Building Predictive Maintenance Model Using ML.NET


Summary

This C# notebook is a continuation from the previous blog post Predictive Maintenance on .NET Platform.

The notebook is completely implemented on .NET platform using C# Jupyter Notebook and Daany – C# data analytics library. There are small differences between this notebook and the notebooks at the official azure gallery portal, but in most cases, the code follows the steps defined there.

The notebook shows how to use .NET Jupyter Notebook with Daany.DataFrame and ML.NET in order to prepare the data and build the Predictive Maintenance Model on .NET platform.

Description

In the previous post, we analyzed 5 data sets with information about telemetry, data, errors and maintenance as well as failure for 100 machines. The data were transformed and analyzed in order to create the final data set for building a machine learning model for Predictive maintenance.

Once we created all features from the data sets, as a final step we created the label column so that it describes if a certain machine will fail in the next 24 hours due to failure a component1, component2, component3, component4 or it will continue to work. . In this part, we are going to perform a part of the machine learning task and start training a machine learning model for predicting if a certain machine will fail in the next 24 hours due to failure, or it will be in functioning normal in that time period.

The model which we are going to build is multi-class classification model sice it has 5 values to predict:

  • component1,
  • component2,
  • component3,
  • component4 or
  • none – means it will continue to work.

ML.NET framework as library for training

In order to train the model, we are going to use ML.NET – Microsoft open source framework for Machine Learning on .NET Platform. First we need to put some preparation codes like:

  • Required Nuget packages,
  • Set of using statements and code for formatting the output:

At the beggining of this notebook, we installed the several NugetPackages in order to complete this notebook. The following code shows using statements, and method for formatting the data from the DataFrame.

//using Microsoft.ML.Data;
using XPlot.Plotly;
using System;
using System.Collections.Generic;
using System.Drawing;
using System.Linq;

//
using Microsoft.ML;
using Microsoft.ML;
using Microsoft.ML.Data;
using Microsoft.ML.Transforms;
using Microsoft.ML.Trainers.LightGbm;
//
using Daany;
using Daany.Ext;
//DataFrame formatter
using Microsoft.AspNetCore.Html;
Formatter.Register((df, writer) =>
{
    var headers = new List();
    headers.Add(th(i("index")));
    headers.AddRange(df.Columns.Select(c => (IHtmlContent) th(c)));
    //renders the rows
    var rows = new List<List>();
    var take = 20;
    //
    for (var i = 0; i < Math.Min(take, df.RowCount()); i++)
    {
        var cells = new List();
        cells.Add(td(df.Index[i]));
        foreach (var obj in df[i]){
            cells.Add(td(obj));
        }
        rows.Add(cells);
    }
    var t = table(
        thead(
            headers),
        tbody(
            rows.Select(
                r => tr(r)))); 
    writer.Write(t);
}, "text/html");

Once we install the Nuget packages and define using statements we are going to define a class we need to create an ML.NET pipeline.

The class PrMaintenanceClass – contains the features (properties) we build in the previous post. We need them to define features in the ML.NET pipeline. The second class we defined is PrMaintenancePrediction we used for prediction and model evaluation.

class PrMaintenancePrediction
{
    [ColumnName("PredictedLabel")]
    public string failure { get; set; }
}
class PrMaintenanceClass
{
    public DateTime datetime { get; set; }
    public int machineID { get; set; }
    public float voltmean_3hrs { get; set; }
    public float rotatemean_3hrs { get; set; }
    public float pressuremean_3hrs { get; set; }
    public float vibrationmean_3hrs { get; set; }
    public float voltstd_3hrs { get; set; }
    public float rotatestd_3hrs { get; set; }
    public float pressurestd_3hrs { get; set; }
    public float vibrationstd_3hrs { get; set; }
    public float voltmean_24hrs { get; set; }
    public float rotatemean_24hrs { get; set; }
    public float pressuremean_24hrs { get; set; }
    public float vibrationmean_24hrs { get; set; }
    public float voltstd_24hrs { get; set; }
    public float rotatestd_24hrs { get; set; }
    public float pressurestd_24hrs { get; set; }
    public float vibrationstd_24hrs { get; set; }
    public float error1count { get; set; }
    public float error2count { get; set; }
    public float error3count { get; set; }
    public float error4count { get; set; }
    public float error5count { get; set; }
    public float sincelastcomp1 { get; set; }
    public float sincelastcomp2 { get; set; }
    public float sincelastcomp3 { get; set; }
    public float sincelastcomp4 { get; set; }
    public string model { get; set; }
    public float age { get; set; }
    public string failure { get; set; }
}

Now that we have defined a class type, we are going to implement the pipeline for this ml model.First, we create MLContext with constant seed, so that the model can be reproduced by any user running this notebook. Then we load the data and split the data into train and test set.

MLContext mlContext= new MLContext(seed:88888);
var strPath="data/final_dataFrame.csv";
var mlDF= DataFrame.FromCsv(strPath);
//
//split data frame on training and testing part
//split at 2015-08-01 00:00:00, to train on the first 8 months and test on last 4 months
var trainDF = mlDF.Filter("datetime", new DateTime(2015, 08, 1, 1, 0, 0), FilterOperator.LessOrEqual);
var testDF = mlDF.Filter("datetime", new DateTime(2015, 08, 1, 1, 0, 0), FilterOperator.Greather);

The summary for the training set is show in the following tables:

Similarly the testing set has the following summary:

Once we have data into application memory, we can prepare the ML.NET pipeline. The pipeline consists of data transformation from the Daany.DataFrame type into collection IDataView. For this task, the LoadFromEnumerable method is used.

//Load daany:DataFrame into ML.NET pipeline
public static IDataView loadFromDataFrame(MLContext mlContext,Daany.DataFrame df)
{
    IDataView dataView = mlContext.Data.LoadFromEnumerable(df.GetEnumerator(oRow =>
    {
        //convert row object array into PrManitenance row
        var ooRow = oRow;
        var prRow = new PrMaintenanceClass();
        prRow.datetime = (DateTime)ooRow["datetime"];
        prRow.machineID = (int)ooRow["machineID"];
        prRow.voltmean_3hrs = Convert.ToSingle(ooRow["voltmean_3hrs"]);
        prRow.rotatemean_3hrs = Convert.ToSingle(ooRow["rotatemean_3hrs"]);
        prRow.pressuremean_3hrs = Convert.ToSingle(ooRow["pressuremean_3hrs"]);
        prRow.vibrationmean_3hrs = Convert.ToSingle(ooRow["vibrationmean_3hrs"]);
        prRow.voltstd_3hrs = Convert.ToSingle(ooRow["voltsd_3hrs"]);
        prRow.rotatestd_3hrs = Convert.ToSingle(ooRow["rotatesd_3hrs"]);
        prRow.pressurestd_3hrs = Convert.ToSingle(ooRow["pressuresd_3hrs"]);
        prRow.vibrationstd_3hrs = Convert.ToSingle(ooRow["vibrationsd_3hrs"]);
        prRow.voltmean_24hrs = Convert.ToSingle(ooRow["voltmean_24hrs"]);
        prRow.rotatemean_24hrs = Convert.ToSingle(ooRow["rotatemean_24hrs"]);
        prRow.pressuremean_24hrs = Convert.ToSingle(ooRow["pressuremean_24hrs"]);
        prRow.vibrationmean_24hrs = Convert.ToSingle(ooRow["vibrationmean_24hrs"]);
        prRow.voltstd_24hrs = Convert.ToSingle(ooRow["voltsd_24hrs"]);
        prRow.rotatestd_24hrs = Convert.ToSingle(ooRow["rotatesd_24hrs"]);
        prRow.pressurestd_24hrs = Convert.ToSingle(ooRow["pressuresd_24hrs"]);
        prRow.vibrationstd_24hrs = Convert.ToSingle(ooRow["vibrationsd_24hrs"]);
        prRow.error1count = Convert.ToSingle(ooRow["error1count"]);
        prRow.error2count = Convert.ToSingle(ooRow["error2count"]);
        prRow.error3count = Convert.ToSingle(ooRow["error3count"]);
        prRow.error4count = Convert.ToSingle(ooRow["error4count"]);
        prRow.error5count = Convert.ToSingle(ooRow["error5count"]);
        prRow.sincelastcomp1 = Convert.ToSingle(ooRow["sincelastcomp1"]);
        prRow.sincelastcomp2 = Convert.ToSingle(ooRow["sincelastcomp2"]);
        prRow.sincelastcomp3 = Convert.ToSingle(ooRow["sincelastcomp3"]);
        prRow.sincelastcomp4 = Convert.ToSingle(ooRow["sincelastcomp4"]);
        prRow.model = (string)ooRow["model"];
        prRow.age = Convert.ToSingle(ooRow["age"]);
        prRow.failure = (string)ooRow["failure"];
        //
        return prRow;
    }));
            
    return dataView;
}

Load the data sets into the app memory:

//Split dataset in two parts: TrainingDataset  and TestDataset          
var trainData = loadFromDataFrame(mlContext, trainDF);
var testData = loadFromDataFrame(mlContext, testDF);

Prior to start training we need to process that data, so that we encoded all non-numerical columns into numerical columns. Also we need to define which columns are going to be part of the Featuresand which one will be label. For this reason we define PrepareData method.

public static IEstimator PrepareData(MLContext mlContext)
{
    //one hot encoding category column
    IEstimator dataPipeline =

    mlContext.Transforms.Conversion.MapValueToKey(outputColumnName: "Label", inputColumnName: nameof(PrMaintenanceClass.failure))
    //encode model column
    .Append(mlContext.Transforms.Categorical.OneHotEncoding("model",outputKind: OneHotEncodingEstimator.OutputKind.Indicator))

    //define features column
    .Append(mlContext.Transforms.Concatenate("Features",
    // 
    nameof(PrMaintenanceClass.voltmean_3hrs), nameof(PrMaintenanceClass.rotatemean_3hrs),
    nameof(PrMaintenanceClass.pressuremean_3hrs),nameof(PrMaintenanceClass.vibrationmean_3hrs),
    nameof(PrMaintenanceClass.voltstd_3hrs), nameof(PrMaintenanceClass.rotatestd_3hrs), 
    nameof(PrMaintenanceClass.pressurestd_3hrs), nameof(PrMaintenanceClass.vibrationstd_3hrs), 
    nameof(PrMaintenanceClass.voltmean_24hrs),nameof(PrMaintenanceClass.rotatemean_24hrs),
    nameof(PrMaintenanceClass.pressuremean_24hrs),nameof(PrMaintenanceClass.vibrationmean_24hrs), 
    nameof(PrMaintenanceClass.voltstd_24hrs),nameof(PrMaintenanceClass.rotatestd_24hrs),
    nameof(PrMaintenanceClass.pressurestd_24hrs),nameof(PrMaintenanceClass.vibrationstd_24hrs), 
    nameof(PrMaintenanceClass.error1count), nameof(PrMaintenanceClass.error2count),
    nameof(PrMaintenanceClass.error3count), nameof(PrMaintenanceClass.error4count), 
    nameof(PrMaintenanceClass.error5count), nameof(PrMaintenanceClass.sincelastcomp1),
    nameof(PrMaintenanceClass.sincelastcomp2),nameof(PrMaintenanceClass.sincelastcomp3),
    nameof(PrMaintenanceClass.sincelastcomp4),nameof(PrMaintenanceClass.model), nameof(PrMaintenanceClass.age) ));

    return dataPipeline;
}

As can be seen, the method converts the label column failure which is a simple textual column into categorical columns containing numerical representation for each different category called Keys.

Now that we have finished with data transformation, we are going to define the Train method which is going to implement ML algorithm, hyper-parameters for it and training process. Once we call this method the method will return the trained model.

//train method
static public TransformerChain Train(MLContext mlContext, IDataView preparedData)
{
    var transformationPipeline=PrepareData(mlContext);
    //settings hyper parameters
    var options = new LightGbmMulticlassTrainer.Options();
    options.FeatureColumnName = "Features";
    options.LearningRate = 0.005;
    options.NumberOfLeaves = 70;
    options.NumberOfIterations = 2000;
    options.NumberOfLeaves = 50;
    options.UnbalancedSets = true;
    //
    var boost = new DartBooster.Options();
    boost.XgboostDartMode = true;
    boost.MaximumTreeDepth = 25;
    options.Booster = boost;
    
    // Define LightGbm algorithm estimator
    IEstimator lightGbm = mlContext.MulticlassClassification.Trainers.LightGbm(options);

    //train the ML model
    TransformerChain model = transformationPipeline.Append(lightGbm).Fit(preparedData);

    //return trained model for evaluation
    return model;
}

Training process and model evaluation

Since we have all required methods, the main program structure looks like:

//prepare data transformation pipeline
var dataPipeline = PrepareData(mlContext);

//print prepared data
var pp = dataPipeline.Fit(trainData);
var transformedData = pp.Transform(trainData);

//train the model
var model = Train(mlContext, trainData);

Once the Train method returns the model, the evaluation phase started. In order to evaluate model, we perform full evaluation with training and testing data.

Model Evaluation with train data set

The evaluation of the model will be performed for training and testing data sets:

//evaluate train set
var predictions = model.Transform(trainData);
var metricsTrain = mlContext.MulticlassClassification.Evaluate(predictions);

ConsoleHelper.PrintMultiClassClassificationMetrics("TRAIN DataSet", metricsTrain);
ConsoleHelper.ConsoleWriteHeader("Train DataSet Confusion Matrix ");
ConsoleHelper.ConsolePrintConfusionMatrix(metricsTrain.ConfusionMatrix);

The model evaluation output:

************************************************************
*    Metrics for TRAIN DataSet multi-class classification model   
*-----------------------------------------------------------
    AccuracyMacro = 0.9603, a value between 0 and 1, the closer to 1, the better
    AccuracyMicro = 0.999, a value between 0 and 1, the closer to 1, the better
    LogLoss = 0.0015, the closer to 0, the better
    LogLoss for class 1 = 0, the closer to 0, the better
    LogLoss for class 2 = 0.088, the closer to 0, the better
    LogLoss for class 3 = 0.0606, the closer to 0, the better
************************************************************
 
Train DataSet Confusion Matrix 
###############################
 

Confusion table
          ||========================================
PREDICTED ||  none | comp4 | comp1 | comp2 | comp3 | Recall
TRUTH     ||========================================
     none || 165 371 |     0 |     0 |     0 |     0 | 1.0000
    comp4 ||     0 |   772 |    16 |    25 |    11 | 0.9369
    comp1 ||     0 |     8 |   884 |    26 |     4 | 0.9588
    comp2 ||     0 |    31 |    22 | 1 097 |     8 | 0.9473
    comp3 ||     0 |    13 |     4 |     8 |   576 | 0.9584
          ||========================================
Precision ||1.0000 |0.9369 |0.9546 |0.9490 |0.9616 |

As can be seen the model predict the values correctly in most cases in the train data set. Now lets see how the model predict the data which have not been part of the raining process.

Model evaluation with test data set

//evaluate test set
var testPrediction = model.Transform(testData);
var metricsTest = mlContext.MulticlassClassification.Evaluate(testPrediction);
ConsoleHelper.PrintMultiClassClassificationMetrics("Test Dataset", metricsTest);

ConsoleHelper.ConsoleWriteHeader("Test DataSet Confusion Matrix ");
ConsoleHelper.ConsolePrintConfusionMatrix(metricsTest.ConfusionMatrix);
************************************************************
*    Metrics for Test Dataset multi-class classification model   
*-----------------------------------------------------------
    AccuracyMacro = 0.9505, a value between 0 and 1, the closer to 1, the better
    AccuracyMicro = 0.9986, a value between 0 and 1, the closer to 1, the better
    LogLoss = 0.0033, the closer to 0, the better
    LogLoss for class 1 = 0.0012, the closer to 0, the better
    LogLoss for class 2 = 0.1075, the closer to 0, the better
    LogLoss for class 3 = 0.1886, the closer to 0, the better
************************************************************
 
Test DataSet Confusion Matrix 
##############################
 

Confusion table
          ||========================================
PREDICTED ||  none | comp4 | comp1 | comp2 | comp3 | Recall
TRUTH     ||========================================
     none || 120 313 |     6 |    15 |     0 |     0 | 0.9998
    comp4 ||     1 |   552 |    10 |    17 |     4 | 0.9452
    comp1 ||     2 |    14 |   464 |    24 |    24 | 0.8788
    comp2 ||     0 |    39 |     0 |   835 |    16 | 0.9382
    comp3 ||     0 |     4 |     0 |     0 |   412 | 0.9904
          ||========================================
Precision ||1.0000 |0.8976 |0.9489 |0.9532 |0.9035 |

We can see, that the model has overall accuracy 99%, and 95% average per class accuracy. The complete nptebook of this blog post can be found .

Your first data analysis with .NET Jupyter Notebook and Daany.DataFrame


Note: The .NET Jupyter notebook for this blog post can be found .

The Structure of Daany.DataFrame

The main part of Daany project is Daany.DataFrame – an c# implementation of a data frame. A data frame is a software component used for handling tabular data, especially for data preparation, feature engineering, and analysis during the development of machine learning models. The concept of Daany.DataFrame implementation is based on simplicity and .NET coding standard. It represents tabular data consisting of columns and rows. Each column has name and type and each row has its index and label.

Usually, rows indicate a zero axis, while columns indicate axis one.

The following image shows a data frame structure:

data frame structure

The basic components of the data frame are:

  • header – list of column names,
  • index – list of object representing each row,
  • data – list of values in the data frame,
  • missing value – data with no values in data frame.

The image above shows the data frame components visually, and how they are positioned in the data frame.

Create Data Frame from a text based file

The data we used are stored in files, and they must be load into application memory in order to be analyzed and transformed. Loading data from files by using Daany.DataFrame is as easy as calling one method.

By using static method DataFrame.FromCsv a user can create data frame object from the csv file. Otherwise, data frame can be persisted on disk by calling static method DataFrame.ToCsv.

The following code shows how to use static methods ToCsv and FromCsv to show persisting and loading data to data frame:

string filename = "df_file.txt";
//define a dictionary of data
var dict = new Dictionary<string, List>
{
    { "ID",new List() { 1,2,3} },
    { "City",new List() { "Sarajevo", "Seattle", "Berlin" } },
    { "Zip Code",new List() { 71000,98101,10115 } },
    { "State",new List() {"BiH","USA","GER" } },
    { "IsHome",new List() { true, false, false} },
    { "Values",new List() { 3.14, 3.21, 4.55 } },
    { "Date",new List() { DateTime.Now.AddDays(-20) , DateTime.Now.AddDays(-10) , DateTime.Now.AddDays(-5) } },

};

//create data frame with 3 rows and 7 columns
var df = new DataFrame(dict);

//first Save data frame on disk and load it
DataFrame.ToCsv(filename, df);

//create data frame with 3 rows and 7 columns
var dfFromFile = DataFrame.FromCsv(filename, sep:',');

//show dataframe
dfFromFile

First, we created a data frame from the dictionary collection. Then we store the data frame to file. After successfully saving, we load the same data frame from the CSV file. The end of the code snippet put asserts in order to prove everything is correctly implemented. The output of the code cell is:

data frame structure

In case the performance is important, you should pass column types to the FromCSV method in order to achieve up to 50% of loading time. For example the following code loads the data from the file, by passing predefined column types:

//defined types of the column 
var colTypes1 = new ColType[] { ColType.I32, ColType.IN, ColType.I32, ColType.STR, ColType.I2, ColType.F32, ColType.DT };
//create data frame with 3 rows and 7 columns
var dfFromFile = DataFrame.FromCsv(filename, sep: ',', colTypes: colTypes1);

And we got the same result: data frame structure

Loading Real Data from the Web

Data can be loaded directly from the web storage by using FromWebstatic method. The following code shows how to load the Concrete Slump Test data from the web. The data set includes 103 data points. There are 7 input variables, and 3 output variables in the data set: Cement, Slag, Fly ash, Water, SP, Coarse Aggr.,Fine Aggr., SLUMP (cm), FLOW (cm), Strength (Mpa). The following code load the Concrete Slump Test data set into Daany DataFrame:

//define web url where the data is stored
var url = "https://archive.ics.uci.edu/ml/machine-learning-databases/concrete/slump/slump_test.data";
//
var df = DataFrame.FromWeb(url);
df.Head(5)

data frame structure

Once we have the data into the application memory, we can perform some statistical calculations. First, let’s see the structure of the data by calling the Describe method:

df.Describe(false)

data frame structure

Now, we see we have a data frame with 103 rows and all columns are of numerical type. The frequency of the data indicated that values are mostly not repeated. From the maximum and minimum values, we can see the data have no outlines since distributions of the values are tends to be normal.

Data Visualization

Let’s perform some visualization just to see how visually data look like. As first let’s see the Slump distribution with respect of SP and Fly ash:

var chart = Chart.Plot(
    new Graph.Scatter()
    {
        x = df["SP"],
        y = df["Fly ash"],
        mode = "markers",
        marker = new Graph.Marker()
        {
            color = df["SLUMP(cm)"].Select(x=>x),
            colorscale = "Jet"
        }
    }
);

var layout = new Layout.Layout(){title="Slump vs. Cement and Slag"};
chart.WithLayout(layout);
chart.WithXTitle("Cement");
chart.WithYTitle("Slag");

display(chart);

data frame structure

From the chart above, we cannot see any relation between those two columns. Let’s see the chart made between Slump and Flow:

var chart = Chart.Plot(
    new Graph.Scatter()
    {
        x = df["SLUMP(cm)"],
        y = df["FLOW(cm)"],
        mode = "markers",
    }
);

var layout = new Layout.Layout(){title="Slump vs. Cement and Slag"};
chart.WithLayout(layout);
chart.WithLegend(true);
chart.WithXTitle("Slump");
chart.WithYTitle("Flow");

display(chart);

data frame structure

We can see some relation in the chart and the relation is positive. This means as Slupm is growing, Flow value grows as well. If we want to measure the relation between the columns we can do that with the following code:

var x1= df["SLUMP(cm)"].Select(x=>Convert.ToDouble(x)).ToArray();
var x2= df["FLOW(cm)"].Select(x=>Convert.ToDouble(x)).ToArray();

//The Pearson coefficient is calculated by
var r=x1.R(x2);
r

The correlation is 0.90 which indicates a strong relationship between those two columns.

The complete .NET Jupyter Notebook for this blog post can be found

Daany – .NET DAta ANalYtics library


Daany - .NET DAta ANalYtics library

Introduction

Daany is .NET data analytics library written in C# and it supposed to be a tool for data preparation, feature engineering and other kinds of data transformations prior to creating ml-ready data set. It is .NET Core based library with ability to run on Windows Linux based distribution and Mac. It is based on .NET Standard 2.1.

Besides data analysis, the library implements a set of statistics or data science features e.g. time series decompositions, optimization performance parameters and similar.

Currently Daany project consists of four main components:

  • Daany.DataFrame,
  • Daany.Stats,
  • Daany.MathStuff and
  • Daany.DataFrame.Ext

The main Daany component is Daany.DataFrame – a data frame implementation for data analysis. It is much like Pandas but the component is not going to follow pandas implementation. It is suitable for doing data exploration and preparation with C# Jupyter Notebook. In order to create or load data into data frame it doesn’t require any predefined class type. In order to defined relevant value type of each column all data are parsed internally during data frame creation. The Daany.DataFrame implements set of powerful features for data manipulation, handling missing values, calculated columns, merging two or more data frames into one, and similar. It is handy for extracting its rows or columns as series of elements and put into the chart to visualizing the data.

Daany.Stat is a collection of statistics features e.g. time series decompositions, optimization, performance parameters and similar.

Daany.Math is a component within data frame with implementation of od matrix and related linear algebra capabilities. It also contains some implementation of other great open source projects. The component is not going to be separate NuGet package.

Daany.DataFrame.Ext contains extensions for Daany.DataFrame component, but they are related to other projects mostly to ML.NET. The Daany.DataFrame should not be dependent on ML.NET and other libraries. So, any future data frame feature which depends on something other than Daany.Math, should be placed in Daany.Ext.

The project is developed as a need to have a set of data transformation features in one library while I am working with machine learning. So, I thought it might help to others. Currently, the library has pretty much data transformation features and might be your number one data analytics library on .NET platform. Collaboration to the project is also welcome.

How to start with Daany

Daany is 100% .NET Core component and can be run on any platform .NET Core supports, from the Windows x86/x64 to Mac or Linux based OS. It can be used by Visual Studio or Visual Studio Code. It consisted of 3 NuGet packages, so the easiest way to start with it is to install the packages in your .NET application. Within Visual Studio create or open your .NET application and open NuGet packages window. Type Daany in the browse edit box and hit enter. You can find four packages starting with Daany. You have few options to install the packages.

  1. Install Daany.DataFrame – only. Use this option if you want only data analysis by using data frame. Once you click Install button, Daany.DataFrame and Daany.Math will be installed into your project app.

  2. Install Daany.Stat package. This package already contains DataFrame, as well as time series decomposition and related statistics features.

Once you install the packages, you can start developing your app using Daany packages.

Using Daany as assembly reference

Since Daany has no dependency to other libraries you can copy three dlls and add them as reference to your project.

file explorer

In order to do so clone the project from ,build it and copy Daany.DataFrame.dll, Daany.Math.dll and Daany.Stat.dll to your project as assembly references. Whole project is just 270 KB.

Using Daany with .NET Jupyter Notebook

Daany library is ideal with .NET Jupyter Notebook, and some of the great notebooks are implemented already, and can be viewed at . The GitHub project contains the code necessary to run the notebooks in Binder, a Jupyter Virtual Environment, and try Daany without any local installation. So the first recommendation is to try Daany with already implemented notebooks using Binder.com.

Namespaces in Daany

Daany project contains several namespaces for separating different implementation. The following list contains relevant namespaces:

  • using Daany – data frame and related code implementation,
  • using Daany.Ext – data frame extensions, used with dependency on third party library,
  • using Daany.MathStuff – math related stuff implemented in Daany,
  • using Daany.Optimizers – set of optimizers like SGD,
  • using Daany.Stat – set of statistics implementations in the project.

That’s all for this post. Next blog posts will show more exciting implementation using Daany.

Predictive Maintenance on .NET Platform


Summary

This article is based on the Azure AI Gallery article: , which includes the data sets used in this article.

However, this notebook is completely implemented on .NET platform using:

  • ,- Jupyter Notebook experience with C# and .NET,
  • – Microsoft open source framework for machine learning, and
  • DAta ANalYtics open source library for data analytics. It can be installed as Nuget package.

There are small differences between this notebook and the notebooks at the official azure gallery portal, but in most cases, the code follows the steps defined there. The purpose of this notebook is to demonstrate how to use .NET Jupyter Notebook with Daany.DataFrame and ML.NET in order to prepare the data and build the Predictive Maintenance Model on .NET platform. But first lets see what is Predictive Maintenance and why is it important.

Quick Introduction to Predictive Maintenance

Simply speaking it is a technique to determine (predict) the failure of the machine component in the near future so that the component can be replaced based on the maintenance plan before it fails and stop the production process. The Predictive maintenance can improve the production process and increase the productivity. By successfully handling with predictive maintenance we are able to achieve the following goals:

  • reduce the operational risk of mission-critical equipment

  • control cost of maintenance by enabling just-in-time maintenance operations

  • discover patterns connected to various maintenance problems

  • provide Key Performance Indicators.

The following image shows different type of maintenance in the production. Predictive Maintenance

Predictive maintenance data collection

In order to handle and use this technique we need a various data from the production, including but not limited to:

  • telemetry data from the observed machines (vibration, voltage, temperature etc)
  • errors and logs data relevant to each machine,
  • failure data, when a certain component is replaced, etc
  • quality and accuracy data, machine properties, models, age etc.

3 Steps in Predictive Maintenance

Usually, every Predictive Maintenance technique should proceed by the following 3 main steps:

  1. Collect Data – collect all possible descriptions,historical and real-time data, usually by using IOT devices, various loggers, technical documentation, etc.

  2. Predict Failures – collected data can be used and transformed into machine learning ready data sets, and build a machine learning model to predict the failures of the components in the set of machines in the production.

  3. React – by obtaining the information which components will fail in the near future, we can activate the process of replacement so the component will be replaced before it fails, and the production process will not be interrupted.

Predict Failures

In this article, the second step will be presented, which will be related to data preparation. In order to predict failures in the production process, a set of data transformations, cleaning, feature engineering, and selection must be performed to prepare the data for building a machine learning model. The data preparation part plays a crucially step in the model building since a quality data preparation will directly reflect on the model accuracy and reliability.

Software requirements

In this article, the complete procedure in data preparation is presented. The whole process is performed using:

  • .NET Core 3.1 – the latest .NET platform version,

  • .NET Jupyter Notebook– .NET implementation of popular Jupyer Notebook,

  • ML.NET – Microsoft open-source framework for Machine Learning on .NET Platform and

  • DaanyDAta ANalYtics library. It can be found at Github but also as Nuget package.

Notebook preparation

In order to complete this task, we should install several Nuget packages and include several using keywords. The following code block shows the using keywords, and additional code related to notebook output format.

Note: nuget package installation must be in the first cell of the Notebook, otherwise the notebook will not work as expected. Hope this will be changed once the final version would be released.

//using Microsoft.ML.Data;
using XPlot.Plotly;
using System;
using System.Collections.Generic;
using System.Drawing;
using System.Linq;
//using statement of Daany package
using Daany;
using Daany.MathStuff;
using Daany.Ext;
//
using Microsoft.ML;
//DataFrame formatter
using Microsoft.AspNetCore.Html;
Formatter<DataFrame>.Register((df, writer) =>
{
    var headers = new List<IHtmlContent>();
    headers.Add(th(i("index")));
    headers.AddRange(df.Columns.Select(c => (IHtmlContent) th(c)));    
    //renders the rows
    var rows = new List<List<IHtmlContent>>();
    var take = 20;  
    //
    for (var i = 0; i < Math.Min(take, df.RowCount()); i++)
    {
        var cells = new List<IHtmlContent>();
        cells.Add(td(df.Index[i]));
        foreach (var obj in df[i])
        {
            cells.Add(td(obj));
        }
        rows.Add(cells);
    }    
    var t = table(
        thead(headers),
        tbody(rows.Select(r => tr(r))));
    
    writer.Write(t);
}, "text/html");

Download the data

In order to start with data preparation, we need data. The data can be found at Azure blob storage. The data is maintained by .

Once the data are downloaded from the blob storage, they will not be downloaded again and they will be used as local copies.

The Data

The data we are using for predictive maintenance can be classified to:

  • telemetry – which collects historical data about machine behavior (voltage, vibration, etc)
  • errors – the data about warnings and errors in the machines
  • maint – data about replacement and maintenance for the machines,
  • machines – descriptive information about the machines,
  • failures – data when a certain machine is stopped, due to component failure.

We load all the files in order to fully prepare data for the training process. The following code sample loads the data in to application memory.

%%time
//Load ALL 5 data frame files
//DataFrame Cols: datetime,machineID,volt,rotate,pressure,vibration
var telemetry = DataFrame.FromCsv("data/PdM_telemetry.csv", dformat: "yyyy-mm-dd hh:mm:ss");
var errors = DataFrame.FromCsv("data/PdM_errors.csv", dformat: "yyyy-mm-dd hh:mm:ss");
var maint = DataFrame.FromCsv("data/PdM_maint.csv", dformat: "yyyy-mm-dd hh:mm:ss");
var failures = DataFrame.FromCsv("data/PdM_failures.csv", dformat: "yyyy-mm-dd hh:mm:ss");
var machines = DataFrame.FromCsv("data/PdM_machines.csv", dformat: "yyyy-mm-dd hh:mm:ss");

Telemetry

The first data source is the telemetry data about machines. It consists of voltage, rotation, pressure, and vibration measurements measured from 100 machines in real-time hourly. The time period the data has been collected is during the year 2015. The following data shows the first 10 records in the dataset.

Predictive Maintenance

A description of the whole dataset is shown on the next cell. As can be seen, we have nearly million records for the machines, which is good starting point for the analysis.

Predictive Maintenance

In case we want to see the visualization of the telemetry data, we can select on of several column and show it.

Predictive Maintenance

Errors

One of the most important information in every Predictive Maintenance system is Error data. Actually errors are non-breaking recorded events while the machine is still operational. The error date and times are rounded to the closest hour since the telemetry data is collected at an hourly rate.

errors.Head()

Predictive Maintenance

//count number of errors 
var barValue = errors["errorID"].GroupBy(v => v)
        .OrderBy(group => group.Key)
        .Select(group => Tuple.Create(group.Key, group.Count()));

//Plot Errors data
var chart = Chart.Plot(
    new Graph.Bar()
    {
       x = barValue.Select(x=>x.Item1),
       y = barValue.Select(x=>x.Item2),
      //  mode = "markers",  
    }
    
);
var layout = new XPlot.Plotly.Layout.Layout() 
    { title = "Error distribution",
     xaxis=new XPlot.Plotly.Graph.Xaxis() { title="Error name" }, 
     yaxis = new XPlot.Plotly.Graph.Yaxis() { title = "Error Count" } };
//put layout into chart
chart.WithLayout(layout);

display(chart)

Predictive Maintenance

Maintenance

The Maintenance is the next PrM component which tells us about scheduled and unscheduled maintenance. The maintenance contains the records which correspond to both regular inspection of components as well as failures. To add the record into the maintenance table a component must be replaced during the scheduled inspection or replaced due to a breakdown. In case the records are created due to breakdowns are called failures. Maintenance contains the data from 2014 and 2015 years.

maint.Head()

Predictive Maintenance

Machines

The data include information about 100 machines which are subject of the Predictive Maintenance analysis. The information includes: model type, and machine age. Distribution of the machine age categorized by the models across production process is shown in the following image:

//Distribution of models across age
var d1 = machines.Filter("model", "model1", FilterOperator.Equal)["age"]
                                    .GroupBy(g => g).Select(g=>(g.Key,g.Count()));
var d2 = machines.Filter("model", "model2", FilterOperator.Equal)["age"]
                                    .GroupBy(g => g).Select(g=>(g.Key,g.Count()));
var d3 = machines.Filter("model", "model3", FilterOperator.Equal)["age"]
                                    .GroupBy(g => g).Select(g=>(g.Key,g.Count()));
var d4 = machines.Filter("model", "model4", FilterOperator.Equal)["age"]
                                    .GroupBy(g => g).Select(g=>(g.Key,g.Count()));
//define bars
var b1 = new Graph.Bar(){ x = d1.Select(x=>x.Item1),y = d1.Select(x=>x.Item2),name = "model1"};
var b2 = new Graph.Bar(){ x = d2.Select(x=>x.Item1),y = d2.Select(x=>x.Item2),name = "model2"};
var b3 = new Graph.Bar(){ x = d3.Select(x=>x.Item1),y = d3.Select(x=>x.Item2),name = "model3"};
var b4 = new Graph.Bar(){ x = d4.Select(x=>x.Item1),y = d4.Select(x=>x.Item2),name = "model4"};
    
//Plot machine data
var chart = Chart.Plot(new[] {b1,b2,b3,b4});
var layout = new XPlot.Plotly.Layout.Layout() 
    { title = "Components Replacements",barmode="stack",
     xaxis=new XPlot.Plotly.Graph.Xaxis() { title="Machine Age" }, 
     yaxis = new XPlot.Plotly.Graph.Yaxis() { title = "Count" } };
//put layout into chart
chart.WithLayout(layout);

display(chart)

Predictive Maintenance

Failures

The Failures data represent the replacements of the components due to the failure of the machines. Once the failure is happened the machine is stopped. This is a crucial difference between Errors and Failures.

failures.Head()

Predictive Maintenance

//count number of failures  
var falValues = failures["failure"].GroupBy(v => v)
        .OrderBy(group => group.Key)
        .Select(group => Tuple.Create(group.Key, group.Count()));

//Plot Failure data
var chart = Chart.Plot(
    new Graph.Bar()
    {
       x = falValues.Select(x=>x.Item1),
       y = falValues.Select(x=>x.Item2),
      //  mode = "markers",  
    }
    
);
var layout = new XPlot.Plotly.Layout.Layout() 
    { title = "Failure Distribution across machines",
     xaxis=new XPlot.Plotly.Graph.Xaxis() { title="Component Name" }, 
     yaxis = new XPlot.Plotly.Graph.Yaxis() { title = "Number of components replaces" } };
//put layout into chart
chart.WithLayout(layout);

display(chart)

Predictive Maintenance

Feature Engineering

This section contains several feature engineering methods used to create features based on the machines’ properties.

Lagged Telemetry Features

First, we are going to create several lagged telemetry data, since telemetry data are classic time series data.

In the following, the rolling mean and standard deviation of the telemetry data over the last 3-hours lag window is calculated for every 3 hours.

//prepare rolling aggregation for each column for average values
var agg_curent = new Dictionary<string, Aggregation>()
 {
    { "datetime", Aggregation.Last }, { "volt", Aggregation.Last }, { "rotate", Aggregation.Last },
    { "pressure", Aggregation.Last },{ "vibration", Aggregation.Last }
  };
//prepare rolling aggregation for each column for average values
var agg_mean = new Dictionary<string, Aggregation>()
 {
    { "datetime", Aggregation.Last }, { "volt", Aggregation.Avg }, { "rotate", Aggregation.Avg },
    { "pressure", Aggregation.Avg },{ "vibration", Aggregation.Avg }
  };
//prepare rolling aggregation for each column for std values
var agg_std = new Dictionary<string, Aggregation>()
{
   { "datetime", Aggregation.Last }, { "volt", Aggregation.Std }, { "rotate", Aggregation.Std },
    { "pressure", Aggregation.Std },{ "vibration", Aggregation.Std }
};
//group Telemetry data by machine ID
var groupedTelemetry = telemetry.GroupBy("machineID");
//calculate rolling mean for grouped data for each 3 hours
var _3AvgValue = groupedTelemetry.Rolling(3, 3, agg_mean)
                 .Create(("machineID", null), ("datetime", null),("volt", "voltmean_3hrs"), ("rotate", "rotatemean_3hrs"),
                         ("pressure", "pressuremean_3hrs"), ("vibration", "vibrationmean_3hrs"));
//show head of the newely generated table
_3AvgValue.Head()

Predictive Maintenance

//calculate rolling std for grouped datat fro each 3 hours
var _3StdValue = groupedTelemetry.Rolling(3, 3, agg_mean)
                 .Create(("machineID", null), ("datetime", null),("volt", "voltsd_3hrs"), ("rotate", "rotatesd_3hrs"),
                         ("pressure", "pressuresd_3hrs"), ("vibration", "vibrationsd_3hrs"));
//show head of the new generated table
_3StdValue.Head()

For capturing a longer term effect 24 hours lag features we are going to calculate rolling avg and std.

//calculate rolling avg and std for each 24 hours
var _24AvgValue = groupedTelemetry.Rolling(24, 3, agg_mean)
                .Create(("machineID", null), ("datetime", null),
                        ("volt", "voltmean_24hrs"), ("rotate", "rotatemean_24hrs"),
                        ("pressure", "pressuremean_24hrs"), ("vibration", "vibrationmean_24hrs"));
var _24StdValue = groupedTelemetry.Rolling(24, 3, agg_std)
                .Create(("machineID", null), ("datetime", null),
                        ("volt", "voltsd_24hrs"), ("rotate", "rotatesd_24hrs"),
                        ("pressure", "pressuresd_24hrs"), ("vibration", "vibrationsd_24hrs"));

Merging telemetry features

Once we have rolling lag features calculated, we can merge them into one data frame:

//before merge all features create set of features from the current values for every 3 or 24 hours
DataFrame _1CurrentValue = groupedTelemetry.Rolling(3, 3, agg_curent)
                            .Create(("machineID", null), ("datetime", null),
                            ("volt", null), ("rotate", null), ("pressure", null), ("vibration", null));

Now that we have basic data frame merge previously calculated data frames with this one.

//merge all telemetry data frames into one
var mergeCols= new string[] { "machineID", "datetime" };
var df1 = _1CurrentValue.Merge(_3AvgValue, mergeCols, mergeCols, JoinType.Left, suffix: "df1");   
                                            
var df2 = df1.Merge(_24AvgValue, mergeCols, mergeCols, JoinType.Left, suffix: "df2");
                                 
var df3 = df2.Merge(_3StdValue, mergeCols, mergeCols, JoinType.Left, suffix: "df3");
                                
var df4 = df3.Merge(_24StdValue, mergeCols, mergeCols, JoinType.Left, suffix: "df4");

At the end of the merging process, select relevant columns.

//select final dataset for the telemetry
var telDF = df4["machineID","datetime","volt","rotate", "pressure", "vibration",
                 "voltmean_3hrs","rotatemean_3hrs","pressuremean_3hrs","vibrationmean_3hrs",
                 "voltmean_24hrs","rotatemean_24hrs","pressuremean_24hrs","vibrationmean_24hrs",
                 "voltsd_3hrs", "rotatesd_3hrs","pressuresd_3hrs","vibrationsd_3hrs",
                 "voltsd_24hrs", "rotatesd_24hrs","pressuresd_24hrs","vibrationsd_24hrs"];

//remove NANs
var telemetry_final = telDF.DropNA();

Now top 5 rows of final telemetry data looks like the following image:

telemetry_final.Head()

Predictive Maintenance

Lag Features from Errors

Unlike telemetry that had numerical values, errors have categorical values denoting the type of error that occurred at a time-stamp. We are going to aggregate categories of the error with different types of errors that occurred in the lag window.

First, encode the errors with One-Hot-Encoding:

var mlContext = new MLContext(seed:2019);
//One Hot Encoding of error column
var encodedErr = errors.EncodeColumn(mlContext, "errorID");

//sum duplicated errors by machine and date
var errors_aggs = new Dictionary<string, Aggregation>();
errors_aggs.Add("error1", Aggregation.Sum);
errors_aggs.Add("error2", Aggregation.Sum);
errors_aggs.Add("error3", Aggregation.Sum);
errors_aggs.Add("error4", Aggregation.Sum);
errors_aggs.Add("error5", Aggregation.Sum);

//group and sum duplicated errors
encodedErr =  encodedErr.GroupBy(new string[] { "machineID", "datetime" }).Aggregate(errors_aggs);

//
encodedErr = encodedErr.Create(("machineID", null), ("datetime", null),
                        ("error1", "error1sum"), ("error2", "error2sum"),
                        ("error3", "error3sum"), ("error4", "error4sum"), ("error5", "error5sum"));
encodedErr.Head()                       

Predictive Maintenance

// align errors with telemetry datetime values so that we can calculate aggregations
var er = telemetry.Merge(encodedErr,mergeCols, mergeCols, JoinType.Left, suffix: "error");
//
er = er["machineID","datetime", "error1sum", "error2sum", "error3sum", "error4sum", "error5sum"];
//fill missing values with 0
er.FillNA(0);
er.Head()   

Predictive Maintenance

//count the number of errors of different types in the last 24 hours, for every 3 hours
//define aggregation
var errors_aggs1 = new Dictionary<string, Aggregation>()
{
  { "datetime", Aggregation.Last },{ "error1sum", Aggregation.Sum }, { "error2sum", Aggregation.Sum }, 
  { "error3sum", Aggregation.Sum },{ "error4sum", Aggregation.Sum },
  { "error5sum", Aggregation.Sum }
};

//count the number of errors of different types in the last 24 hours,  for every 3 hours
var eDF = er.GroupBy(new string[] { "machineID"}).Rolling(24, 3, errors_aggs1);

//
var newdf=  eDF.DropNA();

var errors_final = newdf.Create(("machineID", null), ("datetime", null),
                        ("error1sum", "error1count"), ("error2sum", "error2count"),
                        ("error3sum", "error3count"), ("error4sum", "error4count"), ("error5sum", "error5count"));
errors_final.Head()

Predictive Maintenance

The Time Since Last Replacement

As the main task here is how to create a relevant feature in order to create a quality data set for the machine learning part. One of the good features would be the number of replacements of each component in the last 3 months to incorporate the frequency of replacements.

Furthermore, we can calculate how long it has been since a component is last replaced as that would be expected to correlate better with component failures since the longer a component is used, the more degradation should be expected. As first we are going to encode the maintenance table:

//One Hot Encoding of error column
var encMaint = maint.EncodeColumn(mlContext, "comp");
encMaint.Head()

Predictive Maintenance

//create separate data frames in order to calculate proper time since last replacement 
DataFrame dfComp1 = encMaint.Filter("comp1", 1, FilterOperator.Equal)["machineID", "datetime"];
DataFrame dfComp2 = encMaint.Filter("comp2", 1, FilterOperator.Equal)["machineID", "datetime"];;
DataFrame dfComp3 = encMaint.Filter("comp3", 1, FilterOperator.Equal)["machineID", "datetime"];;
DataFrame dfComp4 = encMaint.Filter("comp4", 1, FilterOperator.Equal)["machineID", "datetime"];;

dfComp4.Head()

Predictive Maintenance

//from telemetry data create helped data frame so we can calculate additional column from the maintenance data frame
var compData = telemetry_final.Create(("machineID", null), ("datetime", null));
%%time
//calculate new set of columns so that we have information the time since last replacement of each component separately
var newCols= new string[]{"sincelastcomp1","sincelastcomp2","sincelastcomp3","sincelastcomp4"};
var calcValues= new object[4];

//perform calculation
compData.AddCalculatedColumns(newCols,(row, i)=>
{
    var machineId = Convert.ToInt32(row["machineID"]);
    var date = Convert.ToDateTime(row["datetime"]);
    
    var maxDate1 = dfComp1.Filter("machineID", machineId, FilterOperator.Equal)["datetime"]
        .Where(x => (DateTime)x <= date).Select(x=>(DateTime)x).Max();
    var maxDate2 = dfComp2.Filter("machineID", machineId, FilterOperator.Equal)["datetime"]
        .Where(x => (DateTime)x <= date).Select(x=>(DateTime)x).Max();
    var maxDate3 = dfComp3.Filter("machineID", machineId, FilterOperator.Equal)["datetime"]
        .Where(x => (DateTime)x <= date).Select(x=>(DateTime)x).Max();
    var maxDate4 = dfComp4.Filter("machineID", machineId, FilterOperator.Equal)["datetime"]
        .Where(x => (DateTime)x <= date).Select(x=>(DateTime)x).Max();
        
    //perform calculation
    calcValues[0] = (date - maxDate1).TotalDays;
    calcValues[1] = (date - maxDate2).TotalDays;
    calcValues[2] = (date - maxDate3).TotalDays;
    calcValues[3] = (date - maxDate4).TotalDays;
    return calcValues;
});
Wall time: 178708.9764ms

Predictive Maintenance

var maintenance_final = compData;
maintenance_final.Head()

Machine Features

The machine data set contains descriptive information about machines like the type of machines and their ages which is the years in service.

machines.Head()

Predictive Maintenance

Joining features into final ML ready data set

As the last step in Feature engineering, we are performing merging all features into one data set.

var merge2Cols=new string[]{"machineID"};
var fdf1= telemetry_final.Merge(errors_final, mergeCols, mergeCols,JoinType.Left, suffix: "er");
var fdf2 = fdf1.Merge(maintenance_final, mergeCols,mergeCols,JoinType.Left, suffix: "mn");
var features_final = fdf2.Merge(machines, merge2Cols,merge2Cols,JoinType.Left, suffix: "ma");
features_final= features_final["datetime", "machineID", 
            "voltmean_3hrs", "rotatemean_3hrs", "pressuremean_3hrs", "vibrationmean_3hrs",
            "voltstd_3hrs", "rotatestd_3hrs", "pressurestd_3hrs", "vibrationstd_3hrs", 
            "voltmean_24hrs", "rotatemean_24hrs", "pressuremean_24hrs", "vibrationmean_24hrs", 
            "voltstd_24hrs","rotatestd_24hrs", "pressurestd_24hrs", "vibrationstd_24hrs", 
            "error1count", "error2count", "error3count", "error4count", "error5count", 
            "sincelastcomp1", "sincelastcomp2", "sincelastcomp3", "sincelastcomp4", 
            "model", "age"];
//

features_final.Head();
DataFrame.ToCsv("data/final_features.csv", features_final);

Define Label Column

The Label in prediction maintenance should be the probability that a machine will fail in the near future due to a failure certain component. If we take 24 hours to be a task for this problem, the label construction is consists of a new column in the feature data set which indicate if certain machine will fail or not in the next 24 hours due to failure one of several components.

With this way we are defining the label as a categorical variable containing: – none – if the machine will not fail in the next 24 hours, – comp1 to comp4

  • if the machine will fail in the next 24 hours due to the failure of certain components.

Since we can experiment with the label construction by applying different conditions, we can implement methods that take several arguments in order to define the general problem.

failures.Describe(false)

Predictive Maintenance

//constructing the label column which indicate if the current machine will 
//fail in the next `predTime` (24 hours as default) due to failur certain component.
//create final data frame from feature df
var finalDf = new DataFrame(features_final);

//group failures by machineID and datetime 
string[] cols = new string[] {  "machineID" , "datetime"};
var failDfgrp = failures.GroupBy(cols);

//Add failure column to  finalDF
var rV = new object[] { "none" };
finalDf.AddCalculatedColumns(new string[]{"failure"}, (object[] row, int i) => rV);

//create new data frame from featuresDF by grouping machineID and datatime
var featureDfGrouped = finalDf["datetime","machineID", "failure"].GroupBy(cols);

//now look for every failure and calculate if the machine will fail in the last 24 hours
//in case two or more components were failed for the ssame machine add new row in df
var failureDfExt = featureDfGrouped.Transform((xdf) =>
{
    //extract the row from featureDfGrouped
    var xdfRow = xdf[0].ToList();
    var refDate = (DateTime)xdfRow[0];
    var machineID = (int)xdfRow[1];

    //now look if the failure contains the machineID
    if(failDfgrp.Group2.ContainsKey(machineID))
    {
        //get the date and calculate total hours
        var dff = failDfgrp.Group2[machineID];

        foreach (var dfff in dff)
        {
            for (int i = 0; i < dfff.Value.RowCount(); i++)
            {
                //"datetime","machineID","failure"
                var frow = dfff.Value[i].ToList();
                var dft = (DateTime)frow[0];
                
                //if total hours is less or equal than 24 hours set component to the failure column
                var totHours = (dft - refDate).TotalHours;
                if (totHours <= 24 && totHours >=0)
                {
                    if (xdf.RowCount() > i)
                        xdf["failure", i] = frow[2];
                    else//in case two components were failed for the same machine and 
                        //at the same time, add new row with new component name
                    {
                        var r = xdf[0].ToList();
                        r[2] = frow[2];
                        xdf.AddRow(r);
                    }
                }
            }
        }
    }
    return xdf;
});

//Now merge extended failure Df with featureDF
var final_dataframe = finalDf.Merge(failureDfExt, cols, cols,JoinType.Left, "fail");

//define final set of columns
final_dataframe = final_dataframe["datetime", "machineID",
"voltmean_3hrs", "rotatemean_3hrs", "pressuremean_3hrs", "vibrationmean_3hrs",
"voltsd_3hrs", "rotatesd_3hrs", "pressuresd_3hrs", "vibrationsd_3hrs",
"voltmean_24hrs", "rotatemean_24hrs", "pressuremean_24hrs", "vibrationmean_24hrs",
"voltsd_24hrs", "rotatesd_24hrs", "pressuresd_24hrs", "vibrationsd_24hrs",
"error1count", "error2count", "error3count", "error4count", "error5count",
"sincelastcomp1", "sincelastcomp2", "sincelastcomp3", "sincelastcomp4",
"model", "age", "failure_fail"];

//rename column
final_dataframe.Rename(("failure_fail", "failure"));
//save the file data frame to disk
DataFrame.ToCsv("data/final_dataFrame.csv",final_dataframe);

Final Data Frame

Lets see how the final_dataframe looks like. It contains 24 columns. Most of the columns are numerical. The Model column is categorical and it should be encoded once we prepare the machine learning part.

Also the label column failure is categorical column containing 5 different categories: none, comp1, comp2, comp3 and comp4. We can also see the data set is not balance, since we have 2785705 none and the rest of the rows in total of 5923 other categories. This is typical unbalanced dataset, and we should be careful when evaluation models, because the model which returns always none value will have more than 97% of accuracy.

final_dataframe.Describe(false)

Predictive Maintenance

In the next part, we are going to implement the training and evaluation process of the Predictive Maintenance model. The full notebook for this blog post can be found

C# Jupyter Notebook Part 2/n


What is .NET Jupyter Notebook

In this blog post, we are going to explore the main features in the new C# Juypter Notebook. For those who used Notebook from other programming languages like Python or R, this would be an easy task. First of all, the Notebook concept provides a quick, simple and straightforward way to present a mix of text and $ \Latex $, source code implementation and its output. This means you have a full-featured platform to write a paper or blog post, presentation slides, lecture notes, and other educated materials.

The notebook consists of cells, where a user can write code or markdown text. Once he completes the cell content confirmation for cell editing can be achieved by Ctrl+Enter or by press run button from the notebook toolbar. The image below shows the notebook toolbar, with a run button. The popup combo box shows the type of cell the user can define. In the case of text, Markdown should be selected, for writing source code the cell should be Code.

run button

To start writing code to C# Notebook, the first thing we should do is install NuGet packages or add assembly references and define using statements. In order to do that, the following code installs several nuget packages, and declare several using statements. But before writing code, we should add a new cell by pressing + toolbar button.

The first few NuGet packages are packages for ML.NET. Then we install the XPlot package for data visualization in .NET Notebook, and then we install a set of Daany packages for data analytics. First, we install Daany.DataFrame for data exploration and analysis, and then Daany.DataFrame.Ext set of extensions for data manipulation used with ML.NET.

//ML.NET Packages
#r "nuget:Microsoft.ML.LightGBM"
#r "nuget:Microsoft.ML"
#r "nuget:Microsoft.ML.DataView"

//Install XPlot package
#r "nuget:XPlot.Plotly"

//Install Daany.DataFrame 
#r "nuget:Daany.DataFrame"
#r "nuget:Daany.DataFrame.Ext"
using System;
using System.Linq;

//Daany data frame
using Daany;
using Daany.Ext;

//Plotting functionalities
using XPlot.Plotly;

//ML.NET using
using Microsoft.ML;
using Microsoft.ML.Data;
using Microsoft.ML.Trainers.LightGbm;

The output for the above code:

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Once the NuGet packages are installed successfully, we can start with data exploration. But before this declare few using statements:

We can define classes or methods globally. The following code implements the formatter method for displaying Daany.DataFrame in the output cell.

// Temporal DataFrame formatter for this early preview
using Microsoft.AspNetCore.Html;
Formatter<DataFrame>.Register((df, writer) =>
{
    var headers = new List<IHtmlContent>();
    headers.Add(th(i("index")));
    headers.AddRange(df.Columns.Select(c => (IHtmlContent) th(c)));
    
    //renders the rows
    var rows = new List<List<IHtmlContent>>();
    var take = 20;
    
    //
    for (var i = 0; i < Math.Min(take, df.RowCount()); i++)
    {
        var cells = new List<IHtmlContent>();
        cells.Add(td(df.Index[i]));
        foreach (var obj in df[i])
        {
            cells.Add(td(obj));
        }
        rows.Add(cells);
    }
    
    var t = table(
        thead(
            headers),
        tbody(
            rows.Select(
                r => tr(r))));
    
    writer.Write(t);
}, "text/html");

For this demo we will used famous Iris data set. We will download the file from the internet, load it by using Daany.DataFrame, a display few first rows. In order to do that we run the folloing code:

var url = "https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data";
var cols = new string[] {"sepal_length","sepal_width", "petal_length", "petal_width", "flower_type"};
var df = DataFrame.FromWeb(url, sep:',',names:cols);
df.Head(5)

The output looks like this: run button

As can be seen, the last line from the previous code has no semicolon, which means the line should be displayed in the output cell. Let’s move on, and implement two new columns. The new columns will be sepal and petal area for the flower. The expression we are going to use is:

$$ PetalArea = petal_width \cdot petal_length;\ SepalArea = sepal_width \cdot sepal_length; $$

As can be seen, the $\LaTeX$ is fully supported in the notebook.

The above formulea is implemented in the following code:

//calculate two new columns into dataset
df.AddCalculatedColumn("SepalArea", (r, i) => Convert.ToSingle(r["sepal_width"]) * Convert.ToSingle(r["sepal_length"]));
df.AddCalculatedColumn("PetalArea", (r, i) => Convert.ToSingle(r["petal_width"]) * Convert.ToSingle(r["petal_length"]));
df.Head(5)

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The data frame has two new columns. They indicate the area for the flower. In order to see basic statistics parameters for each of the defined columns, we call Describe method.

//see descriptive stats of the final ds
df.Describe(false)

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From the table above, we can see the flower column has only 3 values. The most frequent value has a frequency equal to 50, which is an indicator of a balanced dataset.

Data visualization

The most powerful feature in Notebook is a data visualization. In this section, we are going to plot some interesting charts.

In order to see how sepal and petal areas are spread in 2D plane, the following plot is implemented:

//plot the data in order to see how areas are spread in the 2d plane
//XPlot Histogram reference: http://tpetricek.github.io/XPlot/reference/xplot-plotly-graph-histogram.html

var faresHistogram = Chart.Plot(new Graph.Histogram(){x = df["flower_type"], autobinx = false, nbinsx = 20});
var layout = new Layout.Layout(){title="Distribution of iris flower"};
faresHistogram.WithLayout(layout);
display(faresHistogram);

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The chart is also an indication of a balanced dataset.

Now lets plot areas depending on the flower type:

// Plot Sepal vs. Petal area with flower type

var chart = Chart.Plot(
    new Graph.Scatter()
    {
        x = df["SepalArea"],
        y = df["PetalArea"],
        mode = "markers",
        marker = new Graph.Marker()
        {
            color = df["flower_type"].Select(x=>x.ToString()=="Iris-virginica"?1:(x.ToString()=="Iris-versicolor"?2:3)),
            colorscale = "Jet"
        }
    }
);

var layout = new Layout.Layout(){title="Plot Sepal vs. Petal Area & color scale on flower type"};
chart.WithLayout(layout);
chart.WithLegend(true);
chart.WithLabels(new string[3]{"Iris-virginica","Iris-versicolor", "Iris-setosa"});
chart.WithXTitle("Sepal Area");
chart.WithYTitle("Petal Area");
chart.Width = 800;
chart.Height = 400;

display(chart);

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As can be seen from the chart above, flower types are separated almost linearly, since we used petal and sepal areas instead of width and length. With this transformation, we can get a 100% accurate ml model.

Machine Learning

Once we finished with data transformation and visualization we can define the final data frame before machine learning application. To end this we are going to select only two columns for features and one label column which will be flower type.

//create new data-frame by selecting only three columns
var derivedDF = df["SepalArea","PetalArea","flower_type"];
derivedDF.Head(5)

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Since we are going to use ML.NET, we need to declare Iris in order to load the data into ML.NET.

//Define an Iris class for machine learning.
class Iris
{
    public float PetalArea { get; set; }
    public float SepalArea { get; set; }
    public string Species { get; set; }
}
//Create ML COntext
MLContext mlContext = new MLContext(seed:2019);

Then load the data from Daany data frame into ML.NET:

//Load Data Frame into Ml.NET data pipeline
IDataView dataView = mlContext.Data.LoadFromEnumerable<Iris>(derivedDF.GetEnumerator<Iris>((oRow) =>
{
    //convert row object array into Iris row

    var prRow = new Iris();
    prRow.SepalArea = Convert.ToSingle(oRow["SepalArea"]);
    prRow.PetalArea = Convert.ToSingle(oRow["PetalArea"]);
    prRow.Species = Convert.ToString(oRow["flower_type"]);
    //
    return prRow;
}));

Once we have data, we can split it into train and test sets:

//Split dataset in two parts: TrainingDataset (80%) and TestDataset (20%)
var trainTestData = mlContext.Data.TrainTestSplit(dataView, testFraction: 0.2);
var trainData = trainTestData.TrainSet;
var testData = trainTestData.TestSet;

The next step in prepare the data for training is define pipeline for dtaa transformation and feature engineering:

//one encoding output category column by defining KeyValues for each category
IEstimator<ITransformer> dataPipeline =
mlContext.Transforms.Conversion.MapValueToKey(outputColumnName: "Label", inputColumnName: nameof(Iris.Species))

//define features columns
.Append(mlContext.Transforms.Concatenate("Features",nameof(Iris.SepalArea), nameof(Iris.PetalArea)));

Once we completes the preparation paert, we can perform the training part. The training start by calling Fit to the pipeline:

%%time
 // Define LightGbm algorithm estimator
IEstimator<ITransformer> lightGbm = mlContext.MulticlassClassification.Trainers.LightGbm();
//train the ML model
TransformerChain<ITransformer> model = dataPipeline.Append(lightGbm).Fit(trainData);

Once the training is completes, we have trained model which can be evaluated. In order to print the evaluation result with formatting, we are going to install Daany DataFrame extension which has implementation of printing results


//evaluate train set
var predictions = model.Transform(trainData);
var metricsTrain = mlContext.MulticlassClassification.Evaluate(predictions);
ConsoleHelper.PrintMultiClassClassificationMetrics("TRAIN Iris DataSet", metricsTrain);
ConsoleHelper.ConsoleWriteHeader("Train Iris DataSet Confusion Matrix ");
ConsoleHelper.ConsolePrintConfusionMatrix(metricsTrain.ConfusionMatrix);

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//evaluate test set
var testPrediction = model.Transform(testData);
var metricsTest = mlContext.MulticlassClassification.Evaluate(testPrediction);
ConsoleHelper.PrintMultiClassClassificationMetrics("TEST Iris Dataset", metricsTest);
ConsoleHelper.ConsoleWriteHeader("Test Iris DataSet Confusion Matrix ");
ConsoleHelper.ConsolePrintConfusionMatrix(metricsTest.ConfusionMatrix);

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As can be seen, we have a 100% accurate model for Iris flower recognition. Now, let’s add a new column into the data frame called Prediction to have a model prediction in the data frame.
In order to do that, we are evaluating the model on the train and the test data set. Once we have a prediction for both sets, we can join them and add as a separate column in Daany data frame. The following code does exactly what we described previously.

var flowerLabels = DataFrameExt.GetLabels(predictions.Schema).ToList();
var p1 = predictions.GetColumn<uint>("PredictedLabel").Select(x=>(int)x).ToList();
var p2 = testPrediction.GetColumn<uint>("PredictedLabel").Select(x => (int)x).ToList();
//join train and test
p1.AddRange(p2);
var p = p1.Select(x => (object)flowerLabels[x-1]).ToList();
//add new column into df
var dic = new Dictionary<string, List<object>> { { "PredictedLabel", p } };
var dff = derivedDF.AddColumns(dic);
dff.Head()

run button The output above shows the first few rows in the data frame. To see the few last rows from the data frame we call a Tail method.

dff.Tail()

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In this blog post, we saw how can we be more productive when using .NET Jupyter Notebook with Machine Learning and Data Exploration and transformation, by using ML.NET and Daany – DAtaANalYtics library. Complete source code for this notebook can be found at GitHub repo:

How to start with C# Jupyter Notebook


Yesterday at Ignite conference .NET team has announced the Jupyter Notebook for .NET languages C# and F#. This is a huge step ahead for all data scientists who want to do data science and machine learning on the .NET platform. With C# Jupyter Notebook you can perform data exploration and transformation, training, evaluation and testing your Ml models. All operations are performed by code block and you can quickly see the result without running and debugging application every time you want to change something. In order to see how it looks like, in this blog post we are going to explore some of the basic functionalities in C# Jupyter Notebook.

How to Install .NET Jupyter Notebook

In order to install Jupyter Notebook you can see the , anyhow here I am going to present this process because it is very short and easy. Before install .NET Jupyter components, you have to install the latest version of and . Once you have Anaconda installed on your machine, open Anaconda Prompt from Windows Start Menu.

To run Anaconda Prompt you have two options:

  • to open power shell or
  • to open classic command prompt.

Select Anaconda Powershell Prompt, and the powershell window will pop up. Once the powershell prompt is opened we can start with the installation of Jupyter Notebook components. The first step is to install the dotnet try global tool.

Type this to cmd:

dotnet tool install -g dotnet-try

After some time you should get the following message:

Then we need to install .NET Kernel by typing the following command:

dotnet try jupyter install 

Then the following message should appear:

In case you have any problems with the installation please refer to official blog post or post an Issue at .

Also note that this version of Jupyter Notebook is in preview, so not all actions will work as you expected. Now that you have installed C# Jupyter, you can open Jupyter notebook from the Anaconda navigator, or just type Jupyter Notebook in to Anaconda Prompt. Once we did that, your default bowers pops up and shows the starting directory in the Jupyter Notebook. If you click New button, you can see option to create C# and F# notebooks. Press C#, and the new C# notebook will appeared in the browser.

Try some basic stuff in notebook.

In the next blog post we are going to explore more and see some of the coolest features in C# Jupyter Notebook.

In depth LSTM Implementation using CNTK on .NET platform


In this blog post the implementation of the LSTM recurrent neural network in CNTK will be shown in detail. The implementation will cover LSTM implementation based on Hochreiter & Schmidhuber (1997) paper which can be found here . The great blog post about LSTM can also be found at , that explains in details the structure of the LSTM cell, as well as some of the most used LSTM variants. In this blog post the LSTM recurrent network will be implemented using CNTK, a deep learning tool using C# programming language and .NET Core platform. Also in case you want to see how to use pure C# without any additional library for LSTM implementation, you can see great MSDN article: By .

Whole implementation of LSTM RNN is part of ANNdotNET – deep learning tool on .NET platform. More information about the project can be found at GitHub Project page:

Introduction to LSTM Recurrent Network

Classic neural networks are built on the fact that data don’t have any order when entering into the network, and the output depend only on the input features. In case when the output depends on features and previous outputs, the classic feed forward neural network cannot help. The solution for such problem may be neural network which can be recursively provides the previous outputs. This kind of network is called recurrent neural network RNN, and it was introduced by the Hopfields in the 1980s, and later popularized when the back-propagation algorithm was improved in the beginning of 1990s. Simple concept of the recurrent neural network can be shown on the following image.

The current output of the recurrent network is defined by the current input Xt, and also on states related on the previous network outputs ht-1, ht-2,

The concept of the recurrent neural network is simple and easy to implement, but the problem raises during the training phase due to unpredictable gradient behavior. During training phase, gradient problem of neural network can be summarized in two categories: the vanishing and the exploding gradient.

The recurrent neural network is based on back-propagation algorithm, specially developed for the recurrent ANN, which is called back-propagation through time, BPTT.  In vanishing gradient problem parameters updates are proportional to the gradient of the error, which in most cases negligibly small, and results that the corresponding weights are constant and stop the network from further training.

On the other hand, exploding gradient problem refers to the opposite behavior, where the updates of weights (gradient of the cost function) became large in each back-propagation step. This problem is caused by the explosion of the long-term components in the recurrent neural network.

The solution to the above problems is specific design of there current network called Long Short-Term Memory, LSTM. One of the main advantages of the LSTM is that it can provide a constant error flow. In order to provide a constant error flow, the LSTM cell contains set of memory blocks,which have the ability to store the temporal state of the network. The LSTM also has special multiplicative units called gates that control the information flow.

The LSTM cell consists of:

  • input gate – which controls the flow of the input activations into the memory cell,
  • output gate which controls the output flow of the cell activation.
  • forget gate, which filters the information from the input and previous output and decides which one should be remembered or forgot and dropped out.

Besides three gates the LSTM cell contains cell update which is usually tanh layer to be part of the cell state.

In each LSTM cell the three variables are coming into the cell:

  • the current input xt,
  • previous output ht-1 and
  • previous cell state ct-1.

On the other hand, from each LSTM cell two variables are getting out:

  • the current output ht and
  • the current cell state ct.

Graphical representation of the LSTM cell is shown on the following image.

In order to implement LSTM recurrent network, first the LSTM cell should be implemented. The LSTM cell has three gates, and two internal states, which should be determined in order to calculate the current output and current cell state.

The LSTM cell can be define as neural network where the input vector x=\left(x_1,x_2,x_3,\ldots x_t\right)  in time t, maps to the output vector y=\left(y_1,\ y_2,\ \ldots,y_m\right), through the calculation of the following layers:

  • the forget gate sigmoid layer for the time t, ft  is calculated by the previous output ht-1 the input vector xt, and the matrix of weights from the forget layer Wf with addition of corresponded bias bi:

f_t=\sigma\left(W_f\bullet\left[h_{t-1},x_t\right]+b_f\right).

  • the input gate sigmoid layer for the time t, it  is calculated by the previous output ht-1 the input vector xt, and the matrix of weights from the input layer Wi with addition of corresponded bias bi:

i_t=\sigma\left(W_i\bullet\left[h_{t-1},x_t\right]+b_i\right).

  • the cell state in time t, Ct  is calculated from the forget gate 
    ft  and the previous cell state Ct-1. The result is summed wth the input gate it and the cell update state {\widetilde{c}}_t, that is tanh layer calculated by the previous output ht-1 the input vector xt, and the weight matrix for the cell with addition of corresponded bias bi:

C_t=f_t\ \otimes C_{t-1}+\ i_t\otimes\tanh{\left(\ W_C\bullet\left[h_{t-1},x_t\right]+b_C\right).}

  • the output gate sigmoid layer for the time t, ot is calculated by the previous output ht-1, the input vector xt, and the matrix of weights from the output layer Wo with addition of corresponded bias bi:

o_t=\sigma\left(\ W_0\bullet\left[h_{t-1},x_t\right]+b_0\right).

The final stage of the LSTM cell is current output ht calculation. The current output  is calculated with the multiplication operation \otimes between output gate layer and tanh layer of the current cell state Ct .

h_t=o_t\otimes\tanh{\left(C_t\right)}.

The current output ht, has passed through the network as the previous state for the next LSTM cell, or as the input for neural network output layer.

LSTM with Peephole connection

One of the LSTM variant which is implemented in python based CNTK is LSTM with peephole connection which is first introduced by Gers & Schmidhuber (2000). LSTM with peephole connection let each gate (forget, input and output) look at the cell state.

Now the gates with peephole connection can be expressed sothat the started terms of each gates are extended with additional matrix of Ct.So, the forget gate with peephole can be expressed:

f_t=\sigma\left(W_f\bullet\left[{C_{t-1},\ h}_{t-1},x_t\right]+b_f\right).

Similarly, the input gate and the output gate with peephole connection are expressed as:

i_t=\sigma\left(W_i\bullet\left[C_{t-1},\ h_{t-1},x_t\right]+b_i\right),

o_t=\sigma\left(\ W_0\bullet\left[{C_{t-1},h}_{t-1},x_t\right]+b_0\right).

With peephole connection LSTM cell get additional matrix for each gate and the number of LSTM parameters are increased by additional 3mXm parameters, where m – is output dimension.

Implementation of LSTM Recurrent network

The CNTK is Microsoft open source library for deep learning written in C++, but it can be run from various programming languages: Python,C#, R, Java. In order to use the library in C#, the CNTK related Nugget package has to be installed, and the project must be built for 64bit architecture.

  1. So open Visual Studio 2017 and create simple .NET Core Console application.
  2. Then install CNTK GPU Nugget package to your recently created console application.

Once the startup project is created the LSTM CNTK implementation can be started.

Implementation of the LSTM Cell

As stated previously the implementation presented in this blog post is  originally implemented in ANNdotNET – open source project for deep learning on .NET platform. It can be found at official . 

The LSTM recurrent network starts by implementation of the LSTMCell class. The LSTMCell class is derived from the NetworkFoundation class which implements basic neural network operations. The Basic operations are implemented through the implementation of the following methods:

  • Bias – bias parameters implementation
  • Weights – implementation of the weights parameters
  • Layer – implementation of the classic fully connected linear layer
  • AFunction – applying activation function on the layer.

NetworkFoundation class is shown in the next code snippet

///////////////////////////////////////////////////////////////////////////////////////////
// ANNdotNET - Deep Learning Tool on .NET Platform                                                      
// Copyright 2017-2018 Bahrudin Hrnjica                                                                                                                                       //
// This code is free software under the MIT License                                     //
// See license section of https://github.com/bhrnjica/anndotnet/blob/master/LICENSE.md  //
//                                                                                      
// Bahrudin Hrnjica                                                                     
// [email protected]                                                                 
// Bihac, Bosnia and Herzegovina                                                         //
// http://bhrnjica.net                                                                  
//////////////////////////////////////////////////////////////////////////////////////////
using CNTK;
using NNetwork.Core.Common;

namespace NNetwork.Core.Network
{
public class NetworkFoundation
{

public Variable Layer(Variable x, int outDim, DataType dataType, DeviceDescriptor device, uint seed = 1 , string name="")
{
    var b = Bias(outDim, dataType, device);         
    var W = Weights(outDim, dataType, device, seed, name);

    var Wx = CNTKLib.Times(W, x, name+"_wx");
    var l = CNTKLib.Plus(b,Wx, name);

    return l;
}

public Parameter Bias(int nDimension, DataType dataType, DeviceDescriptor device)
{
    //initial value
    var initValue = 0.01;
    NDShape shape = new int[] { nDimension };
    var b = new Parameter(shape, dataType, initValue, device, "_b");
    //
    return b;
}

public Parameter Weights(int nDimension, DataType dataType, DeviceDescriptor device, uint seed = 1, string name = "")
{
    //initializer of parameter
    var glorotI = CNTKLib.GlorotUniformInitializer(1.0, 1, 0, seed);
    //create shape the dimension is partially known
    NDShape shape = new int[] { nDimension, NDShape.InferredDimension };
    var w = new Parameter(shape, dataType, glorotI, device, name=="" ? "_w" : name);
    //
    return w;
}

public Function AFunction(Variable x, Activation activation, string outputName="")
{
    switch (activation)
    {
        default:
        case Activation.None:
            return x;
        case Activation.ReLU:
            return CNTKLib.ReLU(x, outputName);
        case Activation.Softmax:
            return CNTKLib.Sigmoid(x, outputName);
        case Activation.Tanh:
            return CNTKLib.Tanh(x, outputName);
    }
}
}}

As can be seen, methods implement basic neural buildingblocks, which can be apply to any network type. Once the NetworkFoundation baseclass is implemented, the LSTM cell class implementation starts by definingthree properties and custom constructor, that is shown in the following code snippet:

///////////////////////////////////////////////////////////////////////////////////////////
// ANNdotNET - Deep Learning Tool on .NET Platform                                                       
// Copyright 2017-2018 Bahrudin Hrnjica                                                                                                                                       //
// This code is free software under the MIT License                                     //
// See license section of https://github.com/bhrnjica/anndotnet/blob/master/LICENSE.md  //
//                                                                                      
// Bahrudin Hrnjica                                                                     
// [email protected]                                                                 
// Bihac, Bosnia and Herzegovina                                                         //
// http://bhrnjica.net                                                                  
//////////////////////////////////////////////////////////////////////////////////////////
using CNTK;
using NNetwork.Core.Common;

namespace NNetwork.Core.Network.Modules
{
public class LSTM : NetworkFoundation
{
    public Variable X { get; set; } //LSTM Cell Input
    public Function H { get; set; } //LSTM Cell Output
    public Function C { get; set; } //LSTM Cell State

public LSTM(Variable input, Variable dh, Variable dc, DataType dataType, Activation actFun, bool usePeephole, bool useStabilizer, uint seed, DeviceDescriptor device)
{
    //create cell state
    var c = CellState(input, dh, dc, dataType, actFun, usePeephole, useStabilizer, device, ref seed);

    //create output from input and cell state
    var h = CellOutput(input, dh, c, dataType, device, useStabilizer, usePeephole, actFun, ref seed);

    //initialize properties
    X = input;
    H = h;
    C = c;
}

Properties X, H and C, hold current values of the LSTM cell,once the LSTM object is created. The LSTM constructor takes several arguments:

  • the first three are variables for the input, previous output and previous cell state;
  • the activation function of the cell update layer. 

The constructor also contains two arguments for creation a different LSTM variant: peepholes, and self-stabilization, and few other self-explained arguments. The LSTM constructor creates cell state and output by calling CellState and CellOutput methods respectively. Thei mplementation of those methods is shown on the next code snippet:

public Function CellState(Variable x, Variable ht_1, Variable ct_1, DataType dataType, 
    Activation activationFun, bool usePeephole, bool useStabilizer, DeviceDescriptor device, ref uint seed)
{
    var ft = AGate(x, ht_1, ct_1, dataType, usePeephole, useStabilizer, device, ref seed, "ForgetGate");
    var it = AGate(x, ht_1, ct_1, dataType, usePeephole, useStabilizer, device, ref seed, "InputGate");
    var tan = Gate(x, ht_1, ct_1.Shape[0], dataType, device, ref seed);

    //apply Tanh (or other) to gate
    var tanH = AFunction(tan, activationFun, "TanHCt_1" );

    //calculate cell state
    var bft = CNTKLib.ElementTimes(ft, ct_1,"ftct_1");
    var bit = CNTKLib.ElementTimes(it, tanH, "ittanH");

    //cell state
    var ct = CNTKLib.Plus(bft, bit, "CellState");
    //
    return ct;
}

public Function CellOutput(Variable input, Variable ht_1, Variable ct, DataType dataType, DeviceDescriptor device, 
    bool useStabilizer, bool usePeephole, Activation actFun ,ref uint seed)
{
    var ot = AGate(input, ht_1, ct, dataType, usePeephole, useStabilizer, device, ref seed, "OutputGate");

    //apply activation function to cell state
    var tanHCt = AFunction(ct, actFun, "TanHCt");

    //calculate output
    var ht = CNTKLib.ElementTimes(ot, tanHCt,"Output");

    //create output layer in case different dimensions between cell and output
    var c = ct;
    Function h = null;
    if (ht.Shape[0] != ct.Shape[0])
    {
        //rectified dimensions by adding linear layer
        var so = !useStabilizer? ct : Stabilizer(ct, device);
        var wx_b = Weights(ht_1.Shape[0], dataType, device, seed++);
        h = wx_b * so;
    }
    else
        h = ht;

    return h;
}

Above methods have been implemented by using previously defined gates and blocks. The method AGate creates LSTM gate. The method is called two times in order to create forget and input gates. Then the Gate method is called in order to create linear layer for the update cell state. The activation function is provided as the constructor argument. Implementation of AGate and Gate functions is shown in the following code snippet:

public Variable AGate(Variable x, Variable ht_1, Variable ct_1, DataType dataType, bool usePeephole,
    bool useStabilizer, DeviceDescriptor device, ref uint seed, string name)
{
    //cell dimension
    int cellDim = ct_1.Shape[0];
    //define previous output with stabilization of if defined
    var h_prev = !useStabilizer ? ht_1 : Stabilizer(ht_1, device);

    //create linear gate
    var gate = Gate(x, h_prev, cellDim, dataType, device, ref seed);
    if (usePeephole)
    {
        var c_prev = !useStabilizer ? ct_1 : Stabilizer(ct_1, device);
        gate = gate + Peep(c_prev, dataType, device, ref seed);
    }
    //create forget gate
    var sgate = CNTKLib.Sigmoid(gate, name);
    return sgate;
}

private Variable Gate(Variable x, Variable hPrev, int cellDim,
                            DataType dataType, DeviceDescriptor device, ref uint seed)
{
    //create linear layer
    var xw_b = Layer(x, cellDim, dataType, device, seed++);
    var u = Weights(cellDim, dataType, device, seed++,"_u");
    //
    var gate = xw_b + (u * hPrev);
    return gate;
}

As can be seen AGate calls the Gate method in order to create linear layer, and then apply the activation function.

In order to create LSTM variant with peephole connection, as well as LSTM with self-stabilization, two additional methods are implemented. The peephole connection is explained previously. The implementation of Stabilizer methods is based on the implementation found at C# examples on the CNTK github page, with minor modification and re-factorization.

internal Variable Stabilizer(Variable x, DeviceDescriptor device)
{
    //define floating number
    var f = Constant.Scalar(4.0f, device);

    //make inversion of prev. value
    var fInv = Constant.Scalar(f.DataType, 1.0 / 4.0f);

    //create value of 1/f*ln (e^f-1)
    double initValue = 0.99537863;

    //create param with initial value
    var param = new Parameter(new NDShape(), f.DataType, initValue, device, "_stabilize");

    //make exp of product scalar and parameter
    var expValue = CNTKLib.Exp(CNTKLib.ElementTimes(f, param));

    //
    var cost = Constant.Scalar(f.DataType, 1.0) + expValue;

    var log = CNTKLib.Log(cost);

    var beta = CNTKLib.ElementTimes(fInv, log);

    //multiplication of the variable layer with constant scalar beta
    var finalValue = CNTKLib.ElementTimes(beta, x);

    return finalValue;
}

internal Function Peep(Variable cstate, DataType dataType, DeviceDescriptor device, ref uint seed)
{
    //initial value
    var initValue = CNTKLib.GlorotUniformInitializer(1.0, 1, 0, seed);

    //create shape which for bias should be 1xn
    NDShape shape = new int[] { cstate.Shape[0] };

    var bf = new Parameter(shape, dataType, initValue, device, "_peep");

    var peep = CNTKLib.ElementTimes(bf, cstate);
    return peep;
}

The Peep method is based on previous description in the blog post, that simply adds the additional set of parameters which includes the previous cell state into Gates.

Implementation of the LSTM Recurrent Network

Once we have the LSTM cell implementation it is easy toimplement recurrent network based on LSTM. Previously the LSTM is defined withthree input variables: input and two previous state variables. Those previous states should be defined not as real variables but as placeholders, and should be changed dynamically for each iteration. So, the recurrent network starts by defining placeholders of previous output and previous cell state. Then the LSTMcell object is created. Once the the LSTM is created, the actual values is replaced by the previous values by calling the CNTK method PastValue. Then the placeholders are replaced with the past values of the variables. At the end the method return the CNTK Function object, which can be one of two cases, which is controlled by the returnSequence argument:

  • first case where the method returns the full sequence,
  • second case where the methods return the last element of the sequence.
 
/////////////////////////////////////////////////////////////////////////////////////////
// ANNdotNET - Deep Learning Tool on .NET Platform                                      
// Copyright 2017-2018 Bahrudin Hrnjica                                                 
//
// This code is free software under the MIT License                                     
// See license section of  https://github.com/bhrnjica/anndotnet/blob/master/LICENSE.md  
//
// Bahrudin Hrnjica                                                                     
// [email protected]                                                                 
// Bihac, Bosnia and Herzegovina                                                         
// http://bhrnjica.net                                                                  //
////////////////////////////////////////////////////////////////////////////////////////
using CNTK;
using NNetwork.Core.Common;
using NNetwork.Core.Network.Modules;
using System;
using System.Collections.Generic;

namespace NNetwork.Core.Network
{
public class RNN
{
public static Function RecurrenceLSTM(Variable input, int outputDim, int cellDim, DataType dataType, DeviceDescriptor device, bool returnSequence=false,
    Activation actFun = Activation.TanH, bool usePeephole = true, bool useStabilizer = true, uint seed = 1)
{
    if (outputDim &lt;= 0 || cellDim &lt;= 0)
        throw new Exception("Dimension of LSTM cell cannot be zero.");
    //prepare output and cell dimensions 
    NDShape hShape = new int[] { outputDim };
    NDShape cShape = new int[] { cellDim };

    //create placeholders
    //Define previous output and previous cell state as placeholder which will be replace with past values later
    var dh = Variable.PlaceholderVariable(hShape, input.DynamicAxes);
    var dc = Variable.PlaceholderVariable(cShape, input.DynamicAxes);

    //create lstm cell
    var lstmCell = new LSTM(input, dh, dc, dataType, actFun, usePeephole, useStabilizer, seed, device);

    //get actual values of output and cell state
    var actualDh = CNTKLib.PastValue(lstmCell.H);
    var actualDc = CNTKLib.PastValue(lstmCell.C);

    // Form the recurrence loop by replacing the dh and dc placeholders with the actualDh and actualDc
    lstmCell.H.ReplacePlaceholders(new Dictionary&lt;Variable, Variable&gt; { { dh, actualDh }, { dc, actualDc } });

    //return value depending of type of LSTM layer
    if (returnSequence)
        return lstmCell.H;
    else
        return CNTKLib.SequenceLast(lstmCell.H); 

}
}}

As can be seen, the RNN class contains only one static method, which return the CNTK Function object which contains the recurrent network with LSTM cell. The method takes several arguments: input variable, dimension of the output of the recurrent network, dimension of the LSTM cell, and the additional arguments for creation different variants of the LSTM cell.

Implementation of Test Application

Now that the full LSTM based recurrent network is implemented, we are going to provide the test application that can test basic LSTM functionality. The application contains two test methods in order to check:

  • number of LSTM parameters, and
  • output and cell states of the LSTM cell for two iterations.

Testing the correct number of the parameters

The first method implements validation of the correct numberof LSTM parameters. The LSTM cell has three kinds of matrices: U and W and bfor each LSTM component: forget, input and output gate, and cell update.
Let assume the number of input dimension is n,and the number of output is m. Also let assume that dimension number of the cell is equal to output dimension. We can defined the following matrices:

  • U matrix with dimensions of mxn
  • W matrix with dimensions of mxm
  • B matrix (vector) with dimensions 1xm

In total the LSTM has P_{\left(LSTM\right)}=4\bullet\left(m^2+m\bullet n+m\right).

In case the LSTM has peephole connection the the number of parameters is increased with additional C matrix with 1xm parameters.

In total the LSTM with peephole connection has P_{\left(LSTM\right)}=4\bullet\left(m^2+m\bullet n+m\right)+3\bullet1\bullet m. The test method is implemented for n=3, and m=4, so the total number of parameters for default LSTM cell is P(n)=4(9+6+3)=4*18=72. With peephole connection the LSTM cell has P(n)= 4(9+6+3)+3*1*4 = 4*18+3*16 = 72+12=84.

In case the LSTM cell is defined with self-stabilization parameter, the additional 4xm parameters are defined.

Now that we defined parameter number for pure LSTM, with peephole and self-stabilization, we can implement test methods based on n=3 and m=4:

[TestMethod]
public void LSTM_Test_Params_Count()
{
    //define values, and variables
    Variable x = Variable.InputVariable(new int[] { 3 }, DataType.Float, "input");
    Variable y = Variable.InputVariable(new int[] { 4 }, DataType.Float, "output");

    //Number of LSTM parameters
    var lstm1 = RNN.RecurrenceLSTM(x,4,4, DataType.Float,device, Activation.Tanh,true,true,1);

    var ft = lstm1.Inputs.Where(l=&gt;l.Uid.StartsWith("Parameter")).ToList();
    var consts = lstm1.Inputs.Where(l =&gt; l.Uid.StartsWith("Constant")).ToList();
    var inp = lstm1.Inputs.Where(l =&gt; l.Uid.StartsWith("Input")).ToList();

    //bias params
    var bs = ft.Where(p=&gt;p.Name.Contains("_b")).ToList();
    var totalBs = bs.Sum(v =&gt; v.Shape.TotalSize);
    Assert.AreEqual(totalBs,12);
    //weights
    var ws = ft.Where(p =&gt; p.Name.Contains("_w")).ToList();
    var totalWs = ws.Sum(v =&gt; v.Shape.TotalSize);
    Assert.AreEqual(totalWs, 24);
    //update
    var us = ft.Where(p =&gt; p.Name.Contains("_u")).ToList();
    var totalUs = us.Sum(v =&gt; v.Shape.TotalSize);
    Assert.AreEqual(totalUs, 36);
    

    var totalOnly = totalBs + totalWs + totalUs;
    var totalWithSTabilize = totalOnly + totalst;
    var totalWithPeep = totalOnly + totalPh;

    var totalP = totalOnly + totalst + totalPh;
    var totalParams = ft.Sum(v=&gt;v.Shape.TotalSize);
    Assert.AreEqual(totalP,totalParams);
}

Testing the output and cell state values

In this test the network parameters input, previous output and cell states are setup. The result of this test is weather the LSTM cell returns correct output and cell state values for first and second iteration. The implementation of this test is shows on the following code snippet:

public void LSTM_Test_WeightsValues()
{

    //define values, and variables
    Variable x = Variable.InputVariable(new int[] { 2 }, DataType.Float, "input");
    Variable y = Variable.InputVariable(new int[] { 3 }, DataType.Float, "output");

    //data 01
    var x1Values = Value.CreateBatch&lt;float&gt;(new NDShape(1, 2), new float[] { 1f, 2f }, device);
    var ct_1Values = Value.CreateBatch&lt;float&gt;(new NDShape(1, 3), new float[] { 0f, 0f, 0f }, device);
    var ht_1Values = Value.CreateBatch&lt;float&gt;(new NDShape(1, 3), new float[] { 0f, 0f, 0f }, device);

    var y1Values = Value.CreateBatch&lt;float&gt;(new NDShape(1, 3), new float[] { 0.0629f, 0.0878f, 0.1143f }, device);

    //data 02
    var x2Values = Value.CreateBatch&lt;float&gt;(new NDShape(1, 2), new float[] { 3f, 4f }, device);
    var y2Values = Value.CreateBatch&lt;float&gt;(new NDShape(1, 3), new float[] { 0.1282f, 0.2066f, 0.2883f }, device);

    //Create LSTM Cell with predefined previous output and prev cell state
    Variable ht_1 = Variable.InputVariable(new int[] { 3 }, DataType.Float, "prevOutput");
    Variable ct_1 = Variable.InputVariable(new int[] { 3 }, DataType.Float, "prevCellState");
    var lstmCell = new LSTM(x, ht_1, ct_1, DataType.Float, Activation.Tanh, false, false, 1, device);
            

    var ft = lstmCell.H.Inputs.Where(l =&gt; l.Uid.StartsWith("Parameter")).ToList();
    var pCount = ft.Sum(p =&gt; p.Shape.TotalSize);
    var consts = lstmCell.H.Inputs.Where(l =&gt; l.Uid.StartsWith("Constant")).ToList();
    var inp = lstmCell.H.Inputs.Where(l =&gt; l.Uid.StartsWith("Input")).ToList();

    //bias params
    var bs = ft.Where(p =&gt; p.Name.Contains("_b")).ToList();
    var pa = new Parameter(bs[0]);
    pa.SetValue(new NDArrayView(pa.Shape, new float[] { 0.16f, 0.17f, 0.18f }, device));
    var pa1 = new Parameter(bs[1]);
    pa1.SetValue(new NDArrayView(pa1.Shape, new float[] { 0.16f, 0.17f, 0.18f }, device));
    var pa2 = new Parameter(bs[2]);
    pa2.SetValue(new NDArrayView(pa2.Shape, new float[] { 0.16f, 0.17f, 0.18f }, device));
    var pa3 = new Parameter(bs[3]);
    pa3.SetValue(new NDArrayView(pa3.Shape, new float[] { 0.16f, 0.17f, 0.18f }, device));
            
    //set value to weights parameters
    var ws = ft.Where(p =&gt; p.Name.Contains("_w")).ToList();
    var ws0 = new Parameter(ws[0]);
    var ws1 = new Parameter(ws[1]);
    var ws2 = new Parameter(ws[2]);
    var ws3 = new Parameter(ws[3]);
    (ws0).SetValue(new NDArrayView(ws0.Shape, new float[] { 0.01f, 0.03f, 0.05f, 0.02f, 0.04f, 0.06f }, device));
    (ws1).SetValue(new NDArrayView(ws1.Shape, new float[] { 0.01f, 0.03f, 0.05f, 0.02f, 0.04f, 0.06f }, device));
    (ws2).SetValue(new NDArrayView(ws2.Shape, new float[] { 0.01f, 0.03f, 0.05f, 0.02f, 0.04f, 0.06f }, device));
    (ws3).SetValue(new NDArrayView(ws3.Shape, new float[] { 0.01f, 0.03f, 0.05f, 0.02f, 0.04f, 0.06f }, device));
            
    //set value to update parameters
    var us = ft.Where(p =&gt; p.Name.Contains("_u")).ToList();
    var us0 = new Parameter(us[0]);
    var us1 = new Parameter(us[1]);
    var us2 = new Parameter(us[2]);
    var us3 = new Parameter(us[3]);
    (us0).SetValue(new NDArrayView(us0.Shape, new float[] {  0.07f, 0.10f, 0.13f, 0.08f, 0.11f, 0.14f, 0.09f, 0.12f, 0.15f }, device));
    (us1).SetValue(new NDArrayView(us1.Shape, new float[] {  0.07f, 0.10f, 0.13f, 0.08f, 0.11f, 0.14f, 0.09f, 0.12f, 0.15f }, device));
    (us2).SetValue(new NDArrayView(us2.Shape, new float[] {  0.07f, 0.10f, 0.13f, 0.08f, 0.11f, 0.14f, 0.09f, 0.12f, 0.15f }, device));
    (us3).SetValue(new NDArrayView(us3.Shape, new float[] {  0.07f, 0.10f, 0.13f, 0.08f, 0.11f, 0.14f, 0.09f, 0.12f, 0.15f }, device));

    //evaluate 
    //Evaluate model after weights are setup
    var inV = new Dictionary&lt;Variable, Value&gt;();
    inV.Add(x, x1Values);
    inV.Add(ht_1, ht_1Values);
    inV.Add(ct_1, ct_1Values);

    //evaluate output when previous values are zero
    var outV11 = new Dictionary&lt;Variable, Value&gt;();
    outV11.Add(lstmCell.H, null);
    lstmCell.H.Evaluate(inV, outV11, device);
            
    //test  result values
    var result = outV11[lstmCell.H].GetDenseData&lt;float&gt;(lstmCell.H);
    Assert.AreEqual(result[0][0], 0.06286034f);//
    Assert.AreEqual(result[0][1], 0.0878196657f);//
    Assert.AreEqual(result[0][2], 0.114274308f);//

    //evaluate cell state
    var outV = new Dictionary&lt;Variable, Value&gt;();
    outV.Add(lstmCell.C, null);
    lstmCell.C.Evaluate(inV, outV, device);

    var resultc = outV[lstmCell.C].GetDenseData&lt;float&gt;(lstmCell.C);
    Assert.AreEqual(resultc[0][0], 0.114309229f);//
    Assert.AreEqual(resultc[0][1], 0.15543206f);//
    Assert.AreEqual(resultc[0][2], 0.197323829f);//

    //evaluate second value, with previous values as previous state
    //setup previous state and output
    ct_1Values = Value.CreateBatch&lt;float&gt;(new NDShape(1, 3), new float[] { resultc[0][0], resultc[0][1], resultc[0][2] }, device);
    ht_1Values = Value.CreateBatch&lt;float&gt;(new NDShape(1, 3), new float[] { result[0][0], result[0][1], result[0][2] }, device);

    //Prepare for the evaluation
    inV = new Dictionary&lt;Variable, Value&gt;();
    inV.Add(x, x2Values);
    inV.Add(ht_1, ht_1Values);
    inV.Add(ct_1, ct_1Values);

    outV11 = new Dictionary&lt;Variable, Value&gt;();
    outV11.Add(lstmCell.H, null);
    lstmCell.H.Evaluate(inV, outV11, device);

    //test  result values
    result = outV11[lstmCell.H].GetDenseData&lt;float&gt;(lstmCell.H);
    Assert.AreEqual(result[0][0], 0.128203377f);//
    Assert.AreEqual(result[0][1], 0.206633776f);//
    Assert.AreEqual(result[0][2], 0.288335562f);//

    //evaluate cell state
    outV = new Dictionary&lt;Variable, Value&gt;();
    outV.Add(lstmCell.C, null);
    lstmCell.C.Evaluate(inV, outV, device);

    //evaluate cell state with previous value
    resultc = outV[lstmCell.C].GetDenseData&lt;float&gt;(lstmCell.C);
    Assert.AreEqual(resultc[0][0], 0.227831185f);//
    Assert.AreEqual(resultc[0][1], 0.3523231f);//
    Assert.AreEqual(resultc[0][2], 0.4789199f);//
}

In this article the implementation of the LSTM cell is presented in details from the theory and implementation. Also the article contains two test methods in order to prove the correctness of the implementation. The result values of the output and the cell states are compared with manually calculated values.