residualSimilarityModel

Residual comparison-based similarity model for estimating remaining useful life

Description

Use residualSimilarityModel to estimate the remaining useful life (RUL) of a component using a residual comparison-based similarity model. This model is useful when you have degradation profiles for an ensemble of similar components, such as multiple machines manufactured to the same specifications, and you know the dynamics of the degradation process. The historical data for each member of the data ensemble is fitted with a model of identical structure. The degradation data of the test component is used to compute 1-step prediction errors, or residuals, for each ensemble model. The magnitudes of these errors indicate how similar the test component is to the corresponding ensemble members.

To configure a residualSimilarityModel object, use fit, which trains and stores the degradation model for each data ensemble member. Once you configure the parameters of your similarity model, you can then predict the remaining useful life of similar components using predictRUL. For similarity models, the RUL of the test component is estimated as the median statistic of the lifetime span of the most similar components minus the current lifetime value of the test component. For a basic example illustrating RUL prediction, see Update RUL Prediction as Data Arrives.

For general information on predicting remaining useful life, see Models for Predicting Remaining Useful Life.

Creation

Syntax

mdl = residualSimilarityModel

mdl = residualSimilarityModel(initModel)

mdl = residualSimilarityModel(___,Name,Value)

Description

mdl = residualSimilarityModel creates a residual comparison-based similarity model for estimating RUL and initializes the model with default settings.

mdl = residualSimilarityModel(initModel) creates a residual comparison-based similarity model and initializes the model parameters using an existing residualSimilarityModel object initModel.

mdl = residualSimilarityModel(___,Name,Value) specifies user-settable model properties using name-value pairs. For example, residualSimilarityModel('LifeTimeUnit',"days") creates a residual comparison-based similarity model that uses days as a lifetime unit. You can specify multiple name-value pairs. Enclose each property name in quotes.

Input Arguments

initModel — Residual comparison-based similarity model

residualSimilarityModel object

Residual comparison-based similarity model, specified as a residualSimilarityModel object.

Properties

Method — Type of model

"arma2" (default) | "linear" | "arima2" | "poly2" | "exp1" | ...

Type of model trained using the fit function and used for residual generation, specified as one of the following:

• "linear" — Line with offset term

• "poly2" — Second-order polynomial

• "poly3" — Third-order polynomial

• "exp1" — Exponential with offset term

• "exp2" — Sum of two exponentials

• "arma2" — Second-order ARMA model

• "arma3" — Third-order ARMA model

• "arima2" — Second-order ARMA model with noise integration

• "arima3" — Third-order ARMA model with noise integration

Select the model type based on your knowledge of the dynamics of the component degradation process.

You can specify Method:

• Using a name-value pair when you create the model

• Using dot notation after model creation

For more information on estimating ARMA and polynomial models, see armax and polyfit, respectively.

Distance — Distance computation method

"euclidian" (default) | "absolute" | function handle

Distance computation method, specified as one of the following:

• "euclidian" — Use the 2-norm of the residual signal.

• "absolute" — Use the 1-norm of the residual signal.

• Function handle — Use a custom function of the form:

  D = distanceFunction(r)

  where,

  • r is the residual, specified as a column vector.

  • D is the distance, returned as nonnegative scalar.

You can specify Distance:

• Using a name-value pair when you create the model

• Using dot notation after model creation

Models — Parameters of the fitted models

Read-only: cell array

This property is read-only.

Parameters of the fitted models for each member of the training data ensemble, specified as a cell array and assigned by the fit function. The content of Models depends on the type of model used for regression, as specified in Method.

Method	Model Structure	Models Cell Content
"linear"	at + b	Row vector — [a b]
"poly2"	at2 + bt + c	Row vector — [a b c]
"poly3"	at3 + bt2 + ct + d	Row vector — [a b c d]
"exp1"	aebt+c	Row vector — [a b c]
"exp2"	aebt+cedt	Row vector — [a b c d]
"arma2"	Second-order ARMA model: $$A\left(q\right)S\left(t\right)=C\left(q\right)e\left(t\right)$$ where A(q) = [1 a1q-1 a2q-2] C(q) = [1 c1q-1] S(t) is the degradation feature	Structure with fields: A — Row vector [1 a1 a2] C — Row vector [1 c1]
"arma3"	Similar to "arma2", but with A(q) third-order and C(q) second-order	Structure with fields: A — Row vector [1 a1 a2 a2] C — Row vector [1 c1 c2]
"arima2"	Similar to "arma2", but with an additional noise integrator: $$A\left(q\right)S\left(t\right)=\frac{C\left(q\right)}{1-q^{-1}}e\left(t\right)$$	Structure with fields: A — Row vector [1 a1 a2] C — Row vector [1 c1]
"arima3"	Similar to "arma3", but with an additional noise integrator	Structure with fields: A — Row vector [1 a1 a2 a2] C — Row vector [1 c1 c2]

For more information on estimating ARMA and polynomial models, see armax and polyfit, respectively.

ModelMSE — Mean squared error of the estimation for each model

Read-only: vector

This property is read-only.

Mean squared error of the estimation for each model in Models, specified as a vector and assigned by the fit function.

LifeSpan — Ensemble member life spans

Read-only: double vector (default) | vector of duration objects

This property is read-only.

Ensemble member life spans, specified as a double vector or duration object vector and computed from the ensemble member degradation profiles by the fit function.

NumNearestNeighbors — Number of nearest neighbors for RUL estimation

Inf (default) | finite positive integer

Number of nearest neighbors for RUL estimation, specified as Inf or a finite positive integer. If NumNearestNeighbors is Inf, then predictRUL uses all the ensemble members during estimation.

You can specify NumNearestNeighbors:

• Using a name-value pair when you create the model

• Using dot notation after model creation

IncludeTies — Flag to include ties

true (default) | false

Flag to include ties, specified as true or false. When IncludeTies is true, the model includes all neighbors whose distance to the test component data is less than the Kth smallest distance, where K is equal to NumNearestNeigbors.

You can specify IncludeTies:

• Using a name-value pair when you create the model

• Using dot notation after model creation

Standardize — Flag for standardizing residuals

false (default) | true

Flag for standardizing residuals before computing distance, specified as true or false.

When Standardize is true, the residuals are scaled by the inverse square root of the estimated mean squared errors in ModelMSE.

You can specify Standardize:

• Using a name-value pair when you create the model

• Using dot notation after model creation

LifeTimeVariable — Lifetime variable

"" (default) | string

Lifetime variable, specified as a string that contains a valid MATLAB^® variable name or "".

When you train the model using the fit function, if your training data is a:

• table, then LifeTimeVariable must match one of the variable names in the table

• timetable, then LifeTimeVariable one of the variable names in the table or the dimension name of the time variable, data.Properties.DimensionNames{1}

You can specify LifeTimeVariable:

• Using a name-value pair when you create the model

• As an argument when you call the fit function

• Using dot notation after model creation

LifeTimeUnit — Lifetime variable units

"" (default) | string

Lifetime variable units, specified as a string.

The units of the lifetime variable do not need to be time-based. The life of the test component can be measured in terms of a usage variable, such as distance traveled (miles) or fuel consumed (gallons).

DataVariables — Degradation variable names

"" (default) | string | string array

Degradation variable names, specified as a string or string array. The strings in DataVariables must be valid MATLAB variable names.

You can specify DataVariables:

• Using a name-value pair when you create the model

• As an argument when you call the fit function

• Using dot notation after model creation

UseParallel — Flag for using parallel computing

false (default) | true

Flag for using parallel computing for nearest-neighbor searching, specified as either true or false.

You can specify UseParallel:

• Using a name-value pair when you create the model

• Using dot notation after model creation

UserData — Additional model information

[] (default) | any data type or format

Additional model information for bookkeeping purposes, specified as any data type or format. The model does not use this information.

You can specify UserData:

• Using a name-value pair when you create the model

• Using dot notation after model creation

Object Functions

predictRUL	Estimate remaining useful life for a test component
fit	Estimate parameters of remaining useful life model using historical data
compare	Compare test data to historical data ensemble for similarity models

Examples

Train Residual Similarity Model

Load training data.

load('residualTrainVectors.mat')

The training data is a cell array of column vectors. Each column vector is a degradation feature profile for a component.

Create a residual similarity model with default settings.

mdl = residualSimilarityModel;

Train the similarity model using the training data.

fit(mdl,residualTrainVectors)

Train Residual Similarity Model Using Tabular Data

Load training data.

load('residualTrainTables.mat')

The training data is a cell array of tables. Each table is a degradation feature profile for a component. Each profile consists of life time measurements in the "Time" variable and corresponding degradation feature measurements in the "Condition" variable.

Create a residual similarity model that fits the data with a third-order ARMA model and uses an absolute distance metric.

mdl = residualSimilarityModel('Method',"arma3",'Distance',"absolute");

Train the similarity model using the training data. Specify the names of the life time and data variables.

fit(mdl,residualTrainTables,"Time","Condition")

Predict RUL Using Residual Similarity Model

Load training data.

load('residualTrainTables.mat')

The training data is a cell array of tables. Each table is a degradation feature profile for a component. Each profile consists of life time measurements in the "Time" variable and corresponding degradation feature measurements in the "Condition" variable.

Create a residual similarity model that fits the data with a third-order ARMA model and uses hours as the life time unit.

mdl = residualSimilarityModel('Method',"arma3",'LifeTimeUnit',"hours");

Train the similarity model using the training data. Specify the names of the life time and data variables.

fit(mdl,residualTrainTables,"Time","Condition")

Load testing data. The test data contains the degradation feature measurements for a test component up to the current life time.

load('residualTestData.mat')

Predict the RUL of the test component using the trained similarity model.

estRUL = predictRUL(mdl,residualTestData)

estRUL = duration
   85.73 hr

The estimated RUL for the component is around 86 hours.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The predictRUL command supports code generation with MATLAB Coder™ for this RUL model type. Before generating code that uses this model, you must save the model using saveRULModelForCoder. For an example, see Generate Code for Predicting Remaining Useful Life.

• You cannot change any properties of this RUL model at run time.

• For code generation, you must set the Method property of residualSimilarityModel to "linear", "poly2", "poly3". Other values of Method, including the default value "arima", are not supported for code generation.

• If you specify the Distance property of residualSimilarityModel as a function handle, it cannot be an anonymous function.

• See predictRUL for additional limitations on code generation.

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To evaluate these models in parallel, set the UseParallel property to true.

Version History

Introduced in R2018a