How does the algorithm of the residualSimilarityModel looks like?

Dear MATLAB Community,

I actually have a simple question and don't need a super scientific answer. What is the rough algorithm of the residualSimilarityModel?

I know that for the training every ensemble member gets a regression fit based on the equation defined in Method. And then I assume that in case of the command predictRUL() a additonal regression fit is performed for the input data and followed by a kNN classifiaction which checkes witch regression model of the training data is closest to the actual regression model and then predicting the RUL of the closest model.

However, in the description of "Method" is written: "Type of model trained using the fit function and used for residual generation, specified as one of the following:" What is meant by residual generation? This part is confusing me in my assumtion, for what is the residual of the regression model fit used? Somehow, I interpret that I am wrong with my kNN assumtion.

Does somone has a overview of how this model works?

[Marvin Eckert]

Addendum: Thats the discription inside the model

% Residual Similarity model compares the magnitudes of the residuals
% generated by the ensemble models to determine the nearest neighbors of a
% test component's degradation profile. First, each member of the
% historical data ensemble is fitted with a model of identical structure,
% using the "fit" method. Then the test component's degradation data is used
% to compute 1-step prediction errors for each model. The magnitudes of
% these errors serve as indicators of closeness of the test component
% to the historical ensemble members; the smaller the residual,
% the closer the test component is to the member that generated it. You can
% view Residual Similarity model as a special type of Pairwise Similarity
% model that uses the magnitudes of model residuals as a measure of
% distance.
%
% The remaining useful life (RUL) of the test component is estimated as the
% median statistic of the life span of most similar components minus the
% current life time value (see predictRUL).

[Marvin Eckert]

Mhhh ... maybe I wine my question down. Can somone assume what is ment by this sentence?

> Then the test component's degradation data is used to compute 1-step prediction errors for each model (out of the trainings set).

Answer 1

[Ayush Gupta]

1-step prediction for a model is for a time series IT = {Y1, Y2 ,…, YT }.

At time T, we want to forecast YT+1, YT+2, YT+1, YT+2, …, YT+l

Where T is the forecast origin and l is forecast horizon.

1-step ahead forecast = Forecasted value YT+1

= E [YT+1 | YT, YT-1,…., Y1]

And 1-step prediction error is the margin by which it is varying with the actual value.

[Marvin Eckert]

Thanks, for the answer!