Comprehensive Errors-invariables-based model identification (Part 2)

Learning or developing dynamic models from experimental data is crucial in monitoring and control of processes. In general, measurements of both inputs and outputs of a process are subject to noise. Model development from such data is treated under the broad banner of errors-invariables (EIV) identification. The research carried out by our research group during the last five years on this topic has led to a novel approach, known as the dynamic iterative principal component analysis (DIPCA) to comprehensively identify linear time-invariant models and error characteristics from noisy data for single-input, single-output systems. The highlights of the developed method are (i) minimal user intervention with maximal information (ii) strong theoretical support and (iii) comprehensive inference of the system characteristics including model order, delay, parameter estimates and noise covariances ([1]). The method has been ported to a MATLAB-based toolbox with a graphical user interface in the recently RBCDSAI-funded project titled “Comprehensive errors-in-variables-based model identification” for the year 2018-19. Version 1.0 of this toolbox is available for experimentation and testing purposes from the proponent’s website A self-installation app file including the relevant documentation, user manual, test data and links to related published material are provided for download. The toolbox not only encapsulates the basic method but also incorporates certain subtle and advanced features including hypothesis testing (for eigenvalue analysis) and bootstrapping for generating confidence interval for all model parameters and noise covariances.

The objectives of the current proposal are to develop: (i) a concrete theory (using ideas from DIPCA based SISO identification) for identification of EIV multiple input, multiple output (MIMO) systems in the state-space framework, (ii) a theoretical method for residual generation from identified EIV models using tailored Kalman filters, and (iii) a computationally efficient algorithm for the preceding theoretical methods. The expected deliverables of this proposal are: (i) publications (in leading international conferences and journals) describing the proposed methodology for EIV-identification of MIMO systems and (ii) version 2.0 of the existing (version 1.0) toolbox incorporating all of the above developments with enhanced features. The toolbox will not only enable the user to identify models but also carry out significance tests on the estimated parameters, generate residuals and have provision for incorporating any prior information that the user may have about the system characteristics.