Recursive nonlinear-system identification using latent variables

Abstract

In this paper we develop a method for learning nonlinear system models with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood principle we derive a criterion for learning the model. The resulting optimization problem is tackled using a majorization-minimization approach. Finally, we develop a convex majorization technique and show that it enables a recursive identification method. The method learns parsimonious predictive models and is tested on both synthetic and real nonlinear systems.

A flexible state–space model for learning nonlinear dynamical systems

“…To achieve a good performance with such a regularization, the system which generated the data has to be well described by only a few number of the basis functions being 'active', i.e., have non-zero coefficients, which makes the choice of basis functions important and problem-dependent. The recent work by Mattsson et al (2016) is also covering learning of a regularized basis function expansion, however for input-output type of models.…”

Partially coupled gradient estimation algorithm for multivariable equation‐error autoregressive moving average systems using the data filtering technique

“…In most cases, it is not easy to analyse the whole system and to construct the mathematical model based on the analytic approach. Therefore, system identification becomes the first choice when people model a system [10][11][12], and has a wide application in both linear [13] and nonlinear systems [14][15][16][17]. For the multiple-input and multiple-output Box-Jenkins model with disturbances, a two-stage identification method was developed by using the residual model of Kalman filter [18].…”

Flexible Models for Smart Maintenance

“…The starting point in this paper is the latent variable framework (LAVA) [9], which can handle flexible model structures using a data-adaptive regularization, meaning that the regularization parameters are learned automatically from the data instead of being tuned by a user. This facilitates the learning of a diverse set of different components and machines.…”

“…Furthermore, this paper uses similar ideas as in [9] to develop a new method for identifying a unique model for each batch (or unit) that is processed in some machine, even though only a few data samples are collected from each batch. It is shown how this can be used to determine if the behaviour of the machine changes between batches.…”

“…The layout of the paper is as follows. In Section II the method in [9] is presented, together with a discussion on how to apply it to smart maintenance. In Section III a similar idea is used in order to develop a new method for detecting dynamical changes between batches/units.…”