Real-time parameter updating for nonlinear digital twins using inverse mapping models and transient-based features

Abstract

In the context of digital twins, it is essential that a model gives an accurate description of the (controlled) dynamic behavior of a physical system during the system’s entire operational life. Therefore, model updating techniques are required that enable real-time updating of physically interpretable parameter values and are applicable to a wide range of (nonlinear) dynamical systems. As traditional, iterative, parameter updating methods may be computationally too expensive for real-time updating, the inverse mapping parameter updating (IMPU) method is proposed as an alternative. For this method, first, an artificial neural network (ANN) is trained offline using novel features of simulated transient response data. Then, in the online phase, this ANN maps, with little computational cost, a set of measured output response features to parameter estimates enabling real-time model updating. In this paper, various types of transient response features are introduced to update parameter values of nonlinear dynamical systems with increased computational efficiency and accuracy. To analyze the efficacy of these features, the IMPU method is applied to a (simulated) nonlinear multibody system. It is shown that a smart selection of features, based on, e.g., the frequency content of the transient response, can improve the accuracy of the estimated parameter values, leading to more accurate updated models. Furthermore, the generalization capabilities of the ANNs are analyzed for these feature types, by varying the number of training samples and assessing the effect of incomplete training data. It is shown that the IMPU method can predict parameter values that are not part of the training data with acceptable accuracy as well.

Mutual information-based feature selection for inverse mapping parameter updating of dynamical systems

“…In the IMPU method [1], the goal is to update parameter values, stored in p ∈ R np such that the output y ∈ R nout of a generic nonlinear dynamical model,…”

“…As a solution to the problem posed here, in previous work, the authors have proposed the Inverse Mapping Parameter Updating (IMPU) method [1]. This method employs an Artificial Neural Network (ANN) that infers (online) a set of parameter values from a set of features extracted from measured data.…”

“…In contrast, other popular model (parameter) updating methods, e.g., the Extended Kalman Filter (EKF) [3][4][5][6][7], typically require the explicit Equations of Motion (EoMs) of a model. Although the main advantages of the IMPU method over the EKF are mostly of a qualitative nature, the interested reader is referred to [1] for a quantitative comparison. Other conventional (sensitivity-based) parameter updating techniques [8][9][10] require costly iterative computations, which are undesirable.…”

“…In the IMPU method, a wide range of response features can be used: multiple (combinations of) transient-based types, i.e., sampled values of a time-signal, the extrema thereof, and (complex) values of the Fourier-transformed signal, see [1]. In practice, however, some features might be irrelevant as they are barely influenced by the updated parameters.…”

“…Finally, in previous work [1], the IMPU method has only been applied to academic demonstrators that operate in open loop. In this work, this application is extended to an industrial use case.…”