A bootstrap-based approach for parameter and polyspectral density estimation of a non-minimum phase ARMA process

Shanta, Shahnoor; Kadirkamanathan, Visakan

doi:10.1080/00207721.2013.784444

Cited by 2 publications

(1 citation statement)

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“…The bootstrap is a sampling-based method of statistical inference, which as with other ensemble methods is appealing for its simplicity to implement, even for complex models, which is why we use it here. The bootstrap has been widely used with time-series models, including the blockbootstrap and the residual bootstrap [48]- [51]. In this paper we use the stationary bootstrap [52], a type of variable length block-bootstrap, to quantify uncertainty in the recurrent network models.…”

Section: Introductionmentioning

confidence: 99%

Interpretable Deep Learning for Nonlinear System Identification Using Frequency Response Functions With Ensemble Uncertainty Quantification

Jacobs,

Kadirkamanathan,

Anderson

2024

IEEE Access

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We are grateful to the EPSRC support via project Pervasive Sensing for Buried Pipes (Pipebots) under grant EP/S016813/1, https://pipebots.ac.uk/ ABSTRACT Deep learning methods contain powerful tools for modelling nonlinear dynamic systems. However, whilst these models are useful for predicting outputs, they tend to be described by complicated black box equations that lack interpretability. They are therefore not so useful for giving insight into system dynamics, and importantly, insight into why a system produces a certain output in response to a given input. This paper presents a novel method for interpreting and comparing deep learning models for nonlinear system identification, using nonlinear output frequency response functions (NOFRFs). NOFRFs describe nonlinear dynamic system behaviour in the frequency-domain using one-dimensional functions, in a manner similar to how Bode plots are used for analysing linear dynamic systems. This is a classical way of interpreting and understanding system behaviour, e.g. via resonances, and in the case of nonlinear systems, super and sub-harmonics, and energy transfer between frequencies. We also use uncertainty quantification via the bootstrap method to enhance the model interpretation, by propagating the model uncertainty estimates into the frequency-domain. The approach is demonstrated with gated recurrent unit (GRU) and long short term memory (LSTM) models -both are types of recurrent network used in deep learning that are analogous to nonlinear state space models. The results obtained from both a numerical example (a nonlinear mass spring damper system that exhibits energy transfer between frequencies) and a real-world nonlinear system (a magneto-rheological damper) show that it is possible to gain valuable insight and interpretation of the system dynamics from the NOFRFs in a way that is not possible from analysing the time-domain model equations alone.

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Section: Introductionmentioning

confidence: 99%