Learning Nonlinear State-Space Models Using Smooth Particle-Filter-Based Likelihood Approximations

Svensson, Andreas; Lindsten, Fredrik; Schön, Thomas B.

doi:10.1016/j.ifacol.2018.09.216

Cited by 2 publications

(13 citation statements)

References 18 publications

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“…As presented in [32], the main challenge is that likelihood distribution estimation and its derivatives are fundamentally noisy; the main idea of the SPF method is to choose the proposal distribution

q (x_{k}^{i} | x_{k - 1}^{i}, z_{k})

and the resampling weights

w_{k}^{n}

, such that it is entirely independent of parameters

θ

(in this application, the parameters of the degradation model). Based on this choice, it is noted that all the randomly extracted elements, such as particles

x_{0 : T}^{n}

and ancestor indices

a_{1 : T}^{n}

(furthermore are the

a_{1 : T}^{n}

drawn with respect to the

w_{k}^{n}

) in the PF algorithm, became independent of

θ

; this is critical in the analysis and estimation of battery degradation as the true values of the degradation model parameters are unknown, and highly influenced by uncertainty [24].…”

Section: Theoretical Background‐methodologymentioning

confidence: 99%

“…Based on this choice, it is noted that all the randomly extracted elements, such as particles

x_{0 : T}^{n}

and ancestor indices

a_{1 : T}^{n}

(furthermore are the

a_{1 : T}^{n}

drawn with respect to the

w_{k}^{n}

) in the PF algorithm, became independent of

θ

; this is critical in the analysis and estimation of battery degradation as the true values of the degradation model parameters are unknown, and highly influenced by uncertainty [24]. Therefore, this article combines the second‐order empirical degradation model with the SPF algorithm [32] to improve the RUL prediction of LiB battery by smoothing the PF using likelihood approximations scheme.…”

Section: Theoretical Background‐methodologymentioning

confidence: 99%

“…Now, if a certain condition is applied to the realisation of fx n 0:T ; a n 1:T g, the ẑθ estimation will convert into a deterministic function within θ, and any standard optimisation routine can then be implemented to solve (11) and find the maximum likelihood estimate of θ [32].…”

Section: The Proposed Spf Algorithmmentioning

confidence: 99%

“…For this reason, we must repeat the parameter values over k until we roughly arrive at values close to b θ. By inserting (13) and (14) into the particle filter algorithm and combining with an external optimisation loop, an innovative method is proposed and, presented in Table 2 [32]. The steps of the method are:…”

Section: The Proposed Spf Algorithmmentioning

confidence: 99%

“…The structure ofẑ θ k−1 ðθÞ, which is implicitly defined in the function likelihood of the proposed algorithm, might still be utilised by a more suitable optimisation scheme. Its structure can be shown as [32]:…”

Section: The Proposed Spf Algorithmmentioning

confidence: 99%

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Smooth particle filter‐based likelihood approximations for remaining useful life prediction of Lithium‐ion batteries

et al. 2021

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Accurate prediction of the remaining useful life (RUL) in Lithium-ion batteries (LiBs) is a key aspect of managing its health, in order to promote reliable and secure systems, and to reduce the need for unscheduled maintenance and costs. Recent work on RUL prediction has largely focused on refining the accuracy and reliability of the RUL prediction. The author introduces a new online RUL prediction for LiB using smooth particle filter (SPF)-based likelihood approximation method. The proposed algorithm can accurately estimate the unknown degradation model parameters and predict the degradation state by solving the optimisation problem at each iteration, rather than only taking a gradient step, that tends to lead to rapid convergence, avoids instability issues and improves predictive accuracy. From the experimental datasets published by Prognostics Centre of Excellence (PCoE) of NASA, a second order degradation model was created to explore the degradation of LiB, utilising non-linear characteristics and non-Gaussian capacity degradation. RUL prediction was tested with various predicted starting points to assess whether the amount of data and parameters' uncertainty influenced the accuracy of the prediction. Results show that the proposed prediction approach gives improved prediction accuracy and improves the convergence rate in comparison with the particle filter (PF) and other methods such as unscented particle filter (UPF). Since the maximum error of the SPF predicting approach is relatively small, RUL prediction in the best case at the prediction starting point consisting of 80 cycles is 127 cycles. The prediction relative error was approximately 0.024, and the absolute error of the proposed algorithm is around 2 cycles, which is lower than the PF (around 16 cycles). RUL prediction is close to 108 cycles and relative error is around 0.136, while the absolute error prediction is approximately 16. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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q (x_{k}^{i} | x_{k - 1}^{i}, z_{k})

and the resampling weights

w_{k}^{n}

, such that it is entirely independent of parameters

θ

(in this application, the parameters of the degradation model). Based on this choice, it is noted that all the randomly extracted elements, such as particles

x_{0 : T}^{n}

and ancestor indices

a_{1 : T}^{n}

(furthermore are the

a_{1 : T}^{n}

drawn with respect to the

w_{k}^{n}

) in the PF algorithm, became independent of

θ

; this is critical in the analysis and estimation of battery degradation as the true values of the degradation model parameters are unknown, and highly influenced by uncertainty [24].…”

Section: Theoretical Background‐methodologymentioning

confidence: 99%

“…Based on this choice, it is noted that all the randomly extracted elements, such as particles