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1

Modelling of Li-Ion battery state-of-health with Gaussian processes

Dudek Adrian, Baranowski Jerzy

Archives of Electrical Engineering

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2023

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Vol. 72, nr 3

643--659

EN

The problem of lithium-ion cells, which degrade in time on their own and while used, causes a significant decrease in total capacity and an increase in inner resistance. So, it is important to have a way to predict and simulate the remaining usability of batteries. The process and description of cell degradation are very complex and depend on various variables. Classical methods are based, on the one hand, on fitting a somewhat arbitrary parametric function to laboratory data and, on the other hand, on electrochemical modelling of the physics of degradation. Alternative solutions are machine learning ones or non-parametric ones like support-vector machines or the Gaussian process (GP), which we used in this case. Besides using the GP, our approach is based on current knowledge of how to use non-parametric approaches for modeling the electrochemical state of batteries. It also uses two different ways of dealing with GP problems, like maximum likelihood type II (ML-II) methods and the Monte Carlo Markov Chain (MCMC) sampling.

2

A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process

Karagodin Nikita

Probability and Mathematical Statistics

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2022

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Vol. 42, Fasc. 2

195--217

EN

We prove the convergence of the distribution of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.

3

Gaussian process dynamic modeling and backstepping sliding mode control for magnetic levitation system of maglev train

Sun Yougang, Wang Sumei, Lu Yang, Xu Junqi

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 1

49--62

EN

The maglev trains are strongly nonlinear and open-loop unstable systems with external disturbances and parameters uncertainty. In this paper, the Gaussian process method is utilized to get the dynamic parameters, and a backstepping sliding mode controller is proposed for magnetic levitation systems (MLS) of maglev trains. That is, for a MLS of a maglev train, a nonlinear dynamic model with accurate parameters is obtained by the Gaussian process regression method, based on which a novel robust control algorithm is designed. Specifically, the MLS is divided into two sub-systems by a backstepping method. The inter virtual control inputs and the Lyapunov function are constructed in the first sub-system. For the second sub-system, the sliding mode surface is constructed to fulfil the design of the whole controller to asymptotically regulate the airgap to a desired trajectory. The stability of the proposed control method is analyzed by the Lyapunov method. Both simulation and experimental results are included to illustrate the superior performance of the presented method to cope with parameters perturbations and external disturbance.

4

Pickands–Piterbarg Constants for Self-Similar Gaussian Processes

Dębicki Krzysztof, Tabiś Kamil

Probability and Mathematical Statistics

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2020

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Vol. 40, Fasc. 2

297--315

EN

For a centered self-similar Gaussian process {Y (t) : t ∈ [0;∞)} and R≥0 we analyze the asymptotic behavior of [formula], for suitably chosen γ> 0. Additionally, we find bounds for HRY , R > 0, and a surprising relation between HY and the classical Pickands constants.

5

Efficient learning variable impedance control for industrial robots

Li C., Zhang Z., Xia G., Xie X., Zhu Q.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 2

201--212

EN

Compared with the robots, humans can learn to perform various contact tasks in unstructured environments by modulating arm impedance characteristics. In this article, we consider endowing this compliant ability to the industrial robots to effectively learn to perform repetitive force-sensitive tasks. Current learning impedance control methods usually suffer from inefficiency. This paper establishes an efficient variable impedance control method. To improve the learning efficiency, we employ the probabilistic Gaussian process model as the transition dynamics of the system for internal simulation, permitting long-term inference and planning in a Bayesian manner. Then, the optimal impedance regulation strategy is searched using a model-based reinforcement learning algorithm. The effectiveness and efficiency of the proposed method are verified through force control tasks using a 6-DoFs Reinovo industrial manipulator.

6

Mathematical modeling and stochastic stability analysis of viscoelastic nanobeams using higher-order nonlocal strain gradient theory

Pavlović I. R., Pavlović R., Janevski G.

Archives of Mechanics

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2019

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Vol. 71, nr 2

137--153

EN

This paper analyzes stochastic vibrations of a viscoelastic nanobeam under axial loadings. Based on the higher-order nonlocal strain gradient theory and the Liapunov functional method, bounds of the almost sure asymptotic stability of a nanobeam are obtained as a function of retardation time, variance of the stochastic force, higher-order and lower-order scale coefficients, strain gradient length scale, and intensity of the deterministic component of axial loading. Analytical results from this study are first compared with those obtained from the Monte Carlo simulation. Numerical calculations are performed for the Gaussian and harmonic non-white processes as models of axial forces.

7

Use of machine learning algorithm for the better prediction of SR peculiarities of WEDM of Nimonic-90 superalloy

Singh Nain S., Sai R., Sihag P., Vambol S., Vambol V.

Archives of Materials Science and Engineering

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2019

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Vol. 95, nr 1

12--19

EN

Purpose: With the end goal to fulfil stringent structural shape of the component in aeronautics industry, machining of Nimonic-90 super alloy turns out to be exceptionally troublesome and costly by customary procedures, for example, milling, grinding, turning, etc. For that reason, the manufacture and design engineer worked on contactless machining process like EDM and WEDM. Based on previous studies, it has been observed that rare research work has been published pertaining to the use of machine learning in manufacturing. Therefore the current research work proposed the use of SVM, GP and ANN methods to evaluate the WEDM of Nimonic-90. Design/methodology/approach: The experiments have been performed on the WEDM considering five process variables. The Taguchi L 18 mixed type array is used to formulate the experimental plan. The surface roughness is checked by using surface contact profilometre. The evolutionary algorithms like SVM, GP and ANN approaches have been used to evaluate the SR of WEDM of Nimonic-90 super alloy. Findings: The entire models present the significant results for the better prediction of SR peculiarities of WEDM of Nimonic-90 superalloy. The GP PUK kernel model is dominating the entire model. Research limitations/implications: The investigation was carried for the Nimonic-90 super alloy is selected as a work material. Practical implications: The results of this study provide an opportunity to conduct contactless processing superalloy Nimonic-90. At the same time, this contactless process is much cheaper, faster and more accurate. Originality/value: An experimental work has been reported on the WEDM of Udimet-L605 and use of advance machine learning algorithm and optimization approaches like SVM, and GRA is recommended. A study on WEDM of Inconel 625 has been explored and optimized the process using Taguchi coupled with grey relational approach. The applicability of some evolutionary algorithm like random forest, M5P, and SVM also tested to evaluate the WEDM of Udimet-L605.The fuzzy- inference and BP-ANN approached is used to evaluate the WEDM process. The multi-objective optimization using ratio analysis approach has been utilized to evaluate the WEDM of high carbon & chromium steel. But this current research work proposed the use of SVM, GP and ANN methods to evaluate the WEDM of Nimonic-90.

8

On extremal index of max-stable stationary processes

Dębicki K., Hashorva E.

Probability and Mathematical Statistics

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2017

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Vol. 37, Fasc. 2

299--317

EN

In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary proces W(t), t ϵ R, as [wzór] (set 0Z = R if δ = 0) and the extremal index of the associated max-stable stationary process ξW. We derive several new formulas and obtain lower bounds for ΉδW if W is a Gaussian or a Lévy process. As a by-product we show an interesting relation between Pickands constants and lower tail probabilities for fractional Brownian motions.

9

Fault tolerant control using Gaussian processes and model predictive control

Yang X., Maciejowski J. M.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

133--148

EN

Essential ingredients for fault-tolerant control are the ability to represent system behaviour following the occurrence of a fault, and the ability to exploit this representation for deciding control actions. Gaussian processes seem to be very promising candidates for the first of these, and model predictive control has a proven capability for the second. We therefore propose to use the two together to obtain fault-tolerant control functionality. Our proposal is illustrated by several reasonably realistic examples drawn from flight control.

10

Zastosowanie metody Gaussowskiego procesu do identyfikacji charakterystyk zagęszczenia gruntów ziarnistych

Kłos M., Słoński M., Waszczyszyn Z.

Zeszyty Naukowe Politechniki Rzeszowskiej. Budownictwo i Inżynieria Środowiska

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2012

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z. 59, nr 3/IV

41-48

PL

W pracy zastosowano metodę bayesowską Gaussowskiego Procesu (GP). Metoda wyróżnia się brakiem wektora wag i użyciem funkcji kernelowskich oraz macierzy kowariancji w przestrzeni danych wejściowych. Dzięki temu w GP można było formułować stosunkowo proste algorytmy i procedury komputerowe. GP zastosowano do identyfikacji dwóch charakterystyk zagęszczenia gruntów ziarnistych, tj. wilgotności optymalnej oraz maksymalnej gęstości objętościowej. Celem sprawdzenia numerycznej efektywności GP zastosowano ją do analizy nowych danych pomiarowych opisanych w [2], analizowanych w [4] za pomocą semi-baysowskiej sieci neuronowej (SBNN). Wykazano, że dokładność identyfikacji metodą GP jest porównywalna z zaletami SBNN.

EN

In the paper the Gaussian Process (GP) model is discussed as a simple Bayesian for approach to identification analysis. In GP model the weight vector is not applied, which makes the algorithms and computational procedures simpler than those formulated in the Semi-Bayesian Neural Network (SBNN). In the paper it was numerically proved that the application of GP to the identification of compaction parameters for granular soils is numerically efficient, comparable for GP and SBNN applications.

11

Path regularity of Gaussian processes via small deviations

Aurzada F.

Probability and Mathematical Statistics

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2011

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Vol. 31, Fasc. 1

61--78

EN

We study the a.s. sample path regularity of Gaussian processes. To this end we relate the path regularity directly to the theory of small deviations. In particular, we show that if the process is n-times differentiable, then the exponential rate of decay of its small deviations is at most ε-1/n. We also show a similar result if n is not an integer. Further generalizations are given, which parallel the entropy method to determine the small deviations. In particular, the present approach seems to be a probabilistic interpretation of the multiplicativity property of the entropy numbers.

12

Bayesian neural networks and Gaussian processes in identification of concrete properties

Słoński M.

Computer Assisted Mechanics and Engineering Sciences

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2011

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Vol. 18, no. 4

291-302

EN

This paper gives a concise overview of concrete properties prediction using advanced nonlinear regression approach and Bayesian inference. Feed-forward layered neural network (FLNN) with Markov chain Monte Carlo stochastic sampling and Gaussian process (GP) with maximum likelihood hyperparameters estimation are introduced and compared. An empirical assessment of these two models using two benchmark problems are presented. Results on these benchmark datasets show that Bayesian neural networks and Gaussian processes have rather similar prediction accuracy and are superior in comparison to linear regression model.

13

Computer modelling of operating processes for both simulational and experimental investigation of fracture problems

Čačko J.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2001

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Vol. 269, z. 67

7-26

EN

The problem of evaluation and computer modelling of operational processes with both continuous and discontinuous nature is presented in the paper. We suppose the knowledge of statistical characteristics of the continuous component in the frame of correlation theory - frequency probability density function of the distribution and power spectral density or autocorrelation function respectively. A simulation model is based on modelling of time-series with application for gaussian and nongaussian processes. Discontinuous events are assumed as a sequence of various impacts with Poissonian distribution, and they are superimposed to a continuous component. A cumulative damage is continuously evaluated regarding to a closed hysteresis loops counting. A fatigue damage mechanism is represented either by rainflow matrix or by a fatigue damage function. The function is specified using some hypothesis of a fatigue cumulative damage and fatigue failure criteria.

14

Asymptotics of the supremum of scaled Brownian motion

Dębicki K.

Probability and Mathematical Statistics

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2001

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Vol. 21, Fasc. 1

199--212

EN

We consider the problem of estimating the tail of the distribution of the supremum of scaled Brownian motion B(ƒ(t)) processes with linear drift.Using the local time technique we obtain asymptotics and bounds of Pt≥t0(sup(B(ƒ(t))−t)> u), which are expressed in terms of the expected value of thelocal timeof B(ƒ(t))−tprocesses at levelu.As an application we obtain upper bounds for the tail of distribution of the supremum for some Gaussian processes with stationary increments.