scholarly journals The Probabilistic Deconvolution of the Distribution of Relaxation Times with Finite Gaussian Processes

2021 ◽  
Author(s):  
Adeleke Maradesa ◽  
Baptiste Py ◽  
Emanuele Quattrocchi ◽  
Francesco Ciucci
Keyword(s):  
Experimental Data ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Electrochemical Impedance ◽  
Probabilistic Approach ◽  
Relaxation Times ◽  
Electrochemical Systems ◽  
Process Approximation ◽  
Machine Learning Tool ◽  
New Framework

Electrochemical impedance spectroscopy (EIS) is a tool widely used to study the properties of electrochemical systems. The distribution of relaxation times (DRT) has emerged as one of the main methods for the analysis of EIS spectra. Gaussian processes can be used to regress EIS data, quantify uncertainty, and deconvolve the DRT, but current implementations do not constrain the DRT to be positive and can only use the imaginary part of EIS spectra. Herein, we overcome both issues by using a finite Gaussian process approximation to develop a new framework called the finite Gaussian process distribution of relaxation times (fGP-DRT). The analysis on artificial EIS data shows that the fGP-DRT method consistently recovers exact DRT from noise-corrupted EIS spectra while accurately regressing experimental data. Furthermore, the fGP-DRT framework is used as a machine learning tool to provide probabilistic estimates of the impedance at unmeasured frequencies. The method is further validated against experimental data from fuel cells and batteries. In short, this work develops a novel probabilistic approach for the analysis of EIS data based on Gaussian process, opening a new stream of research for the deconvolution of DRT.

Comparative analysis and verification of engineering methods of shallow cracks effect for fracture toughness prediction for reactor pressure vessels

2020 ◽  
pp. 140-165
Author(s):  
V. I. Kostylev ◽  
B. Z. Margolin
Keyword(s):  
Experimental Data ◽  
Fracture Toughness ◽  
Comparative Analysis ◽  
Nuclear Reactor ◽  
Probabilistic Approach ◽  
Pressure Vessels ◽  
Local Methods ◽  
European Method ◽  
Shallow Crack ◽  
Reactor Pressure

The main features of shallow cracks fracture are considered, and a brief analysis of methods allowing to predict the temperature dependence of the fracture toughness KJC (T) for specimens with shallow cracks is given. These methods include DA-method, (JQ)-method, (J-T)-method, “local methods” with its multiparameter probabilistic approach, GP method uses power approach, and also two engineering methods – RMSC (Russian Method for Shallow Crack) and EMSC (European Method for Shallow Crack). On the basis of 13 sets of experimental data for national and foreign steels, a detailed verification and comparative analysis of these two engineering methods were carried out on the materials of the VVER and PWR nuclear reactor vessels considering the effect of shallow cracks.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

scholarly journals Determination of the Distribution of Relaxation Times by Means of Pulse Evaluation for Offline and Online Diagnosis of Lithium-Ion Batteries

Batteries ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 36
Author(s):  
Erik Goldammer ◽  
Julia Kowal
Keyword(s):  
Lithium Ion Batteries ◽  
Electrochemical Impedance ◽  
Sampling Rate ◽  
Relaxation Times ◽  
Low Frequency ◽  
Lithium Ion ◽  
Battery Management ◽  
Time Constants ◽  
Time Domain Data ◽  
Aging Study

The distribution of relaxation times (DRT) analysis of impedance spectra is a proven method to determine the number of occurring polarization processes in lithium-ion batteries (LIBs), their polarization contributions and characteristic time constants. Direct measurement of a spectrum by means of electrochemical impedance spectroscopy (EIS), however, suffers from a high expenditure of time for low-frequency impedances and a lack of general availability in most online applications. In this study, a method is presented to derive the DRT by evaluating the relaxation voltage after a current pulse. The method was experimentally validated using both EIS and the proposed pulse evaluation to determine the DRT of automotive pouch-cells and an aging study was carried out. The DRT derived from time domain data provided improved resolution of processes with large time constants and therefore enabled changes in low-frequency impedance and the correlated degradation mechanisms to be identified. One of the polarization contributions identified could be determined as an indicator for the potential risk of plating. The novel, general approach for batteries was tested with a sampling rate of 10 Hz and only requires relaxation periods. Therefore, the method is applicable in battery management systems and contributes to improving the reliability and safety of LIBs.

scholarly journals The calculation of TV, VT, VV, VV' − rate coefficients for the collisions of the main atmospheric components

1998 ◽  
Vol 16 (7) ◽  
pp. 838-846 ◽  
Author(s):  
A. S. Kirillov
Keyword(s):  
Experimental Data ◽  
Energy Transfer ◽  
Vibrational Energy ◽  
Relaxation Times ◽  
Atmospheric Composition ◽  
Rate Coefficients ◽  
Frequency Change ◽  
Vibrational Energy Transfer ◽  
Ion Chemistry ◽  
Vibrationally Excited

Abstract. The first-order perturbation approximation is applied to calculate the rate coefficients of vibrational energy transfer in collisions involving vibrationally excited molecules in the absence of non-adiabatic transitions. The factors of molecular attraction, oscillator frequency change, anharmonicity, 3-dimensionality and quasiclassical motion have been taken into account in the approximation. The analytical expressions presented have been normalized on experimental data of VT-relaxation times in N2 and O2 to obtain the steric factors and the extent of repulsive exchange potentials in collisions N2-N2 and O2-O2. The approach was applied to calculate the rate coefficients of vibrational-vibrational energy transfer in the collisions N2-N2, O2-O2 and N2-O2. It is shown that there is good agreement between our calculations and experimental data for all cases of energy transfer considered.Key words. Ionosphere (Auroral ionosphere; ion chemistry and composition). Atmospheric composition and structure (Aciglow and aurora).

scholarly journals Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions

2018 ◽  
Vol 30 (11) ◽  
pp. 3072-3094 ◽  
Author(s):  
Hongqiao Wang ◽  
Jinglai Li
Keyword(s):  
Bayesian Inference ◽  
Gaussian Process ◽  
Adaptive Algorithm ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Likelihood Functions ◽  
Inference Problems ◽  
Active Learning Method ◽  
Computationally Intensive ◽  
Process Approximation

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP)–based method to approximate the joint distribution of the unknown parameters and the data, built on recent work (Kandasamy, Schneider, & Póczos, 2015 ). In particular, we write the joint density approximately as a product of an approximate posterior density and an exponentiated GP surrogate. We then provide an adaptive algorithm to construct such an approximation, where an active learning method is used to choose the design points. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for Bayesian computation.

scholarly journals Wavelet-based simulation of random processes from certain classes with given accuracy and reliability

2019 ◽  
Vol 25 (3) ◽  
pp. 217-225
Author(s):  
Ievgen Turchyn
Keyword(s):  
Stochastic Processes ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Random Processes

Abstract We consider stochastic processes {Y(t)} which can be represented as {Y(t)=(X(t))^{s}} , {s\in\mathbb{N}} , where {X(t)} is a stationary strictly sub-Gaussian process, and build a wavelet-based model that simulates {Y(t)} with given accuracy and reliability in {L_{p}([0,T])} . A model for simulation with given accuracy and reliability in {L_{p}([0,T])} is also built for processes {Z(t)} which can be represented as {Z(t)=X_{1}(t)X_{2}(t)} , where {X_{1}(t)} and {X_{2}(t)} are independent stationary strictly sub-Gaussian processes.

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