A derivative-free Gauss–Newton method

Cartis, Coralia; Roberts, Lindon

doi:10.1007/s12532-019-00161-7

Cited by 45 publications

(90 citation statements)

References 34 publications

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“…At a higher C-rate of 0.5C ( Figure 4b) and 2C (Figure 4c), the concentrations become spatially inhomogeneous, which leads to concentration overpotentials that limit the accessible capacity. A Derivative-Free Gauss-Newton method [24] was also used to fit the model to data from a series of constantcurrent discharges of a 17 Ah BBOXX Solar Home battery at intervals of 0.5 A from 3 A to 0.5 A ( Figure 5). Each constant-current discharge is followed by a two-hour rest period during which the current is zero.…”

Section: Resultsmentioning

confidence: 99%

Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model

Sulzer

Chapman

Please

et al. 2019

J. Electrochem. Soc.

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An isothermal porous-electrode model of a discharging lead-acid battery is presented, which includes an extension of concentrated-solution theory that accounts for excluded-volume effects, local pressure variation, and a detailed microscopic water balance. The approach accounts for three typically neglected physical phenomena: convection, pressure diffusion, and variation of liquid volume with state of charge. Rescaling of the governing equations uncovers a set of fundamental dimensionless parameters that control the battery's response. Total volume change during discharge and nonuniform pressure prove to be higher-order effects in cells where variations occur in just one spatial dimension. A numerical solution is developed and exploited to predict transient cell voltages and internal concentration profiles in response to a range of C-rates. The dependence of discharge capacity on C-rate deviates substantially from Peukert's simple power law: charge capacity is concentration-limited at low C-rates, and voltage-limited at high C-rates. The model is fit to experimental data, showing good agreement.

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Section: Resultsmentioning

confidence: 99%

Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model

Sulzer

Chapman

Please

et al. 2019

J. Electrochem. Soc.

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“…Since this budget is much larger than is often used for testing (e.g. [29,4]), we show data profiles with a log-scale for budget, so we can easily compare solvers both for large budgets (to check robustness) and for realistically small budgets. For the CUTEst problems (CR), we used a much smaller budget of 50(n + 1) evaluations, to represent the other regime, where objectives are expensive to evaluate.…”

Section: Solver Settingsmentioning

confidence: 99%

“…Comparisons to Related Software In our numerical results, we compare DFO-LS to DFO-GN [4] and DFBOLS [29], also designed for nonlinear least-squares problems 1 . We find that using different default parameters for noisy problems, coupled with multiple restarts, makes DFO-LS have substantially improved robustness to noise over both DFO-GN and DFBOLS, without the early loss of performance associated with sample averaging and regression models.…”

Section: Introductionmentioning

confidence: 99%

Improving the Flexibility and Robustness of Model-based Derivative-free Optimization Solvers

Cartis

Fiala

Marteau

et al. 2019

ACM Trans. Math. Softw.

Self Cite

128

130

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We present DFO-LS, a software package for derivative-free optimization (DFO) for nonlinear Least-Squares (LS) problems, with optional bound constraints. Inspired by the Gauss-Newton method, DFO-LS constructs simplified linear regression models for the residuals. DFO-LS allows flexible initialization for expensive problems, whereby it can begin making progress from as few as two objective evaluations. Numerical results show DFO-LS can gain reasonable progress on some medium-scale problems with fewer objective evaluations than is needed for one gradient evaluation. DFO-LS has improved robustness to noise, allowing sample averaging, the construction of regression-based models, and multiple restart strategies together with an auto-detection mechanism. Our extensive numerical experimentation shows that restarting the solver when stagnation is detected is a cheap and effective mechanism for achieving robustness, with superior performance over both sampling and regression techniques. We also present our package Py-BOBYQA, a Python implementation of BOBYQA (Powell, 2009), which also implements robustness to noise strategies. Our numerical experiments show that Py-BOBYQA is comparable to or better than existing general DFO solvers for noisy problems. In our comparisons, we introduce a new adaptive measure of accuracy for the data profiles of noisy functions that strikes a balance between measuring the true and the noisy objective improvement.

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“…To fit our model to the data, we minimise the sumof-squares of the voltage prediction error. We do this in Python with both a derivative-based (leastsquares [18]) or derivative-free (DFO-GN [19]) optimisation algorithm.…”

Section: Parameter Fittingmentioning

confidence: 99%

Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part II. Asymptotic Analysis

Sulzer¹,

Chapman²,

Please³

et al. 2019

J. Electrochem. Soc.

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Electrochemical and equivalent-circuit modelling are the two most popular approaches to battery simulation, but the former is computationally expensive and the latter provides limited physical insight. A theoretical middle ground would be useful to support battery management, on-line diagnostics, and cell design. We analyse a thermodynamically consistent, isothermal porous-electrode model of a discharging lead-acid battery. Asymptotic analysis of this full model produces three reduced-order models, which relate the electrical behaviour to microscopic material properties, but simulate discharge at speeds approaching an equivalent circuit. A lumped-parameter model, which neglects spatial property variations, proves accurate for C-rates below 0.1C, while a spatially resolved higher-order solution retains accuracy up to 5C. The problem of parameter estimation is addressed by fitting experimental data with the reducedorder models.

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A derivative-free Gauss–Newton method

Cited by 45 publications

References 34 publications

Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model

Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model

Improving the Flexibility and Robustness of Model-based Derivative-free Optimization Solvers

Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part II. Asymptotic Analysis

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