A genetic algorithms based technique for computing the nonlinear least squares estimates of the parameters of sum of exponentials model

Mitra, Sharmishtha; Mitra, Amit

doi:10.1016/j.eswa.2011.12.033

Cited by 14 publications

(10 citation statements)

References 23 publications

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“…This particular type of problem therefore points towards considering stochastic search methods like GA. In case of time series analysis, it has been shown28 that GA can be used efficiently for sum of exponentials functions. GA parameters can be varied for each selected biophysical model and time complexity may change with each choice.…”

Section: Methodsmentioning

confidence: 99%

“…Also, it reduces the number of iterations (generations) and population size used in the GA (step 2). For example, in time series analysis to have precise results, GA requires population size of 250 with 150 iterations28. With the type of functions describing white matter multi-compartment biophysical models, such a stochastic search will become computationally prohibitive.…”

Section: Methodsmentioning

confidence: 99%

“…The estimation of non-linear parameters is a non-convex problem and is handled first. This is done by stochastic search that utilizes Genetic Algorithms (GA); GAs have been shown to be effective in approximating exponential time series models28. The task to estimate linear parameters amounts to a convex problem and can be solved using standard least squares techniques.…”

mentioning

confidence: 99%

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Microstructure Imaging of Crossing (MIX) White Matter Fibers from diffusion MRI

Farooq

Nam

et al. 2016

Sci Rep

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Diffusion MRI (dMRI) reveals microstructural features of the brain white matter by quantifying the anisotropic diffusion of water molecules within axonal bundles. Yet, identifying features such as axonal orientation dispersion, density, diameter, etc., in complex white matter fiber configurations (e.g. crossings) has proved challenging. Besides optimized data acquisition and advanced biophysical models, computational procedures to fit such models to the data are critical. However, these procedures have been largely overlooked by the dMRI microstructure community and new, more versatile, approaches are needed to solve complex biophysical model fitting problems. Existing methods are limited to models assuming single fiber orientation, relevant to limited brain areas like the corpus callosum, or multiple orientations but without the ability to extract detailed microstructural features. Here, we introduce a new and versatile optimization technique (MIX), which enables microstructure imaging of crossing white matter fibers. We provide a MATLAB implementation of MIX, and demonstrate its applicability to general microstructure models in fiber crossings using synthetic as well as ex-vivo and in-vivo brain data.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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Microstructure Imaging of Crossing (MIX) White Matter Fibers from diffusion MRI

Farooq

Nam

et al. 2016

Sci Rep

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“…By designing a parameter estimation algorithm, which should be incorporated into a feedback system, some drawbacks might arise, such as computational burden [4,5], [11][12][13]; slow convergence rate [14][15][16][17]; long duration of the analysis window [18]; dependency on simplifying pre-defined assumptions [19,20]; existence of biased estimation and high energy consumption of the feedback control system [21]; high sensitivity to noise and disturbance effects [22][23][24]; and failure to track fast continuously varying parameters [25,26].…”

Section: Introductionmentioning

confidence: 99%

Short‐Time Linear Quadratic Form Technique for Estimating Fast‐Varying Parameters in Feedback Loops

Homaeinezhad¹,

Moghaddam²,

Khakpour³

et al. 2015

Asian Journal of Control

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The precision of a closed‐loop controller system designed for an uncertain plant depends strongly upon the maximum extent to which it is possible to track the trend of time‐varying parameters of the plant. The aim of this study is to describe a new parameter estimation algorithm that is able to follow fast‐varying parameters in closed‐loop systems. The short‐time linear quadratic form (STLQF) estimation algorithm introduced in this paper is a technique for tracking time‐varying parameters based on short‐time analysis of the regressing variables in order to minimize locally a linear quadratic form cost function. The established cost function produces a linear combination of errors with several delays. To meet this objective, mathematical development of the STLQF estimation algorithm is described. To implement the STLQF algorithm, the algorithm is applied to a planar mobile robot with fast‐varying parameters of inertia and viscous and coulomb frictions. Next, performance of the proposed algorithm is assessed against noise effects and variation in the type of parameters.

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“…Therefore, some intelligent algorithm for example the genetic algorithm (GA) (Chan et al 2009;Delavar et al 2010), simulated annealing, and particle swarm optimization was developed to calculate the parameters of the kinetic model in recent years. Among those methods, the GA has been widely applied to solve the problem (Mitra and Mitra 2012). In addition, fitting of nonlinear models relies on non-trivial assumptions.…”

Section: Introductionmentioning

confidence: 99%

Investigate the kinetics of coke solution loss reaction with an alkali metal as a catalyst based on the improved genetic algorithm

Zhao

Zhang

Cui

2017

Int J Coal Sci Technol

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The kinetics of coke solution loss reaction with and without sodium carbonate were investigated under the reaction atmosphere of carbon dioxide. The variables of gas flow rate and coke particle size were explored to eliminate the external and internal diffusion, respectively. Then, the improved method combining with the least square and the genetic algorithm was proposed to solve the homogeneous model and the shrinking core model. It was found that the improved genetic algorithm method has good stability by studying the fitness function at each generation. In the homogeneous model, the activation energy with and without sodium carbonate was 54.89 and 95.56 kJ/mol, respectively. And, the activation energy with and without sodium carbonate in the shrinking core model was 49.83 and 92.18 kJ/mol, respectively. Therefore, it was concluded that the sodium carbonate has the catalytic action. In addition, results showed that the estimated conversions were agreed well with the experimental ones, which indicated that the calculated kinetic parameters were valid and the proposed method was successfully developed. Graphical AbstractKeywords Coking Á Kinetic Á Improved genetic algorithm Á Alkali metal Á Catalyst

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A genetic algorithms based technique for computing the nonlinear least squares estimates of the parameters of sum of exponentials model

Cited by 14 publications

References 23 publications

Microstructure Imaging of Crossing (MIX) White Matter Fibers from diffusion MRI

Microstructure Imaging of Crossing (MIX) White Matter Fibers from diffusion MRI

Short‐Time Linear Quadratic Form Technique for Estimating Fast‐Varying Parameters in Feedback Loops

Investigate the kinetics of coke solution loss reaction with an alkali metal as a catalyst based on the improved genetic algorithm

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