Globalized Nelder–Mead method for engineering optimization

Luersen, Marco Antônio; Riche, Rodolphe Le

doi:10.1016/j.compstruc.2004.03.072

Cited by 192 publications

(43 citation statements)

References 4 publications

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“…To achieve this, numerical optimization techniques can be used to obtain a set of coefficients α s by minimization of difference between f n−m and k B T θ n−m . In practice, the globalized bounded Nelder-Mead algorithm 43 is used for the optimization. We note, however, that many other optimization methods can be also used to obtain α s by defining the test function f n = k B T  N s=0 α s α n+s and the target function k B T θ n .…”

Section: Appendix B: Colored Noise Generatormentioning

confidence: 99%

Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism

Bian

et al. 2015

The Journal of Chemical Physics

135

155

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The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model. C 2015 AIP Publishing LLC. [http://dx

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Section: Appendix B: Colored Noise Generatormentioning

confidence: 99%

Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism

Bian

et al. 2015

The Journal of Chemical Physics

135

155

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“…With the results from the previous step, the system to optimize is then given by N nonlinear equations with NZ unknowns of the form shown in Eq. (13). Thus, As mentioned before, there are no restrictions in this equation.…”

Section: B Solve the Nonlinear Problem Using An Optimization Proceduresmentioning

confidence: 76%

“…To this end, a modification of the Nelder and Mead simplex method [11][12][13] was implemented. Such modifications define the stopping criteria and the subspace in which the solution is being optimized.…”

Section: B Solve the Nonlinear Problem Using An Optimization Proceduresmentioning

confidence: 99%

Noise Source Localization and Optimization of Phased-Array Results

Ravetta

Burdisso

2009

AIAA Journal

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A new approach to the deconvolution of acoustic sources has been developed and is presented in this work. The goal of this postprocessing is to simplify the beamforming output by suppressing the side lobes and reducing the sources' main lobes to single (or a small number of) points that accurately identify the noise sources' positions and their actual levels. In this work, a new modeling technique for the beamforming output is proposed. The idea is to use an image-processing-like approach to identify the noise sources from the beamforming maps: that is, recognizing lobe patterns in the beamformed output and relating them to the noise sources that would produce that map. For incoherent sources, the beamforming output is modeled as a superposition of point-spread functions and a linear system is posted. For coherent sources, the beamforming output is modeled as a superposition of complex pointspread functions and a nonlinear system of equations in terms of the sources' amplitudes is posted. As a first approach to solving this difficult problem, the system is solved using a new two-step procedure. In the first step, an approximated linear problem is solved. In the second step, an optimization is performed over the nonzero values obtained in the previous step. The solution to this system of equations renders the sources' positions and amplitudes. In the case of coherent sources, their relative phase can also be recovered. The technique is referred as noise source localization and optimization of phased-array results. A detailed analytical formulation, numerical simulations, and sample experimental results are shown for the proposed postprocessing.

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“…The mathematical equations for all these steps are given below

Reflection : x_{r} = \bar{x} + δ_{1} (x_{h} - \bar{x}),

Expansion : x_{e} = \bar{x} + δ_{2} (x_{r} - \bar{x}),

Contraction : x_{c} = \bar{x} + δ_{3} (x_{h} - \bar{x}),

Shrinkage : x_{e} = \bar{x} + δ_{4} (x_{l} - x_{i}); i = 0, 1, \dots, n,

where δ 1 , δ 2 , δ 3 , and δ 4 are coefficients of reflection, expansion, contraction, and shrinkage, respectively. The typical values of these coefficients have been chosen as 1, 2, 0.5, and 0.5, respectively (Lagarias et al, 1998; Luersen and Riche, 2004). The schematic of the algorithm is shown in Figure 2.…”

Section: Methodsmentioning

confidence: 99%

“…The formulated pre-optimized model is passed to an iterative simplex method with initial parameter vector. The simplex algorithm (Spendley et al, 1962) and its modified version (Nelder and Mead, 1965) has frequently been used in past for many signal processing and engineering-design optimization applications (Luersen and Riche, 2004). Fifteen simulated data sets have been generated with known parameters to verify the correctness of the proposed algorithm.…”

Section: Introductionmentioning

confidence: 99%

Optimal hemodynamic response model for functional near-infrared spectroscopy

Kamran

Jeong

Mannan

2015

Front. Behav. Neurosci.

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Functional near-infrared spectroscopy (fNIRS) is an emerging non-invasive brain imaging technique and measures brain activities by means of near-infrared light of 650–950 nm wavelengths. The cortical hemodynamic response (HR) differs in attributes at different brain regions and on repetition of trials, even if the experimental paradigm is kept exactly the same. Therefore, an HR model that can estimate such variations in the response is the objective of this research. The canonical hemodynamic response function (cHRF) is modeled by two Gamma functions with six unknown parameters (four of them to model the shape and other two to scale and baseline respectively). The HRF model is supposed to be a linear combination of HRF, baseline, and physiological noises (amplitudes and frequencies of physiological noises are supposed to be unknown). An objective function is developed as a square of the residuals with constraints on 12 free parameters. The formulated problem is solved by using an iterative optimization algorithm to estimate the unknown parameters in the model. Inter-subject variations in HRF and physiological noises have been estimated for better cortical functional maps. The accuracy of the algorithm has been verified using 10 real and 15 simulated data sets. Ten healthy subjects participated in the experiment and their HRF for finger-tapping tasks have been estimated and analyzed. The statistical significance of the estimated activity strength parameters has been verified by employing statistical analysis (i.e., t-value > tcritical and p-value < 0.05).

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Globalized Nelder–Mead method for engineering optimization

Cited by 192 publications

References 4 publications

Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism

Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism

Noise Source Localization and Optimization of Phased-Array Results

Optimal hemodynamic response model for functional near-infrared spectroscopy

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