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USE OF A MONTE-CARLO PDF METHOD IN A STUDY OF THE INFLUENCE OF TURBULENT FLUCTUATIONS ON SELECTIVITY IN A JET-STIRRED REACTOR

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APPLIED SCIENTIFIC RESEARCH 1991年第3-4期48卷 271-300页

作者： ROEKAERTS, D 1. Koninklijke/Shell-Laboratorium Amsterdam (Shell Research B.V.) P.O. Box 3003 1003 AA Amsterdam The Netherlands

A model for single-phase turbulent reacting flow is presented and a solution algorithm is described. The model combines the standard k - epsilon model for the velocity field with a transport equation for the probability density function (PDF) of the thermochemical variables. In this equation terms describing spatial transport by velocity fluctuations and mixing on the smallest scales are modelled. The essential advantage of this approach is that the effect of nonlinear kinetics appears in closed form and that the influence of turbulent fluctuations on mean reaction rates is included. A stochastic algorithm for the solution of the PDF transport equation, essentially due to Pope, is described. Cylindrical symmetry is assumed. The PDF is represented by ensembles of N representative values of the thermochemical variables in each cell of a nonuniform finite-difference grid and operations on these elements representing convection, diffusion, mixing and reaction are derived. A simplified model and solution algorithm which neglects the influence of turbulent fluctuations on mean reaction rates is also described. Both algorithms are applied to a selectivity problem in a real reactor studied earlier by Liu and Barkelew. Spatial profiles of mean species mole fractions and of relative selectivity to the target product are obtained. The profiles are clearly different in both models but at the end of the reactor the same selectivity is predicted.

关键词： TURBULENT REACTING FLOW PDF stochastic algorithm SELECTIVITY

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stochastic Primal Dual Fixed Point Method for Composite Optimization

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JOURNAL OF SCIENTIFIC COMPUTING 2020年第1期84卷 16-16页

作者： Zhu, Ya-Nan Zhang, Xiaoqun Shanghai Jiao Tong Univ Inst Nat Sci Sch Math Sci Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ MOE LSC Shanghai 200240 Peoples R China

In this paper we propose a stochastic primal dual fixed point method for solving the sum of two proper lower semi-continuous convex function and one of which is composite. The method is based on the primal dual fixed point method proposed in Chen et al. (Inverse Probl 29:025011, 2013) that does not require subproblem solving. Under some mild condition, the convergence is established based on two sets of assumptions: bounded and unbounded gradients and the convergence rate of the expected error of iterate is of the order O(k(-alpha)) where k is iteration number and alpha is an element of (0, 1]. Finally, numerical examples on graphic Lasso and logistic regressions are given to demonstrate the effectiveness of the proposed algorithm.

关键词： stochastic algorithm Proximal point method Primal dual Fixed point Composite optimization Graphic lasso

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A versatile nonlinear inversion to interpret gravity anomaly caused by a simple geometrical structure

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PURE AND APPLIED GEOPHYSICS 2005年第12期162卷 2557-2571页

作者： Tlas, M Asfahani, J Karmeh, H Atom Energy Commiss Damascus Syria

A geophysical interpretative method is proposed to depth, amplitude coefficient and geometrical shape factor determination of a buried structure from an observed gravity anomaly related to a cylinder or a sphere-like *** method is based on nonlinearly constrained mathematical modelling and also on stochastic optimization approaches. The proposed interpretative method first has been tested on theoretical synthetic models with different random errors at a certain depth, where a very close agreement has been observed between assumed and evaluated parameters. Subsequent field data have been considered for which the interpreted results by other methods are available for comparison. The agreement between the obtained results by the proposed technique and by other geophysical methods is good. A statistical analysis has been also carried out to demonstrate the accuracy and the precision of the suggested interpretative method.

关键词： gravity anomaly mathematical modelling interior penalty function stochastic algorithm

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Recursive computation of the invariant distribution of a diffusion

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BERNOULLI 2002年第3期8卷 367-405页

作者： Lamberton, D Pagès, G Univ Marne la Vallee UMR 8050 Lab Anal & Math Appl F-77454 Champs Sur Marne 2 Marne La Vallee France Univ Paris 06 UMR 7599 Lab Probabil & Modeles Aleatoires F-75252 Paris France

We propose a recursive stochastic algorithm with decreasing step to compute the invariant distribution v of a Brownian diffusion process, in which we approximate v(f) for a wide class of possibly unbounded continuous functions f. We consider a somewhat general setting which includes cases where the diffusion may have several invariant distributions. Our main convergence result contains as a corollary the almost sure central limit theorem. Further, we investigate the weak rate of convergence of the algorithm. We show, in the class of polynomial steps gamma(n) = n(-a), that it can be at most n(1/3) when the white noise has third moment zero and n(1/4) otherwise, where n denotes the number of iterations of the algorithm.

关键词： almost sure central limit theorem central limit theorem diffusion process invariant distribution numerical probability stochastic algorithm

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ASYMPTOTIC LAW IN SEQUENTIAL ESTIMATION OF A CHANGE POINT

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STATISTICS & PROBABILITY LETTERS 1993年第5期16卷 379-390页

作者： DECAMBRY, O ESIEF F-93162 NOISY LE GRANDFRANCE

We are concerned with the change point problem for independent random variables when the distributions before and after the change point are known. We construct a consistent and asymptotically Gaussian sequential esti... 详细信息

关键词： CHANGE POINT stochastic algorithm SEQUENTIAL ESTIMATION ASYMPTOTIC PROPERTIES

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algorithmic research on surface roughness in laser-melted claddings: A review

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SURFACE ENGINEERING 2024年第9-10期40卷 933-944页

作者： Zhao, Changlong Zhang, Zihao Yu, Zice Du, Weilong Changchun Univ Coll Mech & Vehicle Engn Changchun 130022 Jilin Peoples R China

As a breakthrough of the additive manufacturing technology being achieved, many fields have broadly applied laser cladding due to its unique advantages. But the surface characteristics of the cladding layer are not frequently aligned with the standards necessary for industrial use. Consequently, with a particular focus on refining its surface roughness, it has emerged as a significant area of interest among numerous investigators. This paper reviews a variety of methods for optimizing the surface roughness of laser cladding, covering from deterministic algorithms such as Taguchi's method, orthogonal experimental method, gradient descent method, to stochastic algorithms including neural network, genetic algorithm, Gray Wolf algorithm, and even hybrid algorithms combining multiple algorithms like neural network genetic algorithm, adaptive neural fuzzy reasoning algorithm, and improved genetic algorithms for response surface analysis, and so on. Through comparative analysis, it is found that the hybrid algorithms can quickly generate the optimal optimization parameters for the sake of achieving the optimal surface quality since they may combine the accuracy of deterministic algorithms and the robustness of stochastic algorithms. In addition, this paper also looks forward to the future development direction of surface quality optimization methods for laser cladding, aiming at laying a foundation for the research work of high-quality coating preparation.

关键词： laser cladding technology surface roughness deterministic algorithm stochastic algorithm hybrid algorithm

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Development of a Modification of the Particle Collision algorithm (PCA), Providing an Approximate Solution to the Traveling Salesman Problem

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AUTOMATIC DOCUMENTATION AND MATHEMATICAL LINGUISTICS 2024年第1期58卷 1-9页

作者： Syedin, D. Yu. MIREA Russian Technol Univ Dept Corp Informat Syst Moscow Russia Starovoytov Ctr Informat Technol & Syst Execut Pow Moscow Russia

This work is devoted to the development of a modification of the particle collision algorithm (PCA), which provides an approximate solution to the traveling salesman problem. The resulting modification was tested on a... 详细信息

关键词： traveling salesman problem stochastic algorithm combinatorial optimization

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Asynchronous parallel stochastic Quasi-Newton methods

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PARALLEL COMPUTING 2021年 101卷 102721-102721页

作者： Tong, Qianqian Liang, Guannan Cai, Xingyu Zhu, Chunjiang Bi, Jinbo Univ Connecticut Storrs CT 06269 USA Baidu USA Sunnyvale CA 94089 USA

Although first-order stochastic algorithms, such as stochastic gradient descent, have been the main force to scale up machine learning models, such as deep neural nets, the second-order quasi-Newton methods start to draw attention due to their effectiveness in dealing with ill-conditioned optimization problems. The L-BFGS method is one of the most widely used quasi-Newton methods. We propose an asynchronous parallel algorithm for stochastic quasi-Newton (AsySQN) method. Unlike prior attempts, which parallelize only the calculation for gradient or the two-loop recursion of L-BFGS, our algorithm is the first one that truly parallelizes L-BFGS with a convergence guarantee. Adopting the variance reduction technique, a prior stochastic L-BFGS, which has not been designed for parallel computing, reaches a linear convergence rate. We prove that our asynchronous parallel scheme maintains the same linear convergence rate but achieves significant speedup. Empirical evaluations in both simulations and benchmark datasets demonstrate the speedup in comparison with the non-parallel stochastic L-BFGS, as well as the better performance than first-order methods in solving ill-conditioned problems.

关键词： Quasi-Newton method Asynchronous parallel stochastic algorithm Variance reduction

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An improved tabu algorithm applied to global optimizations of inverse problems in electromagnetics

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IEEE TRANSACTIONS ON MAGNETICS 2002年第2期38卷 1069-1072页

作者： Chen, XD Ni, GZ Yang, SY Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China

This paper proposes an improved tabu search algorithm for global optimizations of multimodal functions with continuous variables of inverse problems in electromagnetics. The improvements include the introduction of a multistart process, the new neighborhood generating mechanism, and the memorization of the previously searched subspaces as well as the stop criteria for different termination purposes. The numerical results on solving a mathematical test function reveal that the proposed method is more robust in finding the global optimum compared with other kinds of tabu search algorithms. The shape optimization of an electrode demonstrates its value in practical engineering.

关键词： global optimization inverse problem stochastic algorithm tabu search algorithm

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A New Response Surface stochastic Analysis Method for Spatial Structure Stability-The Reticulated Shell Structure as an Example

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BUILDINGS 2021年第12期11卷 669页

作者： Liu, Huijuan Tondini, Nicola Lu, Xisen Chen, Chunxiang Xu, Zhonggen Guangxi Univ Coll Civil Engn & Architecture Guangxi Key Lab Disaster Prevent & Engn Safety Key Lab Disaster Prevent & Struct SafetyMinist E Nanning 530004 Peoples R China Univ Trento Dept Civil Environm & Mech Engn Via Mesiano 77 I-38123 Trento Italy Guangxi Univ Sch Math & Informat Sci Nanning 530004 Peoples R China Guangxi Univ Sch Mech Engn Nanning 530004 Peoples R China Guangzhou Univ Sch Civil Engn Guangzhou 510006 Peoples R China

For a long time, spatial structures have been widely used. However, compared with the high strength of their material, their stability is weak, and especially sensitive to damage and defects. This feature has increased the engineering industry's high requirements for their stability analysis. As we all know, this problem is more prominent for the reticulated shell structure, which is a classic representative of the spatial structure. However, in the current analysis methods for the stability of reticulated shells, the deterministic analysis method cannot consider the random characteristics of defects. Other random methods, such as the random defect modal method, and many improved methods, require more samples and calculation time. This unfavorable situation makes its engineering application greatly restricted. In addition, the random modal superposition method and derivation method based on Monte Carlo has not fundamentally changed this limitation. In order to fundamentally overcome this traditional shortcoming, this paper comprehensively studies the advantages of the high accuracy of the random defect modal method and the improved method, and at the same time, investigates the speed advantage of the response surface method, and then creates a new stochastic analysis method based on the response surface method. Finally, the analysis results of the calculation examples in this paper prove that it successfully balances and satisfies the dual requirements of accuracy and speed required for calculating the stability of the reticulated shell structure. Moreover, it has universal applicability to different forms of reticulated shells, such as classic 6-point flat domes, traditional reticulated shell structures, and bionic reticulated shell structures, and even other types of spatial structures.

关键词： spatial structure reticulated shell structures stability performance response surface method stochastic algorithm critical load

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