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Deep Neural Network-based Inverse Analysis with Application to a Rockfill Dam

KSCE JOURNAL OF CIVIL ENGINEERING 2024年第1期28卷 155-168页

作者： Shahzadi, Gullnaz Soulaimani, Azzeddine Ecole Technol Super Dept Mech Engn Montreal PQ H3C 1K3 Canada

The availability of significant computational resources has played an essential role in developing advanced numerical models for the design and safety evaluation of complex structures such as rockfill dams. Determining the geomechanical parameters is deemed a crucial but challenging task for effective modelling. The general approach involves using in situ or laboratory tests or experimental relationships from the literature to assess these parameters. These measures, however, do not accurately reflect the actual situation. This paper proposes a data driven approach using deep neural networks and non-deterministic optimization algorithms to identify the soil parameters that will lead to displacements that best approximate the measured data. The methodology is applied to a rockfill dam recently built in Quebec, for which some measurements of inclinometer displacements are available. A finite element model (FEM) of two dimensions generates numerical solutions. A comparative study is performed to account for the heterogeneity of the materials by decomposing the computational domain into subdomains. Subsequently, the inverse analysis uses the surrogate model instead of the full FEM model for rapid computations. A suitable objective function is defined to account for large oscillations in the measurement data. Non-intrusive stochastic optimization algorithms such as Genetic algorithm (GA), Particle Swarm Optimization (PSO), and Differential evolution (DE) are evaluated for the minimization problem. Finally, the case study confirms the capability of the proposed methodology to identify the relevant dam parameters, provide some insights into the performance, and compare three optimization algorithms.

关键词： Deep neural networks Inverse analysis Uncertainty analysis stochastic algorithms Rockfill dam

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Using Decomposed Error for Reproducing Implicit Understanding of algorithms

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EVOLUTIONARY COMPUTATION 2024年第1期32卷 49-68页

作者： Owen, Caitlin A. Dick, Grant Whigham, Peter A. Univ Otago Dept Informat Sci Dunedin New Zealand

Reproducibility is important for having confidence in evolutionary machine learning algorithms. Although the focus of reproducibility is usually to recreate an aggregate prediction error score using fixed random seeds, this is not sufficient. Firstly, multiple runs of an algorithm, without a fixed random seed, should ideally return statistically equivalent results. Secondly, it should be confirmed whether the expected behaviour of an algorithm matches its actual behaviour, in terms of how an algorithm targets a reduction in prediction error. Confirming the behaviour of an algorithm is not possible when using a total error aggregate score. Using an error decomposition framework as a methodology for improving the reproducibility of results in evolutionary computation addresses both of these factors. By estimating decomposed error using multiple runs of an algorithm and multiple training sets, the framework provides a greater degree of certainty about the prediction error. Also, decomposing error into bias, variance due to the algorithm (internal variance), and variance due to the training data (external variance) more fully characterises evolutionary algorithms. This allows the behaviour of an algorithm to be confirmed. Applying the framework to a number of evolutionary algorithms shows that their expected behaviour can be different to their actual behaviour. Identifying a behaviour mismatch is important in terms of understanding how to further refine an algorithm as well as how to effectively apply an algorithm to a problem.

关键词： Genetic programming evolutionary machine learning error decomposition bias-variance trade-off stochastic algorithms geometric semantic genetic programming ensemble learning symbolic regression

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Simulation-based methods for blind maximum-likelihood filter identification

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SIGNAL PROCESSING 1999年第1-2期73卷 3-25页

作者： Cappé, O Doucet, A Lavielle, M Moulines, E Ecole Natl Super Telecommun Dept signal CNRS URA 820 F-75634 Paris 13 France

Blind linear system identification consists in estimating the parameters of a linear time-invariant system given its (possibly noisy) response to an unobserved input signal. Blind system identification is a crucial problem in many applications which range from geophysics to telecommunications, either for its own sake or as a preliminary step towards blind deconvolution (i.e. recovery of the unknown input signal). This paper presents a survey of recent stochastic algorithms, related to the expectation-maximization (EM) principle, that make it possible to estimate the parameters of the unknown linear system in the maximum likelihood sense. Emphasis is on the computational aspects rather than on the theoretical questions. A large section of the paper is devoted to numerical simulations techniques, adapted from the Markov chain Monte Carlo (MCMC) methodology, and their efficient application to the noisy convolution model under consideration. (C) 1999 Published by Elsevier Science B.V. All rights reserved.

关键词： blind system identification maximum likelihood estimation expectation maximization (EM) stochastic algorithms Markov chain Monte Carlo (MCMC)

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DISCRETE TIME MARKOVIAN AGENTS INTERACTING THROUGH A POTENTIAL

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ESAIM-PROBABILITY AND STATISTICS 2013年第1期17卷 614-634页

作者： Budhiraja, Amarjit Del Moral, Pierre Rubenthaler, Sylvain Univ N Carolina Dept Stat & Operat Res Chapel Hill NC 27515 USA Univ Bordeaux 1 Bordeaux Math Inst INRIA Bordeaux Sud Ouest F-33405 Talence France Univ Nice Sophia Antipolis Lab Math JA Dieudonne F-06108 Nice France

A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the 'gradient' of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport in response to external stimulus such as a chemical gradient. One of the basic mathematical challenges is to develop a general theory of stability for such interacting Markovian systems and for the corresponding nonlinear Markov processes that arise in the large agent limit. Such a theory would be key to a mathematical understanding of the interactive structure formation that results from the complex feedback between the agents and the potential field. It will also be a crucial ingredient in developing simulation schemes that are faithful to the underlying model over long periods of time. The goal of this work is to study qualitative properties of the above stochastic system as the number of particles (N) and the time parameter (n) approach infinity. In this regard asymptotic properties of a deterministic nonlinear dynamical system, that arises in the propagation of chaos limit of the stochastic model, play a key role. We show that under suitable conditions this dynamical system has a unique fixed point. This result allows us to study stability properties of the underlying stochastic model. We show that as N -> infinity, the stochastic system is well approximated by the dynamical system, uniformly over time. As a consequence, for an arbitrarily initialized system, as N -> infinity and n -> infinity, the potential field and the empirical measure of the interacting particles are shown to converge to the unique fixed point of the dynamical system. In general, simulation

关键词： Interacting Markov chains agent based modeling multi-agent systems propagation of chaos non-linear Markov processes stochastic algorithms stability particle approximations swarm simulations chemotaxis reinforced random walk

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Analysis of the applicability and results of swarm intelligence tools for the positioning of Energy Storage Systems

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年 163卷

作者： Divasson-J, Asier Santamaria, Itxaso Aranzabal Landaribar, Miren T. Bedialauneta Aguirre, Paula Castillo Univ Deusto Unibertsitate Etorb 24 Bilbao 48007 Biscay Spain Univ Basque Country UPV EHU Ingeniero Torres Quevedo Pl 1 Bilbao 48013 Biscay Spain Univ Basque Country UPV EHU Otaola Hiribidea 29 Gipuzkoa 20600 Eibar Spain

The integration of renewable energy is transforming traditional energy systems, blurring the distinction between producers and consumers and shifting towards a distributed grid network. This change demands innovative approaches to optimize Energy Storage Systems (ESS) and manage grid incidents efficiently, all without significant infrastructural changes. While optimization algorithms like Swarm Intelligence are gaining traction, critical aspects, such as worst-case scenario analysis in distribution networks, remain underexplored. This study addresses this gap by applying stochastic optimization techniques to determine the optimal placement and capacity of ESS in a medium voltage radial distribution system, using the IEEE 33-bus model. The findings highlight the importance of considering worst-case scenarios, offering a balanced evaluation of current methodologies. This research provides valuable insights for improving system flexibility and resilience, contributing to more effective and practical energy optimization strategies in real-world applications.

关键词： Energy storage systems Distribution systems Electrical systems Optimization stochastic algorithms

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Mean-square performance of a convex combination of two adaptive filters

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2006年第3期54卷 1078-1090页

作者： Arenas-García, J Figueiras-Vidal, AR Sayed, AH Univ Calif Los Angeles Adapt Syst Lab Dept Elect Engn Los Angeles CA 90095 USA Univ Carlos III Madrid Dept Signal Theory & Commun Leganes 28911 Spain

Combination approaches provide an interesting way to improve adaptive filter performance. In this paper, we study the mean-square performance of a convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination is adapted by means of a stochastic gradient algorithm in order to minimize the error of the overall structure. General expressions are derived that show that the method is universal with respect to the component filters, i.e., in steady-state, it performs at least as well as the best component filter. Furthermore, when the correlation between the a priori errors of the components is low enough, their combination is able to outperform both of them. Using energy conservation relations, we specialize the results to a combination of least mean-square filters operating both in stationary and in nonstationary scenarios. We also show how the universality of the scheme can be exploited to design filters with improved tracking performance.

关键词： adaptive filtering convex combination energy conservation stochastic algorithms

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Average Competitive Learning Vector Quantization

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2014年第6期43卷 1288-1303页

作者： Salomon, Luis A. Fort, Jean-Claude Lozada-Chang, Li-Vang Inst Math Toulouse Toulouse France Univ Paris 05 Paris France Univ La Habana Fac Matemat & Comput CP-10400 Havana Cuba

We propose a new algorithm for vector quantization:Average Competitive Learning Vector Quantization (ACLVQ). It is a rather simple modification of the classical Competitive Learning Vector Quantization (CLVQ). This new formulation give us similar results for the quantization error to those obtained by the CLVQ and reduce considerably the computation time to achieve the optimal quantizer. We establish the convergence of the method via the Kushner-Clark approach, and compare the two algorithms via the Central Limit Theorem. A simulation study is carried out showing the good performance of our proposal.

关键词： Asymptotic convergence Kushner-Clark method Optimal quantization stochastic algorithms

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Zeroth-order algorithms for nonconvex-strongly-concave minimax problems with improved complexities

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JOURNAL OF GLOBAL OPTIMIZATION 2023年第2-4期87卷 709-740页

作者： Wang, Zhongruo Balasubramanian, Krishnakumar Ma, Shiqian Razaviyayn, Meisam Univ Calif Davis Dept Math Davis CA 95616 USA Univ Calif Davis Dept Stat Davis CA USA Univ Southern Calif Dept Ind & Syst Engn Los Angeles CA USA

In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first consider a deterministic version of the problem. We design and analyze the Zeroth-Order Gradient Descent Ascent (ZO-GDA) algorithm, and provide improved results compared to existing works, in terms of oracle complexity. We also propose the Zeroth-Order Gradient Descent Multi-Step Ascent (ZO-GDMSA) algorithm that significantly improves the oracle complexity of ZO-GDA. We then consider stochastic versions of ZO-GDA and ZO-GDMSA, to handle stochastic nonconvex minimax problems. For this case, we provide oracle complexity results under two assumptions on the stochastic gradient: (i) the uniformly bounded variance assumption, which is common in traditional stochastic optimization, and (ii) the Strong Growth Condition (SGC), which has been known to be satisfied by modern over-parameterized machine learning models. We establish that under the SGC assumption, the complexities of the stochastic algorithms match that of deterministic algorithms. Numerical experiments are presented to support our theoretical results.

关键词： Minimax problem Zeroth-order algorithms Oracle complexity Gradient descent ascent stochastic algorithms

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IterML: A Fast, Robust Algorithm for Estimating Signals With Finite Rate of Innovation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2013年第21期61卷 5324-5336页

作者： Wein, Alex Srinivasan, Lakshminarayan Univ Calif Los Angeles Neural Signal Proc Lab Dept Radiol Los Angeles CA 90095 USA

Recently, various methods have emerged for sub-Nyquist sampling and reconstruction of signals with finite rate of innovation (FRI). These methods seek to sample parametric signals at close to their information rate and later reconstruct the parameters of interest. Some proposed reconstruction algorithms are based on annihilating filters and root-finding. stochastic methods based on Gibbs sampling were subsequently proposed with the intent of improving robustness to noise, but these may run too slowly for some real-time applications. We present a fast maximum-likelihood-based deterministic greedy algorithm, IterML, for reconstructing FRI signals from noisy samples. We show in simulation that it achieves comparable or better performance than previous algorithms at a much lower computational cost. We also uncover a fundamental flaw in the application of MMSE (minimum mean squared error) estimation, a technique employed by some existing methods, to the problem in question.

关键词： Finite rate of innovation sampling maximum likelihood estimation Prony's method annihilating filter method Gibbs sampling stochastic algorithms

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Fluid simulation with the geometric cluster Monte Carlo algorithm

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COMPUTING IN SCIENCE & ENGINEERING 2006年第2期8卷 20-29页

作者： Luijten, E Univ Illinois Urbana IL 61801 USA

Building on earlier approaches, the geometric cluster algorithm permits the efficient simulation of cases in which conventional simulation methods fail, such as mixtures of different-sized particles. Starting from the celebrated Metropolis Monte Carlo algorithm, the author describes the development of cluster methods for magnetic systems and their connection with the geometric cluster algorithm.

关键词： Monte Carlo Methods stochastic algorithms Complex Fluids Cluster Methods

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