[ { "id": "authors:7awkn-98013", "collection": "authors", "collection_id": "7awkn-98013", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120905-165531861", "type": "book_section", "title": "Hybrid Subset Simulation Method for Dynamic Reliability Problems", "book_title": "Proceedings of the 9th International Conference on Structural Safety and Reliability", "author": [ { "family_name": "Ching", "given_name": "J.", "orcid": "0000-0001-6028-1674", "clpid": "Ching-Jianye" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" } ], "abstract": "A hybrid Subset Simulation approach is proposed for reliability estimation for general dynamical\nsystems subject to stochastic excitation. This new stochastic simulation approach combines the advantages\nof the two previously proposed Subset Simulation methods, Subset Simulation with Markov Chain Monte\nCarlo (MCMC) algorithm and Subset Simulation with splitting. The new method employs the MCMC algorithm\nbefore reaching an intermediate failure level and splitting after reaching the level to exploit the causality\nof dynamical systems. Two examples are presented to demonstrate the effectiveness of the new approach and\nto compare with the previous two Subset Simulation methods. The results show that the new method is robust\nto the choice of proposal distribution for the MCMC algorithm and to the intermediate failure events selected\nfor Subset Simulation.", "isbn": "978-90-5966-056-4", "publisher": "Millpress", "place_of_publication": "Rotterdam, Netherlands", "publication_date": "2012-11-13", "pages": "2001-2008" }, { "id": "authors:7htvw-jed88", "collection": "authors", "collection_id": "7htvw-jed88", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120905-164022640", "type": "book_section", "title": "Application of Subset Simulation Methods to Reliability Benchmark Problems", "book_title": "Proceedings of the 9th International Conference on Structural Safety and Reliability", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Ching", "given_name": "J.", "orcid": "0000-0001-6028-1674", "clpid": "Ching-Jianye" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "This paper presents the reliability analysis of three benchmark problems using three variants of\nSubset Simulation. The original version of Subset Simulation, SubSim/MCMC, employs a Markov chain\nMonte Carlo (MCMC) method to simulate samples conditional on intermediate failure events; it is a general\nmethod that is applicable to all the benchmark problems. A later version of Subset Simulation, Sub-\nSim/Splitting, is applicable to first-passage problems involving deterministic causal dynamical systems; it\nuses splitting of excitation time histories rather than MCMC to generate the conditional samples. The latest\nversion, SubSim/Hybrid, combines the advantages of MCMC and splitting and is also applicable to firstpassage\nproblems. Results show that all three Subset Simulation methods are effective in high-dimensional\nproblems and that some computational efficiency can be gained by adopting the splitting and hybrid strategies\nwhen calculating the reliability for the first-passage benchmark problems.", "isbn": "978-90-5966-056-4", "publisher": "Millpress", "place_of_publication": "Rotterdam, Netherlands", "publication_date": "2012-11-13", "pages": "2079-2084" }, { "id": "authors:nz8ev-rsq88", "collection": "authors", "collection_id": "nz8ev-rsq88", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120306-082708524", "type": "article", "title": "Bayesian post-processor and other enhancements of Subset Simulation for estimating failure probabilities in high dimensions", "author": [ { "family_name": "Zuev", "given_name": "Konstantin M.", "orcid": "0000-0003-2174-700X", "clpid": "Zuev-K-M" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "Siu-Kui", "orcid": "0000-0002-0228-1796", "clpid": "Au-Siu-Kui" }, { "family_name": "Katafygiotis", "given_name": "Lambros S.", "clpid": "Katafygiotis-Lambros-S" } ], "abstract": "Estimation of small failure probabilities is one of the most important and challenging computational problems in reliability engineering. The failure probability is usually given by an integral over a high-dimensional uncertain parameter space that is difficult to evaluate numerically. This paper focuses on enhancements to Subset Simulation (SS), proposed by Au and Beck, which provides an efficient algorithm based on MCMC (Markov chain Monte Carlo) simulation for computing small failure probabilities for general high-dimensional reliability problems. First, we analyze the Modified Metropolis algorithm (MMA), an MCMC technique, which is used in SS for sampling from high-dimensional conditional distributions. The efficiency and accuracy of SS directly depends on the ergodic properties of the Markov chains generated by MMA, which control how fast the chain explores the parameter space. We present some observations on the optimal scaling of MMA for efficient exploration, and develop an optimal scaling strategy for this algorithm when it is employed within SS. Next, we provide a theoretical basis for the optimal value of the conditional failure probability p_0, an important parameter one has to choose when using SS. We demonstrate that choosing any p_0 \u2208 [0.1, 0.3] will give similar efficiency as the optimal value of p0. Finally, a Bayesian post-processor SS+ for the original SS method is developed where the uncertain failure probability that one is estimating is modeled as a stochastic variable whose possible values belong to the unit interval. Simulated samples from SS are viewed as informative data relevant to the system's reliability. Instead of a single real number as an estimate, SS+ produces the posterior PDF of the failure probability, which takes into account both prior information and the information in the sampled data. This PDF quantifies the uncertainty in the value of the failure probability and it may be further used in risk analyses to incorporate this uncertainty. To demonstrate SS+, we consider its application to two different reliability problems: a linear reliability problem and reliability analysis of an elasto-plastic structure subjected to strong seismic ground motion. The relationship between the original SS and SS+ is also discussed.", "doi": "10.1016/j.compstruc.2011.10.017", "issn": "0045-7949", "publisher": "Elsevier", "publication": "Computers and Structures", "publication_date": "2012-02", "volume": "92-93", "pages": "283-296" }, { "id": "authors:xrmjb-bm314", "collection": "authors", "collection_id": "xrmjb-bm314", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120817-154248962", "type": "article", "title": "Discussion of Paper by F. Miao and M. Ghosn, \"Modified Subset Simulation for Reliability Analysis of Structural Systems\"", "author": [ { "family_name": "Au", "given_name": "S. K.", "orcid": "0000-0002-0228-1796", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Zuev", "given_name": "K. M.", "orcid": "0000-0003-2174-700X", "clpid": "Zuev-K-M" }, { "family_name": "Katafygiotis", "given_name": "L. S.", "clpid": "Katafygiotis-Lambros-S" } ], "abstract": "The subject paper presents a 'Regenerative Adaptive Subset\nSimulation' (RASS) algorithm that includes some modifications to\nthe original Subset Simulation algorithm for calculating small failure\nprobabilities for dynamic systems that was first proposed by\nAu and Beck in [1]. In particular, the authors state that their proposed\nmodifications overcome some limitations of the original\nMetropolis\u2013Hastings algorithm used in Subset Simulation, including\nthe 'burn-in' problem and the difficulty of the selection of the\nproposal distribution. This discussion intends to clarify several issues\nassociated with the paper.", "doi": "10.1016/j.strusafe.2011.09.003", "issn": "0167-4730", "publisher": "Elsevier", "publication": "Structural Safety", "publication_date": "2012-01", "series_number": "1", "volume": "34", "issue": "1", "pages": "379-380" }, { "id": "authors:f2fav-n4v30", "collection": "authors", "collection_id": "f2fav-n4v30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120810-115858828", "type": "article", "title": "Application of subset simulation methods to reliability benchmark problems", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Ching", "given_name": "J.", "orcid": "0000-0001-6028-1674", "clpid": "Ching-Jianye" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "This paper presents the reliability analysis of three benchmark problems using three variants of Subset Simulation. The\noriginal version of Subset Simulation, SubSim/MCMC, employs a Markov chain Monte Carlo (MCMC) method to simulate samples conditional on intermediate failure events; it is a general method that is applicable to all the benchmark\nproblems. SubSim/Splitting is a variant of Subset Simulation applicable to first-passage problems involving deterministic\ndynamical systems. It makes use of trajectory splitting for generating conditional samples. Another variant, SubSim/\nHybrid, uses a combined MCMC/Splitting strategy and so it has the advantages of MCMC and splitting; it is applicable\nto uncertain and deterministic dynamical systems. Results show that all three Subset Simulation variants are effective in\nhigh-dimensional problems and that some computational efficiency can be gained by exploiting and incorporating system\ncharacteristics into the simulation procedure.", "doi": "10.1016/j.strusafe.2006.07.008", "issn": "0167-4730", "publisher": "Elsevier", "publication": "Structural Safety", "publication_date": "2007-07", "series_number": "3", "volume": "29", "issue": "3", "pages": "183-193" }, { "id": "authors:rw3kq-vcn43", "collection": "authors", "collection_id": "rw3kq-vcn43", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120905-163324297", "type": "book_section", "title": "Benchmark Study on Reliability Estimation in Higher Dimensions of Structural Systems \u2013 An Overview", "book_title": "Proceedings of the 6th European Conference on Structural Dynamics", "author": [ { "family_name": "Schu\u00ebller", "given_name": "G. I.", "clpid": "Schu\u00ebller-G-I" }, { "family_name": "Pradlwater", "given_name": "H. J.", "clpid": "Pradlwater-H-J" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "S. K.", "orcid": "0000-0002-0228-1796", "clpid": "Au-Siu-Kui" }, { "family_name": "Katafygiotis", "given_name": "L. S.", "clpid": "Katafygiotis-L-S" }, { "family_name": "Ghanem", "given_name": "R.", "clpid": "Ghanem-R" } ], "contributor": [ { "family_name": "Soize", "given_name": "C.", "clpid": "Soize-C" }, { "family_name": "Schueller", "given_name": "G. I.", "clpid": "Schueller-G-I" } ], "abstract": "This work is concerned with a Benchmark study on reliability estimation of structural systems,\nwhich was suggested in 2004 and is currently in progress (Institute of Engineering Mechanics, University of\nInnsbruck, 2004). The Benchmark study attempts to assess various recently proposed alternatives for reliability\nestimation with respect to their accuracy and computational efficiency. The emphasis of this study is on\nsystems which include a large number of random variables. For this purpose three problems have been chosen\nwhich cover a wide range of cases of interest in engineering practice and involve linear and non-linear systems\nwith uncertainties in the material properties and/or the loading conditions. The present work provides an\noverview of the Benchmark study and of the methods compared, as well as the current status of the results obtained.", "isbn": "9059660331", "publisher": "Milpress", "place_of_publication": "Rotterdam", "publication_date": "2005-09", "pages": "717-722" }, { "id": "authors:d5mf2-fvr37", "collection": "authors", "collection_id": "d5mf2-fvr37", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120817-164316371", "type": "article", "title": "Hybrid Subset Simulation Method for Reliability Estimation of Dynamical Systems Subject to Stochastic Excitation", "author": [ { "family_name": "Ching", "given_name": "J.", "orcid": "0000-0001-6028-1674", "clpid": "Ching-Jianye" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" } ], "abstract": "A hybrid Subset Simulation approach is proposed for reliability estimation for general dynamical systems subject to stochastic excitation.\nThis new stochastic simulation approach combines the advantages of the two previously proposed Subset Simulation methods, Subset\nSimulation with Markov Chain Monte Carlo (MCMC) algorithm and Subset Simulation with splitting. The new method employs the MCMC\nalgorithm before reaching an intermediate failure level and splitting after reaching the level to exploit the causality of dynamical systems.\nThe statistical properties of the failure probability estimators are derived. Two examples are presented to demonstrate the effectiveness of the\nnew approach and to compare with the previous two Subset Simulation methods. The results show that the new method is robust to the choice\nof proposal distribution for the MCMC algorithm and to the intermediate failure events selected for Subset Simulation.", "doi": "10.1016/j.probengmech.2004.09.001", "issn": "0266-8920", "publisher": "Elsevier", "publication": "Probabilistic Engineering Mechanics", "publication_date": "2005-07", "series_number": "3", "volume": "20", "issue": "3", "pages": "199-214" }, { "id": "authors:yg5s0-8qm79", "collection": "authors", "collection_id": "yg5s0-8qm79", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120817-165053206", "type": "article", "title": "Reliability Estimation for Dynamical Systems Subject to Stochastic Excitation using Subset Simulation with Splitting", "author": [ { "family_name": "Ching", "given_name": "J.", "orcid": "0000-0001-6028-1674", "clpid": "Ching-Jianye" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "A new subset simulation approach is proposed for reliability estimation for dynamical systems subject to stochastic excitation. The basic idea of subset simulation is to factor a small failure probability into a product of larger failure\nprobabilities conditional on intermediate failure events. The new method proposed in this work does not require Markov\nChain Monte Carlo simulation, in contrast to the original method, to estimate the conditional probabilities;\ninstead, only direct Monte Carlo simulation is needed. The method employs splitting of a trajectory that reaches an\nintermediate failure level into multiple trajectories subsequent to the corresponding first passage time. The new\napproach still enjoys most of the advantages of the original subset simulation, e.g. it is applicable to general causal\ndynamical systems and it is robust with respect to the dimension of the uncertain input variables. The statistical properties\nof the failure probability estimators are presented, where it is shown that they are unbiased and formulas are\nderived to assess the error of estimation, including the coefficient of variation. We also discuss the selection of intermediate\nfailure events and the number of samples for each failure level. The resulting algorithm is simple and easy to\nimplement. Two examples are presented to demonstrate the effectiveness of the new approach, and the results are compared\nwith the original subset simulation and with direct Monte Carlo simulation.", "doi": "10.1016/j.cma.2004.05.028", "issn": "0045-7825", "publisher": "Elsevier", "publication": "Computer Methods in Applied Mechanics and Engineering", "publication_date": "2005-04-08", "series_number": "12-16", "volume": "194", "issue": "12-16", "pages": "1557-1579" }, { "id": "authors:98zpx-w6115", "collection": "authors", "collection_id": "98zpx-w6115", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110607-105851426", "type": "book_section", "title": "Reliability of dynamic systems using stochastic simulation", "book_title": "Structural dynamics: EURODYN 2005", "author": [ { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" } ], "contributor": [ { "family_name": "Soize", "given_name": "Christian", "clpid": "Soize-C" }, { "family_name": "Schu\u00ebller", "given_name": "Gerhart I.", "clpid": "Schu\u00ebller-G-I" } ], "abstract": "An overview is given of the use of stochastic simulation to estimate first-passage failure probabilities\nfor dynamic reliability problems. Also, two methods are described that were developed recently by the\nauthors which give much better computational efficiency than Monte Carlo Simulation when estimating small\nfailure probabilities: ISEE (Importance Sampling using Elementary Events) for linear dynamic systems and\nSubset Simulation for general problems, including those with nonlinear dynamics.", "isbn": "90-5966-033-1", "publisher": "Millpress", "place_of_publication": "Rotterdam", "publication_date": "2005", "pages": "23-30" }, { "id": "authors:j4dha-heb66", "collection": "authors", "collection_id": "j4dha-heb66", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PORes04b", "type": "article", "title": "Effect of Seismic Risk on Lifetime Property Value", "author": [ { "family_name": "Porter", "given_name": "Keith A.", "clpid": "Porter-K-A" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Shaikhutdinov", "given_name": "Rustem V.", "clpid": "Shaikhutdinov-R-V" }, { "family_name": "Au", "given_name": "Siu Kui", "clpid": "Au-Siu-Kui" }, { "family_name": "Mizukoshi", "given_name": "Kaoru", "clpid": "Mizukoshi-K" }, { "family_name": "Miyamura", "given_name": "Masamitsu", "clpid": "Miyamura-M" }, { "family_name": "Ishida", "given_name": "Hiroshi", "clpid": "Ishida-H" }, { "family_name": "Moroi", "given_name": "Takafumi", "clpid": "Moroi-T" }, { "family_name": "Tsukada", "given_name": "Yasu", "clpid": "Tsukada-Y" }, { "family_name": "Masuda", "given_name": "Manabu", "clpid": "Masuda-M" } ], "abstract": "We examine seismic risk from the commercial real estate investor's viewpoint. We present a methodology to estimate the uncertain net asset value (NAV) of an investment opportunity considering market risk and seismic risk. For seismic risk, we employ a performance-based earthquake engineering methodology called assembly-based vulnerability (ABV). For market risk, we use evidence of volatility of return on investment in the United States. We find that uncertainty in NAV can be significant compared with investors' risk tolerance, making it appropriate to adopt a decision-analysis approach to the investment decision, in which one optimizes certainty equivalent, CE, as opposed to NAV. Uncertainty in market value appears greatly to exceed uncertainty in earthquake repair costs. Consequently, CE is sensitive to the mean value of earthquake repair costs but not to its variance. Thus, to a real estate investor, seismic risk matters only in the mean, at least for the demonstration buildings examined here.", "doi": "10.1193/1.1810536", "issn": "8755-2930", "publisher": "Earthquake Spectra", "publication": "Earthquake Spectra", "publication_date": "2004-11", "series_number": "4", "volume": "20", "issue": "4", "pages": "1211-1237" }, { "id": "authors:tdrw7-v5071", "collection": "authors", "collection_id": "tdrw7-v5071", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120817-165443909", "type": "article", "title": "Structural Damage Detection and Assessment using Adaptive Markov Chain Monte Carlo Simulation", "author": [ { "family_name": "Yuen", "given_name": "Ka-Veng", "orcid": "0000-0002-1755-6668", "clpid": "Yuen-Ka-Veng" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "Siu Kui", "clpid": "Au-Siu-Kui" } ], "abstract": "This paper uses Bayesian updating of dynamic models of structures to perform all four levels of structural\ndamage detection and assessment: damage indication, its location and severity, and its impact on the structural\nreliability. The numerical integration that is required in Bayesian updating is known to be computationally\nprohibitive for problems with high dimensions. The proposed approach uses Markov chain Monte Carlo\nsimulation based on the Metropolis\u2013Hastings algorithm to tackle this problem in conjunction with an adaptive\nconcept to obtain information about the important regions of the updated probability distribution in an\nefficient manner. The Markov chain samples are then used to estimate the damage probabilities by statistical\naveraging for damage detection and assessment. The proposed approach is illustrated using the ASCE-IASC\nfour-storey benchmark structure for various amounts of modal data that produce globally identifiable, locally\nidentifiable and unidentifiable cases.", "doi": "10.1002/stc.47", "issn": "1545-2255", "publisher": "John Wiley & Sons", "publication": "Structural Control and Health Monitoring", "publication_date": "2004-09", "series_number": "4", "volume": "11", "issue": "4", "pages": "327-347" }, { "id": "authors:k7tcn-fsj05", "collection": "authors", "collection_id": "k7tcn-fsj05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120912-151520978", "type": "book_section", "title": "Reliability Estimation for Dynamical Systems Subject to Stochastic Excitation using Subset Simulation with Splitting", "author": [ { "family_name": "Ching", "given_name": "Jianye", "orcid": "0000-0001-6028-1674", "clpid": "Ching-Jianye" }, { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" } ], "abstract": "A new Subset Simulation approach is proposed in this paper for reliability estimation for\ndynamical systems subject to stochastic excitation. The basic idea of Subset Simulation is to\nconsider a small failure probability as a product of larger failure probabilities conditional on\nintermediate failure events. This new approach does not require Markov Chain Monte Carlo\nsimulation, in contrast to the original method, to generate conditional samples for estimating\nthe conditional probabilities; instead, only direct Monte Carlo simulation is needed. The\nmethod employs splitting of a trajectory that reaches an intermediate failure level into multiple\ntrajectories subsequent to its first passage time. This exploits an important feature of causal\ndynamical systems, namely, the distribution of the future excitation subsequent to the first\npassage time and conditional on the previous excitation is just equal to its unconditional\ncounterpart. The statistical properties of the failure probability estimates are presented, where\nit is shown that the estimates are unbiased and formulas are derived to assess the error of\nestimation, including the coefficient of variation of the estimates. The resulting algorithm is\nsimple and easy to implement. Two examples are presented to demonstrate the effectiveness\nof the new approach, also to compare with the original Subset Simulation and with direct\nMonte Carlo simulation.", "publisher": "Curran Associates", "publication_date": "2004-07" }, { "id": "authors:wvpfv-ttt61", "collection": "authors", "collection_id": "wvpfv-ttt61", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120829-115334989", "type": "article", "title": "Two-Stage Structural Health Monitoring Approach for Phase I Benchmark Studies", "author": [ { "family_name": "Yuen", "given_name": "Ka-Veng", "orcid": "0000-0002-1755-6668", "clpid": "Yuen-Ka-Veng" }, { "family_name": "Au", "given_name": "Siu Kui", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" } ], "abstract": "This paper presents a two-stage structural health monitoring methodology and applies it to the Phase I benchmark study\nsponsored by the IASC-ASCE Task Group on Structural Health Monitoring. In the first stage, modal parameters are identified using\nmeasured structural response from the undamaged system and then from the (possibly) damaged system. In the second stage, these data\nare used to update a parametrized structural model of the system using Bayesian system identification. The approach allows one to obtain\nnot only estimates of the stiffness parameters but also the probability that damage in any substructure exceeds any specified threshold\nexpressed in terms of a fractional stiffness loss. It successfully identifies the location and severity of damage in all cases of the benchmark\nproblem.", "doi": "10.1061/(ASCE)0733-9399(2004)130:1(16)", "issn": "0733-9399", "publisher": "American Society of Civil Engineers", "publication": "Journal of Engineering Mechanics", "publication_date": "2004-01", "series_number": "1", "volume": "130", "issue": "1", "pages": "16-33" }, { "id": "authors:0d89f-mff20", "collection": "authors", "collection_id": "0d89f-mff20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120829-115643890", "type": "article", "title": "Subset Simulation and its Application to Seismic Risk Based on Dynamic Analysis", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "A method is presented for efficiently computing small failure probabilities encountered in seismic risk problems involving\ndynamic analysis. It is based on a procedure recently developed by the writers called Subset Simulation in which the central idea is that\na small failure probability can be expressed as a product of larger conditional failure probabilities, thereby turning the problem of\nsimulating a rare failure event into several problems that involve the conditional simulation of more frequent events. Markov chain Monte\nCarlo simulation is used to efficiently generate the conditional samples, which is otherwise a nontrivial task. The original version of\nSubset Simulation is improved by allowing greater flexibility for incorporating prior information about the reliability problem so as to\nincrease the efficiency of the method. The method is an effective simulation procedure for seismic performance assessment of structures\nin the context of modern performance-based design. This application is illustrated by considering the failure of linear and nonlinear\nhysteretic structures subjected to uncertain earthquake ground motions. Failure analysis is also carried out using the Markov chain samples\ngenerated during Subset Simulation to yield information about the probable scenarios that may occur when the structure fails.", "doi": "10.1061/(ASCE)0733-9399(2003)129:8(901)", "issn": "0733-9399", "publisher": "American Society of Civil Engineers", "publication": "Journal of Engineering Mechanics", "publication_date": "2003-08", "series_number": "8", "volume": "129", "issue": "8", "pages": "901-917" }, { "id": "authors:0v3fj-jxq39", "collection": "authors", "collection_id": "0v3fj-jxq39", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120829-120814856", "type": "article", "title": "Importance Sampling in High Dimensions", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "This paper draws attention to a fundamental problem that occurs in applying importance sampling to 'high-dimensional' reliability problems, i.e., those with a large number of uncertain parameters. This question of applicability carries an important bearing on the potential use of importance sampling for solving dynamic first-excursion problems and static reliability problems for structures with a large number of uncertain structural model parameters. The conditions under which importance sampling is applicable in high dimensions are investigated, where the focus is put on the common case of standard Gaussian uncertain parameters. It is found that importance sampling densities using design points are applicable if the covariance matrix associated with each design point does not deviate significantly from the identity matrix. The study also suggests that importance sampling densities using random pre-samples are generally not applicable in high dimensions.", "doi": "10.1016/S0167-4730(02)00047-4", "issn": "0167-4730", "publisher": "Elsevier", "publication": "Structural Safety", "publication_date": "2003-04", "series_number": "2", "volume": "25", "issue": "2", "pages": "139-163" }, { "id": "authors:cn7zx-z5m14", "collection": "authors", "collection_id": "cn7zx-z5m14", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120919-153417896", "type": "book_section", "title": "Robust Reliability of Stochastic Structural Systems under Stochastic Excitation", "book_title": "Structural dynamics - EURODYN 2002 : proceedings of the 4th international conference on structural dynamics, Munich, Germany, 2-5 September 2002", "author": [ { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" } ], "abstract": "This paper presents the concept of robust dynamic reliability where the uncertainties in the dynamic\nloading and structural modelling are treated probabilistically. Efficient evaluation of this robust reliability,\nwhich is formulated as a multi-dimensional probability integral, requires advanced computational methodologies\nother than numerical integration or standard Monte Carlo simulation. Some advanced simulation methods\nthat have been recently developed by the authors are reviewed, namely, ISEE (Importance Sampling using Elementary\nEvents) and adaptive importance sampling and subset simulation, both of which use Markov chain\nMonte Carlo simulation. In particular, ISEE is dedicated to, and is extremely efficient for, evaluating first-passage\nprobabilities for linear dynamical systems. Subset simulation, on the other hand, is applicable for\ngeneral dynamical systems and is most suitable for a combined treatment of both loading and structural parameter\nuncertainties in high dimensions.", "isbn": "905809510 X", "publisher": "Swets & Zeitlinger", "place_of_publication": "Lisse, Netherlands", "publication_date": "2002-09", "pages": "331-336" }, { "id": "authors:gae5n-h5149", "collection": "authors", "collection_id": "gae5n-h5149", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120919-155317476", "type": "book_section", "title": "Application of Subset Simulation to Seismic Risk Analysis", "author": [ { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" } ], "contributor": [ { "family_name": "Smyth", "given_name": "Andrew", "clpid": "Smyth-A" } ], "abstract": "This paper presents the application of a new reliability method called Subset Simulation to seismic risk analysis of a structure, where the exceedance of some performance quantity, such as the peak\ninterstory drift, above a specified threshold level is considered for the case of uncertain seismic excitation. This involves analyzing the well-known but difficult first-passage failure problem. Failure analysis\nis also carried out using results from Subset Simulation which yields information about the probable\nscenarios that may occur in case of failure. The results show that for given magnitude and epicentral distance (which are related to the 'intensity' of shaking), the probable mode of failure is due to a\n'resonance effect.' On the other hand, when the magnitude and epicentral distance are considered to be\nuncertain, the probable failure mode correspondsto the occurrence of 'large-magnitude, small epicentral\ndistance' earthquakes.", "publisher": "Columbia University", "publication_date": "2002-06" }, { "id": "authors:v47j7-pkp85", "collection": "authors", "collection_id": "v47j7-pkp85", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120810-105626108", "type": "article", "title": "Bayesian Updating of Structural Models and Reliability using\n Markov Chain Monte Carlo Simulation", "author": [ { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" } ], "abstract": "In a full Bayesian probabilistic framework for \"robust\" system identification, structural response predictions and performance reliability are updated using structural test data D by considering the predictions of a whole set of possible structural models that are\nweighted by their updated probability. This involves integrating h(\u03b8)p(\u03b8|D) over the whole parameter space, where \u03b8 is a parameter vector defining each model within the set of possible models of the structure, h(\u03b8) is a model prediction of a response quantity of interest,\nand p(\u03b8|D) is the updated probability density for \u03b8, which provides a measure of how plausible each model is given the data D. The evaluation of this integral is difficult because the dimension of the parameter space is usually too large for direct numerical integration and\np(\u03b8|D) is concentrated in a small region in the parameter space and only known up to a scaling constant. An adaptive Markov chain\nMonte Carlo simulation approach is proposed to evaluate the desired integral that is based on the Metropolis-Hastings algorithm and a\nconcept similar to simulated annealing. By carrying out a series of Markov chain simulations with limiting stationary distributions equal\nto a sequence of intermediate probability densities that converge on p(\u03b8|D), the region of concentration of p(\u03b8|D) is gradually portrayed.\nThe Markov chain samples are used to estimate the desired integral by statistical averaging. The method is illustrated using simulated\ndynamic test data to update the robust response variance and reliability of a moment-resisting frame for two cases: one where the model\nis only locally identifiable based on the data and the other where it is unidentifiable.", "doi": "10.1061/(ASCE)0733-9399(2002)128:4(380)", "issn": "0733-9399", "publisher": "American Society of Civil Engineers", "publication": "Journal of Engineering Mechanics", "publication_date": "2002-04", "series_number": "4", "volume": "128", "issue": "4", "pages": "380-391" }, { "id": "authors:02x3x-32z39", "collection": "authors", "collection_id": "02x3x-32z39", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120925-141745375", "type": "book_section", "title": "Probabilistic Damage Detection Using Markov Chain Simulation with Application to a Benchmark Problem", "book_title": "Proceedings of the 3rd World Conference on Structural Control", "author": [ { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Yuen", "given_name": "K. V.", "orcid": "0000-0002-1755-6668", "clpid": "Yuen-Ka-Veng" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" } ], "contributor": [ { "family_name": "Casciati", "given_name": "Fabio", "clpid": "Casciati-F" } ], "abstract": "A Markov chain simulation method is presented to evaluate the integrals giving the\nprobability of damage and updated reliability based on dynamic data in a Bayesian\nprobabilistic approach to damage detection and assessment. The method is based\non the Metropolis-Hastings algorithm and an adaptive procedure to gain information\nabout the important regions of the updated probability distribution in an efficient\nmanner. Statistical averaging over the Markov chain samples is used to estimate the\ndamage probability for each substructure and the updated reliability. The method is\nillustrated by applying it to modal data from the ASCE four-story benchmark structure\nto perform damage detection and assessment by giving the likely locations of the\ndamage, its severity and its impact on the interstory-drift reliability of the structure.", "isbn": "0471489808", "publisher": "Wiley", "place_of_publication": "Chichester, NY", "publication_date": "2002-04", "pages": "1065-1070" }, { "id": "authors:t41ph-mex06", "collection": "authors", "collection_id": "t41ph-mex06", "cite_using_url": "https://resolver.caltech.edu/CaltechEERL:2002.EERL-2002-04", "type": "monograph", "title": "Impact of Seismic Risk on Lifetime Property Values", "author": [ { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Porter", "given_name": "Keith A.", "clpid": "Porter-K-A" }, { "family_name": "Shaikhutdinov", "given_name": "R. V.", "clpid": "Shaikhutdinov-R-V" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Mizukoshi", "given_name": "K.", "clpid": "Mizukoshi-K" }, { "family_name": "Miyamura", "given_name": "M.", "clpid": "Miyamura-M" }, { "family_name": "Ishida", "given_name": "H.", "clpid": "Ishida-H" }, { "family_name": "Moroi", "given_name": "T.", "clpid": "Moroi-T" }, { "family_name": "Tsukada", "given_name": "Y.", "clpid": "Tsukada-Y" }, { "family_name": "Masuda", "given_name": "M.", "clpid": "Masuda-M" } ], "abstract": "This report presents a methodology for establishing the uncertain net asset value, NAV, of a real-estate investment opportunity considering both market risk and seismic risk for the property. It also presents a decision-making procedure to assist in making real-estate investment choices under conditions of uncertainty and risk-aversion. It is shown that that market risk, as measured by the coefficient of variation of NAV, is at least 0.2 and may exceed 1.0. In a situation of such high uncertainty, where potential gains and losses are large relative to a decision-maker's risk tolerance, it is appropriate to adopt a decision-analysis approach to real-estate investment decision-making. A simple equation for doing so is presented. The decision-analysis approach uses the certainty equivalent, CE, as opposed to NAV as the basis for investment decision-making. That is, when faced with multiple investment alternatives, one should choose the alternative that maximizes CE. It is shown that CE is less than the expected value of NAV by an amount proportional to the variance of NAV and the inverse of the decision-maker's risk tolerance, [rho]. \n\nThe procedure for establishing NAV and CE is illustrated in parallel demonstrations by CUREE and Kajima research teams. The CUREE demonstration is performed using a real 1960s-era hotel building in Van Nuys, California. The building, a 7-story non-ductile reinforced-concrete moment-frame building, is analyzed using the assembly-based vulnerability (ABV) method, developed in Phase III of the CUREE-Kajima Joint Research Program. The building is analyzed three ways: in its condition prior to the 1994 Northridge Earthquake, with a hypothetical shearwall upgrade, and with earthquake insurance. This is the first application of ABV to a real building, and the first time ABV has incorporated stochastic structural analyses that consider uncertainties in the mass, damping, and force-deformation behavior of the structure, along with uncertainties in ground motion, component damageability, and repair costs. New fragility functions are developed for the reinforced concrete flexural members using published laboratory test data, and new unit repair costs for these components are developed by a professional construction cost estimator. Four investment alternatives are considered: do not buy; buy; buy and retrofit; and buy and insure. It is found that the best alternative for most reasonable values of discount rate, risk tolerance, and market risk is to buy and leave the building as-is. However, risk tolerance and market risk (variability of income) both materially affect the decision. That is, for certain ranges of each parameter, the best investment alternative changes. This indicates that expected-value decision-making is inappropriate for some decision-makers and investment opportunities. It is also found that the majority of the economic seismic risk results from shaking of S[subscript a] < 0.3g, i.e., shaking with return periods on the order of 50 to 100 yr that cause primarily architectural damage, rather than from the strong, rare events of which common probable maximum loss (PML) measurements are indicative. \n\nThe Kajima demonstration is performed using three Tokyo buildings. A nine-story, steel-reinforced-concrete building built in 1961 is analyzed as two designs: as-is, and with a steel-braced-frame structural upgrade. The third building is 29-story, 1999 steel-frame structure. The three buildings are intended to meet collapse-prevention, life-safety, and operational performance levels, respectively, in shaking with 10%exceedance probability in 50 years. The buildings are assessed using levels 2 and 3 of Kajima's three-level analysis methodology. These are semi-assembly based approaches, which subdivide a building into categories of components, estimate the loss of these component categories for given ground motions, and combine the losses for the entire building. The two methods are used to estimate annualized losses and to create curves that relate loss to exceedance probability. The results are incorporated in the input to a sophisticated program developed by the Kajima Corporation, called Kajima D, which forecasts cash flows for office, retail, and residential projects for purposes of property screening, due diligence, negotiation, financial structuring, and strategic planning. The result is an estimate of NAV for each building. A parametric study of CE for each building is presented, along with a simplified model for calculating CE as a function of mean NAV and coefficient of variation of NAV. The equation agrees with that developed in parallel by the CUREE team. \n\nBoth the CUREE and Kajima teams collaborated with a number of real-estate investors to understand their seismic risk-management practices, and to formulate and to assess the viability of the proposed decision-making methodologies. Investors were interviewed to elicit their risk-tolerance, r, using scripts developed and presented here in English and Japanese. Results of 10 such interviews are presented, which show that a strong relationship exists between a decision-maker's annual revenue, R, and his or her risk tolerance, [rho is approximately equal to] 0.0075R[superscript 1.34]. The interviews show that earthquake risk is a marginal consideration in current investment practice. Probable maximum loss (PML) is the only earthquake risk parameter these investors consider, and they typically do not use seismic risk at all in their financial analysis of an investment opportunity. For competitive reasons, a public investor interviewed here would not wish to account for seismic risk in his financial analysis unless rating agencies required him to do so or such consideration otherwise became standard practice. However, in cases where seismic risk is high enough to significantly reduce return, a private investor expressed the desire to account for seismic risk via expected annualized loss (EAL) if it were inexpensive to do so, i.e., if the cost of calculating the EAL were not substantially greater than that of PML alone. \n\nThe study results point to a number of interesting opportunities for future research, namely: improve the market-risk stochastic model, including comparison of actual long-term income with initial income projections; improve the risk-attitude interview; account for uncertainties in repair method and in the relationship between repair cost and loss; relate the damage state of structural elements with points on the force-deformation relationship; examine simpler dynamic analysis as a means to estimate vulnerability; examine the relationship between simplified engineering demand parameters and performance; enhance category-based vulnerability functions by compiling a library of building-specific ones; and work with lenders and real-estate industry analysts to determine the conditions under which seismic risk should be reflected in investors' financial analyses.", "publisher": "California Institute of Technology", "publication_date": "2002-01-01" }, { "id": "authors:m7b6w-kbc81", "collection": "authors", "collection_id": "m7b6w-kbc81", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120809-162908584", "type": "article", "title": "Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation", "author": [ { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" } ], "abstract": "A new simulation approach, called 'subset simulation', is proposed to compute small failure probabilities encountered in reliability analysis of engineering systems. The basic idea is to express the failure probability as a product of larger conditional failure probabilities by introducing intermediate failure events. With a proper choice of the conditional events, the conditional failure probabilities can be made sufficiently large so that they can be estimated by means of simulation with a small number of samples. The original problem of calculating a small failure probability, which is computationally demanding, is reduced to calculating a sequence of conditional probabilities, which can be readily and efficiently estimated by means of simulation. The conditional probabilities cannot be estimated efficiently by a standard Monte Carlo procedure, however, and so a Markov chain Monte Carlo simulation (MCS) technique based on the Metropolis algorithm is presented for their estimation. The proposed method is robust to the number of uncertain parameters and efficient in computing small probabilities. The efficiency of the method is demonstrated by calculating the first-excursion probabilities for a linear oscillator subjected to white noise excitation and for a five-story nonlinear hysteretic shear building under uncertain seismic excitation.", "doi": "10.1016/S0266-8920(01)00019-4", "issn": "0266-8920", "publisher": "Elsevier", "publication": "Probabilistic Engineering Mechanics", "publication_date": "2001-10", "series_number": "4", "volume": "16", "issue": "4", "pages": "263-277" }, { "id": "authors:8egeq-9hr04", "collection": "authors", "collection_id": "8egeq-9hr04", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120924-143920520", "type": "book_section", "title": "Bayesian Updating of Nonlinear Model Predictions using Markov Chain Monte Carlo Simulation", "book_title": "18th Biennial Conference on Mechanical Vibration and Noise", "author": [ { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Yuen", "given_name": "K.-V.", "orcid": "0000-0002-1755-6668", "clpid": "Yuen-Ka-Veng" } ], "abstract": "The usual practice in system identification is to use system\ndata to identify one model from a set of possible models and\nthen to use this model for predicting system behavior. In contrast,\nthe present robust predictive approach rigorously combines\nthe predictions of all the possible models, appropriately weighted\nby their updated probabilities based on the data. This Bayesian\nsystem identification approach is applied to update the robust reliability\nof a dynamical system based on its measured response\ntime histories. A Markov chain simulation method based on the\nMetropolis-Hastings algorithm and an adaptive scheme is proposed\nto evaluate the robust reliability integrals. An example for\nupdating the reliability of a Duffing oscillator is given to illustrate\nthe proposed method.", "isbn": "0791835464", "publisher": "American Society of Mechanical Engineers", "place_of_publication": "New York, NY", "publication_date": "2001-09", "pages": "821-828" }, { "id": "authors:k8csm-w1659", "collection": "authors", "collection_id": "k8csm-w1659", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120809-162001049", "type": "article", "title": "First Excursion Probabilities for Linear Systems by Very Efficient Importance Sampling", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "An analytical study of the failure region of the first excursion reliability problem for linear dynamical systems subjected to Gaussian white noise excitation is carried out with a view to constructing a suitable importance sampling density for computing the first excursion failure probability. Central to the study are 'elementary failure regions', which are defined as the failure region in the load space corresponding to the failure of a particular output response at a particular instant. Each elementary failure region is completely characterized by its design point, which can be computed readily using impulse response functions of the system. It is noted that the complexity of the first excursion problem stems from the structure of the union of the elementary failure regions. One important consequence of this union structure is that, in addition to the global design point, a large number of neighboring design points are important in accounting for the failure probability. Using information from the analytical study, an importance sampling density is proposed. Numerical examples are presented, which demonstrate that the efficiency of using the proposed importance sampling density to calculate system reliability is remarkable.", "doi": "10.1016/S0266-8920(01)00002-9", "issn": "0266-8920", "publisher": "Elsevier", "publication": "Probabilistic Engineering Mechanics", "publication_date": "2001-07", "series_number": "3", "volume": "16", "issue": "3", "pages": "193-207" }, { "id": "authors:chx8g-bre39", "collection": "authors", "collection_id": "chx8g-bre39", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120924-144441807", "type": "book_section", "title": "Probabilistic System Identification with Unidentifiable Models", "book_title": "Proceedings of the 8th International Conference on Structural Safety and Reliability", "author": [ { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" } ], "contributor": [ { "family_name": "Corotis", "given_name": "R. B.", "clpid": "Corotis-R-B" }, { "family_name": "Schu\u00ebller", "given_name": "G. I.", "clpid": "Schu\u00ebller-G-I" }, { "family_name": "Shinozuka", "given_name": "M.", "clpid": "Shinozuka-M" } ], "abstract": "In a Bayesian probabilistic framework for system identification, the performance reliability for a\nstructure can be updated using structural test data D by considering the reliability predictions of a\nwhole set of possible structural models that are weighted by their updated probability. This involves\nintegrating h(\u0398)p(\u0398|D) over the whole parameter space, where \u0398 is a parameter vector\ndefining each model within the set of possible models of the structure, h(\u0398) is the structural reliability\npredicted by the model and p(\u0398|D) is the updated probability density for \u0398 which provides\na measure of how plausible each model is given the data D. The resulting integral, called the\nupdated 'robust' reliability integral, is difficult to evaluate because the dimension of the parameter\nspace is usually too large for direct numerical integration. In practical applications, the variation of\np(\u0398|D) is usually more dominant than h(\u0398), and thus methods for evaluating the integral are differentiated\nby the topological characteristics of p(\u0398|D). In the 'identifiable' case, p(\u0398|D) is\npeaked at a finite number of 'optimal points' and asymptotic methods can be used to approximate\nthe integral using information at the optimal points. The evaluation of the integral in the 'unidentifiable'\ncase, where p(\u0398|D) is concentrated in the neighborhood of a manifold S of lower dimension\nthan the parameter space, is much more difficult. Standard Monte Carlo simulation or importance\nsampling fail because the important region of the integrand, which is in the neighborhood of\nthe manifold S, is often of complicated geometry and has small volume in the parameter space.\nDeterministic search methods for computing an asymptotic approximation of the robust reliability\nintegral have appeared in the literature, which discretize the manifold S using a finite number of\nrepresentative points and then approximate p(\u0398|D) as a discrete probability mass distribution\namong the representative points. The complexity and computational effort associated with such\nmethods arc expected to grow in a similar manner to that of direct numerical integration, making\nthe method practical only when the dimension of the manifold is small.\n\nThis paper presents a Markov chain Monte Carlo simulation method to evaluate the robust reliability\nintegral without the need for optimization to find the manifold S. It is based on the Metropolis-\nHastings algorithm augmented with an adaptive scheme to gain information about the\nmanifold in a gradual manner. By carrying out a series of Markov chain simulations with limiting\nstationary distributions equal to a sequence of intermediate PDFs that converge on p(\u0398|D), the\nregion of significant probability density of p(\u0398|D) is gradually portrayed. The Markov chain\nsamples can be used to estimate the robust reliability integral by statistical averaging. The method\nis illustrated using simulated modal test data to update the robust reliability of a two-story moment-resisting\nframe where the model is not identifiable based on the data.", "isbn": "905809197X", "publisher": "Balkema", "place_of_publication": "Lisse, Netherlands", "publication_date": "2001-06", "pages": "29" }, { "id": "authors:pjg8m-5xa39", "collection": "authors", "collection_id": "pjg8m-5xa39", "cite_using_url": "https://resolver.caltech.edu/CaltechEERL:2001.EERL-2001-02", "type": "monograph", "title": "On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment", "author": [ { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" } ], "abstract": "In a probabilistic assessment of the performance of structures subjected to uncertain environmental loads such as earthquakes, an important problem is to determine the probability that the structural response exceeds some specified limits within a given duration of interest. This problem is known as the first excursion problem, and it has been a challenging problem in the theory of stochastic dynamics and reliability analysis. In spite of the enormous amount of attention the problem has received, there is no procedure available for its general solution, especially for engineering problems of interest where the complexity of the system is large and the failure probability is small.\n\nThe application of simulation methods to solving the first excursion problem is investigated in this dissertation, with the objective of assessing the probabilistic performance of structures subjected to uncertain earthquake excitations modeled by stochastic processes. From a simulation perspective, the major difficulty in the first excursion problem comes from the large number of uncertain parameters often encountered in the stochastic description of the excitation. Existing simulation tools are examined, with special regard to their applicability in problems with a large number of uncertain parameters. Two efficient simulation methods are developed to solve the first excursion problem. The first method is developed specifically for linear dynamical systems, and it is found to be extremely efficient compared to existing techniques. The second method is more robust to the type of problem, and it is applicable to general dynamical systems. It is efficient for estimating small failure probabilities because the computational effort grows at a much slower rate with decreasing failure probability than standard Monte Carlo simulation. The simulation methods are applied to assess the probabilistic performance of structures subjected to uncertain earthquake excitation. Failure analysis is also carried out using the samples generated during simulation, which provide insight into the probable scenarios that will occur given that a structure fails.", "publisher": "California Institute of Technology", "publication_date": "2001-01-01" }, { "id": "authors:xshmz-rcv16", "collection": "authors", "collection_id": "xshmz-rcv16", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120829-133858966", "type": "article", "title": "Monitoring Structural Health Using a Probabilistic Measure", "author": [ { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" }, { "family_name": "Vanik", "given_name": "Michael W.", "clpid": "Vanik-M-W" } ], "abstract": "A Bayesian probabilistic methodology for structural\nhealth monitoring is presented. The method uses a\nsequence of identified modal parameter data sets to continually\ncompute the probability of damage. In this approach,\na high likelihood of a reduction in model stiffness at a location\nis taken as a proxy for damage at the corresponding\nstructural location. The concept extends the idea of using\nas indicators of damage the changes in model parameters\nidentified using a linear finite-element model and modal\nparameter data sets from the structure in undamaged and\npossibly damaged states. This extension is needed because\nof uncertainties in the updated model parameters that in\npractice obscure health assessment. These uncertainties\narise due to effects such as variation in the identified modal\nparameters in the absence of damage, as well as unavoidable\nmodel error. The method is illustrated by simulating\non-line monitoring, wherein specified modal parameters are\nidentified on a regular basis and the probability of damage\nfor each substructure is continually updated. Examples\nare given for abrupt onset of damage and progressive\ndeterioration.", "doi": "10.1111/0885-9507.00209", "issn": "1093-9687", "publisher": "Wiley", "publication": "Computer-Aided Civil and Infrastructure Engineering", "publication_date": "2001-01", "series_number": "1", "volume": "16", "issue": "1", "pages": "1-11" }, { "id": "authors:7a826-tn043", "collection": "authors", "collection_id": "7a826-tn043", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120809-153753425", "type": "article", "title": "Entropy-Based Optimal Sensor Location for Structural Model Updating", "author": [ { "family_name": "Papadimitriou", "given_name": "Costas", "orcid": "0000-0002-9792-0481", "clpid": "Papadimitriou-Costas" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" } ], "abstract": "A statistical methodology is presented for optimally locating the sensors in a structure for the\npurpose of extracting from the measured data the most information about the parameters of the model used\nto represent structural behavior. The methodology can be used in model updating and in damage detection\nand localization applications. It properly handles the unavoidable uncertainties in the measured data as well\nas the model uncertainties. The optimality criterion for the sensor locations is based on information entropy,\nwhich is a unique measure of the uncertainty in the model parameters. The uncertainty in these parameters is\ncomputed by a Bayesian statistical methodology, and then the entropy measure is minimized over the set of\npossible sensor configurations using a genetic algorithm. The information entropy measure is also extended\nto handle large uncertainties expected in the pretest nominal model of a structure. In experimental design,\nthe proposed entropy-based measure of uncertainty is also well-suited for making quantitative evaluations\nand comparisons of the quality of the parameter estimates that can be achieved using sensor configurations\nwith different numbers of sensors in each configuration. Simplified models for a shear building and a truss\nstructure are used to illustrate the methodology.", "doi": "10.1177/107754630000600508", "issn": "1741-2986", "publisher": "SAGE Publications", "publication": "Journal of Vibration and Control", "publication_date": "2000-07", "series_number": "5", "volume": "6", "issue": "5", "pages": "781-800" }, { "id": "authors:a6hpv-kwk25", "collection": "authors", "collection_id": "a6hpv-kwk25", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120809-154136247", "type": "article", "title": "Bayesian Probabilistic Approach to Structural Health Monitoring", "author": [ { "family_name": "Vanik", "given_name": "M. W.", "clpid": "Vanik-M-W" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" } ], "abstract": "A Bayesian probabilistic methodology for structural health monitoring is presented. The method\nuses a sequence of identified modal parameter data sets to compute the probability that continually updated\nmodel stiffness parameters are less than a specified fraction of the corresponding initial model stiffness parameters.\nIn this approach, a high likelihood of reduction in model stiffness at a location is taken as a proxy for\ndamage at the corresponding structural location. The concept extends the idea of using as indicators of damage\nthe changes in structural model parameters that are identified from modal parameter data sets when the structure\nis initially in an undamaged state and then later in a possibly damaged state. The extension is needed, since\neffects such as variation in the identified modal parameters in the absence of damage, as well as unavoidable\nmodel error, lead to uncertainties in the updated model parameters that in practice obscure health assessment.\nThe method is illustrated by simulating on-line monitoring, wherein specified modal parameters are identified\non a regular basis and the probability of damage for each substructure is continually updated.", "doi": "10.1061/(ASCE)0733-9399(2000)126:7(738)", "issn": "0733-9399", "publisher": "American Society of Civil Engineers", "publication": "Journal of Engineering Mechanics", "publication_date": "2000-07", "series_number": "7", "volume": "126", "issue": "7", "pages": "738-745" }, { "id": "authors:enemw-nwp60", "collection": "authors", "collection_id": "enemw-nwp60", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120925-163206969", "type": "book_section", "title": "Subset Simulation \u2013 A New Approach to Calculating Small Failure Probabilities", "book_title": "Monte Carlo simulation : proceedings of the International Conference on Monte Carlo Simulation, Principality of Monaco, 18-21 June 2000", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "contributor": [ { "family_name": "Schu\u00ebller", "given_name": "G. I.", "clpid": "Schu\u00ebller-G-I" }, { "family_name": "Spanos", "given_name": "P. D.", "clpid": "Spanos-P-D" }, { "family_name": "Shinozuka", "given_name": "Masanobu", "clpid": "Shinozuka-M" } ], "abstract": "A new simulation approach, called 'subset simulation', is proposed to compute small failure\nprobabilities. The basic idea is to express the failure probability as a product of larger conditional failure\nprobabilities by introducing intermediate failure events. With a proper choice of the intermediate failure\nevents, the original problem of calculating a small failure probability, which is computationally demanding,\nis reduced to calculating a sequence of conditional probabilities, which are efficiently estimated by\nsimulation using a special Markov chain. The proposed method is robust to the number of uncertain\nparameters and efficient in computing small probabilities. An example of calculating the first-excursion\nprobability of a five-story shear building under uncertain seismic excitation is presented to demonstrate\nthe efficiency of the method.", "isbn": "9058091880", "publisher": "Balkema", "place_of_publication": "Rotterdam, Netherlands", "publication_date": "2000-07", "pages": "287-293" }, { "id": "authors:0a2h7-16w19", "collection": "authors", "collection_id": "0a2h7-16w19", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120925-162729567", "type": "book_section", "title": "Calculation of First Excursion Probabilities by Subset Simulation", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "A new simulation approach, called 'subset simulation', is applied to computing small first excursion probabilities\nfor dynamical systems with stochastic excitations. The basic idea is to express the first excursion\nprobability as a product of larger conditional failure probabilities by introducing intermediate failure boundaries.\nWith a proper choice of the intermediate boundaries, the original problem of calculating a small failure\nprobability, which is computationally demanding, is reduced to calculating a sequence of conditional probabilities,\nwhich are efficiently estimated by simulation using a special Markov chain. The proposed method is\nrobust to the type of structural model (e.g., linear or nonlinear) and stochastic excitation model (e.g., stationary\nor nonstationary). Numerical studies are presented to demonstrate the efficiency of the method.", "publisher": "Notre Dame", "publication_date": "2000-07" }, { "id": "authors:v48vc-63c89", "collection": "authors", "collection_id": "v48vc-63c89", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120925-162939719", "type": "book_section", "title": "Updating Robust Reliability using Markov Chain Simulation", "book_title": "Monte Carlo simulation : proceedings of the International Conference on Monte Carlo Simulation, Principality of Monaco, 18-21 June 2000", "author": [ { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" }, { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" } ], "contributor": [ { "family_name": "Schu\u00ebller", "given_name": "Gerhart I.", "clpid": "Schu\u00ebller-G-I" }, { "family_name": "Spanos", "given_name": "P. D.", "clpid": "Spanos-P-D" }, { "family_name": "Shinozuka", "given_name": "Masanobu", "clpid": "Shinozuka-M" } ], "abstract": "A Markov chain simulation method based on the Metropolis-Hastings algorithm and simulated\nannealing is proposed to update the robust reliability integrals based on a Bayesian statistical\napproach. It is applied to update the reliability of a structure based on its identified natural frequencies.", "isbn": "9058091880", "publisher": "Balkema", "place_of_publication": "Lisse, Netherlands", "publication_date": "2000-06", "pages": "499-440" }, { "id": "authors:9b2s7-qha66", "collection": "authors", "collection_id": "9b2s7-qha66", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120925-163435058", "type": "book_section", "title": "Two-Stage System Identification Results for Benchmark Structure", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Yuen", "given_name": "K.-V.", "orcid": "0000-0002-1755-6668", "clpid": "Yuen-Ka-Veng" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "contributor": [ { "family_name": "Tassoulas", "given_name": "J. L.", "clpid": "Tassoulas-J-L" } ], "abstract": "This paper reports on Cases 1{3 of the benchmark study sponsored by the IASC-ASCE\nTask Group on Structural Health Monitoring which is defined in Johnson et al. [1].\nThese cases involve damage detection in the weak direction only of the test structure\nusing a 12 DOF linear shear building model during the analysis. Cases 1 and 3 use\ndata generated by broad-band excitation of the USC 12 DOF model at each floor and\nat the roof only, respectively. Case 2 uses data generated by broad-band excitation of\nthe HKUST 120 DOF model at each floor.", "publisher": "Dept. of Civil Engineering, University of Texas at Austin", "publication_date": "2000-05" }, { "id": "authors:kpmrm-khf89", "collection": "authors", "collection_id": "kpmrm-khf89", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120926-084723457", "type": "book_section", "title": "A Performance-Based Optimal Design Methodology Incorporating Multiple Criteria", "book_title": "12th World Conference on Earthquake Engineering, Auckland, New Zealand", "author": [ { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Irfanoglu", "given_name": "Ayhan", "orcid": "0000-0001-8334-6717", "clpid": "Irfanoglu-Ayhan" }, { "family_name": "Papadimitriou", "given_name": "Costas", "orcid": "0000-0002-9792-0481", "clpid": "Papadimitriou-Costas" }, { "family_name": "Au", "given_name": "Siu Kui", "clpid": "Au-Siu-Kui" } ], "abstract": "A general framework is presented for optimal design based on multiple design criteria which is\nsuitable for performance-based design of structural systems operating in an uncertain dynamic\nenvironment. Reliability-based design criteria are used to maintain user-specified levels of\nstructural safety by properly taking into account the uncertainties in the seismic loads that a\nstructure may experience during its lifetime, as well as modeling uncertainties. Code-based\nrequirements are easily incorporated into the optimal design. The methodology is demonstrated\nwith a simple example involving the design of a three-story steel-frame building for which the\nground motion uncertainty is characterized by a probabilistic response spectrum developed from a\nstandard seismic hazard analysis.", "isbn": "0958215405", "publisher": "New Zealand Society for Earthquake Engineering", "place_of_publication": "Upper Hutt, N.Z", "publication_date": "2000-02", "pages": "Article No 344" }, { "id": "authors:2xkn3-ddt64", "collection": "authors", "collection_id": "2xkn3-ddt64", "cite_using_url": "https://resolver.caltech.edu/CaltechEERL:2000.EERL-2000-01", "type": "monograph", "title": "On the solution of first-excursion failure problem for linear systems by efficient simulation", "author": [ { "family_name": "Au", "given_name": "Siu-Kui", "orcid": "0000-0002-0228-1796", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" } ], "abstract": "An analytical study of the failure region of the first-excursion reliability problem for linear dynamical systems subjected to Gaussian white noise excitation is carried out with a view to constructing a suitable importance sampling density for computing the first-excursion failure probability. Central to the study are 'elementary failure regions', which are defined as the failure region in the load space corresponding to the failure of a particular output response at a particular instant. Each elementary failure region is completely characterized by its design point, which can be computed readily using impulse response functions of the system. It is noted that the complexity of the first-excursion problem stems from the structure of the union of the elementary failure regions. One important consequence of this union structure is that, in addition to the global design point, a large number of neighboring design points are important in accounting for the failure probability. Using information from the analytical study, an importance sampling density is proposed. Numerical examples are presented, which demonstrate that the efficiency of using the proposed importance sampling density to calculate system reliability is remarkable.", "publisher": "California Institute of Technology", "publication_date": "2000-01-01" }, { "id": "authors:pa2gv-3p067", "collection": "authors", "collection_id": "pa2gv-3p067", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120829-135654997", "type": "article", "title": "Reliability of Uncertain Dynamical Systems with Multiple Design Points", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Papadimitriou", "given_name": "C.", "orcid": "0000-0002-9792-0481", "clpid": "Papadimitriou-Costas" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "Asymptotic approximations and importance sampling methods are presented for evaluating a class of\nprobability integrals with multiple design points that may arise in the calculation of the reliability of\nuncertain dynamical systems. An approximation based on asymptotics is used as a first step to provide a\ncomputationally efficient estimate of the probability integral. The importance sampling method utilizes\ninformation of the integrand at the design points to substantially accelerate the convergence of available\nimportance sampling methods that use information from one design point only. Implementation issues\nrelated to the choice of importance sampling density and sample generation for reducing the variance of\nthe estimate are addressed. The computational efficiency and improved accuracy of the proposed methods\nis demonstrated by investigating the reliability of structures equipped with a tuned mass damper for which\nmultiple design points are shown to contribute significantly to the value of the reliability integral.", "doi": "10.1016/S0167-4730(99)00009-0", "issn": "0167-4730", "publisher": "Elsevier", "publication": "Structural Safety", "publication_date": "1999-06", "volume": "21", "pages": "113-133" }, { "id": "authors:pqsfs-z6m36", "collection": "authors", "collection_id": "pqsfs-z6m36", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120829-134911107", "type": "article", "title": "A New Adaptive Importance Sampling Scheme for Reliability Calculations", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "abstract": "An adaptive importance sampling methodology is proposed to compute the multidimensional integrals\nencountered in reliability analysis. It is based on a Markov simulation algorithm due to Metropolis et al.\n(Metropolis, Rosenbluth, Rosenbluth and Teller, Equations of state calculatons by fast computing\nmachines. Journal of Chemical Physics, 1953;21(6): 1087-1092). In the proposed methodology, samples are\nsimulated as the states of a Markov chain and are distributed asymptotically according to the optimal\nimportance sampling density. A kernel sampling density is then constructed from these samples which is\nused as the sampling density in an importance sampling simulation. The Markov chain samples populate\nthe region of higher probability density in the failure region and so the kernel sampling density approximates the optimal importance sampling density for a large variety of shapes of the failure region. This\nadaptive feature is insensitive to the probability level to be estimated. A variety of numerical examples\ndemonstrates the accuracy, efficiency and robustness of the methodology.", "doi": "10.1016/S0167-4730(99)00014-4", "issn": "0167-4730", "publisher": "Elsevier", "publication": "Structural Safety", "publication_date": "1999-06", "series_number": "2", "volume": "21", "issue": "2", "pages": "135-158" }, { "id": "authors:e1xd3-0kn34", "collection": "authors", "collection_id": "e1xd3-0kn34", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120926-092031273", "type": "book_section", "title": "Treatment of Multiple Design Points in Reliability Methods", "book_title": "Proceedings Fourth International Conference on Stochastic Structural Dynamics", "author": [ { "family_name": "Au", "given_name": "S. K.", "clpid": "Au-Siu-Kui" }, { "family_name": "Papadimitriou", "given_name": "C.", "orcid": "0000-0002-9792-0481", "clpid": "Papadimitriou-Costas" }, { "family_name": "Beck", "given_name": "J. L.", "clpid": "Beck-J-L" } ], "contributor": [ { "family_name": "Spencer", "given_name": "B. F.", "clpid": "Spencer-B-F" }, { "family_name": "Johnson", "given_name": "E. A.", "clpid": "Johnson-E-A" } ], "abstract": "Asymptotic approximations and importance sampling methods are developed for evaluating\na class of probability integrals with multiple design points that may arise in the calculation of\nthe reliability of uncertain systems. The asymptotic approximation is used as a first step to provide\na computationally efficient estimate of the probability integral. The importance sampling method utilizes\ninformation available about the location of multiple design points and the asymptotic estimates for\neach design point in order to substantially accelerate the convergence of available importance sampling\nmethods that use information from one design point only. Implementation issues related to the choice of\nimportance sampling density and sample generation for reducing the variance of the estimate and accelerating\nconvergence are addressed. The computational efficiency and improved accuracy of the proposed\napproximations are demonstrated by investigating the reliability of a ten story building equipped with\na tuned mass damper for which multiple design points are encountered and the contribution from more\nthan one design point to the value of the reliability integral is significant.", "isbn": "9058090248", "publisher": "Balkema", "place_of_publication": "Rotterdam, Netherlands", "publication_date": "1998-08", "pages": "179-186" }, { "id": "authors:z4d8v-4p036", "collection": "authors", "collection_id": "z4d8v-4p036", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120926-094216808", "type": "book_section", "title": "Entropy-based Optimal Sensor Location for Structural Damage Detection", "author": [ { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Papadimitriou", "given_name": "Costas", "orcid": "0000-0002-9792-0481", "clpid": "Papadimitriou-Costas" }, { "family_name": "Au", "given_name": "Siu-Kui", "clpid": "Au-Siu-Kui" }, { "family_name": "Vanik", "given_name": "Michael W.", "clpid": "Vanik-M-W" } ], "abstract": "A statistical methodology is presented for optimally locating the sensors in a structure for the purpose of extracting\nfrom the measured data the most information about the parameters of the model used to represent structural\nbehavior. The methodology can be used in model updating and in damage detection and localization. It properly\nhandles the unavoidable uncertainties in the measured data as well as the model uncertainties. The optimality\ncriterion for the sensor locations is based on information entropy which is a unique measure of the uncertainty in the\nmodel parameters. The uncertainty in these parameters is computed by the Bayesian statistical methodology and\nthen the entropy measure is minimized over the set of possible sensor configurations using a genetic algorithm. The\ninformation entropy measure is also extended to handle large uncertainties expected in the pre-test nominal model\nof a structure. In experimental design, the proposed entropy-based methodology provides a rational procedure for\ncomparing and evaluating the benefits of adding more sensors in the structure against the benefits of exciting and\nobserving (measuring) more modes using the existing number of sensors. Simplified models for building and bridge\nstructures are used to illustrate the methodology.", "doi": "10.1117/12.310604", "publisher": "SPIE", "publication_date": "1998-03" } ]