[ { "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: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: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: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: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: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: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: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: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: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: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" } ]