Bayesian Network Enhanced with Structural Reliability Methods: Methodology

We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced Bayesian network (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence structures, as present in infrastructure and structural systems, and they facilitate Bayesian updating of the model when new information becomes available. On the other hand, SRMs enable accurate assessment of probabilities of rare events represented by computationally demanding, physically-based models. By combining the two methods, the eBN framework provides a unified and powerful tool for efficiently computing probabilities of rare events in complex structural and infrastructure systems in which information evolves in time. Strategies for modeling and efficiently analyzing the eBN are described by way of several conceptual examples. The companion paper applies the eBN methodology to example structural and infrastructure systems

Standard Penetration Test-Based Probabilistic and Deterministic Assessment of Seismic Soil Liquefaction Potential

This paper presents new correlations for assessment of the likelihood of initiation (or “triggering”) of soil liquefaction. These new correlations eliminate several sources of bias intrinsic to previous, similar correlations, and provide greatly reduced overall uncertainty and variance. Key elements in the development of these new correlations are (1) accumulation of a significantly expanded database of field performance case histories; (2) use of improved knowledge and understanding of factors affecting interpretation of standard penetration test data; (3) incorporation of improved understanding of factors affecting site-specific earthquake ground motions (including directivity effects, site-specific response, etc.); (4) use of improved methods for assessment of in situ cyclic shear stress ratio; (5) screening of field data case histories on a quality/uncertainty basis; and (6) use of high-order probabilistic tools (Bayesian updating). The resulting relationships not only provide greatly reduced uncertainty, they also help to resolve a number of corollary issues that have long been difficult and controversial including: (1) magnitude-correlated duration weighting factors, (2) adjustments for fines content, and (3) corrections for overburden stress

Incorporating Parameter Uncertainty into Attenuation Relationships

Strong ground motion attenuation relationships estimate the mean and variance of ground shaking as it decreases with distance from an earthquake source. Current relationships use “classical” regression techniques that treat the input variables or parameters as exact, neglecting the uncertainties associated with the measurement of ground acceleration, moment magnitude, site-to-source distance, shear wave velocity, etc. This leads to a poorly constrained estimate of the uncertainty of strong ground motions. This paper discusses the work in progress on; a) estimating the statistics of parameter uncertainty, and b) incorporating the parameter uncertainty into the regression of strong motion attenuation data using a Bayesian framework. The results are an improved understanding of the uncertainties inherent in the phenomena of strong ground motion attenuation, a reduced and better defined model variance, and better constrained estimates of rarer events associated with ground accelerations towards the tail of the distribution

Optimal design with probabilistic objective and constraints

Title: Optimal design with probabilistic objective and constraints Journal Issue: Journal of Engineering Mechanics-ASCE, 132(1) Publication Date: 01-01-2006.Significant challenges are associated with solving optimal structural design problems involving the failure probability in the objective and constraint functions. In this paper, we develop gradient-based optimization algorithms for estimating the solution of three classes of such problems in the case of continuous design variables. Our approach is based on a sequence of approximating design problems, which is constructed and then solved by a semi-infinite optimization algorithm. The construction consists of two steps: First, the failure probability terms in the objective function are replaced by auxiliary variables resulting in a simplified objective function. The auxiliary variables are determined automatically by the optimization algorithm. Second, the failure probability constraints are replaced by a parameterized first-order approximation. The parameter values are determined in an adaptive manner based on separate estimations of the failure probability. Any computational reliability method, including FORM, SORM and Monte Carlo simulation, can be used for this purpose. After repeatedly solving the approximating problem, an approximate solution of the original design problem is found, which satisfies the failure probability constraints at a precision level corresponding to the selected reliability method. The approach is illustrated by a series of examples involving optimal design and maintenance planning of a reinforced concrete bridge girder

Compression and inference algorithms for Bayesian network modeling of infrastructure systems

The Bayesian network (BN) is an ideal tool for modeling and assessing the reliability of civil infrastructure, particularly when the information about the system and its components is uncertain and evolves in time. One of the major limitations of the BN framework, however, is the size and complexity of the system that can be tractably modeled as a BN. This is due to the size of the conditional probability table (CPT) associated with the system node in the BN model, which grows exponentially with the number of components in the system. In this paper, we present novel compression and inference algorithms that utilize compression techniques to achieve significant savings in memory storage of the system CPT. In addition, heuristics developed to improve the computational efficiency of the algorithms are presented. An application to an example system demonstrates the gains in both memory and computation time requirements achieved by the proposed algorithms.Non UBCUnreviewedThis collection contains the proceedings of ICASP12, the 12th International Conference on Applications of Statistics and Probability in Civil Engineering held in Vancouver, Canada on July 12-15, 2015. Abstracts were peer-reviewed and authors of accepted abstracts were invited to submit full papers. Also full papers were peer reviewed. The editor for this collection is Professor Terje Haukaas, Department of Civil Engineering, UBC Vancouver.Facult

Operational modal analysis using variational Bayes

Operational modal analysis is the primary tool for modal parameters identification in civil engineering. Bayesian statistics offers an ideal framework for analyzing uncertainties associated with the identified modal parameters. However, the exact Bayesian analysis is usually intractable due to the high computation demanding in obtaining the posterior distributions of modal parameters. In this paper, the variational Bayes is employed to provide an approximated solution. Working with the state space representation of a dynamic system, the joint distribution of the state transition matrix and observation matrix as well as the joint distribution of the process noise and measurement error are firstly obtained analytically using conjugate priors, then the distributions of modal parameters are extracted from these obtained joint distributions based on sampling because no closed form solution exists. A numerical simulation example demonstrates the performance of the proposed approach. The variational Bayes yields a consistent estimation of modal parameters although the variability is slightly under-estimated. Moreover, the variational Bayes is more flexible than the Laplace approximation and much more efficient than Monte Carlo sampling.Non UBCUnreviewedThis collection contains the proceedings of ICASP12, the 12th International Conference on Applications of Statistics and Probability in Civil Engineering held in Vancouver, Canada on July 12-15, 2015. Abstracts were peer-reviewed and authors of accepted abstracts were invited to submit full papers. Also full papers were peer reviewed. The editor for this collection is Professor Terje Haukaas, Department of Civil Engineering, UBC Vancouver.Facult