Bayesian analysis of uncertainty for structural engineering applications

There has been recent interest in differentiating aleatory and epistemic uncertainties within the structural engineering context. Aleatory uncertainty, which is related to the inherent physical randomness of a system, has substantially different effects on the analysis and design of structures as compared with epistemic uncertainty, which is knowledge based. Bayesian techniques provide powerful tools for integrating, in a rigorous manner, the two types of uncertainties. In a purely probabilistic viewpoint, the uncertainties merge, resulting in widened probability densities. From the viewpoint of design or experimentation, however, the two types of uncertainties have widely different effects. The purpose of this paper is to develop insight into these effects, using Bayesian-based analytical expressions for the aleatory and epistemic uncertainties. The paper goes beyond standard Bayesian conjugate distributions by incorporating the effects of model uncertainty, where the applicability of two or more analytical models are used to describe the structure of interest. The influence of multiple model uncertainties is explored for two problems: the Bayesian updating process as data is acquired, and the design of simple parallel systems.     

Application of machine learning algorithms for the evaluation of seismic soil liquefaction potential

This study investigates the performance of four machine learning (ML) algorithms to evaluate the earthquake-induced liquefaction potential of soil based on the cone penetration test field case history records using the Bayesian belief network (BBN) learning software Netica. The BBN structures that were developed by ML algorithms-K2, hill climbing (HC), tree augmented naive (TAN) Bayes, and Tabu search were adopted to perform parameter learning in Netica, thereby fixing the BBN models. The performance measure indexes, namely, overall accuracy (OA), precision, recall, F-measure, and area under the receiver operating characteristic curve, were used to evaluate the training and testing BBN models’ performance and highlight the capability of the K2 and TAN Bayes models over the Tabu search and HC models. The sensitivity analysis results showed that the cone tip resistance and vertical effective stress are the most sensitive factors, whereas the mean grain size is the least sensitive factor in the prediction of seismic soil liquefaction potential. The results of this study can provide theoretical support for researchers in selecting appropriate ML algorithms and improving the predictive performance of seismic soil liquefaction potential models.     

Adaptive sampling strategy for characterizing spatial distribution of soil liquefaction potential using cone penetration test

Characterizing spatial distribution of soil liquefaction potential is critical for assessing liquefaction-related hazards (e.g. building damages caused by liquefaction-induced differential settlement). However, in engineering practice, soil liquefaction potential is usually measured at limited locations in a specific site using in situ tests, e.g. cone penetration tests (CPTs), due to the restrictions of time, cost and access to subsurface space. In these cases, liquefaction potential of soil at untested locations requires to be interpreted from limited measured data points using proper interpolation method, leading to remarkable statistical uncertainty in liquefaction assessment. This underlines an important question of how to optimize the locations of CPT soundings and determine the minimum number of CPTs for achieving a target reliability level of liquefaction assessment. To tackle this issue, this study proposes a smart sampling strategy for determining the minimum number of CPTs and their optimal locations in a self-adaptive and data-driven manner. The proposed sampling strategy leverages on information entropy and Bayesian compressive sampling (BCS). Both simulated and real CPT data are used to demonstrate the proposed method. Illustrative examples indicate that the proposed method can adaptively and sequentially select the required number and optimal locations of CPTs.     

Probabilistic models of combinations of stochastic loads for limit state design

When more than one load act on a structure, the maximum intensity of the combined load effect needs to be evaluated. Turkstra's rule is often used in reliability-based limit state design because of its simplicity; however, the approximation is unconservative. This paper presents the theoretical expressions of the cumulative distribution function (cdf) of the maximum intensity during a reference period taking the temporal variation of load intensity into account. Theoretical investigation and numerical examples show that the theoretical expression provides a fairly good estimate regardless of the statistical characteristics of the load processes. To avoid considering time-dependency in determining a design point, it is proposed to consider the intensities of the load processes at the time when the combination takes its maximum value. Based on the observation that the cross section of the joint probability density function (pdf) of these intensities cut by the limit state surface is similar to that of the joint pdf of the basic random variables, the design point is determined in the basic variable space using AFOSM.     

Optimal probabilistic design of seismic dampers for the protection of isolated bridges against near-fault seismic excitations

A probabilistic, simulation-based framework is presented in this paper for risk assessment and optimal design of supplemental dampers for multi-span bridge systems supported on abutments and intermediate piers through isolation bearings. The adopted bridge model explicitly addresses nonlinear characteristics of the isolators and the dampers, the dynamic behavior of the abutments, and the effect of pounding between the neighboring spans against each other as well as against the abutments. Nonlinear dynamic analysis is used to evaluate the bridge performance, and a realistic stochastic ground motion model is presented for describing the time history of future near-fault ground motions and relating their characteristics to the seismic hazard for the structural site. A probabilistic foundation is used to address the various sources of structural and excitation uncertainties and ultimately characterize the seismic risk for the bridge. This risk is given by the expected value of the system response over the adopted probability models. Stochastic simulation is used for evaluating the multi-dimensional integral representing this expected value and for performing the associated optimization when searching for the most favorable damper characteristics. An efficient probabilistic sensitivity analysis is also established for identifying the importance of each of the uncertain model parameters in affecting the overall risk. An illustrative example is presented that considers the design of nonlinear viscous dampers for the protection of a two-span bridge.     

A stable CS-FEM for the static and seismic stability of a single square tunnel in the soil where the shear strength increases linearly with depth

A numerical procedure using a stable cell-based smoothed finite element method (CS-FEM) is presented for estimation of stability of a square tunnel in the soil where the shear strength increases linearly with depth. The kinematically admissible displacement fields are approximated by uniform quadrilateral elements in conjunction with the strain smoothing technique, eliminating volumetric locking issues and the singularity associated with the Mohr–Coulomb model. First, a rich set of simulations was performed to compute the static stability of a square tunnel with different geometries and soil conditions. The presented results are in excellent agreement with the upper and lower bound solutions using the standard finite element method (FEM). The stability charts and tables are given for practical use in the tunnel design, along with a newly proposed formulation for predicting the undrained stability of a single square tunnel. Second, the seismic stability number was computed using the present numerical approach. Numerical results reveal that the seismic stability number reduces with an increasing value of the horizontal seismic acceleration (α_h), for both cases of the weightless soil and the soil with unit weight. Third, the link between the static and seismic stability numbers is described using corrective factors that represent reductions in the tunnel stability due to seismic loadings. It is shown from the numerical results that the corrective factor becomes larger as the unit weight of soil mass increases; however, the degree of the reduction in seismic stability number tends to reduce for the case of the homogeneous soil. Furthermore, this advanced numerical procedure is straightforward to extend to three-dimensional (3D) limit analysis and is readily applicable for the calculation of the stability of tunnels in highly anisotropic and heterogeneous soils which are often encountered in practice.     

Estimation of non-linear continuous time models for the heat exchange dynamics of building integrated photovoltaic modules

This paper focuses on a method for linear or non-linear continuous time modelling of physical systems using discrete time data. This approach facilitates a more appropriate modelling of more realistic non-linear systems. Particularly concerning advanced building components, convective and radiative heat interchanges are non-linear effects and represent significant contributions in a variety of components such as photovoltaic integrated façades or roofs and those using these effects as passive cooling strategies, etc. Since models are approximations of the physical system and data is encumbered with measurement errors it is also argued that it is important to consider stochastic models.