Probabilistic Engineering Mechanics最新文献

A novel method for analyzing the reliability of structures under non-stationary stochastic seismic excitations, considering the combined effect of multiple structural demand extreme values, is proposed. The spectral representation method is employed to establish a non-stationary stochastic seismic excitation model, and based on the theory of first-passage probability, multiple integral formulas for seismic reliability under multidimensional limit states are derived. The extreme value distribution is established using the Gamma mixture model (GMM). The equations for estimating the model parameters are derived based on both fractional moments and moment-generating functions, while the determination of the number of gamma distribution components is guided by the probability distribution and statistical characteristics of the samples. The joint probability density function (JPDF) for multiple demand extreme values is established by incorporating copula functions to account for correlation, and the fitting accuracy of different copula functions is assessed. The proposed method is illustrated using reinforced concrete (RC) frame structures. The results demonstrate that the fitting accuracy of extreme value distribution can be enhanced by adjusting the number of gamma distribution components in the GMM, which exhibits high accuracy in fitting both the main and tail regions. The presence of correlation can induce variations in the JPDF, thereby exerting an influence on the failure probability. Consequently, disregarding correlation is not conducive to reliability analysis.

The concept of Bayesian active learning has recently been introduced from machine learning to structural reliability analysis. Although several specific methods have been successfully developed, significant efforts are still needed to fully exploit their potential and to address existing challenges. This work proposes a quasi-Bayesian active learning method, called ‘Quasi-Bayesian Active Learning Cubature’, for structural reliability analysis with extremely small failure probabilities. The method is established based on a cleaver use of the Bayesian failure probability inference framework. To reduce the computational burden associated with the exact posterior variance of the failure probability, we propose a quasi posterior variance instead. Then, two critical elements for Bayesian active learning, namely the stopping criterion and the learning function, are developed subsequently. The stopping criterion is defined based on the quasi posterior coefficient of variation of the failure probability, whose numerical solution scheme is also tailored. The learning function is extracted from the quasi posterior variance, with the introduction of an additional parameter that allows multi-point selection and hence parallel distributed processing. By testing on four numerical examples, it is empirically shown that the proposed method can assess extremely small failure probabilities with desired accuracy and efficiency.

The effects of evolutionary wind spectra with different modulation functions on the nonstationary buffeting responses of suspension bridges are uncertain. After considering the nonlinear buffeting force of a twin-box girder, the buffeting responses of a cross-sea suspension bridge under four nonstationary wind speed models with two uniform modulation and two nonuniform modulation functions were investigated in this paper. Through the evolutionary spectral theory, the nonstationary wind speed models at the bridge site with four typical modulation functions were generated and then validated from the autocorrelation and power spectrum density. The results show that the mean and root-mean-square error (RMSE) values of vertical and horizontal wind speeds by using nonuniform modulation functions (NMF1 and NMF2) were much larger than those by using uniform modulation functions (uMF1 and uMF2). Moreover, most of the peak and RMSE values for the torsional and lateral displacement under the NMF1 are the largest, while the RMSE values of the vertical displacement without the modulation function are the largest. With the increase of the circular frequency $\gamma$ or decrease of the initial phase $\theta$ in the cosine function of time-varying mean wind speeds, the RMS values in three displacement responses of the bridge deck become larger.

There is an increasing interest in investigating the effects of input uncertainties on dynamic systems. The probabilistic analyses for a vibrator-ground (VG) interaction system are rare and the effects of system uncertainties need to be revealed. This study aims to present an approach for the probabilistic performance-based analysis of the VG system under multi-source uncertainties. The probabilistic model of the VG system is constructed on the basis of the Monte Carlo (MC) simulation combined with the Latin Hypercube Sampling (LHS) method, while the artificial neural networks optimized by the genetic algorithms are employed to reduce the large computational expenses in the MC simulation. Then, a multi-criteria sensitivity analysis is presented by using a technique for order preference by similarity to ideal solution (TOPSIS) to evaluate the effects of input uncertainties on the dynamic performance of the vibrator. Finally, a probabilistic simulation analysis of the VG system is conducted by implementing the presented approach. The results demonstrate the effectiveness of the presented probabilistic performance-based analysis approach for the VG system and evaluate the effects of input uncertainties on the dynamic performance of the system.

The multi-mode system failure probability function (SFPF) can quantify how the distribution parameters of the random input vector affect the system safety and decouple the system reliability-based design optimization model. However, for a problem with a time-consuming implicit performance function and rare failure domain, efficiently solving the SFPF remains significantly challenging. Therefore, in this study, two efficient algorithms are proposed, namely, the meta model-based importance sampling and cross entropy-based importance sampling. The contributions of this study are twofold. The first is constructing a single-loop optimal importance sampling density (SL-OISD) method to decouple the double-loop framework for analyzing the SFPF. The second is establishing two methods to efficiently approximate the SL-OISD and complete the SFPF estimation. The first method is based on the meta model of the system performance function, which is abbreviated as SL-Meta-IS. The second method is based on minimizing the cross entropy between the Gaussian mixture density model and SL-OISD, which is abbreviated as SL-CE-IS. To reduce the number of evaluating the system performance function when approximating the SL-OISD, sampling the SL-OISD, and identifying the state of the samples for completing the SFPF estimation, an adaptive Kriging model of the system performance function is introduced into SL-Meta-IS and SL-CE-IS. Owing to decoupling the double-loop framework into a single-loop framework, replacing the time-consuming system performance function with the economic Kriging model, and employing importance sampling variance reduction techniques to address issues related to the rare failure domain, the proposed SL-Meta-IS and SL-CE-IS methods greatly enhance the efficiency of SFPF estimations. The numerical and practical examples demonstrate that the two proposed methods are superior to the existing algorithms; moreover, the efficiency of SL-CE-IS is higher than that of SL-Meta-IS.

Identifying the seismic failure modes of beam-column joints (BCJs) is crucial for the safety and integrity of reinforced concrete (RC) buildings or structures withstanding seismic forces. However, traditional identification methods fail to provide any indication about the uncertainties within their predictions, which is beneficial for evaluating, interpreting and improving these predictions. This study develops a probabilistic identification method for seismic failure modes of BCJs using Gaussian process (GP) with a deep kernel, which integrates the representational power of deep neural networks with the flexible structure of kernel functions to accurately represent the evolution characteristics of seismic failure modes of BCJs. Analysis results demonstrated the potential of the proposed method for improving the classification accuracy of traditional GPs, as well as its superiority over the prediction accuracy of traditional shear-resistance design methods and machine learning techniques. Furthermore, the proposed method also provides an efficient approach to estimate the uncertainties within their predictions for seismic failure modes of BCJs.

The small failure probability problem of stochastic structures is investigated by using two types of surrogate models and the subset simulation method in conjunction with parallel computation. To achieve high computational efficiency, the explicit expression of dynamic responses of stochastic structures is first derived in the form based on the explicit time-domain method. Then, the small failure probability analysis of stochastic structures is efficiently carried out through the Monte Carlo simulation method utilizing explicit expressions. To avoid the repeated calculation for the coefficient matrices or vectors of the explicit expression of stochastic structures, two types of surrogate models, e.g., the backpropagation neural network model and the Kriging model, are introduced to obtain these matrices or vectors for each parameter sample of the stochastic structures. The computational cost is further reduced by using the subset simulation method to generate conditional samples which follow the rule of Metropolis-Hastings. Furthermore, in virtue of the independence of the surrogate models for each time instant and the independence of dynamic analysis for each sample, parallel computation is embedded in the proposed approach, which can fully exploit the characteristics of the proposed approach and further improve the computational efficiency of dynamic reliability analysis. Numerical examples are given to illustrate the validity of the proposed hybrid approach.

Seismic reliability analysis of actual slopes considering the spatial variability of soil materials is crucial. However, for the discretization of large-scale random fields, high-precision finite element analysis and analysis of small failure probability events, the random analysis of slopes under seismic loads is inefficient. To address this situation, this study proposes a collaborative reliability analysis framework based on the modified linear estimation method (MLEM) and optimized subset simulation (OSS). First, the random field of the uncertain parameters of the Jinping-I left bank slope model is efficiently discretized by the MLEM, and a sensitivity analysis is carried out. Then, considering the adoption of different degrees of cross-correlation of the sensitive random parameters, the OSS method is used to perform random finite element analysis on the coarse mesh model. Finally, the fine mesh samples are obtained according to the response conditioning method (RCM). The MLEM is used to ensure the consistency of the two sets of random fields, and the seismic failure probability and reliability index of the slope under different cross-correlation coefficients of uncertain parameters are obtained. The results suggest that the degree of cross-correlation of parameters has a great influence on the seismic reliability of the slope. Considering that the shear strength parameters of geotechnical materials are often negatively correlated, the fine analysis based on a fine model is necessary.

The conditional simulation of non-Gaussian excitations utilizing records from the monitoring system is of great significance for hazard mitigation. To this end, this paper proposes a novel conditional non-Gaussian simulation method. In this method, the Unified Hermite Polynomial Model (UHPM) is used to describe the transformation relationship between recorded and unrecorded non-Gaussian processes and their underlying Gaussian counterparts. Meanwhile, an explicit transformation model between their correlation functions is also provided. Then, the covariance matrix of Fourier coefficients of the underlying Gaussian processes is constructed. Based on this covariance matrix, the conditional samples of Fourier coefficients are generated and substituted into the Spectral Representation Method (SRM) to perform the conditional simulation of the underlying Gaussian processes. Finally, the conditionally simulated samples of the underlying Gaussian processes are transformed into the non-Gaussian samples by the UHPM. To showcase the precision and efficacy of the proposed method, two numerical examples involving the conditional simulations of non-Gaussian ground motions and non-Gaussian wind pressure coefficients are provided.

To accurately predict the ultimate drift capacity of reinforced concrete (RC) columns failed in flexure mode under seismic loading, a probabilistic methodology is proposed to correct the biases in deterministic models and establish probabilistic models. Probabilistic correction models are constructed based on Bayesian updating, which can consider potential critical influences and also yield probability distribution associated with the model parameters and predictions. The probabilistic models are simplified to identify the significant informative terms by Bayesian updating. Then, the influences of the physical properties and size of the sample on the probabilistic models are discussed. The results show that the Bayesian-based correction method can increase the accuracy of predictions and quantify uncertainties. Additionally, adding new samples with different physical properties in Bayesian updating can expand the scope of application of probabilistic models, and the sample size should be at least two times the number of variables involved in Bayesian updating.