Probabilistic Engineering Mechanics最新文献

One of the key elements of probabilistic seismic risk assessment studies is the fragility curve, which represents the conditional probability of failure of a mechanical structure for a given scalar measure derived from seismic ground motion. For many structures of interest, estimating these curves is a daunting task because of the limited amount of data available; data which is only binary in our framework, i.e., only describing the structure as being in a failure or non-failure state. A large number of methods described in the literature tackle this challenging framework through parametric log-normal models. Bayesian approaches, on the other hand, allow model parameters to be learned more efficiently. However, the impact of the choice of the prior distribution on the posterior distribution cannot be readily neglected and, consequently, neither can its impact on any resulting estimation. This paper proposes a comprehensive study of this parametric Bayesian estimation problem for limited and binary data. Using the reference prior theory as a cornerstone, this study develops an objective approach to choosing the prior. This approach leads to the Jeffreys prior, which is derived for this problem for the first time. The posterior distribution is proven to be proper (i.e., it integrates to unity) with the Jeffreys prior but improper with some traditional priors found in the literature. With the Jeffreys prior, the posterior distribution is also shown to vanish at the boundaries of the parameters’ domain, which means that sampling the posterior distribution of the parameters does not result in anomalously small or large values. Therefore, the use of the Jeffreys prior does not result in degenerate fragility curves such as unit-step functions, and leads to more robust credibility intervals. The numerical results obtained from two different case studies—including an industrial example—illustrate the theoretical predictions.

In recent years, focus has been shifted towards predictive maintenance in an effort to improve the reliability of operating structures. Processing structural response data obtained from in-situ sensors during operation can provide added value towards this direction. Structural Health Monitoring (SHM) methods are uniquely suited for this task; however, accounting for the effect of stochastic structural loads is critical for their robustness. In this work, a framework based on Maximum Likelihood Estimation (MLE) is presented, whose goal is to obtain inferences on typically unobservable quantities that describe stochastic structural loading. A structural beam is employed as a demonstrative case study, that is subjected to point loads with stochastic magnitude and application points. The hyperparameters that govern their underlying probability distribution functions (pdf) are the quantities of inferential interest. The inverse (load) identification process is performed using a marginalized MLE objective, where stochastic Monte Carlo (MC) integration is employed to perform the marginalization and Genetic Algorithms (GAs) are used as the optimizer. The Cramer–Rao (CR) lower bound is used to produce 95 % Confidence Intervals (CIs) to quantify estimation uncertainty.

Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations requires reliable kernel density estimates computed from an ensemble of system realizations. However, in several real world signals such as Big Data, only a single system realization is available—making it impossible to estimate a reliable kernel density. This study presents an approach for detecting P-type bifurcations using unreliable density estimates. The approach creates an ensemble of objects from Topological Data Analysis (TDA) called persistence diagrams from the system’s sole realization and statistically analyzes the resulting set. We compare several methods for replicating the original persistence diagram including Gibbs point process modelling, Pairwise Interaction Point Modelling, and subsampling. We show that for the purpose of predicting a bifurcation, the simple method of subsampling exceeds the other two methods of point process modelling in performance.

This paper aims to propose a new hybrid Machine Learning (ML) with Bayesian Optimization (BO) methods for predicting the patch loading resistance, P_u of longitudinally unstiffened plate girders. A total of 354 tests of the unstiffened plate girder under patch loading are collected and used for the training and testing to establish the proposed models. Five ML models including Support Vector Machines (SVM), Decision Tree (DT), Gradient Boosted Tree (GBT), Extreme Gradient Boosting algorithm (XGBoost), and CatBoost regression (CAT) are employed, and the BO method is used to optimize the hyperparameters of these ML models, in order to show which of them is best-suited for prediction of the PLR of longitudinally unstiffened plate girders. It was found that the BO-GBT presents the best accuracy compared to others. The performance of the BO-GBT model is validated by comparing its predictive results with the current design standards and the existing formulae. Additionally, the Shapley Additive Explanations (SHAP) method is employed to evaluate the importance and contributions of each input variable on the proposed model, and a Graphical User Interface (GUI) tool is developed to conveniently estimate the P_u of the unstiffened plate girders. Finally, the BO-GBT model is used to develop a support tool for finding suitable geometric dimensions and material properties of longitudinally unstiffened girder under patch loading in the preliminary design stage. The optimization tool is accessible online for the users for more convenient use in practical design purposes.

Quantifying the near-fault effect and establishing a reasonable model of near-fault pulse-like ground motions are particularly important for seismic design of structures in near-fault regions. Given the pronounced randomness associated with earthquakes, this study first proposes a novel stochastic model of near-fault pulse-like ground motions by combining the improved finite-fault model (IFFM) and the multivariate copula-based velocity-pulse model (CVPM). Further, a probability density evolution method (PDEM) based stochastic simulation method is developed, by which the model parameters can be determined in a unified probability space so as to ensure the consistency of two independent models. For illustrative purposes, the observed records collected from the 1999 Chi-Chi earthquake are used to generate new stochastic ground motions set. Two ground motions sets based on classical stochastic simulation methods are also presented for comparison. Numerical results show that the proposed method for stochastic simulation of near-fault pulse-like ground motions is reliable; the statistics of peak ground accelerations and spectral characteristics of simulated samples are consistent with station records. Besides, the proposed method accommodates the noteworthy randomness and proportion consistency of components associated with near-fault pulse-like ground motions, making it suitable for the stochastic response and reliability analysis of seismic structures in near-fault regions. This superiority is challenging to classical stochastic simulation methods that lack reasonable consideration of randomness and correlation associated with model parameters.

A modified failure chance measure (FCM) was proposed to assess the safety degree of structures under the influence of twofold random uncertainty. This uncertainty arises from random inputs with random distribution parameters. The aim of this paper is to effectively evaluate the safety degree of structures in such conditions. This paper introduces a method named dimensional reduction technique-based maximum entropy principle to address the issue at hand. The proposed method utilizes maximum entropy principle method to efficiently approach optimal probability density characteristics while adhering to the constraints imposed by fractional moments. Additionally, the dimensional reduction strategy is employed to estimate fractional moments, resulting in a linear increase in computational cost with respect to the dimensionality. The primary contribution of this work involves the detailed decoupling of the double-uncertainty analysis used to estimate FCM into a single-uncertainty analysis. This approach allows for the innovative re-use of the same group integral grid points to estimate different fractional moments required for solving FCM. The results of applying the proposed method to solve FCM under acceptable accuracy demonstrate that the number of evaluations required for the performance function can be reduced to less than 100 when the uncertainty dimensionality is limited to 20. This finding confirms the high efficiency of the proposed method for solving FCM.

The uncertain mechanical parameters of clay layer under torrential rain are the key to the dynamic evolution process and stability assessment of landslide geological hazards. Due to the complex environment, engineering geology and physical chemistry process, the mechanical parameters of clay layer show significant spatial variability and correlation. In addition, due to technical and economic conditions constraints, the actual investigation and test data of soft cohesive soil are very limited, which seriously restricts the stability evaluation of clay slope and the prevention of instability disaster. To characterize anisotropic spatial variations of uncertain mechanical parameters for clay layer using incomplete probability data, the elastic modulus, Poisson ratio and shear strength under saturated conditions were measured, and statistical data and variation properties of uncertain mechanical parameters were analyzed. A modeling approach was proposed for characterizing incomplete probability data of clay layer. The accuracy of the proposed approach is verified by comparison of the statistical characteristic for measured data and simulated data. A novel linear fitting method was proposed for assessing scale of fluctuation and autocorrelation distances. The variability and correlation of uncertain mechanical properties for soft cohesive soil layer are discussed. The results show that the mechanical properties of the clay layer are uncertain in spatial position. Both the original observation data and the simulated data of three mechanical parameters have symmetrical correlation structure. The clay layer display the horizontal layered structure on the soil profile, and the vertical autocorrelation distances are shorter than the horizontal distances. This paper clearly illustrates the anisotropic spatial variations of uncertain mechanical parameters for clay layer using incomplete probability data and it can provide scientific data for the uncertainty analysis and risk assessment of clay slope under torrential rain conditions.

This study derives a novel higher-order spectral representation method (HOSRM) to represent and simulate multi-dimensional fourth-order non-Gaussian random physical fields. The method primarily extends the traditional second-order spectral representation method (SRM) for simulating non-Gaussian random physical fields by introducing higher-order cumulant function tensors and trispectrum tensors, thereby accomplishing the modeling of fourth-order non-Gaussian random physical fields (symmetric nonlinear physical fields) from a frequency domain perspective. In an endeavor to enhance the simulation efficiency of this theoretical framework, the Fast Fourier Transform (FFT) algorithm is astutely amalgamated into the simulation. This integration contributes significantly to the augmentation of computational efficiency. Furthermore, exhaustive derivations and proofs are presented for the first-order, second-order, and fourth-order ensemble properties of simulated fourth-order non-Gaussian random physical fields. Subsequently, the reliability and accuracy of the proposed algorithm framework are validated through numerical simulations of two two-dimensional and two three-dimensional non-Gaussian random physical fields. The findings demonstrate that the simulated sample function effectively captures the probability characteristics of the random field, including mean, variance, and kurtosis. Finally, an in-depth analysis of numerical simulation results highlights the difference between the proposed method and the traditional second-order spectral representation method, which further underscores the distinctive attributes and potential superiority of the proposed method.

Under random and interval hybrid uncertainties, solving hybrid reliability based design optimization (HRBDO) can acquire an optimal balance between structural performance and reliability. Since solving HRBDO includes a triple nested framework involving minimum analysis of performance function (PF), failure probability constraint analysis and design parameter optimization, the computational complexity of HRBDO is high, especially for dealing with complex structures. Therefore, a quantile-based sequential optimization and reliability assessment method (QSORA) is proposed for reducing the computational complexity of HRBDO. In the proposed QSORA for HRBDO, failure probability constraint is firstly transformed into minimum PF (MPF) quantile one corresponding to target failure probability. Then, approximating the difference between PF and its target quantile at current iteration by that at previous one, the failure probability constraint analysis is decoupled from the design parameter optimization. Moreover, by approximating the minimum point of the PF with respect to the interval input in the current iteration by that in the previous one, the minimum analysis of PF is separated from the design parameter optimization. By the separation of minimum analysis and failure probability constraint analysis from the design parameter optimization in the proposed QSORA, the triple nested framework of HRBDO is decoupled sequentially as the deterministic design optimization, the minimum analysis of the PF and the target MPF quantile estimation, and this way of reconstructing the HRBDO from the triple nested framework to three single-loop frameworks can significantly enhance the efficiency of solving HRBDO. Furthermore, the MPF quantile at the current design parameter is estimated by stochastic collocation based statistical moment method, in which the stochastic collocation method is employed to efficiently estimate the MPF moment to approximate the probability density function of MPF. The efficiency and accuracy of the QSORA are validated by four numerical and engineering examples finally.

Underplatform dampers (UPDs) mitigate turbine blade vibrations in aeroengines through friction dissipation generated by the contact interface. However, in UPD design, uncertainties are often overlooked, including manufacturing discrepancies, excitation forces, and wear factors, leading to suboptimal predictions of structural dynamic responses. This study presents a dynamic model for the blade-UPD system with cyclic symmetric attributes, which simulates uncertainties using statistical methods. An efficient algorithm using adaptive techniques is proposed to construct polynomial chaos expansions (PCE) for precise and efficient uncertainty quantification (UQ) in turbine blades with UPDs. Further, the influence of single/multiple parameter uncertainties on the dynamic characteristics of the blade-UPD is explored. Sobol' indices are then employed to assess the sensitivity of uncertain factors to the vibration reduction properties of UPDs. The findings suggest that the new approach, which offers precise UQ at minimal computational cost, outperforms traditional methods like Ordinary Least Squares (OLS) and Sparse Least Angle Regression (LARS). Observations reveal a significant impact of parameter uncertainties on blade-UPD dynamic responses, which manifest as "resonance bands" and "frequency shifts" in some cases. Sensitivity analysis indicates noticeable variations in Sobol' indices for each uncertainty parameter as the excitation frequency changes. Specifically, the uncertainty in the friction coefficient demonstrates pronounced sensitivity to amplitude when slip occurs at the contact interface. Furthermore, the observed "drop" phenomenon in Sobol' indices is explained.