Probabilistic Engineering Mechanics最新文献

Engineering problems are mainly defined in implicit processes; hence, the fully probabilistic analyses, e.g., Monte Carlo simulations (MCS), are expensive to implement. In practice, two approaches to overcome the issues are either reducing the size of simulations or developing surrogate models for actual problems. The latter does not sacrifice the size of MCS and requires less insight into probabilistic calculation; hence, it is preferable to most engineers. This study proposes an efficient framework to develop reliable and accurate surrogate models by considering data at the limit state margins (LS data). Effects of involving LS data in the training process and performances of the proposed metamodels are investigated for most issues relating to reliability analyses, including nonlinear performance functions, multiple failure modes, and implicitly defined problems. Two machine learning algorithms, including artificial neural networks and the Gaussian process, are employed to prove the ability of the proposed method. Investigations reveal that the limit state data plays a vital role in developing accurate surrogate models for reliability analyses, and accumulating them into the training dataset helps quickly construct accurate metamodels. This work contributes a practical framework for reliability analyses because the LS data can be detected easily without insight into probabilistic calculations.

To efficiently estimate the main effects and total effects of uncertain distribution parameters on the uncertainty of failure probability, we construct single-loop estimation formulas by introducing auxiliary variables through the equal probability transformation. This approach circumvents the original nested triple-loop process. For generating samples used in the derived single-loop estimation formulas, direct Monte Carlo simulation can be employed. To reduce the number of samples in Monte Carlo simulation, the important sampling technique can be integrated into the proposed single-loop estimation formulas. Additionally, to enhance the efficiency of identifying the states (failure or safety) of all used samples, an adaptive Kriging model can be introduced. Subsequently, the adaptive Kriging model coupled with Monte Carlo simulation, and the adaptive Kriging model coupled with the importance sampling technique, are integrated into the derived single-loop formulas to concurrently and efficiently estimate the main effects and total effects of uncertain distribution parameters. The results of three case studies validate the accuracy and efficiency of the proposed method.

Time-dependent kinematic reliability of a motion mechanism is critical for optimizing its operational performance. Dynamic factors, including material deterioration and wear in the joints, are disregarded in the prior study. As such, the envelope method is employed to undertake time-dependent kinematic reliability analysis of motion mechanisms, accounting for dynamic factors. Firstly, a decoupling strategy is proposed for decoupling the time-dependent motion error stemming from motion input and the dynamic factors. Thus, the kinematic reliability is delineated into two distinct temporal parameter-dependent issues. Subsequently, the envelope function is extended to solve the kinematic reliability. The expansion temporal points determination function (ETPDF) in the envelope function is approximated using a first-order method coupled with an active learning Kriging mode. After the expansion temporal points are found, the time-dependent reliability can be efficiently calculated via a multivariate Gaussian integral. Finally, the effectiveness and accuracy of the proposed method is verified by means of a 4-bar function generating mechanism.

This paper extends the recently developed method of separable Gaussian neural networks (SGNN) to obtain solutions of the Fokker–Planck–Kolmogorov (FPK) equation in high-dimensional state space. Several challenges when extending SGNN to high-dimensional state space are addressed including proper definition of domain for placing Gaussian neurons and region for data sampling, and numerical integration issue of evaluating marginal probability density functions. Three benchmark nonlinear dynamic systems with increasing complexity and dimension are examined with the SGNN method. In particular, the steady-state probability density of the response is obtained with the SGNN method and compared with the results of extensive Monte Carlo simulations. It should be pointed out that some solutions of high-dimensional FPK equations for nonlinear dynamic systems would be very difficult to obtain without SGNN.

The OOR (out-of-roundness) wheel is one of the main excitation sources causing vehicle vibration. However, the OOR wheel occurs randomly, indicating that the vibration behavior of a vehicle cannot be comprehensively evaluated using a deterministic approach. Thus, a probability analysis framework is proposed to obtain vehicle vibration characteristics while considering the randomness of the OOR wheel. The probability model of the random OOR wheel is derived by reducing the high-dimensional variables into a few independent variables of the radius, amplitude, and phase. Then, the vertical vehicle-track coupled system with OOR wheels is modelled. A DPIM (direct probability integral method) is further developed to analyze the evolution of excitation to response probabilities. Finally, the statistics of the random vibration of the vehicle are calculated. The proposed framework is verified using a numerical case. Results show that the PDF (probability density function) shape of the vehicle random vibration, induced by the Gaussian-distributed OOR wheel, deviates from the Gaussian distribution due to the nonlinear wheel/rail contact force. Instead, it exhibits a right-skewed shape, significantly impacting the dynamic performance. As the mean or coefficient of variation of the OOR wheel amplitude increases linearly, the reliability of the vehicle Sperling index experiences a quadratic or double-sloping decrease. Consequently, a maintenance threshold for OOR wheel amplitudes is given based on reliability considerations. Compared to Monte Carlo simulation, the proposed framework offers a computational efficiency improvement of at least one order of magnitude.

To address the substantial computational burden associated with probability density evolution method (PDEM) in structural reliability analysis, this study proposes a novel look-ahead learning function named stepwise truncated variance reduction (STVR), integrating polynomial chaos Kriging (PCK) and PDEM. Three key features of STVR are highlighted. First, it enables quantifying the maximum reduction in predictive errors of PCK within the regions of interest (ROI) when adding a new point. Second, closed-form expression for STVR is derived through Kriging update formulas, eliminating the need for computationally intensive Gauss–Hermite quadrature or extensive conditional simulations of PCK. Third, a dynamic adjustment procedure is proposed for the probability level-related parameter in STVR, with the aim of achieving a good balance between the exploitation and exploration of ROI during the sequential experimental design process. The performance of STVR is demonstrated through two benchmark analytical functions and three numerical examples of varying complexity. Results indicate that the dynamic adjustment procedure for the probability level-related parameter in STVR outperforms the empirical setting of a minor value. Then, STVR proves more advantageous than existing pointwise and look-ahead learning functions, particularly in addressing complex dynamic reliability problems.

Monte Carlo numerical simulations for generating stationary Gaussian random time-domain signal samples fulfil an important role in random fatigue life prediction. Control parameters such as the random seed, the sampling frequency and the number of sampling points in the numerical simulations have significant effects on the time-domain random fatigue life. In this paper, the effects are investigated systematically by utilizing commonly used power spectrum samples and engineering materials, and so a new method for optimizing the control parameter values is proposed. The proposed method solves the critical problem found in many papers that the relative error between the frequency-domain fatigue life and the time-domain fatigue life increases with the slope K of the S–N curve. Furthermore, it observably reduces the sampling variability of time-domain fatigue life for the large slope K, which will help the related researchers to establish better frequency-domain models for fatigue life prediction by using the time-domain fatigue life values as standard data.

This paper presents a framework for robust topology optimization of bridges under random traffic loading. Traffic loading is simulated using a stream of random moving loads parameterized by their masses, speeds, directions, and arrival times. The stochastic reduced-order model approach is combined with the equivalent static load method to achieve uncertainty-informed dynamic response topology optimization. The stochastic reduced-order model approach propagates uncertainty and reduces problem dimension, whereas the equivalent static load method is employed for dynamic response topology optimization. The effectiveness of the proposed optimization framework is demonstrated using several numerical examples. The proposed framework is found to be effective in optimizing structures under traffic loading, making it a promising solution for the topological design of bridges.

This work addresses the critical task of accurately estimating failure probabilities in dynamic systems by utilizing a probabilistic load model based on a set of data with similar characteristics, namely the relaxed power spectral density (PSD) function. A major drawback of the relaxed PSD function is the lack of dependency between frequencies, which leads to unrealistic PSD functions being sampled, resulting in an unfavorable effect on the failure probability estimation. In this work, this limitation is addressed by various methods of modeling the dependency, including the incorporation of statistical quantities such as the correlation present in the data set. Specifically, a novel technique is proposed, incorporating probabilistic dependencies between different frequencies for sampling representative PSD functions, thereby enhancing the realism of load representation. By accounting for the dependencies between frequencies, the relaxed PSD function enhances the precision of failure probability estimates, opening the opportunity for a more robust and accurate reliability assessment under uncertainty. The effectiveness and accuracy of the proposed approach is demonstrated through numerical examples, showcasing its ability to provide reliable failure probability estimates in dynamic systems.

To quantify the fatigue behaviour of materials, a Wöhler diagram is required. The state of the art shows that, over the years, numerous approaches suitable for determining Wöhler curves have been devised and validated through large fatigue data sets. The variation in experimental fatigue data elicits the use of statistics for analysis and design purposes. By focusing on the medium-cycle fatigue regime (i.e., failures in the range 10³÷10⁷ cycles to failure), this paper reviews relevant statistical approaches, particularly the methods suggested by the American Society for Testing Materials (ASTM) as well as the International Institute of Welding (IIW) and the so-called Linear Regression Method (LRM). Their responses were assessed on virtual data sets tailored to satisfy specific statistical requirements as well as experimental fatigue data sets from the literature. While the scatter bands at two times or less of the spread are similar for all approaches, the ASTM approach is seen to be the most conservative.