Probabilistic Engineering Mechanics最新文献

Accurate modeling of the turbulent wind field is a crucial component of risk analysis for structures to windborne debris damage. Existing studies typically simplify the complexities of wind turbulence, and the potential influence on the accuracy of debris flight modeling has not been systematically demonstrated. This study takes a multi-layered approach to numerically simulate the flight trajectory of spherical debris in a turbulent wind field. Complexities are incrementally added to the simulated wind field to systematically investigate the influence of spatial correlation and non-Gaussian features of turbulence on debris flight behavior. The sensitivity of debris flight behavior to turbulent wind features will inform the design of debris flight tracking wind tunnel tests and building façade debris vulnerability modeling efforts.

Reliability assessment is a crucial aspect of the design and operation of structures, particularly in balancing safety and cost considerations. This paper introduces a novel method for evaluating the performance-based target reliability of floating wind turbine platforms in offshore environments. The method focuses on the platform's motion modes and wave frequencies, which significantly influence the system's structural integrity and performance. An improved limit state function is proposed to enhance the accuracy of reliability calculations, specifically for steady-state conditions. The platform's six degrees of freedom motions are carefully analyzed to investigate their dependence on wave frequencies. By considering the time response of these motions and accounting for uncertainties in wave characteristics, wave impact directions, and wind effects, a comprehensive reliability analysis is conducted to assess the stability modes of the platform. This paper introduces the term 'Reliability Performance-Based' (RPB) analysis as a new concept to evaluate the system's reliability at a given performance level. Furthermore, an optimal target reliability index is defined to address the economic aspect of the design process. The proposed methodology's PEB analysis focuses on capturing uncertainties in wave characteristics and wind effects on floating wind turbine platforms. This includes a detailed examination of wave and wind-induced loads and their propagation through the system concerning its performance level. Statistical models were integrated to quantify these uncertainties, applying Monte Carlo simulations to assess their effects on the platform's reliability. This approach allows for a nuanced understanding of the interactions between environmental factors and structural responses, enhancing the precision of our reliability assessments. It enables the consideration of economic efficiency alongside safety, ensuring a balanced approach to the design and operation of the floating wind turbine platform. By providing a comprehensive reliability assessment framework, it aids in the optimization of design and decision-making processes for floating wind turbine platforms.

Modeling complex joints in structures entails significant time and effort, necessitating simplifications. Epistemic uncertainties arising from low-fidelity modeling can be quantified through probabilistic model updating. However, finding a surrogate physical model to represent simplified joint configurations poses challenges. Additionally, establishing a Bayesian formulation capable of incorporating structural parameters of connections is necessary. This study employs a validated simplifying parameterization approach for surrogate modeling of complex semi-rigid connections in a benchmark laboratory steel grid. It proposes a modal probabilistic Bayesian methodology to quantify uncertainties in the structure's joints. Three modal-based objective functions are utilized for finite element model updating. The modal properties of the structure are extracted by experimental modal analysis during an impact test, which will be utilized in the model updating process. Deterministic and probabilistic structural parameter estimations are integrated to enhance the robustness of the Bayesian technique. Furthermore, a guideline for selecting optimal hyperparameters is provided. Results demonstrate that utilizing deterministically estimated parameters as prior knowledge can facilitate and improve modal probabilistic model updating for structures with complex joints. Also, it is found that despite significant simplifications of joints, structural parameter tolerance around the maximum a posteriori estimate in surrogate models remains low.

Based on the improved interval operation theory, an improved expression of the return period wind speed interval prediction is constructed by using an approximate first-order Taylor series expansion. According to the measured wind speed data in Beijing, Jinan, Nanjing, Wuxi, Shanghai and Shenzhen, the improved method and the traditional method are respectively used to predict the interval of the return period wind speed. Furthermore, the interval results predicted by the improved method and the traditional method are compared and analyzed under the same confidence level. Results show that the improved method has good applicability for different parameter estimation methods under the condition of certain extreme value distribution model, and the interval prediction results of the return period wind speed are basically stable. Compared with the interval results predicted by the traditional method, the interval predicted by the improved method is more likely to be close to or contain the exact solution of the return period wind speed, which has higher prediction accuracy. In addition, the calculation process of the improved method is relatively simple and can realize the simplified calculation of interval prediction.

A statistical model calibration problem is known to have unstable or non-unique optimal solutions due to its ill-posed inverse nature, which is further complicated by limited test data availability due to time and cost constraints. To overcome these challenges and improve the identifiability of calibration parameters, this study proposes a novel statistical model calibration framework. The proposed method integrates input test data for unknown model variables and output test data for a system response, employing a bivariate form of copula function to model the probability distribution while accounting for the correlations between unknown model variables. Furthermore, a sample-averaged log-likelihood is used as a calibration metric, assuming conditional independence to reflect input and output test data evenly in a single metric. Optimization-based model calibration (OBMC) is performed to identify the probability models that maximize the calibration metric for a given set of input and output test data, among candidates of marginal probability distributions and copula functions. Consequently, this proposed method enhances the identifiability of calibration parameters and overcomes insufficient data issues by taking observations of unknown model variables into account in the statistical model calibration procedure. The proposed framework is validated using numerical examples.

The high-reliability lifetime estimation of the lifting lug is of significant importance, as it is the most crucial component of the aerial bomb. This paper focuses on the high-reliability lifetime of the three-parameter Weibull distribution for lifting lug fatigue data. A novel method is developed to generate estimates of reliability lifetime according to the generalized fiducial inference, whose prior is calculated by the failure data. A posterior distribution is obtained based on Bayesian theory to compute the point estimate and the confidence interval of the generalized fiducial inference for reliability lifetime using the Monte Carlo Markov chain method. Subsequently, it is compared with the non-informative prior Bayesian inference. A Monte Carlo simulation demonstrates that the proposed method outperforms the non-informative prior Bayesian inference. The lower confidence limit of the generalized fiducial inference for the reliability lifetime exhibis satisfactory coverage probabilities. Finally, fatigue tests are performed on 18 lifting lugs under variable loads. The point estimate and the lower confidence limit of the high-reliability lifetime are estimated, which can illustrate the applicability of the proposed method.

The damping of a structure has often been modeled as linear hysteretic damping (LHD), so its corresponding equation of motion (EOM) is an integro-differential equation that involves the Hilbert transform of response displacement. As a result, the system is non-causal in nature, and it is challenging to compute its nonstationary response statistics under evolutionary stochastic excitation. This article develops an efficient solution method to obtain closed-form solutions for various nonstationary response statistics, including the evolutionary power spectrum (EPS), correlation function and mean square values. The novel solution method utilizes the concept of causalization time to introduce a “causalized” impulse response function (IRF), by which causal response statistics are computed based on a pole-residue approach. This approach requires obtaining a pole-residue form of the transfer function (TF) from the frequency response function (FRF) of the system, which is readily obtained from the EOM. Subsequently, the desired response statistics are obtained by shifting the causal response statistics back to the original time. To obtain the pole-residue form of the TF, two steps are necessary: (1) taking the inverse Fourier transform of the FRF of the oscillator to obtain a discrete IRF and (2) using the Prony-SS method to decompose this discrete IRF to obtain the pole residues associated with the TF. The correctness of the proposed method is numerically verified by Monte Carlo simulations through examples of hysteretic damping and mixed viscous-hysteretic damping oscillators that are subjected to white noise, modulated white noise and modulated Kanai–Tajimi model random excitations.

A new method is proposed to compute the probability density of the multi-dimensional nonlinear dynamical system perturbed by a combined excitation of Gaussian and Poisson white noises. We first deduce a probability-density solver from the Euler–Maruyama scheme of the stochastic system and the corresponding Chapman–Kolmogorov equation. This solver actually is an explicit numerical formula of the probability density of the solution to this stochastic system. To compute the probability density, we propose an efficient algorithm for this solver, which actually is the implementation of a numerical integration. Furthermore, we prove this solver is an approximated solution of the corresponding forward Kolmogorov equation. Numerical examples are conducted to illustrate our probability-density solver.

Operator learning frameworks have recently emerged as an effective scientific machine learning tool for learning complex nonlinear operators of differential equations. Since neural operators learn an infinite-dimensional functional mapping, it is useful in applications requiring rapid prediction of solutions for a wide range of input functions. A task of a similar nature arises in many applications of uncertainty quantification, including reliability estimation and design under uncertainty, each of which demands thousands of samples subjected to a wide range of possible input conditions, an aspect to which neural operators are specialized. Although the neural operators are capable of learning complex nonlinear solution operators, they require an extensive amount of data for successful training. Unlike the applications in computer vision, the computational complexity of the numerical simulations and the cost of physical experiments contributing to the synthetic and real training data compromise the performance of the trained neural operator model, thereby directly impacting the accuracy of uncertainty quantification results. We aim to alleviate the data bottleneck by using multi-fidelity learning in neural operators, where a neural operator is trained by using a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. We propose the multi-fidelity wavelet neural operator, capable of learning solution operators from a multi-fidelity dataset, for efficient and effective data-driven reliability analysis of dynamical systems. We illustrate the performance of the proposed framework on bi-fidelity data simulated on coarse and refined grids for spatial and spatiotemporal systems.

In spite of recent advancements in reliability analysis, high-dimensional and low-failure probability problems remain challenging because many samples and function calls are required for an accurate result. Function calls lead to a sharp increase in computational cost in terms of time. For this reason, an active learning algorithm is proposed using Kriging metamodel, where an unsupervised algorithm is used to select training samples from random samples for the first and second iterations. Then, the metamodel is improved iteratively by enriching the concerned domain with samples near the limit state function and samples obtained from a space-filling design. Hence, rapid convergence with the minimum number of function calls occurs using this active learning algorithm. An efficient stopping criterion has been developed to avoid premature or late-mature terminations of the metamodel and to regulate the accuracy of the failure probability estimations. The efficacy of this algorithm is examined using relative error, number of function calls, and coefficient of efficiency in five examples which are based on high-dimensional and low-failure probability with random and interval variables.