Probabilistic Engineering Mechanics最新文献

A method is proposed for characterizing and simulating both stationary and fully non-stationary stochastic ground motions. This method is based on discrete filtered white noise models, including single and double filtered, with the latter is introduced to suppress low-frequency components. Specifically, the proposed method expresses seismic ground motion as a linear combination of products involving orthogonal random variables and deterministic functions. Further, by defining high-dimensional orthogonal random variables as orthogonal functions of extremely low dimensional elementary random variables, efficient dimension-reduction (DR) of primitive ground motion process can be achieved. To illustrate this concept, three distinct categories of random orthogonal functions involving only one or two elementary random variables are examined, employing filtered white noise models to simulate ground motion acceleration processes, thereby demonstrating the accuracy and efficiency of the proposed method. Simultaneously, recommendations for employing the proposed method in simulations are provided based on an analysis of the impacts of various parameters on random ground motion processes. Case studies demonstrate the accuracy and robustness of the proposed method compared to Monte Carlo (MC) methods. Furthermore, case studies on fully non-stationary ground motion highlight the practical applicability of the proposed method in engineering.

During operational phases, maglev trains encounter track irregularities, presenting a formidable challenge to the integrity of their control systems owing to the inherently stochastic nature, a challenge accentuated in the context of high-speed maglev trains. This study aims to comprehensively examine control parameters within the context of stochastic excitation resulting from track irregularities. Through the development of a rigorous stochastic response analysis model utilizing the pseudo excitation method, the investigation delves into the dynamics of an EMS-type high-speed maglev train-rigid track system. Evaluation indices, derived from the power spectral density of the maglev train's response, are established to quantify both control stability and operational stability. Subsequently, based on these indices, a recommended range of PD control parameters is proposed, accounting for the requirements stipulated by the evaluation metrics. The study elucidates that variation in PD control parameters exert discernible effects on the system's stability, primarily altering the nature frequency and damping ratio. Specifically, control stability demonstrates a positive correlation with increasing PD control parameters, while operational stability exhibits a nuanced relationship—initially bolstered by escalating proportional coefficients but subsequently tempered, albeit gradually, with heightened derivative coefficients. The delineated range of values for PD control parameters is meticulously determined, considering pertinent physical parameters of the electromagnetic system, such as mass, static suspension current, and static suspension gap, alongside factors like the Sperling indicator and suspension gap variation.

Although stochastic averaging methods have proven effective in solving the responses of nonlinear oscillators with a strong stiffness term under broadband noise excitations, these methods appear to be ineffective when dealing with oscillators that have a strong inertial nonlinearity term (also known as coordinate-dependent mass) or multiple potential wells. To address this limitation, a radial basis function neural network (RBFNN) algorithm is applied to predict the responses of oscillators with both a strong inertia nonlinearity term and multiple potential wells. The well-known Gaussian functions are chosen as radial basis functions in the model. Then, the approximate stationary probability density function (PDF) is expressed as the sum of Gaussian basis functions (GBFs) with weights. The squared error of the approximate solution for the Fokker-Plank-Kolmogorov (FPK) function is minimized using the Lagrange multiplier method to determine optimal weight coefficients. Three examples are presented to demonstrate how inertia nonlinearity terms and potential wells affect the responses. The mean square errors between Monte Carlo simulations (MCS) and RBFNN predictions are provided. The results indicate that RBFNN predictions align perfectly with those obtained from MCS.

The simulation of multivariate ergodic stochastic processes is critical for structural dynamic analysis and reliability evaluation. Although the traditional spectral representation method (SRM) has a wide application in many areas, it is highly inefficient in simulating stochastic processes with many simulation points or long durations due to the significant computational cost associated with matrix factorizations concerning frequency. To address the encountered challenge, this paper presents an efficient approach for simulating ergodic stochastic processes with limited frequencies. Central to this approach is a fusion of the adaptive spectral sampling and the non-uniform fast Fourier transform (NUFFT) techniques. The adaptive spectral sampling of the envelope spectrum enables the determination of limited non-equispaced frequencies, which are randomly sampled according to a uniform distribution. Thus, the Cholesky decomposition is only required at limited specific frequencies, which dramatically reduces the computational cost of matrix factorizations. Since the randomly sampled frequencies are not equispaced, utilizing FFT to accelerate the summation of trigonometric functions becomes impractical. Then, the NUFFT that adapts the non-equispaced sampling points is employed instead to expedite this process with the non-uniform increment approximated through reduced interpolation. By taking the wind field simulation of a long-span suspension bridge as an example, a parametric analysis is conducted to investigate the effect of random frequencies on the simulation error of the developed approach and the convergence of spectra. Finally, the developed approach is further validated by focusing on the spectra and probabilistic density functions of the simulated wind samples, and the simulation performance is compared with that of the traditional approach. The analytical results demonstrate the efficiency and accuracy of the developed approach in simulating ergodic stochastic processes.

A probabilistic framework for the expected damage estimation of RC half-joints under traffic load is proposed. Taking into account the uncertainties in geometrical features and mechanical properties, and introducing a probabilistic model for the traffic load, the proposed procedure links the structural response of RC half-joints, described by fragility curves, to financial consequences, according to the Loss-Based Design (LBD). In addition to the reliability of RC Gerber bridges, as impacted by the structural response of RC half-joints, the procedure allows to identify proper strengthening interventions focusing on cost-effectiveness and efficiency. The improved level of information regarding the structural performance of bridges can become the basis for more rational decision making as part of risk management strategies. The procedure is applied to the RC Gerber bridge “Annone” (Italy), which is investigated, as case study, in the as-built configuration and assuming a strengthening intervention.

Efficiently merging fatigue datasets from diverse sources has proven to be a strategic approach for enhancing the reliability of fatigue assessment and design within industry, while concurrently streamlining costs and time. Statistical parametric analysis is an approach that can be applied to fatigue datasets to determine whether the datasets can be deemed statistically significant (different) or statistically insignificant (similar). This paper systematically employed statistical parametric test-statistic hypotheses to assess significance. To validate this approach the paper used as a case study, fatigue data sets generated from varied notched specimens with hole diameters ranging from 0 mm to 3 mm, in addition to data from the literature. In particular, gross stresses were utilized to ensure that the only means to identify differences in the fatigue datasets was through statistical analysis. This approach was observed to work well for geometries with differences in notch geometry as small as 1 mm and was able to identify notch insensitivity in cast iron. Thus, this method can be used to differentiate fatigue datasets based on statistical parameters rather than other physical parameters.

A time-dependent reliability model for pre-stressed metal/polymer/metal composite structures subject to interlayer slip failure is developed in this study, allowing for predicting the probability of failure of the whole structure under multi-axial random multi-peak impact loads and transport vibration. A multi-Gaussian envelope model with uniform modulations is proposed to model random multi-peak impact loads, and the inverse sampling method is employed to model random transport vibration. An interlayer slip physics model is developed based on the contact surface friction mechanism under multi-axial vibration load and the stress-relaxation constitutive model. By implementing the interlayer slip physics model in the finite element method framework via the user-material routine, the geometry effect of the structure can be dealt with, and the reliabilities at an arbitrary location of the structure can be obtained. The proposed method is demonstrated using engineering examples. The results show that the proposed reliability assessment method provides a viable and systematical procedure of computing the time-dependent reliability of composite structures as a whole under multi-axial impact loads and vibrations.

To establish an accurate model for determining the shear strength parameters of sliding surfaces while considering the variability and uncertainty of geotechnical parameters, a reliability back analysis method for parameters based on Bayesian theory and a three-dimensional slope stability analysis method are proposed in this paper. First, the prior information of shear strength parameters is updated according to the field test information based on Bayesian theory. Then, combined with the reliability theory, the influences of different two-dimensional and three-dimensional sliding surface shapes on the parameters back analysis are studied. The results show that the uncertainty of parameters decreases with the increase in the amount of test data after introducing the test data to update the mastered parameter information based on Bayesian theory, and it is of great significance to consider the shape and three-dimensional effect of the sliding surface accurately to improve the accuracy of parameter determination and slope stability analysis.

The serviceability of tall timber buildings due to wind-induced vibrations is often a governing design criterion. However, accurate modelling of such buildings for their serviceability is a challenge, partly because certain non-structural building elements (e.g. plasterboards, façade, screed) act structurally, and no guidelines exist on how to effectively include them in the model. Model updating may be helpful in revealing their as-built characteristics. This paper presents findings of a surrogate-based Bayesian model updating of a lightweight eight-storey cross-laminated-timber building. In particular, the focus was on patterns and correlations between mass distribution and modal characteristics, as well as the effects of joints, non-structural building elements, and the foundation. Model updating utilised the results of ambient vibration testing, which is commonly used in civil engineering for structural identification or health monitoring, however, it generally offers a relatively low number of identified modes. To this end, the study investigates the sensitivity of the updating process to the number of modes involved in the analysis.

In the estimation of extreme wind speed, the effect of wind direction is usually ignored. Nevertheless, as a vital parameter of the wind, it should be reasonably taken into consideration. Nowadays, the influence of wind direction can be considered through directional wind speed or directly regarding it as a variable. Based on wind speed data of climate stations, the wind directions are divided into uniform and non-uniform sectors. Copula function is then applied to establish the joint distribution of directional wind speed. The effect of the partition of directional sectors is discussed subsequently. Meanwhile, a joint distribution model of wind speed and wind direction based on copula function is also set up. According to the joint distribution, extreme wind speeds under specified wind directions are estimated based on conditional probability. Besides, extreme wind speeds considering wind directionality based on the aforementioned two methods are compared. Results show that the classification of wind direction will affect the estimation of extreme wind speed. In addition, the estimation of extreme wind speed under specified wind direction based on the joint distribution of wind speed and wind direction does not reflect the actual wind characteristics. Through the comparison of different methods considering directionality, the result based on the joint distribution of directional wind speed seems more reasonable.