Probabilistic Engineering Mechanics最新文献

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.

The transition and mean first-passage time(MFPT) in a fractional-order bistable system, excited by multiplicative non-Gaussian noise and additive Gaussian white noise, are investigated. Utilizing the fractional-order minimum mean square error criterion and the path integral approach, we derive approximate expressions for both the steady-state probability distribution function and the MFPT. The results show that the noise correlation strength, non-Gaussian parameter, Gaussian noise strength and fractional order can induce phase transitions. The MFPT exhibits a peak as a function of non-Gaussian noise intensity, demonstrating the noise-enhanced stability phenomenon, while the MFPT displays a consistent, monotonic relationship as a function of Gaussian white noise intensity. Numerical simulations are conducted to validate theoretical results, which show a reasonably high degree of consistency.

In this paper, a fatigue life prediction model based on the amplitude probability density function under broadband multimodal stochastic vibration response is presented. An analysis method is proposed to address the dispersion of the third- and fourth-order normalized moments of rain-flow amplitude distributions. The unified relationships between the first four-order normalized moments of rain-flow amplitude distributions and the spectral parameters are established to determine the model parameters. Through comparison with other frequency-domain methods and based on the tail probability density distribution of rain-flow amplitude, the proposed model offers more precise and stable fitting results under broadband multimodal response power spectra.

In this paper, a novel approach, based on the principle of the deep learning method, is proposed to study the stochastic responses of vehicle-bridge system (VBS) subjected to near fault earthquakes (NFEs), which also considers the effects of uncertain parameters. To generate the training data as the input of the proposed deep learning model, the dynamic formulas of the VBS are deduced by Newmark-β method. The proposed analysis model comprises three modules: the CNN module for seismic data feature extraction, the Attention Mechanism module for enhancing the selection for information between time series to improve the accuracy and efficiency of the final prediction, and the Bidirectional Gated Recurrent Unit (BiGRU) for predicting VBS responses. The mapping connection between earthquake action and the system response is established. The BiGRU model is capable of conveying both the excitation's randomness and the system's uncertain parameters. An actual railway cable-stayed bridge subjected to the running railway vehicle and NFEs is utilized to verify the proposed model. The uncertain train weight, bridge damping ratio and the randomness of NFEs are incorporated into the dynamic responses analysis of VBS. As a result, the time-varying responses obtained by the proposed model show significant agreement with results from a validated dynamic VBS framework. The mean value and standard deviation (STD) of the responses obtained by the proposed method are also compared with those by the Monte Carlo method and probability density evolution method. Therefore, both the individual sample of the dynamic response and the statistical data from diverse stochastic responses are chosen to validate the model's accuracy and efficiency in the VBS analysis under NFEs. In addition, the effects of the stochastic characteristics on the system's random vibrations are also explored through the time-histories of statistical data and the probability density function of the absolute maximum of responses.

One crucial element of a seismic performance evaluation approach is to appropriately account for the stochastic characteristics of SGMs and the uncertainty associated with material properties. Furthermore, the incidence angle of seismic waves may be influenced by topographic and geological factors, leading to uncertainty and randomness. This variability in incident angles has the potential to cause unforeseen structural damage. However, the current seismic design code of underground structures has commonly assumed the vertical or horizontal seismic input method in underground engineering. From the uncertain point of view, the multi-source uncertainties that incorporate the nonstationary SMGs, seismic input angles, and material parameters utilized to conduct the seismic performance assessment of HTs remain a challenge in current seismic design and performance evaluation. To overcome this challenge, the Generalized F-discrepancy method, the generalized PDEM, and the equivalent extreme-value event are introduced to conduct stochastic dynamic analysis and develop the appropriate fragility curves of HTs considering the multi-source uncertainties. The results demonstrate that the probability of damage of the HT obtained by multi-source uncertainties is significantly different in analyzing the single uncertain and two uncertainties. Moreover, it can be concluded that the multi-source uncertainties can cause more seismic demand than the single uncertain and two uncertainties under different earthquake intensity levels for the HT. In light of this, it is strongly suggested that seismic design and performance assessment of HTs take into account the relevant aspects, such as the input angles, the random features of seismic waves, and the material parameters.

Lattice structures can provide high strength with modest weight. For this reason, they are found in many natural systems at the microscopic level and have also been adopted in engineering at many scales. Assessment of the load-bearing capacity of such structures is crucial and cannot ignore considerations of imperfections, whether due to natural factors if the material exists naturally or to manufacturing defects if it is created artificially. Defects can affect many geometrical aspects of the lattice such as the shape of cells and the thickness and the waviness of trusses. In this paper, we will focus on the first aspect, investigating the effect of variation of the shape of the cells by applying a perturbation to the periodic configuration for common geometries. The failure load of these systems is evaluated by means of an upper bound limit analysis through linear programming, varying the relative density of the lattice and the intensity of imperfections. The failure load is addressed by statistical moments and probability density functions.

Performance-based earthquake engineering (PBEE) is a popular direction in the earthquake community, and at this stage, risk-based PBEE has become mainstream. In the risk-based probabilistic framework, seismic fragility analysis constitutes the most important link, and corresponding research on the mainshock–aftershock sequence has received widespread attention in recent years. Since a mainshock is often accompanied by multiple aftershocks and there is great uncertainty in the vibration characteristics of aftershocks, a seismic fragility analysis of structures under a stochastic mainshock-multi-aftershock sequence is meaningful and necessary. The corresponding questions, such as how to derive the multi-dimensional analytical fragility form under a stochastic mainshock-multi-aftershock sequence and how to correlate multiple intensity measures with multiple demand parameters, still require further investigation. In this paper, a direct analytical derivation of the multi-dimensional seismic fragility spaces of structures under nonstationary stochastic mainshock-multi-aftershock sequences is introduced. The methodology framework, implementation steps, and application examples are also provided in detail. Moreover, two scenarios, the one-mainshock-one-aftershock and one-mainshock-two-aftershocks, are considered, and the obtained multi-dimensional analytical fragility spaces for both scenarios are validated. In general, the matching accuracy of the fragility results for both scenarios is proven to be high, and the direct analytical derivation of the multi-dimensional fragility spaces is validated to be ideally consistent, which further provides a reference for multi-dimensional risk analysis under nonstationary stochastic mainshock-multi-aftershock sequences in future work.

The Physical Synthesis Method (PSM) stands out as a robust framework for conducting structural reliability analyses due to its clear conceptual foundation. However, this approach often necessitates significant computational resources when addressing scenarios with small failure probabilities. In response to this challenge, this study introduces a layer assigned probability space partition method designed to identify pivotal points based on the ultimate bearing capacity failure criterion of structural components within the PSM framework. Drawing inspiration from Harbitz's β-sphere, this method effectively utilizes the minimum reliability index of components to discern essential representative points within the probability space, thus streamlining computations. The efficacy of this approach is showcased through two case studies: a simply supported beam and a six-story reinforced concrete frame. The outcomes demonstrate that the proposed method, when integrated with PSM, exhibits a substantial enhancement in efficiency compared to the conventional Monte Carlo method. Besides, under equivalent computational resources, it achieves superior computational accuracy compared to the importance sampling method, particularly in scenarios with small failure probabilities. Furthermore, by introducing the notion of a common safe domain, this method addresses challenges in structural reliability analyses involving multiple failure surfaces.

With the growing use of composite materials, the need for high-fidelity simulation techniques of the related behavior increases. One important aspect to take into account is the uncertainty of the response due to fluctuations of the material parameters of the constituent materials of the homogenized composite. This inherent randomness leads to stochastic stresses on the microscale and uncertain macroscale response. Until now, the viscoelastic response of the matrix material seriously hindered the application of efficient methods to predict the composite material behavior. In this work, a novel method based on the time-separated stochastic mechanics (TSM) is developed to address this problem. We present how the uncertainty of the microscale stresses of a representative volume element and the homogenized macroscale stresses can be approximated with a low number of deterministic finite element simulations. Quantities of interest are the expectation, standard deviation, and the probability distribution function of the stresses on micro- and macroscale. The results showcase that the TSM is able to approximate the reference results very well at a minimal fraction of the computational cost needed for Monte Carlo simulations.

Reliability analysis poses a significant challenge for complex structures with stringent reliability requirements. While Sequential Importance Sampling (SIS) and Subset Simulation (SUS) have proven highly effective in addressing high-dimensional problems with small failure probabilities, the computational burden of mechanical simulations remains substantial due to the time-consuming nature of numerical simulation processes. Consequently, this paper introduces a novel approach, denoted as AK-SIS, which combines SIS with Kriging metamodeling specifically designed to address computational challenges associated with small failure probabilities. The fundamental principle of this approach involves utilizing AK-MCS technology (Echard et al., 2011) [1] as a precursor to the SIS approach to initially generate metamodels. These metamodels are then employed in lieu of performance functions in subsequent steps, significantly reducing the number of function calls required to simulate complex engineering problems when applying SIS techniques directly. By inheriting the advantages of SIS, AK-SIS has demonstrated its suitability for reliability analysis in scenarios involving high-dimensional spaces and small fault probabilities. Furthermore, AK-SIS is not limited by the shape of the failure domain, eliminates the need to solve the design point, and is particularly well-suited for analyzing reliability in cases of discontinuous failure domains, multiple failure domains, as well as complex failure domains and rare events. The efficacy of AK-SIS is substantiated through rigorous evaluation encompassing nonlinear, high-dimensional examples, and an engineering application. These empirical validations collectively contribute to a robust methodological framework for reliability analysis of intricate structures characterized by stringent reliability requirements.