Probabilistic Engineering Mechanics最新文献

In recent years, the active learning reliability method that combines the Kriging model and Monte Carlo simulation (AK-MCS) has emerged as a promising approach due to its computational efficiency and accuracy. However, the commonly used learning functions, such as the expected feasibility function (EFF), U function, H function, and expected risk function (ERF), can only select one training point at each iteration which is time-wasteful when parallel computing is available. Therefore, this paper proposes a parallel active learning Kriging strategy, namely P-AK-MCS, for structural reliability analysis. By introducing an influence function that reflects the impact of the added point on the original learning function, four parallel learning functions are constructed: pseudo-U (PU) function, pseudo-EFF (PEFF), pseudo-H (PH) function, and pseudo-ERF (PERF). These functions aim to identify multiple training points at each iteration without requiring additional functional evaluations. The effectiveness of the proposed method is validated using four examples. The results demonstrate that compared to the standard AK-MCS, the proposed P-AK-MCS significantly reduces the number of computation loops and greatly decreases computational costs. Moreover, the total number of functional evaluations required is similar to that of the standard AK-MCS and remains insensitive to the number of multiple training points.

Traditionally, regulations employ semi-probabilistic methods with partial safety factors to control design limits. Calibrating these partial safety factors involves estimating the target reliability level and optimizing the partial safety factor values in order to minimize the deviation of the safety index between the considered design scenarios and the target value. This procedure necessitates performing a demanding amount of reliability analyses and is often carried out for simplified design situations. Therefore, high computational costs must be accepted for design problems formulated with complex computational models. This study implements a meta-modeling approach based on active learning in the partial safety calibration procedure, enabling its application to computationally intensive problems. Subsequently, the approach is applied to the running safety of ballasted high-speed railway bridges. This limit state implicitly accounts for the phenomenon of ballast destabilization, the occurrence of which disturbs the load path from the rail level to the bridge structure. The dramatic increase in train operating speeds in recent decades has increased the possibility of this design limit state being violated due to resonance. Despite the evident safety concerns, the adopted safety factors appear to be solely based on engineering judgments rather than calibration through higher-level reliability analysis. Therefore, the proposed calibration method is employed to determine the corresponding partial safety factors for various maximum allowable operating train speeds. The newly calibrated partial safety factors allow for a permissible maximum vertical acceleration of the bridge deck approximately 25% higher than the conventional design approaches. Therefore, incorporating these factors into the design procedure may lead to the construction of lighter bridges.

Wind tunnel experiment is an essential measure for acquiring wind pressure information on the surface of structures. However, it is hard to acquire the complete wind pressure field information because of the restrictions of the measuring equipment capability or inner space of rigid experimental models. For this reason, this paper proposes a reliable wind pressure field reconstruction method using a variance-extended Kriging sequence interpolation. Besides the commonly deterministic reconstruction generated via conventional methods, this method can achieve the reconstruction of wind pressure coefficient time history or statistical moments at any required instant or location from the probabilistic perspective. More importantly, it can effectively avoid the repetitive procedure in addressing the sequence interpolation problem. Numerical examples are employed to illustrate the performance of the proposed method. The experimental result demonstrates that this method can provide a reliable reconstruction of the wind pressure field, and thus may have a great potential in practice.

In the engineering field, time-variant reliability analysis (TRA) is used to measure the safety level of structures under time-variant uncertainties. Lacking in information or data, some uncertainties cannot be directly quantified as stochastic models, which results in the simultaneous existence of aleatory and epistemic uncertainties in most of problems. In general, stochastic and interval models are respectively used to describe aleatory and epistemic uncertainties. For the hybrid TRA (HTRA) problem considering the two kinds of uncertainties, the existing method needs to excessively evaluate the original time-variant limit-state function, which is too expensive for engineering problems. To address this issue, we propose the concept of bound-most-probable point trajectory (BMPPT) which can be used to construct the approximation of the limit-state hyper-surface. Moreover, we develop a HTRA method based on approximating BMPPT which can further improve the computational efficiency. First, based on time discretization, we transform the HTRA problem into a time-independent series-system reliability problem which can be solved by searching the bound-most-probable point (BMPP) at all discrete time instants. Then, with the BMPPT, the lower and upper bounds of the time-variant limit-state function are linearized into two Gaussian processes. Finally, the expansion optimal linear estimation and Monte Carlo simulation are performed to estimate the time-variant reliability. To avoid excessive BMPP searches, the active learning Kriging is used to approximate the BMPPT. Two numerical examples including a cantilever beam, and a 10-bar truss, and two engineering applications of the solid rocket engine shell and the rocket inter-stage structure are investigated, and the results reveal that the proposed method can solve the HTRA problems with high accuracy and efficiency.

The operational safety of high-speed trains traversing ballasted bridges is contingent upon the prevention of the ballast destabilization, which can interrupt load transfer from the rail to the bridge. Current design regulations indirectly address this limit-state by specifying a threshold value for the vertical acceleration of the superstructure. This value represents the condition at which the inertial forces induced by train passage exceed the resistive forces. However, this approach is based on limited experimental data and the influence of numerous parameters remains unexplored. As a result, reliability analyses pertaining to running safety are hampered by a lack of knowledge, leading to greater epistemic uncertainties. In this study, the impact of such uncertainties on this dynamic system is investigated using surrogate-based Imprecise Structural Reliability Analysis (ISRA). For this purpose, parametric probability boxes are used to represent lower and upper bounds of the cumulative distribution function for basic random variables with epistemic uncertainties and surrogate models are adaptively trained to reduce computational costs. The obtained results show that neglecting the influence of epistemic uncertainties can lead to permissible operating train speed higher than the speed corresponding to the desired reliability level. In this study, an overestimation of about 13% was observed on average. Furthermore, the rough analyses carried out show that taking epistemic uncertainties into account can lead to a reduction of the system characteristic safety factor by up to 30%. This significant reduction underlines the importance of expanding the available knowledge on the phenomenon of ballast instability.

Finite Element Simulations in solid mechanics are nowadays common practice in engineering. However, considering uncertainties based on this powerful method remains a challenging task, especially when nonlinearities and high stochastic dimensions have to be taken into account. Although Monte Carlo Simulation (MCS) is a robust method, the computational burden is high, especially when a nonlinear finite element analysis has to be performed behind each sample. To overcome this burden, several “model-order reduction” techniques have been discussed in the literature. Often, these studies are limited to quite smooth responses (linear or smooth nonlinear models and moderate stochastic dimensions).

This paper presents systematic studies of the promising Sparse Polynomial Chaos Expansion (SPCE) method to investigate the capabilities and limitations of this approach using MCS as a benchmark. A nonlinear damage mechanics problem serves as a reference, which involves random fields of material properties. By this, a clear limitation of SPCE with respect to the stochastic dimensionality could be shown, where, as expected, the advantage over MCS disappears.

As part of these investigations, options to optimise SPCE have been studied, such as different error measures and optimisation algorithms. Furthermore, we have found that combining SPCEs with sensitivity analysis to reduce the stochastic dimension improves accuracy in many cases at low computational cost.

This paper uses statistical linearization to analyze a state space system controlled by a class of semi-active on-off control. The control input is proportional to a feedback state, while the coefficient of proportionality is switched based on the sign of the product of feedback state and a control state. The explicit simultaneous equations are derived to obtain the system's statistics. The usefulness of the approach is demonstrated through 4 examples. In the example of vibration isolation system, the analytical best performance of skyhook control is found. In the example of mass damper system, the analytical best performance of groundhook control is presented. In the example of quarter-car suspension system, the skyhook-groundhook control is optimized. At last, in the example of 4-mass system, the clipped-linear-quadratic-regulator control is demonstrated.

This study proposes an innovative Two-phase method, based on the Langlie method and the D-optimality criterion, to overcome the intrinsic shortcomings of the staircase method used in estimating the fatigue limit distribution. This paper identifies the current challenges and provides an overview of existing solutions, setting the goal of developing an efficient data collection protocol. It further explains the application of D-optimality criterion and describes the Two-phase protocol, accompanied by a relevant example. The most significant advantage of this approach is its minimal requirement for pre-test information. A simulation-based study was executed to analyze the sensitivity of the input parameters and compare the effectiveness of the proposed method with the traditional staircase and Bayesian optimized method. The numerical simulations reveal that the proposed method offers improved estimation performance for the mean and standard deviation of the fatigue limit distribution, even with minimal pre-test information.

Failure-probability (FP) global sensitivity (FP-GS) can measure the average effect of random input on FP, and it is significant in reliability-based design optimization. The key of FP-GS is estimating the conditional FPs on the different realizations of random inputs, which usually requires a time-demanding double-loop structure analysis. This paper originally discovers a reliability updating perspective to efficiently estimate FP-GS, in which all required conditional FPs can be approximated by the posterior FPs based on reliability updating strategy, and the double-loop structure is avoided in estimating the conditional FPs required by FP-GS. In the proposed novel reliability updating based FP-GS analysis method, all conditional FPs required by FP-GS are derived with the likelihood function on the given quasi observations, and they can be simultaneously estimated by a single random input sample set for analyzing the unconditional FP. To reduce the computational cost further, adaptive Kriging model is updated to replace the performance function for efficiently estimating the unconditional FP and all conditional FPs required by FP-GS. Several examples are presented to verify the efficiency and accuracy of the proposed novel reliability updating method for estimating the FP-GS.

Various metamodeling approaches are applied in conjunction with Monte Carlo simulation and or the second moment-based method for reliability analyses of underground tunnels. However, there is no study regarding the suitability of such metamodels for reliability analyses of tunnels. An attempt is made here to make a comparative assessment of different metamodeling approaches for tunnel reliability analysis to comprehend the performances of various metamodels from the subset of machine learning methods. In doing so, the least square method based polynomial response surface method (RSM), mostly used in tunnel reliability analyses, and its improved version i.e., moving least square method-based RSM, are taken up for comparison. Further, the most successful empirical risk minimization-based Kriging model and the structural risk minimization principle-based support vector regression model are considered for comparison. Also, the sparse Bayesian regression found to be useful in solving various structural reliability analysis problems, is taken up for the present comparative study. Two numerical examples demonstrate the effectiveness of the selected metamodels in tunnel reliability analysis. It has been generally noted that the Kriging and SVR-based metamodels outperform in reliability estimates of underground tunnels.