Full-Scale Train-to-Train Impact Test and Multi-Body Dynamic Simulation Analysis

When a train crashes with another train at a high speed, it will lead to significant financial losses and societal costs. Carrying out a train-to-train crash test is of great significance to reproducing the collision response and assessing the safety performance of trains. To ensure the testability and safety of the train collision test, it is necessary to analyze and predict the dynamic behavior of the train in the whole test process before the test. This paper presents a study of the dynamic response of the train in each test stage during the train-to-train crash test under different conditions. In this study, a 1D/3D co-simulation dynamics model of the train under various load conditions of driving, collision and braking has been established based on the MotionView dynamic simulation software. The accuracy of the numerical model is verified by comparing with a five-vehicle formations train-to-train crash test data. Sensitivities of several key influencing parameters, such as the train formation, impact velocity and the vehicle mass, are reported in detail as well. The results show that the increase in the impact velocity has an increasing effect on the movement displacement of the vehicle in each process. However, increasing the vehicle mass and train formation has almost no effect on the running displacement of the braking process of the traction train. By sorting the variables in descending order of sensitivity, it can be obtained that impact speed > train formation > vehicle mass. The polynomial response surface method (PRSM) is used to construct the fitting relationship between the parameters and the responses.

Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling

Polynomial Regression Surface (PRS) is a commonly used surrogate model for its simplicity, good interpretability, and computational efficiency. The performance of PRS is largely dependent on its basis functions. With limited samples, how to correctly select basis functions remains a challenging problem. To improve prediction accuracy, a PRS modeling approach based on multitask optimization and ensemble modeling (PRS-MOEM) is proposed for rational basis function selection with robustness. First, the training set is partitioned into multiple subsets by the cross validation method, and for each subset a sub-model is independently constructed by optimization. To effectively solve these multiple optimization tasks, an improved evolutionary algorithm with transfer migration is developed, which can enhance the optimization efficiency and robustness by useful information exchange between these similar optimization tasks. Second, a novel ensemble method is proposed to integrate the multiple sub-models into the final model. The significance of each basis function is scored according to the error estimation of the sub-models and the occurrence frequency of the basis functions in all the sub-models. Then the basis functions are ranked and selected based on the bias-corrected Akaike’s information criterion. PRS-MOEM can effectively mitigate the negative influence from the sub-models with large prediction error, and alleviate the uncertain impact resulting from the randomness of training subsets. Thus the basis function selection accuracy and robustness can be enhanced. Seven numerical examples and an engineering problem are utilized to test and verify the effectiveness of PRS-MOEM.

Reliability and reliability-based sensitivity analysis of self-centering buckling restrained braces using meta-models

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.

Thermal optimization research of oil-immersed transformer winding based on the support machine response surface

In this paper, the CFD (computational fluid dynamics) model is established for the low voltage winding region of an oil-immersed transformer according to the design parameters, and the detailed temperature distribution within the region is obtained by numerical simulation. On this basis, the RSM (response surface methodology) is adopted to optimize the structure parameters with the purpose of minimizing the hot spot temperature. After a sequence of designed experiments, the second-order polynomial response surface and the SVM (support vector machine) response surface are established respectively. The analysis of their errors shows that the SVM response surface can be better used to fit the approximation. Finally, the PSO (particle swarm optimization) algorithm is employed to get the optimal structure parameters of the winding based on the SVM response surface. The results show that the optimization method can significantly reduce the hot spot temperature of the winding, which provides a guiding direction for the optimal design of the winding structure of transformers.

Design of a Segmented Mirror with a Global Radius of Curvature Actuation System: Contributions of Multiple Surrogates

Due to fabrication difficulties, separately-polished segmented mirrors cannot meet the co-phasing surface shape error requirements in the segmented telescope system. Applying the global radius of curvature (GRoC) actuation system for the individual segments has become an effective solution in space-based telescopes. In this paper, we designed a segmented mirror with a GRoC actuation system. The direct optimization by numerical simulations has low computational efficiency and is not easy to converge for optimizing the actuation point’s position on the segmented mirror. For this problem, three common surrogates, including polynomial response surface (PRS), radial basis function neural network (RBFNN), and kriging (KRG), were summed to propose the multiple surrogates (MS) which have the higher approximate ability. The surrogates were then optimized through the multi-island genetic algorithm (MIGA), and the segmented mirror met the design requirement. Compared with direct optimization through numerical simulations, the results show that the proposed multiple-surrogate-based optimization (MSBO) methodology saves computational cost significantly. Besides, it can be deployed to solve other complex optimization problems.

Experimental, numerical, and multi-objective optimization investigations on the energy absorption features of single- and bi-layer deep-drawn cups

In this article, the energy absorption features of single- and bi-layer deep-drawn cups (S- and B-cups, respectively) under a quasi-static axial loading are investigated experimentally and numerically. The S-cups were made of 304L stainless steel and explosively welded B-cups were composed of aluminum and 304L stainless steel layers. A multi-objective optimization was performed on specific energy absorption and initial peak force based on the polynomial response surface method. Furthermore, to compare the energy absorption features of deep-drawn cups, two groups of 304L stainless steel tubes (with the same mass or the same height as the S-cups) were axially compressed. The experimental results indicated that the S-cups experienced total energy absorption and mean crush force approximately 24% and 51% greater than those of tubes with the same mass and thickness, respectively. Furthermore, the total efficiency and specific total efficiency of the S-cups were approximately 0.23 and 1.82 times greater than those of tubes with the same height and thickness. Moreover, the energy absorbing effectiveness factor of B-cups was approximately twice of the S-cup.

Selecting the Best Quantity and Variety of Surrogates for an Ensemble Model

Surrogate modeling techniques are widely used to replace the computationally expensive black-box functions in engineering. As a combination of individual surrogate models, an ensemble of surrogates is preferred due to its strong robustness. However, how to select the best quantity and variety of surrogates for an ensemble has always been a challenging task. In this work, five popular surrogate modeling techniques including polynomial response surface (PRS), radial basis functions (RBF), kriging (KRG), Gaussian process (GP) and linear shepard (SHEP) are considered as the basic surrogate models, resulting in twenty-six ensemble models by using a previously presented weights selection method. The best ensemble model is expected to be found by comparative studies on prediction accuracy and robustness. By testing eight mathematical problems and two engineering examples, we found that: (1) in general, using as many accurate surrogates as possible to construct ensemble models will improve the prediction performance and (2) ensemble models can be used as an insurance rather than offering significant improvements. Moreover, the ensemble of three surrogates PRS, RBF and KRG is preferred based on the prediction performance. The results provide engineering practitioners with guidance on the superior choice of the quantity and variety of surrogates for an ensemble.

Fatigue Reliability Analysis of Motor Hanger for High-Speed Train Based on Bayesian Updating and Subset Simulation

In order to more accurately analyze the fatigue reliability of motor hanger for high-speed train and reduce the influence of uncertain factors, a Bayesian statistical method is introduced to propose a novel fatigue reliability analysis method based on Bayesian updating and subset simulation. First, considering the influence of various uncertain parameters on the first principal stress (FPS) of motor hanger, the ANSYS parametric design language (APDL) is used to establish the parametric model. The D-optimal design of experiment is carried out to calculate the FPS of the motor hanger. Second, the experimental data is fitted by the least square method to establish a polynomial response surface function which characterizes the FPS of the motor hanger, and analysis of variance (ANOVA) is carried out. On this basis, the variation trend of the FPS under parameter fluctuation is calculated, and its probability distribution characteristics are obtained. Based on the MATLAB platform, the Bayesian updating method is adopted to correct the probability and statistical characteristics of the FPS to improve the accuracy of prediction. Finally, the subset simulation (SS) method is used to calculate the fatigue failure probability of the motor hanger. The research results show that the proposed method helps to improve the accuracy and efficiency of fatigue reliability analysis.