The design and integration of suspension parameters directly affects the riding quality of a rail vehicle. This study is intended to develop an approach to the optimization of suspension parameters of rail vehicles based on a virtual prototype Kriging model. To construct the virtual prototype Kriging model, a virtual prototype model of a rail vehicle and its suspension system was established based on a vertical model for its dynamics and using virtual prototype software. A virtual prototype Kriging model of a rail vehicle based on riding quality was also proposed, in which the training sample was obtained as different combinations of suspension parameters using the virtual prototype and dynamics simulations based on the design of experiments method. On this basis, an optimization model of the suspension parameters was established, in which the objective function was the Kriging model of the riding quality index. The optimized combination of suspension parameters was determined using the Multi-Island Genetic Algorithm. The dynamics simulation results before and after optimization for different rail profiles indicated that the riding quality was significantly improved, which demonstrated the universality and effectiveness of this approach.

The spatial correlation function (SCF) is an important part of the Kriging surrogate model that describes the sample data structure, and the SCF affects the fitting accuracy of the Kriging surrogate model directly. In a Kriging surrogate model, a single SCF is typically selected to describe the sample data structure, which may cause sample information loss and fitting error. A new Kriging surrogate model for combination forecasting (CF-Kriging) was constructed by integrating of linear weighted approach based on the combination forecasting method, in which the differences in the sample information described by the diverse SCFs for the same sample data structure were considered. The integrity of the sample information of the CF-Kriging model was improved using single-SCF Kriging surrogate models as sub-models and considering the minimum mean absolute percentage error as the improved target for the fitting accuracy. The effectiveness of the CF-Kriging surrogate model was demonstrated using four test functions and two engineering problems, which indicated that the CF-Kriging surrogate model could effectively improve the fitting accuracy and the fitting stability of an ordinary Kriging surrogate model.

This research is intended to develop a suspension parameter optimization approach based on a virtual prototype surrogate model of rail vehicles considering the coupling effects of suspension parameters. In order to analyze the effects on the dynamic indexes, which were affected by the suspension parameters, a virtual prototype model of a rail vehicle was established. The indexes of lateral ride quality and motion stability were obtained under different combinations of suspension parameters by design of experiment and simulation of virtual prototype. For constructing objective function of multi-objective optimization model for suspension parameters, the suspension parameters that have significant effects on ride quality and motion stability simultaneously were taken as the design variables, and thereafter Kriging models of lateral ride quality index, derailment coefficient, and reduction ratio of wheel load were obtained. On this basis, the multi-objective optimization model of suspension parameters was established, in which the objective function was combined with the three Kriging models. Then, the Pareto optimal solution set and concrete value of suspension parameters were sought using the NSGA-II algorithm. The dynamic simulation results indicated that both ride quality and motion stability of the rail vehicle had been improved after the multi-objective optimization of suspension parameters.

The deep-water pipeline connector (DPC) is a key piece of equipment for the connection of multiple facilities located in different positions of the subsea production system. Its sealing reliability affects the safety of the production system directly during oil and gas exploration. Although the reliability assessment methods of the DPC have been investigated, previous studies have mostly been carried out under a single mechanical field. To determine the DPC reliability considering thermo-mechanical coupling, this paper establishes random load models of working pressure and temperature by using the Gaussian function, and the stochastic finite element model of the DPC is constructed to obtain the sealing performance under coupling conditions. A Kriging–Sobol sensitivity analysis method is developed to obtain the main variables influencing the sealing performance for the purpose of decreasing the computational cost of the ordinary sensitivity analysis. A reliability assessment approach based on the cross entropy-importance sampling-Kriging method is introduced to analyze the DPC reliability, and a sealing reliability assessment method of DPC under thermo-mechanical coupling conditions is finally formed. An engineering case is taken to verify the effectiveness of the proposed method. The results show that the reliability analysis accuracy of the proposed method is almost agreed with the Monte Carlo method, but the computational cost can be reduced 85.61%, which indicates that the proposed method provides designers with a fast method with an acceptable computational cost to assess the reliability of the DPC connector under coupling conditions.

The VX gasket is an important part of the wellhead connector for a subsea Christmas tree. Optimization of the gasket’s structure can improve the connector’s sealing performance. In this paper, we develop an optimization approach for the VX gasket structure, taking into consideration working load randomness, based on the Kriging surrogate model-NSGA-II algorithm. To guarantee the simulation accuracy, a random finite element (R-FE) model of the connector’s sealing structure was constructed to calculate the gasket’s sealing performance under random working load conditions. The working load’s randomness was simulated using the Gaussian distribution function. To improve the calculation efficiency of the sealing performance for individuals within the initial populations, Kriging surrogate models were constructed. These models accelerated the optimization speed, where the training sample was obtained using an experimental method design and the constructed R-FE model. The effectiveness of the presented approach was verified in the context of a subsea Christmas tree wellhead connector, which matched the 20'' casing head. The results indicated that the proposed method is effective for VX gasket structure optimization in subsea connectors, and that efficiency was significantly enhanced compared to the traditional FE method.

In order to enhance the pertinency of suspension parameters optimization for a rail vehicle, this research intends to reveal the influence rule of suspension parameters on dynamic performance using sensitivity analysis method based on a virtual prototype response surface method model. Dynamic indexes in different combinations of suspension parameters are simulated using the virtual prototype, which is established using SIMPACK based on a multi-body dynamic model. And the response surface method models of dynamic indexes are constructed with the training samples, which are composed of the simulated dynamic indexes and the corresponding suspension parameters. The sensitivity analysis method is presented, taking a derivative with respect to the response surface method model. Then, the sensitivity analysis results of suspension parameters on dynamic performance of a rail vehicle are obtained in less computation time using the presented sensitivity analysis method. The results indicate that different suspension parameters affect different dynamic indexes of a rail vehicle, and there is a mutual coupling between the lateral stability, derailment coefficient, and wheel reduction rate.