Random/Cognitive Hybrid Uncertainty Analysis of Ship Multitasking Cabin Layout

A new hybrid uncertainty analysis method and its application to squeal analysis with random and interval variables

A comparative study of two interval-random models for hybrid uncertainty propagation analysis

Multiobjective robust optimization for crashworthiness design of foam filled thin-walled structures with random and interval uncertainties

Reliability analysis of motion mechanism under three types of hybrid uncertainties

For robust design optimization (RDO) of electrical machines, cases with random uncertainty and interval uncertainty are generally investigated separately. Accordingly, the performance fluctuation analysis under uncertainty is based on random method and interval method respectively. However, the problem with hybrid uncertainties can also be met yet rarely researched. Under this circumstance, the uncertainty analysis methods for a single type of uncertainty may no longer be applicable, which challenges the robust optimization conduction. For effective RDO of electrical machines with hybrid uncertainties, this article presents a robust optimizer based on evolutionary algorithms and the polynomial chaos Chebyshev interval (PCCI) method. The PCCI method is utilized for effectively modeling the fluctuations caused by the hybrid uncertainty with a small number of samples. As additional enhancements, the filtering strategy for the algorithm with deterministic constraints is proposed to reduce the solutions that require robustness analysis in each iteration and accelerate the optimization further while not affecting the global convergence ability. A design example of a brushless DC motor considering hybrid uncertainties is analyzed and optimized. The results confirm the feasibility of the proposed method.

The present study investigates the hybrid reliability modeling of structures in which the inputs contain both random variables and interval variables. Hybrid uncertainty is divided into three categories, including random variables mixed with random variables, interval variables mixed with interval variable, and random variables mixed with interval variables. In order to perform the reliability analysis of structural systems, first, the Bayes method is proposed in the present study to obtain distribution parameters of random variables. Moreover, the self‐sample method is introduced to obtain the interval boundaries based on the least available measuring data. Then, the reliability models are established for three situations and the reliability indices are defined and derived accordingly. The abovementioned three types of reliability indices outline the general situation of structural systems. Finally, the specific calculation process is described in details through different examples. Furthermore, the accuracy and efficiency of the proposed method is discussed by comparing the results obtained from the Monte Carlo simulation and those of other methods. The obtained results indicate that the performance of the proposed model in solving reliability modeling problems is better.

In the traditional uncertainty-based analyses and optimizations of the automotive powertrain mounting system (PMS), uncertain parameters are usually treated as either random variables or interval variables. In this article, an efficient analysis and optimization method is proposed for PMS designs with hybrid random and interval uncertainties. An efficient analysis method, named the hybrid perturbation–finite difference method (HPFDM), is first derived to calculate the uncertain responses of the natural frequencies (NFs) and the decoupling ratios (DRs) of the PMS. Then, an optimization model of the PMS with hybrid uncertainties is established based on the HPFDM, where the uncertain responses of the relevant NFs and DRs are taken to create optimization constraints and optimization objectives. With the aid of the HPFDM, the nested optimization model can be solved efficiently. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.

Hybrid uncertain analysis for structural–acoustic problem with random and interval parameters

Probabilistic interval analysis for structures with uncertainty

Concerning the issue of high-dimensions, hybrid uncertainties of randomness and intervals including implicit and highly nonlinear limit state function, reliability analysis based on the hybrid uncertainty reliability mode combining with back propagation neural network (HU-BP neural network) is proposed in this paper. Random variables and interval variables are as input layer of the neural network, after the training and approximation of the neural network, the response variables are obtained through the output layer. Reliability index is calculated by solving the optimization model of the most probable point (MPP) searching in the limit state band. Two numerical cases are used to demonstrate the method proposed in this paper, and finally the method is employed to solving an engineering problem of the aerospace friction plate. For this high nonlinear, small failure probability problem with interval variables, this method could achieve a good analysis result.

Time response of structure with interval and random parameters using a new hybrid uncertain analysis method

Hybrid uncertain analysis for steady-state heat conduction with random and interval parameters

In practical engineering, it is a cost-consuming problem to consider the time-variant reliability of both random variables and interval variables, which usually requires a lot of calculation. Therefore, a time-variant reliability analysis approach with hybrid uncertain variables is proposed in this paper. In the design period, the stochastic process is discretized into random variables. Simultaneously, the original random variables and the discrete random variables are converted into independent normal variables, and the interval variables are changed into standard variables. Then it is transformed into a hybrid reliability problem of static series system. At different times, the limited state functions are linearized at the most probable point (MPP) and at the most unfavorable point (MUP). The transformed static system reliability problem with hybrid uncertain variables can be solved effectively by introducing random variables. To solve the double-loop nested optimization in the hybrid reliability calculation, an effective iterative method is proposed. Two numerical examples and an engineering example demonstrate the validity of the present approach.

Robust mechanism synthesis with random and interval variables

This paper presents the displacement, stress and reliability analysis of structures with a mixture of random and interval parameters under uncertain static loads. The structural displacement and stress responses are random interval variables when some structural parameters/loads are modelled as random variables and others are considered as intervals. The random interval perturbation method and random interval moment method are employed to predict the random interval structural response. The structural reliability is not a deterministic value but an interval as the structural responses are random interval variables. The expressions for lower and upper bounds of reliability index, probability of failure and reliability of structural elements and systems are then developed by using the combination of the structural reliability theory and interval approach. Truss and frame structures are used as examples to demonstrate the validity and feasibility of the presented methods. The probabilistic and interval characteristics of structural static response and reliability are investigated and some useful conclusions are given.