A Probability-Interval Hybrid Uncertainty Analysis Method Based on the Arbitrary Polynomial Chaos-Chebyshev Interval Expansion

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

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

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

Data-driven polynomial chaos-interval metamodel for dynamics and reliability analysis under hybrid uncertainty

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.

Reliability analysis of motion mechanism under three types of hybrid uncertainties

Dynamic response analysis of structure with hybrid random and interval uncertainties

This paper proposes a methodology for sampling-based design optimization in the presence of interval variables. Assuming that an accurate surrogate model is available, the proposed method first searches the worst combination of interval variables for constraints when only interval variables are present or for probabilistic constraints when both interval and random variables are present. Due to the fact that the worst combination of interval variables for probability of failure does not always coincide with that for a performance function, the proposed method directly uses the probability of failure to obtain the worst combination of interval variables when both interval and random variables are present. To calculate sensitivities of constraints and probabilistic constraints with respect to interval variables by the sampling-based method, the behavior of interval variables at the worst case is defined by utilizing the Dirac delta function. Then, Monte Carlo simulation is applied to calculate constraints and probabilistic constraints with the worst combination of interval variables, and their sensitivities. The important merit of the proposed method is that it does not require gradients of performance functions and transformation from X-space to U-space for reliability analysis after the worst combination of interval variables is obtained, thus there is no approximation or restriction in calculating the sensitivities of constraints or probabilistic constraints. Numerical results indicate that the proposed method can search the worst case probability of failure with both efficiency and accuracy and that it can perform design optimization with mixture of random and interval variables by utilizing the worst case probability of failure search.

This paper proposes a methodology for sampling-based design optimization in the presence of interval variables. Assuming that an accurate surrogate model is available, the proposed method first searches the worst combination of interval variables for constraints when only interval variables are present or for probabilistic constraints when both interval and random variables are present. Due to the fact that the worst combination of interval variables for probability of failure does not always coincide with that for a performance function, the proposed method directly uses the probability of failure to obtain the worst combination of interval variables when both interval and random variables are present. To calculate sensitivities of the constraints and probabilistic constraints with respect to interval variables by the sampling-based method, behavior of interval variables at the worst case is defined by the Dirac delta function. Then, Monte Carlo simulation is applied to calculate the constraints and probabilistic constraints with the worst combination of interval variables, and their sensitivities. A merit of using an MCS-based approach in the X-space is that it does not require gradients of performance functions and transformation from X-space to U-space for reliability analysis, thus there is no approximation or restriction in calculating sensitivities of constraints or probabilistic constraints. Numerical results indicate that the proposed method can search the worst case probability of failure with both efficiency and accuracy and that it can perform design optimization with mixture of random and interval variables by utilizing the worst case probability of failure search.

Identifying the optimal cabin layout is an important way to improve the efficiency of ship systems and ensure the efficient circulation of personnel and materials. The ship task state refers to the state maintained by the joint actions of ship machinery and equipment, cargo, and personnel when facing different jobs and tasks during operation. A cabin layout that facilitates multitasking states can improve the efficiency of collaboration between systems and ensure the operation of the ship. The demand for human flow and logistics is different in multitasking states. To express the demand in mathematical form, there is a certain random uncertainty in the numerical quantification of the demand. Thus, to better meet the needs of different states, the coefficient values of each state can be integrated using special methods. Ensuring values’ initial preference to the greatest extent inevitably produces a degree of cognitive uncertainty. Therefore, uncertainty analysis is necessary for cabin layout design to be used for multitasking states. In this paper, a deterministic optimization platform of cabin layout in multitasking states is obtained. Adjacent and circulating strength coefficients are obtained through numerical quantization of the demand for human flow and logistics. The random uncertainty in the input values of two coefficients was represented by random variables, and the cognitive uncertainty was represented by interval variables. In order to solve the problem of two types of variables, a random-interval hybrid uncertainty model was established. Through random intervalization and interval randomization, three cases, of random variables, interval variables, and random variables and interval variables, were studied. The probability distribution of the model function was used to evaluate the influence of different compositions of uncertainty parameters on the robustness of the cabin layout scheme. The necessity and effectiveness of uncertainty analysis in multitasking cabin layout are discussed below.

Response analysis of an accelerating unbalanced rotating system with both random and interval variables

A sensitivity analysis method to evaluate the impacts of random and interval variables on the probability box

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.

In many practical engineering problems, distributions of some random variables may not be precisely known or even only the variation ranges can be given, due to which the Reliability-Based Design Optimization (RBDO) methods cannot be applied directly. In this paper, a hybrid RBDO model is established to deal with hybrid uncertainties including random variables with interval distribution parameters and coexistence of random and interval variables. The hybrid uncertainties lead to an interval of reliability, thus giving rise to a triple-loop optimization problem, which burdens the computational effort significantly. Therefore, an extended Sequential Optimization and Reliability Assessment (SORA) method is proposed, where the worst-case point over the bounded domain of interval uncertainty is employed to replace reliability constraint with deterministic optimization. Therefore, the hybrid RBDO problem can be efficiently solved by a series of deterministic optimization procedures. The efficiency and accuracy of the proposed method are illustrated through several numerical examples.

Error modelling and motion reliability analysis of a multi-DOF redundant parallel mechanism with hybrid uncertainties