Arbitrary Distribution Parameters Research Articles

Meta model-based importance sampling combined with adaptive Kriging method for estimating failure probability function

The failure probability function (FPF) can provide the entire effect of the distribution parameter in the concerned region on failure probability (FP), which is important for decoupling the optimal parameter search and constraint analysis in the FP-constrained design optimization. To improve the efficiency of solving the FPF, this paper combines meta model-based importance sampling with adaptive Kriging (Meta-IS-AK). First, based on the theoretical optimal importance sampling density (ISD) for estimating the FP (ISD-FP) at the given distribution parameter, the theoretical optimal ISD for solving FPF (ISD-FPF) is constructed using an integral operator. Then, a Kriging model of the performance function is adaptively trained to establish the quasi-optimal ISD-FPF for approximating the optimal performance function, and a simple rejection sampling (SRS) method is designed to extract the samples of the quasi-optimal ISD-FPF. For recognizing the state of the ISD-FPF sample and completing the IS estimation of FPF, the Kriging model is secondly updated to establish ISD-FPF in the sample pool comprising these ISD-FPF samples. Using the proposed method, the whole FPF corresponding to arbitrary distribution parameters can be obtained using one IS reliability analysis based on the constructed ISD-FPF. Four examples and an application illustrate the advantages of the proposed method.

Interplay of chordwise stiffness and shape on performance of self-propelled flexible flapping plate

The locomotion of a flapping flexible plate with different shapes and non-uniform chordwise stiffness distribution in a stationary fluid is studied numerically. The normalized effective bending stiffness K∗ for three-dimensional plates with arbitrary stiffness distribution and shape parameters is proposed, and the overall bending stiffness of non-uniform plates with different shapes is reasonably characterized. It is found that the propulsion performance in terms of cruising speed and efficiency of the self-propelled flapping plate mainly depends on the effective bending stiffness. Plates with moderate flexibility K∗ show better propulsion performance. Meanwhile, both a large area moment of the plate and a flexible anterior are favorable to significantly improve their propulsive performance. The evolution of vortical structures and the pressure distribution on the upper and lower surfaces of the plate are analyzed, and the inherent mechanism is revealed. These findings are of great significance to the optimal design of propulsion systems with different fins or wings.

Reliability analysis and optimization design on equilibrium elbow

Equilibrium elbow is a key mechanical component in the self-propelled artillery system and the reliability analysis of the component is necessary to the safety of the whole system. In this paper, the equilibrium elbow model is established to analyze the reliability and reliability sensitivity of arbitrary distribution parameters. Three main failure modes and the times of loading action have been taken into account when analyzing the reliability sensitivity. Numerical method for reliability calculation is presented based on four moment method and the reliability sensitivity model of mean and variance values with random structural parameters were established. Based on the results of the reliability sensitivity analysis, reliability robust optimization design has been studied to enhance the reliability of equilibrium elbow and decrease the reliability sensitivity of mean and variance value. Application of the proposed approach could provide a practical routine for mechanical optimization and design.

Design Optimization Method for Composite Components Based on Moment Reliability-Sensitivity Criteria

AbstractIn this paper, a Reliability-Sensitivity Based Design Optimization (RSBDO) methodology for the design of the ceramic matrix composites (CMCs) components has been proposed. A practical and efficient method for reliability analysis and sensitivity analysis of complex components with arbitrary distribution parameters are investigated by using the perturbation method, the respond surface method, the Edgeworth series and the sensitivity analysis approach. The RSBDO methodology is then established by incorporating sensitivity calculation model into RBDO methodology. Finally, the proposed RSBDO methodology is applied to the design of the CMCs components. By comparing with Monte Carlo simulation, the numerical results demonstrate that the proposed methodology provides an accurate, convergent and computationally efficient method for reliability-analysis based finite element modeling engineering practice.

Frequency Reliability-Based Robust Design of the Suspension Device of a Jarring Machine with Arbitrary Distribution Parameters

The frequency reliability with arbitrary distribution parameters in the stochastic dynamic structure system of practical engineering and its related theories were studied deeply in the paper. The frequency reliability method of avoiding resonance was proposed by mechanical dynamics, stochastic finite element method, and reliability theory. Then the frequency reliability formula with arbitrary distribution parameters was deduced through Edgeworth series method. Furthermore, the frequency reliability sensitivity method was presented based on the frequency reliability research, which provided a preliminary efficient way to analyze how each random parameter contributed to the system reliability. Moreover, the frequency reliability-based robust design method of the stochastic dynamic structure system was obtained by robust and optimization technology on the basis of frequency reliability and sensitivity method, which helped designers to establish acceptable parameter values and to determine the fluctuations of the parameters for the safe operations. Meanwhile, a numerical example of the suspension device of a jarring machine with arbitrary distribution parameters was provided and studied, the numerical results were in agreement with practice, which demonstrated the efficiency and accuracy of the proposed methods.

Dynamic Reliability Sensitivity Design of Cutting Tool with Arbitrary Distribution Parameters

The variation rules of strength, load, and reliability of cutting tool are studied with a change in time, and a model is established for dynamic reliability of cutting tool under the random load acting. By combining the theory of reliability design with the method of sensitivity analysis, the computational method of dynamic reliability sensitivity design with arbitrary distribution parameter is proposed based on the methods Edgeworth and perturbation, and the problem of dynamic reliability sensitivity design of cutting tool distributed arbitrary distribution is solved as well as the variation rules of dynamic reliability sensitivity are given. The variation of reliability is studied as design parameters change a little, which provides theoretical data for dynamic reliability design of cutting tool

Reliability Design of Car Suspension Coil Spring Based on Maximum Entropy Method

A practical and effective numerical method of reliability design with arbitrary distribution parameters is proposed in the paper. And techniques from the maximum entropy method, the reliability design theory and probabilistic engineering design are employed to present an approach for the reliability design with arbitrary distribution parameters. Therefore maximizing the entropy of the state equation distribution should lead to the least biased estimate of its form, which helps us analyze the reliability design of automobile components from an elementarily.

Dynamic Reliability Sensitivity Design of Mechanical Components with Arbitrary Distribution Parameters

The variation rules of strength, load, and reliability of mechanical components are studied with a change in time, and a model is established for dynamic reliability of mechanical components under the random load acting. By combining the theory of reliability design with the method of sensitivity analysis, the computational method of dynamic reliability sensitivity design with arbitrary distribution parameter is proposed based on the methods Edgeworth and perturbation, and the problem of dynamic reliability sensitivity design of mechanical components distributed arbitrary distribution is solved as well as the variation rules of dynamic reliability sensitivity are given. The variation of reliability is studied as design parameters change a little, which provides theoretical data for dynamic reliability design of mechanical components.

Reliability-based sensitivity of mechanical components with arbitrary distribution parameters

This paper presents a reliability-based sensitivity method for mechanical components with arbitrary distribution parameters. Techniques from the perturbation method, the Edgeworth series, the reliability-based design theory, and the sensitivity analysis approach were employed directly to calculate the reliability-based sensitivity of mechanical components on the condition that the first four moments of the original random variables are known. The reliability-based sensitivity information of the mechanical components can be accurately and quickly obtained using a practical computer program. The effects of the design parameters on the reliability of mechanical components were studied. The method presented in this paper provides the theoretic basis for the reliability-based design of mechanical components.

Research on New Numerical Calculation Method for Reliability of Mechanical Strength Based on Blind Number Theory

The uncertainty variable in mechanical design is expressed in blind number and the relation among variables is expressed in the operation rule of blind number; By combining the reliability design theory with blind number calculating method, the reliability of the mechanical elements with arbitrary distribution parameters and discrete test data is discussed; and a numerical method for mechanical reliability based on blind numbers is presented. Besides, the typical examples show that the method is reasonable and effective.

Reliability-Based Sensitivity Design of Mechanical Components with Arbitrary Distribution Parameters

In the reliability-based analysis of mechanical joints, as each factor has different effect on the failure of mechanical joints, the effects of design parameters on reliability of the mechanical joints are determined with the reliability-based sensitivity analysis method. Furthermore, the reliability of mechanical joints can be effectively designed. As a matter of fact, if a change of a certain random parameter has great effect on the reliability of mechanical joints, the parameter must be strictly controlled in the course of design and manufacture to ensure reliability. Whereas if a change of a certain random parameter has unobvious effect on the reliability of mechanical joints, it can be treated as a deterministic value to reduce the complexity of the analysis. In this paper, based on the reliability design theory, the sensitivity analysis method and the fourth moment technique, the reliability sensitivity of the mechanical joints with arbitrary distribution parameters is extensively discussed and a numerical method for reliability sensitivity design is presented. The variation regularities of reliability sensitivity are obtained and the effects of design parameters on reliability of the mechanical joints are studied. The method presented in this paper provides reasonable and necessary reliability basis for the design, manufacture, use and evaluation of the mechanical joints.

Robust Reliability Design of Banjo Flange With Arbitrary Distribution Parameters

The perturbation method, the Edgeworth series, the reliability-based optimization, the reliability sensitivity technique, and the robust design are employed to present a practical and effective approach for the robust reliability design of the Banjo flange with arbitrary distribution parameters on the condition of known first four moments of original random variables. The theoretical formulas of robust reliability design for the Banjo flange with arbitrary distribution parameters are obtained. The respective program can be used to obtain the robust reliability design parameters of the Banjo flange with arbitrary distribution parameters accurately and quickly.

Reliability sensitivity of automobile components with arbitrary distribution parameters

Techniques from the perturbation method, the Edgeworth series, the reliability-based design theory, and the sensitivity analysis approach are employed to present a practical and efficient method for the reliability sensitivity of automobile components with arbitrary distribution parameters. On the condition of first four moments of original random variables known, the reliability sensitivity theory and case studies are researched. The respective program can be used to obtain the reliability sensitivity of automobile components with arbitrary distribution parameters accurately and quickly.

Optimal and Near-Optimal Decisions for Procurement and Allocation of a Critical Resource with a Stochastic Consumption Rate

Management of critical resources having uncertain consumption rates is perhaps the most common challenge encountered by businesses in discharging their numerous functions, e.g., inventory distribution, marketing, finance, production, personnel, etc. It involves making two key decisions optimally: (1) How much of each critical resource must be procured (replenishment quantity decision), and, having procured, (2) How much of each resource should be allocated among the competing entities (allocation decision). The finance/inventory literature thus far has addressed the allocation decision in an optimal fashion using certain ranking algorithms. However, the optimal replenishment decisions have not yet been addressed optimally except under a restrictive assumption called the allocation assumption. Using the illustration of a periodic-review, stochastic-demand, fixed-route, centralized, multi-echelon distribution system in this paper, we propose a non-ranking allocation policy that is faster than those existing in the literature and also develop an optimal replenishment algorithm that is independent of the allocation assumption. Furthermore, we allow our distribution system a greater flexibility than that allowed in the literature thus far--we explicitly permit fixed delivery routes, arbitrary demand distribution parameters, non-identical delivery leadtimes simultaneously with a positive order leadtime. The major empirical contribution of this work is to demonstrate, through an extensive simulation study, that computationally efficient heuristic, called the hybrid heuristic, performs close to optimal, even for the systems with high demand uncertainty. Intriguingly, the bottom line finding of our computational experiments is that while the probability of violation of the allocation assumption itself is very sensitive to the system demand uncertainty, it is relatively insensitive to the expected system inventory costs in the vicinity of the optimal region. We also develop hand- computable theoretical lower and upper bounds on system replenishment quantity and expected system cost per period that require a single Normal distribution table look-up.