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The multi-objective optimum design of stationary flat-plate solar collectors under probabilistic uncertainty is considered. The clear day solar beam radiation and diffuse radiation at the location of the solar collector are estimated. Three objectives are considered in the optimization problem formulation: maximization of the annual average incident solar energy, maximization of the lowest month incident solar energy, and minimization of the cost. The game theory methodology is used for the solution of the three objective constrained optimization problem. A parametric study is conducted with respect to changes in the standard deviation of the mean values of random variables and probability of constraint satisfaction. The present study is expected to help designers in creating optimized solar collectors based on specified requirements. [DOI: 10.1115/1.4002133]

In this paper, based on Shcaff residual strength theory, the effect of abrasion is considered while the strength degradation of parts is studied. Based on the maximum abrasion, a stress-strength interference model considering strength degradation and abrasion is established. Then, the reliability and reliability sensitivity of vehicle parts are analyzed by using the first-order second moment and random perturbation method, and they are verified by the Monte Carlo method. The fitting results are good. It provides a more practical analysis method for engineering analysis. At the same time, based on the correlation between variables, the effect of correlation coefficient on the reliability of vehicle tension rod is discussed. The reliability index and reliability of the correlation coefficient of vehicle tension rod are analyzed, and the reliability sensitivity of the correlation coefficient is also analyzed. At the same time, the gradient reliability of vehicle tension rod geometry is analyzed based on strength degradation theory. Found that if the influence of multiple correlation coefficients on reliability is increased (decreased), then the influence of parameter correlation on reliability will further increase (decrease). On the contrary, if the influence of multiple correlation coefficients on reliability increases and decreases, the reliability change needs to be analyzed specifically. In other words, the influence of multiple correlation coefficients on reliability will produce superposition effect. It provides a new direction for the study of correlation coefficient. [ABSTRACT FROM AUTHOR]

Fuzzy analysis can be used to model the uncertainties present in structures. In particular, the fuzzy finite element method can be used to find the response of structures (isotropic or composite) involving uncertainties. For the integrated structural control of a system, the design of a fuzzy optimal controller is explored. In the past few years, some researchers have tried to design a fuzzy optimal controller based on the Takagi and Sugeno model. In this work, a different (new) approach is proposed for the design of a controller in the context of fuzzy optimal control theory. In most practical applications, the structural and material parameters vary considerably and are subject to uncertainties, mainly due to the uncontrollable aspects associated with the manufacturing and assembly of composite materials. These uncertainties, in many cases, cannot be modeled probabilistically because the probability distributions of the uncertain parameters are not usually known. Also, in some situations, the parameters are known only in linguistic form. A fuzzy finite element approach has been developed for the analysis of structures with fuzzy parameters. Using the deterministic optimal control theory as a basis, a fuzzy optimal control theory is developed so that the controller can be used to act as either a regulator or a tracking system. The control of a planar truss is presented to demonstrate the feasibility and applicability of the methodology presented.

A new hybrid genetic algorithm is presented for the solution of mixed-discrete nonlinear design optimization. In this approach, the genetic algorithm (GA) is used mainly to determine the optimal feasible region that contains the global optimum point, and the hybrid negative subgradient method integrated with discrete one-dimensional search is subsequently used to replace the GA to find the final optimum solution. The hybrid genetic algorithm, combining the advantages of random search and deterministic search methods, can improve the convergence speed and computational efficiency compared with some other GAs or random search methods. Several practical examples of mechanical design are tested using the computer program developed. The numerical results demonstrate the effectiveness and robustness of the proposed approach.

Many engineering optimization problems can bc considered as multistage decision-making problems. If the system involves uncertainty in the form of linguistic parameters and vague data, a fuzzy approach is to be used for its description. The solution of such problems can be accomplished through fuzzy dynamic programming. However, most of the existing fuzzy dynamic programming algorithms cannot deal with mixed-discrete design variables in the optimization of mechanical systems containing fuzzy information. They often assumed that a fuzzy goal is imposed only on the final state for simplicity, the values of fuzzy goal and other parameters need to be predefined, and an optimal solution is obtained in the continuous design space only. To better reflect the nature of uncertainties present in real-life optimization problems, a mixed-discrete fuzzy dynamic programming (MDFDP) approach is proposed in this work for solving multistage decision-making problems in mixed-discrete design space with a fuzzy goal and a fuzzy state imposed on each stage. The method can also be extended to solve general mixed-discrete fuzzy nonlinear programming problems if their corresponding crisp problems can be solved using dynamic programming approaches. The feasibility and versatility of the proposed method are illustrated by considering the design of a four-bar truss and the reliability-based optimization of a gearbox. To the authors' knowledge, this work represents the first fuzzy dynamic programming method reported in the literature for dealing with mixed-discrete optimization problems.

Although much attention has been focused on the development and applications of fuzzy optimization, multiobjective programming, and mixed-discrete optimization methods separately, fuzzy multiobjective optimization problems in mixed-discrete design space have not been addressed in the literature. It is mainly because of the lack of mature and robust theories of mixed-discrete and multiobjective optimization. In most practical applications, designers often encounter problems involving imprecise or fuzzy information, multiple objectives, and mixed-discrete design variables. A new method is presented in which the fuzzy A formulation and game theory techniques are combined with a mixed-discrete hybrid genetic algorithm for solving mixed-discrete fuzzy multiobjective programming problems. Three example problems, dealing with the optimal designs of a two-bar truss, a conical convective spine, and a 25-bar truss, demonstrate that the method can be flexibly and effectively applied to various kinds of engineering design problems to obtain more realistic and satisfactory results in an imprecise environment.

The modeling, analysis, and design of large and complex composite structures involve the use of the finite element approach. In most practical applications the structural and material parameters vary considerably and are subject to uncertainties, mainly because of the uncontrollable aspects associated with the manufacturing and assembly of composite materials. In many cases, the probabilistic methods cannot be applied because the probability distributions of the uncertain parameters are not usually known. Also, in some situations the parameters are known only in linguistic form. In this work, the uncertainties encountered in composite structures, which can be described in linguistic terms or in imprecise form, are modeled as fuzzy parameters. A fuzzy finite element analysis technique is developed for the analysis of laminated beams, involving fuzziness, possibly in the boundary conditions as well. The fuzzy beam element can undergo axial, bending, and transverse shear deformations. Using the basic concepts of the deterministic finite element theory, as well as fuzzy computations and fuzzy matrix operations, a fuzzy beam element is developed. The fuzzy beam element is used for the static and eigenvalue analysis of beams involving imprecise data and/or information. A numerical example is presented to demonstrate the feasibility and applicability of the methodology presented.

Fiber-reinforced composite materials have been used very widely and have emerged as a major class of structural materials in recent years. They are either used or being considered for use as substitutes for metals in many weight-critical components in aerospace and other industries. In most practical applications, the material parameters vary considerably and are subject to uncertainties, mainly due to the uncontrollable aspects associated with the manufacturing process. The probabilistic methods cannot be applied easily because the exact probability distributions of the uncertain parameters are not known. Also, in some situations, the parameters of a composite material are known only in linguistic form. Hence, fuzzy concepts are introduced to model the uncertainties encountered in composite materials, which may he described in uncertain terms or in imprecise/linguistic form as fuzzy parameters. When the basic fuzzy arithmetic computations, such as fuzzy addition, subtraction, multiplication, and division, and fuzzy square root and fuzzy trigonometry computations are used, different composite material mechanics expressions are explored, and the fuzzy analysis of fiber-reinforced composite material mechanics is presented. Numerical examples are given to demonstrate the feasibility and applicability of the approach. Other types of uncertainties, such as interval and probabilistic parameters, can also be accommodated with the approach.