Anoop K. Dhingra

Fuzzy multicriteria models for quality function deployment

Abstract An integrated formulation and solution approach to Quality Function Deployment (QFD) is presented. Various models are developed by defining the major model components (namely, system parameters, objectives, and constraints) in a crisp or fuzzy way using multiattribute value theory combined with fuzzy regression and fuzzy optimization theory. The proposed approach would allow a design team to reconcile tradeoffs among the various performance characteristics representing customer satisfaction as well as the inherent fuzziness in the system. In addition, the modeling approach presented makes it possible to assess separately the effects of possibility and flexibility inherent or permitted in the design process on the overall design. Knowledge of the impact of the possibility and flexibility on customer satisfaction can also serve as a guideline for acquiring additional information to reduce fuzziness in the system parameters as well as determine how much flexibility is warranted or possible to improve a design. The proposed modeling approach would be applicable to a wide spectrum of design problems where multiple design criteria and functional design relationships are interacting and/or conflicting in an uncertain, qualitative, and fuzzy way.

A cooperative fuzzy game theoretic approach to multiple objective design optimization

Abstract The utility and applicability of cooperative game theory in an engineering design process is examined. It is shown how game theory may be used as a tool for solving multiple objective optimization (MOO) problems. The concepts in cooperative game theory and fuzzy set theory are combined to yield a new optimization method referred to herein as cooperative fuzzy games. The concept of cooperative fuzzy games can be applied to solve not only well- and ill-structured single and MOO problems, but also preliminary decision making and design problems where only a feasible solution is sought and no objective functions are specified. A completely general formulation capable of solving decision making problems with partly crisp and partly fuzzy objective functions, as well as partly crisp and partly fuzzy constraints is presented. It is shown that existing techniques for solving crisp and fuzzy mathematical programming problems are special cases of this general formulation. The computational procedure is illustrated via an application to a MOO problem dealing with the design of high speed mechanisms.

Reliability and redundancy apportionment using crisp and fuzzy multiobjective optimization approaches

Abstract The reliability of a multistage system with several components in each stage can be improved either by using more reliable components, or by adding redundant components in parallel in any stage. In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting goals. For example, in the reliability based design of a system, the designer may be required to maximize the reliability and minimize the cost, weight or volume. This work considers the problem of reliability allocation for multistage systems with components having time-dependent reliability. Two multiobjective optimization techniques are presented, coupled with heuristic procedures, to solve the mixed integer nonlinear programming problems. A generalization of the problem in the presence of vague information results in an ill-structured reliability apportionment problem. The solution of such multiobjective problems is also presented in the present work using the techniques of fuzzy optimization.

Nonlinear membership functions in multiobjective fuzzy optimization of mechanical and structural systems

An application of fuzzy mathematical programming techniques to multiple objective design problems is presented. Two examples dealing with the multiobjective design of mechanical and structural systems are considered. The concept of a Pareto-optimal and fuzzy Pareto-optimal solution is discussed, and it is shown that the resulting formulation yields Pareto-optimal solutions. The fundamental assumption in fuzzy mathematical programming applications involving the use of linear membership functions is critically examined. Several nonlinear shapes for the membership functions of the fuzzy sets are proposed, consistent with varying perceptions of the designer, and are analyzed to determine their impact on the overall design process. These shapes correspond to what we define as the coefficient of membership satiation. It is seen that optimum designs for both examples are strongly influenced by the sign of the membership satiation coefficient.

OPTIMAL PLACEMENT OF ACTUATORS IN ACTIVELY CONTROLLED STRUCTURES

The paper deals with the influence of actuator/sensor locations and feedback gains on the optimum design of actively controlled structures. Two related problems are addressed. The first is a parametric study dealing with the effect of number and location of actuators on the minimum weight structural design, while satisfying constraints on the closed loop eigenvalues and damping ratios. The second problem addresses the optimal placement of actuators with the damping augmentation provided by the control action being used as the performance criterion. A solution methodology which allows for an integrated determination of feedback gains and actuator/sensor locations while maximizing the energy dissipated by the controller is presented. Since the actuator locations are spatially discrete whereas the feedback gains are continuous, the resulting optimization problem has mixed discrete-continuous design variables. This problem is solved using a hybrid optimization method which is a synergistic blend of artificial...

Closed-form displacement and coupler curve analysis of planar multi-loop mechanisms using Grobner bases

Abstract The displacement analysis problem for planar and spatial mechanisms can be written as a system of algebraic equations in particular as a system of multi-variate polynomial equations. Elimination theory based on resultants and polynomial continuation are some of the methods which have been used to solve this problem. This paper explores an alternate approach, based on Grobner bases, to solve the displacement analysis problem for planar mechanisms. It is shown that the reduced set of generators obtained using Buchbergers algorithm for Grobner bases not only yields the input–output polynomial for the mechanism, but also provides comprehensive information on the number of closures and the relationships between various links of the mechanism. Numerical examples illustrating the applicability of Grobner bases to displacement analysis of 10- and 12-link mechanisms, and determination of coupler curve equation for an 8-link mechanism are presented. It is seen that even though the Grobner bases method is versatile enough to handle finitely solvable as well as over-constrained systems of equations, it can run into computational problems due to rapidly growing numerical coefficients and/or the set of generators. The examples presented show how these difficulties can be overcome by artificially decoupling complex mechanisms to help facilitate their closed-form analysis.

An efficient approach for reliability-based topology optimization

This article presents an efficient approach for reliability-based topology optimization (RBTO) in which the computational effort involved in solving the RBTO problem is equivalent to that of solving a deterministic topology optimization (DTO) problem. The methodology presented is built upon the bidirectional evolutionary structural optimization (BESO) method used for solving the deterministic optimization problem. The proposed method is suitable for linear elastic problems with independent and normally distributed loads, subjected to deflection and reliability constraints. The linear relationship between the deflection and stiffness matrices along with the principle of superposition are exploited to handle reliability constraints to develop an efficient algorithm for solving RBTO problems. Four example problems with various random variables and single or multiple applied loads are presented to demonstrate the applicability of the proposed approach in solving RBTO problems. The major contribution of this article comes from the improved efficiency of the proposed algorithm when measured in terms of the computational effort involved in the finite element analysis runs required to compute the optimum solution. For the examples presented with a single applied load, it is shown that the CPU time required in computing the optimum solution for the RBTO problem is 15–30% less than the time required to solve the DTO problems. The improved computational efficiency allows for incorporation of reliability considerations in topology optimization without an increase in the computational time needed to solve the DTO problem.

DISCRETE AND CONTINUOUS VARIABLE STRUCTURAL OPTIMIZATION USING TABU SEARCH

A memory-based combinatorial optimization technique is adapted into a search procedure for solving single and multiobjective structural optimization problems. This approach, known as tabu search, employs two complementary mechanisms, namely tabu restrictions and aspiration criteria for constraining and guiding the search in the design space. A non-Markovian function utilizing recent search history is used to constrain the search by classifying certain moves as forbidden or tabu whereas a short term memory function, providing strategic forgetting, is used to free up the search process. Numerical results obtained using three different tabu search strategies for single and multiobjective design of structures with discrete-continuous variables are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that, in several instances, the optimum solutions obtained using tabu search outperform the optimum solutions obtaine...

Closed-form displacement analysis of 8, 9 and 10-link mechanisms

Abstract This paper presents closed-form solutions to the displacement analysis problem of planar 8-link mechanisms with 1 degree-of-freedom (DOF). Using the successive elimination procedure presented herein, the degrees of the input–output (I/O) polynomials as well as the number of assembly configurations for all 71 mechanisms resulting from 16 8-link kinematic chains are presented. It is shown that the displacement analysis problems for these mechanisms can be classified into nine distinct structures each of which can be reduced into a univariate polynomial devoid of any extraneous roots. This univariate polynomial corresponds to the I/O polynomial of the mechanism. Three numerical examples illustrating the applicability of the successive elimination procedure to the displacement analysis of 8-link mechanisms are presented. The first example deals with the determination of I/O polynomial for an 8-link mechanism which does not contain any 4-link loops. The second and third examples address in detail some of the problems associated with the conversion of transcendental loop closure equations into an algebraic form using tangent half-angle substitutions. An application of the proposed approach to the displacement analysis of spherical 8-link mechanisms is also presented.

TOPOLOGICAL OPTIMIZATION OF TRUSS STRUCTURES USING SIMULATED ANNEALING

A design procedure for integrating topological decision making in the framework of structural optimization is presented. The proposed approach facilitates (i) generation and evaluation of alternate structural topologies, and (ii) development of detailed designs for promising concepts. In contrast with the ground-structure approach, the proposed method allows for an introduction of new members in an existing topology. This is done using 0-1 variables to represent topological decisions involving a choice between alternative designs. Since the topological variables are discrete in nature and the member cross-sections are assumed to be continuous, the topological optimization problem has mixed discrete-continuous variables. This problem is solved using a simulated annealing approach wherein the search for an optimum topology is simulated as a relaxation of the stochastic structural system. A probabilistic acceptance criterion is used to accept/reject candidate designs. Numerical results obtained using simulat...