Evidence based uncertainty models and particle swarm optimization for multiobjective optimization of engineering systems

The present work develops several methodologies for solving engineering analysis and design problems involving uncertainties and evidences from multiple sources. The influence of uncertainties on the safety/failure of the system and on the warranty costs (to the manufacturer) are also investigated. Both single and multiple objective optimization problems are considered. A methodology is developed to combine the evidences available from single or multiple sources in the presence (or absence) of credibility information of the sources using modified Dempster Shafer Theory (DST) and Fuzzy Theory in the design of uncertain engineering systems. To optimally design a system, multiple objectives, such as to maximize the belief for the overall safety of the system, minimize the deflection, maximize the natural frequency and minimize the weight of an engineering structure under both deterministic and uncertain parameters, and subjected to multiple constraints are considered. We also study the various combination rules like Dempster's rule, Yager's rule, Inagaki's extreme rule, Zhang's center combination rule and Murphy's average combination rule for combining evidences from multiple sources. These rules are compared and a selection procedure was developed to assist the analyst in selecting the most suitable combination rule to combine various evidences obtained from multiple sources based on the nature of evidence sets. A weighted Dempster Shafer theory for interval-valued data (WDSTI) and weighted fuzzy theory for intervals (WFTI) were proposed for combining evidence when different credibilities are associated with the various sources of evidence. For solving optimization problems which cannot be solved using traditional gradient-based methods (such as those involving nonconvex functions and discontinuities), a modified Particle Swarm Optimization (PSO) algorithm is developed to include dynamic maximum velocity function and bounce method to solve both deterministic multi-objective problems and uncertain multi-objective problems (vertex method is used in addition to the modified PSO algorithm for uncertain parameters). A modified game theory approach (MGT) is coupled with the modified PSO algorithm to solve multi-objective optimization problems. In case of problems with multiple evidences, belief is calculated for a safe design (satisfying all constraints) using the vertex method and the modified PSO algorithm is used to solve the multi-objective optimization problems. The multiobjective problem related to the design of a composite laminate simply supported beam with center load is also considered to minimize the weight and maximize buckling load using modified game theory. A comparison of different warranty policies for both repairable and non repairable products and an automobile warranty optimization problem is considered to minimize the total warranty cost of the automobile with a constraint on the total failure probability of the system. To illustrate the methodologies presented in this work, several numerical design examples are solved. We finally present the conclusions along with a brief discussion of the future scope of the research.