Optimum Design of Mechanical Systems Involving Interval Parameters

The imprecision or uncertainty present in many engineering systems can be modeled using probabilistic, fuzzy or interval methods. This work presents the optimum design of uncertain mechanical systems using interval analysis for the prediction of system response. Each of the uncertain parameters is defined by a range of values. Since the interval ranges of response parameters is found to increase with an increase in the number and/or ranges of input interval parameters with the use of interval arithmetic operations, a truncation procedure is used to obtain approximate but reasonably accurate response of the system. This procedure is found to be simple, economical and fairly accurate. The optimum design of a brake is considered to illustrate the computational aspects of the methods. The procedures outlined in this work are quite general and can be used for the design of any uncertain mechanical system when either the probability distribution functions or the preference information of uncertain parameters are unknown.