A Reduced-Parameter Mathematical Surrogate Model for Improving Measurement Accuracy of Mechanical Systems Using Experimental Techniques

Modeling of a larger mechanical system is inherently difficult due to the complexity of individual processes and the interaction between multiple processes. Using a polynomial model based on experimental results to obtain an input-output relationship offers an easier option than establishing a mathematical model in the case of an Open Loop Controller. Such input-output relationship is workable but sometimes experiences computational burden due to a higher degree of the polynomial. Surrogate modeling is commonly used as a method to overcome this difficulty through an approximation by reducing the degree of complexity of the relationship. Surrogate models based on statistical principles, which correlate multiple inputs and required outputs, are opaque to the system parameters. These system parameters can be optimized to improve the measurement performance and hence input-output relationship by either the polynomial model or its surrogate does not serve the purpose of optimization. A surrogate of a mathematical model based on experimentation is proposed here. The method involves developing mathematical models of subsystems using minimum parameters. The complexity of each subsystem is reduced by retaining dominant parameters and eliminating non-influential parameters. To improve the measurement accuracy of the optimization, model an experimental method has evolved where parameters are attuned appropriately to accommodate the effect of eliminated parameters. This technique is demonstrated by establishing a mathematical model for a pendulum-ball system.