A dynamic system differs from a static system in that it contains signal factor and the target value depends on the level of the signal factor set by the system operator. The aim of optimizing a multi-response dynamic system is to find a setting combination of input controllable factors that would result in optimum values of all response variables at all signal levels. The most commonly used performance metric for optimizing a multi-response dynamic system is the composite desirability function (CDF). The advantage of using CDF is that it is a simple unit less measure and it has a good foundation in statistical practice. However, the problem with the CDF is that it does not consider the variability of the individual response variables. Moreover, if the specification limits for the response variables are not provided the CDF cannot be computed. In this paper, a new performance metric for multi-response dynamic system, called multiple regression-based weighted signal-to-noise ratio (MRWSN) is proposed, which overcome the limitations of CDF. Two sets of experimental data on multi-response dynamic systems, taken from literature, are analysed using both CDF-based and the proposed MRWSN-based approaches for optimization. The results show that the MRWSN-based approach also results in substantially better optimization performance than the CDF-based approach.

Optimization of a multi-response dynamic system aims at finding out a setting combination of input controllable factors that would result in optimum values for all response variables at all signal levels. In real life situation, often the multiple responses are found to be correlated. The main advantage of PCA-based approaches is that it takes into account the correlation among the multiple responses. Two PCA-based approaches that are commonly used for optimization of multiple responses in dynamic system are PCA-based technique for order preference by similarity to ideal solution (TOPSIS) and PCA-based multiple criteria evaluation of the grey relational model (MCE-GRM). This paper presents a new PCA-based approach, called PCA-based utility theory (UT) approach, for optimization of multiple dynamic responses and compares its optimization performance with other existing PCA-based approaches. The results show that the proposed PCA-based UT method is superior to the other PCA-based approaches.

Ultrasonic machining (USM) process has multiple performance measures, e.g. material removal rate (MRR), tool wear rate (TWR), surface roughness (SR) etc., which are affected by several process parameters. The researchers commonly attempted to optimize USM process with respect to individual responses, separately. In the recent past, several systematic procedures for dealing with the multi-response optimization problems have been proposed in the literature. Although most of these methods use complex mathematics or statistics, there are some simple methods, which can be comprehended and implemented by the engineers to optimize the multiple responses of USM processes. However, the relative optimization performance of these approaches is unknown because the effectiveness of different methods has been demonstrated using different sets of process data. In this paper, the computational requirements for four simple methods are presented, and two sets of past experimental data on USM processes are analysed using these methods. The relative performances of these methods are then compared. The results show that weighted signal-to-noise (WSN) ratio method and utility theory (UT) method usually give better overall optimisation performance for the USM process than the other approaches.