Fundamental Principles of Response Curves and Surfaces

Yi Liu ； Yulin Ye ； Zhangdong Wei ； Chongyang Wang ； Chuhan Wang ； Yanzhou Li ； Chengcheng Shen ； Haojie Zang ； Luhang Li ； Yile Pan ； Lin Wang

《Frontiers in Science and Engineering》 1卷7期 (2021/10) Pp. 135-142

https://doi.org/10.29556/FSE.202110_1(7).0021

摘要

Optimization refers to improving the performance of a system, process or product in order to get the maximum benefit from it. The term optimization is often used in analytical chemistry as a means of finding conditions under which a program is applied to produce the best possible response. Traditionally, optimization in analytical chemistry is achieved by monitoring the effect of one factor on the experimental response at a time. When only one parameter changes, the other parameters remain unchanged. This optimization technique is called one variable at a time. Its main drawback is that it does not take into account the interaction between the research variables. Therefore, this technique does not describe the complete effect of parameters on the response. Another disadvantage of single factor optimization is that the number of experiments needed to carry out the research increases, which leads to the increase of time and cost, as well as the increase of reagent and material consumption. In order to overcome this problem, the multivariate statistical technique is used to optimize the analysis method. Response surface methodology (RSM) is one of the most relevant multivariate techniques. Response surface method is a set of mathematical and statistical techniques based on polynomial equation fitting experimental data. It must describe the behavior of data set for statistical prediction. When one or a group of interesting answers are affected by multiple variables, it can be well applied. The goal is to optimize the levels of these variables at the same time to achieve the best system performance. Before applying RSM method, we need to select an experimental design to determine which experiments should be carried out in the experimental area. There are some experimental matrices for this. When the data set does not show curvature, the experimental design of first-order model (such as factorial design) can be used. However, in order to make the response function approximate to the experimental data that cannot be described by linear function, quadratic response surface design should be used, such as third-order factorial, Box Behnken, central composite and Doehlert design. This paper discusses the basic principle of response curve and response surfaces.

關鍵字

Response Surface Methodology ； Response Curves ； Response Surfaces ； Optimization

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