Learning records of data analysis (II) -- simple use of response surface method and design expert

Data analysis learning records （ Two ）— Response surface method and Design-Expert Simple use

 notes ： This article refers to the blog link ：https://www.biomart.cn/experiment/793/2714853.htm

One introduction

Response surface method （Response surface methodology） Explanation on Baidu Encyclopedia ：

“ Response surface method is a statistical test method for optimizing random processes . The goal is to find the quantitative law between the test index and each factor , Find out the best combination of each factor level . Actively collect data on the basis of multiple linear regression , To obtain a regression equation with better properties . The complex multi-dimensional space surface established is closer to the actual situation , The number of test groups required is relatively small , It is widely used in simulation and system dynamics .”

For me, how to understand it more simply and intuitively is the primary consideration when I teach myself . The first point , Why do we need to use response surface method ？ Here we will introduce another most commonly used process optimization method , Single factor test .

Single factor test is based on the assumption that there is no interaction between various factors , Change only one factor at a time , Other factors need to be kept at a constant level , Then study the influence of different test levels on the response value .

In reality, the influencing factors of the process are very complex , And there is usually some interaction between factors , When there are many experimental factors , We need several single factor analysis and a long test cycle to optimize each factor one by one , Such efficiency is not necessarily too low .

At this time, we have to mention a process optimization method with higher efficiency than single factor analysis , That's it Orthogonal test . Orthogonal test can consider many factors at the same time , Under the condition of reasonably reducing the number of tests of single factor analysis , Looking for the best factor level combination , The primary and secondary factors affecting the results are obtained through variance analysis , However, when dealing with the interaction between factors, the orthogonal test needs to design the interaction table , When the interaction between factors is more complex , The workload of orthogonal test will also increase .

therefore ..

Response surface method came into being . Response surface method is also called regression design , In fact, after understanding the analysis principle of response surface method, its name is not difficult to understand , It establishes a primary term including all significant factors on the basis of multiple linear regression 、 The quadratic term and the first-order interaction term between any two factors , It can be said to be set statistics 、 Mathematical and computer integrated statistical process optimization methods .

Response surface method through the design of a reasonable number of experiments , Accurately study the relationship between each factor and the response value we want , Quickly and effectively determine the best conditions of multi factor system .

Two example

Here I found a document , Combine the data analysis Design-expert Software for response surface analysis . There are two common methods of response surface ： Central composite experimental design （central composite design,CCD） and Box-Behnken Experimental design （BBD）.

Common response surface design and analysis software are Matlab、SAS and Design-Expert. In the relevant response surface that has been published （RSM） In the paper of optimization experiment ,Design-Expert Is the most widely used software .

Reference information ：
[1] Hu Dong , Ke LingChao , Zhangjingyu , etc. . Response surface methodology was used to design and optimize the fermentation medium for avermectin chemical synthesis [J]. Chinese Journal of antibiotics , 2018, 043(008):1055-1061.

First open the software , Select new analysis , Then select response surface analysis , Choose the second Box-Behnken , Pictured ：

We fill in the data table in the literature , Enter the number of corresponding factors and the absolute factors in the test （ The default is 0）, Then enter the name and unit of the factor 、 Maximum and minimum , Click on continue Go to the next page ：

Fill in the response value we want to optimize here , Only A response value , by Avermectin increases the percentage , So we filled in , Unit is **%**, Click on continue：

The response value data at the back of the table above needs to be entered manually , Corresponding to the data in the above table .
After typing, we click Analysis Of R1：Transform tab , Generally, you can choose the default value . If there are other requirements , You can find the detailed description of each mode according to your needs and instructions, and then choose .

FitSummary, Look at the suggested factors .

Model Take the default value of the tab , Click on ANOVA tab , Show ANOVA , Significance test of variance , Coefficient significance test regression equation .

Click on Diagnostics tab , Click the options on the left side in turn , The first thing to show is Normal Plot, Uneven normal distribution diagram , The closer the point in the figure is to the straight line, the better .

The second one shows the corresponding relationship between the residual error and the predicted value of the equation , The more scattered and irregular the distribution, the better .

Finally, the corresponding relationship between the predicted value and the actual value of the test is shown , The closer the point is to the same straight line, the better .

And then click Influence Click later Report Enter the result interface , The data is shown in the figure , Include the actual measured value of the test （ Left ） And equation prediction （ Right ）.

And then click Model Graphs View contour map , The contour map examines the impact of each of the two factors on the dependent variable , And form contour lines by fitting equations , It is a two-dimensional plane figure , A better range can be found through this figure .

The three-dimensional response surface graph can more intuitively see the influence of the two factors , You can intuitively find out the optimal range , The two-dimensional contour map just seen is the projection of the three-dimensional response surface map on the bottom .

Next is the key optimization condition options , Determine the value range of each factor according to the actual situation , Then proceed 「 Response value target 」 The determination of , Each experiment has a different purpose , For example, here we want to find the optimal culture conditions that can maximize the yield of avermectin , But in other experiments, the requirements for the target need the maximum , There is a minimum value required , Sometimes it is necessary to stabilize the result in a certain range or a fixed value . Then the corresponding situation can be selected in these four modes .

Click on Solutions tab , You can see the optimal value obtained through analysis , Generally, many schemes are listed , The first solution is to maximize the result of taking the optimal value of each factor , For the predicted value .

above ！！！ If there is something wrong , Welcome to exchange and point out .