Design process of response surface optimization method
First, the experimental design.
1, single factor experiment
In order to provide a reasonable numerical range for the experimental design of response surface method, a single factor experiment is needed before the experimental design of response surface method.
2. Experimental design of response surface method.
Taking extraction temperature (a), ethanol concentration (b) and extraction time (c) as independent variables, and the quality of momordicin in the experiment as the response value, the response surface experiment was designed according to Box-Behnken design principle. Then analyze it according to the experimental results.
1. Open the software Design-Expert, and set the independent variable, unit and its range. The arrow refers to setting the number of independent variables.
2. Set the objective function and unit. The arrow indicates the number of objective functions.
3. Design-Expert software generates the experiment, completes the experiment according to the figure below, and fills in the results in the table below.
Second, the result analysis
1. First, click the Analyze button to test the significance of the linear function, the 2FI model, the second-order model and the third-order model, and recommend the appropriate model by comparing the data of the model significance test, mismatch test and correlation test. For the results of this test scheme, the second-order model is recommended.
Then click the ANOVA button to conduct variance analysis and significance test according to the selected model. In the analysis of variance, the significance of constant term, linear term, quadratic term interaction term and square term affecting quadratic equation model will be tested.
2. Analysis of variance
The greater the F value, the smaller the P value, and the more significant the correlation coefficient may be. Through variance analysis, the model (prob > f value < 0.05) is significant, and the model (prob > f value < 0.0 1) is extremely significant. The primary terms A, B, C, interaction terms AB, AC, BC, secondary terms A 2, B 2, C 2 and missing terms have the same meanings as the model.
In the variance analysis table of regression equation, the prob > f value of the model is required to be less than 0.0 1, which shows that the response surface regression model has reached a very significant level, indicating that the fitting accuracy is good, and the response surface approximation model can be used for subsequent optimization design. Lackofit prob > f value >: 0.05, the missing item is not important. (If it is significant here, check whether the results of the repeated experimental group are correct. ) The primary terms A, B, C, the interactive terms AB, AC, BC, and the secondary terms A 2, B 2, C 2 are as significant as possible.
It can be seen that the prob > f values of the first-order items A, B and C, the interaction item BC, and the second-order items A 2, B 2 and C 2 are all less than 0.0 1, indicating that the quality of momordicin is extremely significant, and the prob > f value of the interaction item AB is less than 0.05, indicating that the quality of momordicin extracted is significantly affected, while other factors are not significant. Temperature >; Ethanol concentration (compare the size of F).
The greater the meta-correlation coefficient R2, the better the correlation. AdjR-Squared and predr-squared (radj2-rpred2 < 0.2) are high and close, then the regression model can fully explain the technological process; If it is not high, it means that the process explanation is not sufficient, and it is necessary to consider whether there are other significant influencing factors. CV < 10%, which shows that the experiment has high reliability and accuracy.
AdeqPrecision is the ratio of effective signal to noise, and it is considered reasonable if it is greater than 4. As can be seen from the above figure, the fitted regression equation conforms to the above test principle and has good adaptability.
Third, the distribution map
1, click Diagnose to give the normal probability distribution of residuals, the distribution of residuals and predicted values, and the distribution of predicted values and actual values. If the model has good adaptability, the normal probability distribution of residual should be a straight line; The distribution of residuals and predicted values is irregular; The distribution of residual and predicted values should be as straight as possible. It can be seen from the figure that the response surface method is suitable for fitting the model.
2. Click on the model diagram, and the response surface method overcomes the shortcoming that the orthogonal experiment can't give an intuitive image. According to the quadratic equation, the three-dimensional response surface and isoline diagram of the interaction between experimental factors were made respectively, and the influence of the interaction of the other two factors on the quality of momordica charantia saponin was investigated under the condition that the central value of one factor was fixed.
Response surface and contour map can directly reflect the influence of interaction on response value. The steeper the surface, the denser the contour, and the more significant the influence. The closer the contour line is to the ellipse, the stronger the interaction between these two factors.
3. The following figure shows the influence of the interaction of extraction temperature and ethanol concentration on the quality of bitter gourd protein when the extraction time is at the central level. Under the condition of low ethanol concentration, with the increase of extraction time, the quality of momordica charantia saponin increased first and then decreased.
When the ethanol concentration is high, the quality of the extracted momordica charantia protein is improved with the extension of reaction time. The slope of response surface is steep, the contour line is oval, and the value of prob > f is less than 0.05, which shows that the interaction of extraction temperature and ethanol concentration has a significant impact on the quality of extracted momordica charantia saponin.
Fourth, response surface optimization results
Click the numerical value in optimization, and the first set of data in the solution is the optimization result of response surface. When the Chinese coordinates in the 3D map are garbled, put the mouse on the 3D map and right-click to select the graphic preference.
Click the icon t, select the graphic label-—Face Name from the list, and select Microsoft JhengHei, that is, Microsoft is black from the drop-down list.