Advanced Materials & Sustainable Manufacturing 2024 , 1, 10003 7 of 14 The constraints are the upper and lower limits of the range of each parameter in the actual case. To obtain better results, the limits of the error function are added to the constraints, as in Equation (9):
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(9)
Table 4 shows a comparison table of the errors in solving the parameters under different methods with the number of known parameters of 5, 4, 3, 2 and 1. The errors of the values in the table are in the form of percentages. From the table it can be seen that the solution result of nonlinear programming is better than that of NSGA-II. Nonlinear programming needs to be assigned reasonable initial values before running the model, so it is already closer to reasonable values in the first run. But it is difficult to provide feasible initial solutions to determine upper and lower limits of parameters or when there are more parameters. So nonlinear programming is assumed already closer to the reasonable values in the first run. When the upper and lower limits of parameters are not easy to determine or when there are more parameters to assign, it will not be possible to determine a suitable initial value. NSGA-II, on the other hand, uses random assignment of values in the first run, which can be applied to all cases. Normally, the more parameters are known, the more accurate the solution will be, whereas if there are only two or one known parameter values, the solution will no longer be credible. In this paper only five of these cases are listed, the rest are similar. It can be concluded that the method can, to some extent, solve the problem of missing parameter values in the process of model calculation. Moreover, it is a relatively general method that can be used to solve the missing parameters in any process where the mechanistic equations can be established. When the range of parameters is known, the nonlinear programming solution is used; when the range of parameters is unknown and initial values are difficult to assign, NSAG-II is used to solve. Table 4. Comparison of solution error results. 5 4 3 2 1 NLP (%) NSGA-II (%) NLP (%) NSGA-II (%) NLP (%) NSGA-II (%) NLP (%) NSGA-II (%) NLP (%) NSGA-II (%) M is - - - - - - - - - - P is - - - - - - - - 369 891 M iw - - - - - - 2 47 2 61 T iw - - - - 10 22 8 15 7 27 M oc - - 0 0 0 0 0 0 0 0 T oc 9 11 9 12 18 24 18 1 18 3 T ow 1 1 1 1 7 13 5 22 3 31 M ow 0 0 0 0 0 0 2 47 2 61 3.2. Prediction Model Considering that the production process is a relatively complex, non-linear, highly coupled and uncertain process, a correlation analysis between the parameters of the collected characteristics is necessary to eliminate irrelevant variables. The Pearson correlation coefficients of each collected variable with the exhaust air temperature and humidity are calculated, and it is generally considered that a correlation coefficient with an absolute value greater than 0.4 represents a moderate correlation. In this study, the characteristic variables with correlation coefficients greater than 0.4 were selected as inputs to the model. Figure 4 shows the results of the correlation analysis.
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