PoLogCem 4.2. How to build the nonlinear regression models for the pollution generated by a cement plant? The images presented in the next figures illustrate the steps to follow in designing the data models. Firstly, the user will select the output measurement and then push the DISPLAY TABLE button and the results will be displayed as correspondence table for the selected output measurement with all the values of the input measurements for the corresponding output. Both classical and piecewise modeling is possible. In the Fig. 6, is shown a classical modeling. Considering interval data, the piecewise modeling is possible as shown in the Fig. 7. Press here to see the table of data The selection of the output model Here, there is the table containing the data related to dependent (Y) and independent (X) variables. Fig. 6. The automatic loading of values for the output dependent variable 4-6 The table of intervals to be considered for the selected parameter The data can be exported to XLD / Dbase files Fig. 7. Piecewise modelling Functions defined by user. After solving the model, the coefficients are shown in the third column. Press the button to solve the model. Fig. 8. Defining the structure of the regression model In order to determine the mathematical models the following information is valuable: the output measurement must be selected and then in the left-down table will be filled 4-7 the linear/nonlinear functions in a manner enabling us to obtain a model with the following expression: y = A0+ A1*F1(x1, ..., xm) + A2*F2(x1, ..., xm) + AnFn(x1, x2, …, xm), where m is the number of independent variables, and y is the dependent variable. The functions F1, F2,…, Fm must be defined by the user in the editing window (the right ^ down corner in the Fig. 8). Let us denote by Yk si Yk the measured respective the computed output variable, and by Y , the mean value of the variable Y given by the values Yk , k = 1, 2, … . Let Sy be the deviance to the mean of the measured data, and S ^ be the deviance from the mean of the data obtained after the solving of the y M M ^ regression model. Therefore, S y = ∑ (Yk − Y ) 2 and S ^ = ∑ (Yk − Y ) 2 . To compare the y k =1 k =1 measured model against de regression model, the software uses the following indicator S^ (adequacy level): R 2 = Y . SY The adequacy index Press button for more Knowledge to be added in the Database Rules. It is shown the measured versus modeled data in the case of the dependent variable. Fig. 9. Updating the Knowledge Database Note: The software PoLogCem uses the notation R instead of R2 (Fig. 8 and Fig. 9). After the model was created (the structure was established and the coefficients were found) it will be added (using the button APPEND TO DATABASE RULES) to the existing general set of rules (Fig. 9). The name (label) of the new rule is automatically generated. The rules are needed to the optimization module. 4-8

© Copyright 2018