Fig. 2. Turbo-generator at the Chankanaab Turbo-Gas Central. Fig. 1. Graphical depiction of a generic GT system. Monitored variables in the Mitsubishi single shaft Turbo-Generator Model MS6001 that are related to fuel flow. Table 1 Monitored variables in the Mitsubishi single shaft Turbo-Generator Model MS6001 that are related to exhaust gas temperature. 2.3. Problem statement and data Table 2 Fig. 4. Plots show 3D point clouds of the real data collected from the GT unit. Fig. 5. Graphical depiction of the basic GP algorithm. Summary of median performance by each algorithm on each problem. Table 4 Table 5 Fig. 6(a) shows the training error on the Flow problem and Fig. 6(b) shows the same for the Temperature problem. Conversely, Fig. 6(c) shows the test error on the Flow problem while Fig. 6(d) shows the same for the Temperature problem. Summary p-values of the pairwise Friedman test with Benjamini—Hochberg correc- tion for the test performance on the Flow problem; an asterisk (*) indicates that the null hypothesis can be rejected at the w=0.05 significance level. Table 6 Summary p-values of the pairwise Friedman test with Benjamini-Hochberg correc- tion for the test performance on the temperature problem; an asterisk (*) indicates that the null hypothesis can be rejected at the w=0.05 significance level. Fig. 6. Experimental results showing the train (a and b) and test (c and d) performance of all algorithms on each problem, flow (a and c) and temperature (b and d). Fig. 7. Plots show 3D point clouds of the real data collected from the GT unit and the output of the best models produced by the GP-LS method. Summary of median performance by each algorithm on each problem, comparins GP-LS with other machine learning methods. 4.3. Comparison with other machine learning methods these methods with GP-LS based on the size of the models each method produces. For both MARS,” and FFX? we used the freely available toolboxes provided by the authors using their default configuration. Table 7 Fig. 8. Experimental results showing the train test performance of all algorithms on each problem, flow (a) and temperature (b) "ig. 9. Experimental results showing the size of the solutions generated by GP-LS, MARS and FFC on both problems: (a) flow; and (b) temperature Summary p-values of the pairwise Friedman test with Benjamini-Hochberg correction for the test performance on the Flow problem; an asterisk (*) indicates that the nul hypothesis can be rejected at the w=0.05 significance level. Table 9 Summary p-values of the pairwise Friedman test with Benjamini-Hochberg correction for the test performance on the Flow problem; an asterisk (*) indicates that the nul hypothesis can be rejected at the w= 0.05 significance level. difference between the methods on the Flow problem, with the statistical tests suggesting that the best performance is achieved by SR, SVM, FFX and GP-LS. On the other hand, on the Temper- ature problem two methods stand out: MARS and GP-LS achieve the lowest median performance and the statistical test suggesting that there is no significant difference between their median per- formance. However, if we analyze the boxplots of Fig. 8 we can see that the lowest error was produced by GP-LS. real-world task. Comprehensive experimental validation clearly shows that GP-LS outperforms all other GP variants on both prob- lems, with clear statistical significance in the detected differences among the methods. In particular, we would emphasize that the largest improvement, relative to the other methods, was achieved by GP-LS on the temperature prediction problem. This is important to mention since the temperature can cause the most harm to a GT system if it fluctuates outside normal operating ranges, mak- ing accurate predictive models for this variable a desirable tool for real-world system monitoring.
