Using data-based surrogate models for function development and calibration has been proven to be an efficient approach. Current methods are often restricted to stationary or quasi-stationary processes, but many processes of high practical relevance are dynamic, e.g. the air system or the power train. One popular approach to extend data-based regression algorithms for modelling (quasi-)stationary processes towards dynamic processes is the non-linear auto regressive exogenous variable (NARX) approach. Using the NARX approach requires the selection of relevant inputs or features to aid the regression algorithm. To summarize the results on the different problem instances we discuss the performance of the feature selection method and then discuss the regression algorithms considering the computational effort. A final recommendation combines both results. On the feature selection task the CART method yields the best results both in the peak performance as well as robustness over all problem instances. The only drawback is the occasional failure to compute suitable NARX structures. This is easily counteracted by the small computational effort required. The MOCO (multiple objective combinatorial optimization) method performs not as well especially considering the significant computational resources required for obtaining good results. Still, the MOCO NARX approach performed robustly on all problem instances and provided sparse results with good performance. This may be relevant for a subsequent process analysis. Finally, the BF approach did not perform that bad, especially if combined with suitable regression algorithms. This indicates that the feature selection problem is not that critical, at least on the problem instances under investigation. In respect to the regression algorithms the SGP delivered the best peak performance over all problem instances, if given a suitable feature set. Considering the average performance over multiple feature sets per problem instance both SVR (support vector regression) and MLP (multi-layer perceptrons) come close to the performance of the SGP and all three must be considered as robust regression algorithms for the transient modelling task. The performance of the rest of the regression algorithms is more difficult to judge. Of course, the Linear and Quadratic algorithms fail on the SISO (single input single output) model. But, on the other problem instances they perform not as bad compared to the other algorithms. This could be attributed to the noise levels involved, but may also indicate that these problem instances are not too complicated. The Quadratic and Local-Linear algorithms perform well on a number of problem instances, but fail on the HC problem instance as well as on unsuitable NARX feature sets. These outliers ruin the results, especially since the set of problem instances is rather small. The GP (gobal programming) algorithm performs not as well, similar to the LoLiMoT (local linear model tree) algorithm. In case of LoLiMoT this may be attributed to unsuitable parameter settings which have not been studied in detail. This can also hold true for other algorithms, thus any scientific challenges to our results are welcome.
Comparison of alternative approaches to auto-regressive modelling of dynamic systems
2011
13 Seiten, 10 Bilder, 11 Tabellen, 16 Quellen
Conference paper
English
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