## 5 Results  
The evaluation of the procedure is made by means of artificial data in which the positions of the outliers are given. As already mentioned, the developed algorithm is currently integrated into the inferential modelling platform of the unit responsible for Advanced Control and Simulation Solutions within ABB's (Asea Brown Boveri) industry division. Experimental results using sensor measurements of temperature, and pressure in a Distillation Column are presented in this session. In particular, a process is taken into consideration, and this is represented by a dryer section within a paper mill, and it uses steam at different pressures for the drying. The measured quantities are, as already mentioned, temperature, pressures, flow rates, moisture, and levels, and they include process variables, set point variables, manipulated variables, and disturbances. Figure 7 shows the result obtained from the offline mode to validate the presented algorithm. Figure 7a shows data with artificial outliers. In Figure 7b, all of the outliers are correctly detected, and no misclassifications occur using the proposed algorithm with no priori knowledge of the noise. It is possible to notice that almost 100% of outliers are detected in the data in the right way. The rate of the incorrect outliers detected in the data can be higher in the first part of the classification because of the initialisation part of the algorithm in which a statistic is built using the local Lipschitz approach already discussed. The initial standard deviation of the local Lipschitz constant is very small when the algorithm starts. The starting phase can take some samples, normally 15-20 samples. It is the weak point of the procedure being a stochastic one, and, in some cases, it can be not robust. The most difficult situation is if the standard deviation of the local Lipschitz constant is small. The algorithm considered in [5] and the one presented in this contribution are compared. The upper parts of Figures 8-10 show the results using an algorithm developed in [5] (median filter technique) based on an application of the wavelet filter in the distillation column case. They are compared with the proposed algorithm in which they are shown in the lower parts of the same figures. To summarise the results, it is possible to notice that the proposed algorithm with respect to that proposed in [5] results to be \"more aggressive\" in the sense that, presumably, it eliminates data that does not belong to the fault set. This is due to the fact that, with respect to the algorithm developed in [5], which is based on a median filter technique, this new method is statistically based, and it is sensible for the chosen threshold (soft, hard and very hard threshold). More in detail, in Figure 8, a data set from the distillation column case has been contaminated with the outliers. As it can be seen, the MAD algorithm performs much better than the wavelet based one. The MAD algorithm removes all of the outliers and does not remove any measurements that are not outliers. On the other hand, the wavelet based approach removes some of the measurement noise and, more seriously, also some of the signals. Figure 8: Comparison between (**a**) the presented algorithm in [10] and (**b**) that wavelet based on [5] proposed here. Figure 7: Simulations by using wavelet algorithms without a priori knowledge on the noise. (**a**) data with artificial outliers; (**b**) outliers correctly detected. Figure 10: Comparison between (**a**) the presented algorithm in [10] and (**b**) that wavelet based on [5] proposed here. Figure 9: Comparison between (**a**) the presented algorithm in [10] and (**b**) that wavelet based on [5] proposed here. Misclassifications of the outliers can be particularly found in the first part of the data, as it can be seen from Figure 7. The detected rate of the faulty outliers in the data expands in the first part of the classification. The sampling period is usually requested in a linear case to be one-tenth of the \"dominating\" system time constant.