Academia.eduAcademia.edu

Figure 9 – uploaded by Niranjan Roy

See full PDFdownloadDownload figure
Noise reduction using radial basis neural network For each signal, reduction calculated. reduction averaging 00 samples of noisy test data are created and the nois These values are summarized in Table 9 and show a nois between 75% and 81%. Results in this paper clearly dem onstrate the power of the soft computing framework for automated decisior making under uncer ainty. The approach uses the concept of “hybridizatio1 in soft computing” where using different techniques such as neural networks genetic algorithms and fuzzy logic together gives better results than if eacl method is used individually [36]. The “hybridization” process uses th¢ strengths of each different approach to attack the problem.

Table 9 Noise reduction using radial basis neural network For each signal, reduction calculated. reduction averaging 00 samples of noisy test data are created and the nois These values are summarized in Table 9 and show a nois between 75% and 81%. Results in this paper clearly dem onstrate the power of the soft computing framework for automated decisior making under uncer ainty. The approach uses the concept of “hybridizatio1 in soft computing” where using different techniques such as neural networks genetic algorithms and fuzzy logic together gives better results than if eacl method is used individually [36]. The “hybridization” process uses th¢ strengths of each different approach to attack the problem.

Related Figures (18)

R. Verma et al. | Appl. Math. Comput. xxx (2005) xxx-xxx model used to obtain fault signatures or the measurement uncertainties of the signal changed, the diagnostic systems have to be redeveloped. Since there are many different engines operating with different airlines, there are likely to be many possible combinations of fault signatures and measurement uncertainties for the fault isolation systems which need to be developed. Very often the pro- cess of redeveloping the underlying numerics or rules for the diagnostic system is a trial and error process that can be very tedious and require considerable human effort.
R. Verma et al. | Appl. Math. Comput. xxx (2005) xxx-xxx model used to obtain fault signatures or the measurement uncertainties of the signal changed, the diagnostic systems have to be redeveloped. Since there are many different engines operating with different airlines, there are likely to be many possible combinations of fault signatures and measurement uncertainties for the fault isolation systems which need to be developed. Very often the pro- cess of redeveloping the underlying numerics or rules for the diagnostic system is a trial and error process that can be very tedious and require considerable human effort.
Signature for module faults
Signature for module faults
Fig. 1. Change in fault isolation success rate with increasing number of fuzzy sets. simulated measurement deitas using the typical standard deviations tor “EGI, "N1, ‘N2, and "W Fig. 1 shows t F as 4.23 °C, 0.25%, 0.17% and 0.50%, respectively. he success rate for the optimal GFS as the number of fuzzy sets is increased from 2 to 9. For each value of N in this figure, the optimal val- ues of x are calcu ated using Algorithm 3. For only 2 fuzzy sets, the success rate is about 80% and quickly rises as the number of sets increases. The number N = 6 is selected by Algorithm 3 as the point where the GFS is optimal with a minimum num with six sets as th ber of sets. Fig. 2 shows the success rate of the fuzzy system e GA generations’ progress. In this case, only two generations
Fig. 1. Change in fault isolation success rate with increasing number of fuzzy sets. simulated measurement deitas using the typical standard deviations tor “EGI, "N1, ‘N2, and "W Fig. 1 shows t F as 4.23 °C, 0.25%, 0.17% and 0.50%, respectively. he success rate for the optimal GFS as the number of fuzzy sets is increased from 2 to 9. For each value of N in this figure, the optimal val- ues of x are calcu ated using Algorithm 3. For only 2 fuzzy sets, the success rate is about 80% and quickly rises as the number of sets increases. The number N = 6 is selected by Algorithm 3 as the point where the GFS is optimal with a minimum num with six sets as th ber of sets. Fig. 2 shows the success rate of the fuzzy system e GA generations’ progress. In this case, only two generations
Fig. 2. Evolution of success rate for fuzzy system with 6 sets with generations of genetic algorithm.
Fig. 2. Evolution of success rate for fuzzy system with 6 sets with generations of genetic algorithm.
Midpoints of two fuzzy sets Table 2
Midpoints of two fuzzy sets Table 2
Midpoints of three fuzzy sets
Midpoints of three fuzzy sets
Midpoints of four fuzzy sets Midpoints of five fuzzy sets
Midpoints of four fuzzy sets Midpoints of five fuzzy sets
Fig. 3. Discretization of universe of exhaust gas temperature using two fuzzy sets. Midpoints of six fuzzy sets
Fig. 3. Discretization of universe of exhaust gas temperature using two fuzzy sets. Midpoints of six fuzzy sets
Fig. 4. Discretization of universe of exhaust gas temperature using three fuzzy sets. descretization. In Fig. 7, the optimal level of discretization with six fuzzy sets i: achieved.
Fig. 4. Discretization of universe of exhaust gas temperature using three fuzzy sets. descretization. In Fig. 7, the optimal level of discretization with six fuzzy sets i: achieved.
Fig. 5. Discretization of universe of exhaust gas temperature using four fuzzy sets. R. Verma et al. | Appl. Math. Comput. xxx (2005) xxx-xxx
Fig. 5. Discretization of universe of exhaust gas temperature using four fuzzy sets. R. Verma et al. | Appl. Math. Comput. xxx (2005) xxx-xxx
Fig. 6. Discretization of exhaust gas temperature using five fuzzy sets.
Fig. 6. Discretization of exhaust gas temperature using five fuzzy sets.
Fig. 7. Discretization of universe of exhaust gas temperature using six fuzzy sets. R. Verma et al. | Appl. Math. Comput. xxx (2005) xxx-xxx Table 7 Rules for optimal fuzzy system with six fuzzy sets
Fig. 7. Discretization of universe of exhaust gas temperature using six fuzzy sets. R. Verma et al. | Appl. Math. Comput. xxx (2005) xxx-xxx Table 7 Rules for optimal fuzzy system with six fuzzy sets
Results for optimal fuzzy system and manually designed system Table 8
Results for optimal fuzzy system and manually designed system Table 8
Fig. 8. Success rate in fault isolation with increasing noise levels in data.
Fig. 8. Success rate in fault isolation with increasing noise levels in data.
Fig. 9. Noisy and filtered AEGT signal simulating HPC fault. where x~ and x~ are the Ath entries of the centers of the ith and jth hidden units. We have used p= 5. When the centers and widths of the RBF units have been chosen, then the NV = 100 training samples are processed through the hid- den nodes to generate an H x N matrix, called A. Let T be the Mx N desired output matrix for the training patterns and M = 100 is the number of output nodes. The objective is to find the weights that minimize the error between the actual output and the desired output of the network. Essentially, we are try- ing to minimize the objective (cost) function
Fig. 9. Noisy and filtered AEGT signal simulating HPC fault. where x~ and x~ are the Ath entries of the centers of the ith and jth hidden units. We have used p= 5. When the centers and widths of the RBF units have been chosen, then the NV = 100 training samples are processed through the hid- den nodes to generate an H x N matrix, called A. Let T be the Mx N desired output matrix for the training patterns and M = 100 is the number of output nodes. The objective is to find the weights that minimize the error between the actual output and the desired output of the network. Essentially, we are try- ing to minimize the objective (cost) function
Fig. 10. Noisy and filtered AWF signal simulating LPT fault. CADASIL, OVI, CLV, AVY. Noise is added to the ideal signal using a baseline value oo of typical stan dard deviations for “EGT, “NI, ‘N2, and “WF as 4.23 °C, 0.25%, 0.17% anc 0.50%, respectively. The filtered signal in Figs. 9 and 10 show considerabk noise reduction while preserving the nature of the step edge. This data repre sents one noisy signal for each measurement. The visual quality of the datz is considerably improved. Similar results are obtained for all the signals corre sponding to the faults in Table 1. To summarize these results concisely, the fol. lowing noise reduction measure is defined based on the mean absolute erro: (MAB) criteria.
Fig. 10. Noisy and filtered AWF signal simulating LPT fault. CADASIL, OVI, CLV, AVY. Noise is added to the ideal signal using a baseline value oo of typical stan dard deviations for “EGT, “NI, ‘N2, and “WF as 4.23 °C, 0.25%, 0.17% anc 0.50%, respectively. The filtered signal in Figs. 9 and 10 show considerabk noise reduction while preserving the nature of the step edge. This data repre sents one noisy signal for each measurement. The visual quality of the datz is considerably improved. Similar results are obtained for all the signals corre sponding to the faults in Table 1. To summarize these results concisely, the fol. lowing noise reduction measure is defined based on the mean absolute erro: (MAB) criteria.
Related topics:
Applied MathematicsComputer ScienceGenetic Fuzzy SystemsGAS TURBINEPerformance ModelFault IsolationFuzzy SystemRadial Basis Function Neural NetworkMeasurement UncertaintyFuzzy Logic System
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved