Adaptive threshold computation for CUSUM-type procedures in change detection and isolation problems. (English) Zbl 1452.62135
Summary: Statistical methods dealing with change detection and isolation in dynamical systems are based on algorithms deriving from hypothesis testing. As for any statistical test, the problem of threshold choice has to be addressed by taking into account the constraints fixed by the supervisors and the nonstationary nature of the stochastic systems under supervision. A procedure for obtaining adaptive thresholds in change detection or diagnosis algorithms of CUSUM-type rules is proposed. This procedure is carried out through a large number of simulations. The advantage of such an adaptive threshold, when compared with a fixed threshold, is its adaptation to the time evolution of the probability distribution of the test statistic, in order to guarantee constant rates of false alarm or false diagnosis, fixed by the supervisor.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
| 62L10 | Sequential statistical analysis |
| 62L15 | Optimal stopping in statistics |
| 62P30 | Applications of statistics in engineering and industry; control charts |
| 94A13 | Detection theory in information and communication theory |
| 93E10 | Estimation and detection in stochastic control theory |
References:
| [1] | Basseville, M.; Nikiforov, I., Detection of Abrupt Changes: Theory and Applications (1993), Prentice-Hall · Zbl 1407.62012 |
| [2] | Bastin, G.; Dochain, D., On-line Estimation and Adaptive Control of Bioreactors (1990), Elsevier |
| [3] | Blanke, M.; Kinnaert, M.; Lunze, J.; Staroswiecki, M., Diagnosis and Fault-Tolerant Control (2003), Springer · Zbl 1023.93001 |
| [4] | Ding, S.X., Zhang, P., Frank, P.M., 2003. Application of probabilistic robustness technique to the fault detection system design. In: Proceedings of the 42nd IEEE Conference on Decision and Control; Ding, S.X., Zhang, P., Frank, P.M., 2003. Application of probabilistic robustness technique to the fault detection system design. In: Proceedings of the 42nd IEEE Conference on Decision and Control |
| [5] | El Falou, W.; Khalil, M.; Duchêne, J.; Hewson, D., Automatic threshold determination for a local approach of change detection in long-term signal recordings, EURASIP Journal on Advances in Signal Processing, 2007 (2007), Article ID 24748 · Zbl 1168.94463 |
| [6] | Frank, P. M., Analytical and qualitative model based fault diagnosis — A survey and some new results, Eur. J. Control, 2, 6-28 (1996) · Zbl 0857.93015 |
| [7] | Frisen, M., 2007. Optimal sequential surveillance for finance, public health, and other areas. Research report, Statistical Research Unit, Department of Economics, Göteborg University, Sweden; Frisen, M., 2007. Optimal sequential surveillance for finance, public health, and other areas. Research report, Statistical Research Unit, Department of Economics, Göteborg University, Sweden · Zbl 1170.62059 |
| [8] | Kim, S.-H.; Alexopoulos, C.; Tsui, K.-L.; Wilson, J., A distribution-free tabular CUSUM chart for autocorrelated data, IIE Trans., 39, 3, 317-330 (2007) |
| [9] | Knoth, S., Computation of the ARL for CUSUM-\(S^2\) schemes, Comput. Statis. Data Anal., 51, 2, 499-512 (2006) · Zbl 1157.62562 |
| [10] | Lai, T. L., Sequential changepoint detection in quality control and dynamical systems, J. Roy. Statist. Soc. Ser. B, 57, 613-658 (1995) · Zbl 0832.62072 |
| [11] | Lai, T. L., Information bounds and quick detection of parameter changes in stochastic systems, IEEE Trans. Inf. Theory., 44, 2917-2929 (1998) · Zbl 0955.62084 |
| [12] | Lai, T. L., Sequential multiple hypothesis testing and efficient fault detection-isolation in stochastic systems, IEEE Trans. Inf. Theory., 46, 595-608 (2000) · Zbl 0994.62078 |
| [13] | Lai, T. L.; Shan, J. Z., Efficient recursive algorithms for detection of abrupt changes in signals and systems, IEEE Trans. Autom. Control., 44, 952-966 (1999) · Zbl 0956.93060 |
| [14] | Le, K., Huang, Z., Moon, C.W., Tzes, A., 1997. Adaptive thresholding — a robust fault detection approach. In: Proceedings of the 36nd IEEE Conference on Decision and Control; Le, K., Huang, Z., Moon, C.W., Tzes, A., 1997. Adaptive thresholding — a robust fault detection approach. In: Proceedings of the 36nd IEEE Conference on Decision and Control |
| [15] | Lorden, G., Procedures for reacting to a change in distribution, Ann. Math. Statist., 42, 1897-1908 (1971) · Zbl 0255.62067 |
| [16] | Moustakides, G., Optimal procedures for detecting change in distribution, Ann. Statist., 14, 1379-1387 (1986) · Zbl 0612.62116 |
| [17] | Nikiforov, I., A generalized change detection problem, IEEE Trans. Inform. Theory, 41, 171-187 (1995) · Zbl 0826.93064 |
| [18] | Nikiforov, I., A simple recursive algorithm for diagnosis of abrupt changes in random signals, IEEE Trans. Inform. Theory, 46, 2740-2746 (2000) · Zbl 1002.94514 |
| [19] | Nikiforov, I., A lower bound for the detection/isolation delay in a class of sequential tests, IEEE Trans. Inform. Theory, 49, 3037-3046 (2003) · Zbl 1301.94035 |
| [20] | Oskiper, T.; Poor, H. V., Online activity detection in a multiuser environment using the matrix CUSUM algorithm, IEEE Trans. Inform. Theory, 48, 477-493 (2002) · Zbl 1071.94515 |
| [21] | Page, E. S., Continuous inspection schemes, Biometrika, 41, 100-115 (1954) · Zbl 0056.38002 |
| [22] | Ritov, Y., Decision theoric optimality of the CUSUM procedure, Ann. Statist., 18, 1464-1469 (1990) · Zbl 0712.62073 |
| [23] | Shi, Z.; Gu, F.; Lennox, B.; Ball, A. D., The development of an adaptive threshold for model-based fault detection of a nonlinear electro-hydraulic system, Control Eng. Practice, 3, 11, 1357-1367 (2005) |
| [24] | Tartakovsky, A.; Rozovskii, B.; Blazek, R.; Kim, H., Detection of intrusions in information systems by sequential change-point methods, Stat. Methodol., 3, 252-293 (2006) · Zbl 1248.94032 |
| [25] | Willsky, A. S.; Jones, H. L., A generalized likelihood ratio approach to detection and estimation of jumps in linear systems, IEEE Trans. Automat. Control, 21, 108-112 (1976) · Zbl 0316.93038 |
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