Analyzing high-dimensional thresholds for fault detection and diagnosis using active learning and Bayesian statistical modeling



yuning He


Many Fault Detection and Diagnosis (FDD) systems use dis- crete models for fault detection and analysis. Complex indus- trial systems generally have hundreds of sensors, which are used to provide data to the FDD system. Usually, the FDD wrapper code discretizes each sensor value individually and ignores any non-linearities as well as correlations between different sensor signals. This can easily lead to overly con- servative threshold settings potentially resulting in many false alarms.

In this paper, we describe an advanced statistical framework that uses Bayesian dynamic modeling and active learning techniques to detect and characterize a threshold surface and shape in a high-dimensional space. The use of active learning techniques can drastically reduce the effort to study threshold surfaces. Automated Bayesian modeling of complex thres- hold surfaces has the potential to improve quality and perfor- mance of traditional wrapper code, which often uses hyper- cube thresholds.

How to Cite

He, yuning. (2015). Analyzing high-dimensional thresholds for fault detection and diagnosis using active learning and Bayesian statistical modeling. Annual Conference of the PHM Society, 7(1).
Abstract 56 | PDF Downloads 50



bayesian statistics, high-dimensional threshold surface

Abdelwahed, S., Dubey, A., Karsai, G., & Mahadevan, N. (2011). Model-based tools and techniques for real- time system and software health management. Ma- chine Learning and Knowledge Discovery for Engi- neering Systems Health Management, 285.
Cohn, D. A. (1996). Neural network exploration using opti- mal experimental design. Advances in Neural Informa- tion Processing Systems, 6(9), 679–686.
Gramacy, R., & Polson, N. (2011). Particle learning of Gaussian process models for sequential design and op- timization. Journal of Computational and Graphical Statistics, 20(1), 467–478.
Gramacy, R. B. (2005). Bayesian treed Gaussian process models (Unpublished doctoral dissertation). University of California at Santa Cruz. (http://faculty papers/gra2005-02.pdf)
Gramacy, R. B. (2007, June 13). TGP: An R package for Bayesian nonstationary, semiparametric nonlinear re- gression and design by Treed Gaussian Process mod- els. Journal of Statistical Software, 19(9), 1–46.
He, Y. (2012). Variable-length functional output prediction and boundary detection for an adaptive flight control simulator ( (Unpubl. doct. dissertation) ). UC Santa
He, Y. (2015). Online detection and modeling of safety boundaries for aerospace applications using active learning and Bayesian statistic. In Proc. International Joint Conference on Neural Networks (IJCNN).
Jones, D., Schonlau, M., & Welch, W. J. (1998). Efficient global optimization of expensive black box functions. Journal of Global Optimization, 13, 455–492.
MacKay, D. J. C. (1992). Information–based objective func- tions for active data selection. Neural Computation, 4(4), 589–603.
Mahadevan, N., & Karsai, G. (2000–2014). Fact tool suite.
Pearl, J. (1988). Probabilistic reasoning in intelligent sys- tems: Networks of plausible inference. Morgan Kauf- mann.
Ranjan, P., Bingham, D., & Michailidis, G. (2008). Se- quential experiment design for contour estimation from complex computer codes. Technometrics, 50(4), 527– 541.
Rysdyk, R., & Calise, A. (1998). Fault tolerant flight control via adaptive neural network augmentation. AIAA Amer- ican Institute of Aeronautics and Astronautics, AIAA- 98-4483, 1722–1728.
Taddy, M. A., Gramacy, R. B., & Polson, N. G. (2011). Dy- namic trees for learning and design. Journal of the American Statistical Association, 106(493), 109-123.
Wickham, H. (2008). Practical tools for exploring data and models ( (Unpubl. doctoral dissertation) ). Iowa State.
Technical Research Papers