The fault detection problem is investigated for discrete-time linear uncertain systems. Instead of designing a fault detection system from the viewpoint of observer design for robust residual generation, an adaptive threshold approach is proposed to attain robustness against disturbance and norm-bounded model uncertainty. The main goal of the research is to develop a threshold design method that could establish an appropriate trade-off between false alarms and missed fault detection in the presence of model uncertainty. For this purpose, the H_∞ optimization technique is adopted in the linear matrix inequality framework to compute the unknown parameters of an adaptive threshold. It is shown that the proposed fault detection system based on an adaptive threshold depends only on the system parameters and the control input of the monitored system. It is independent of robust residual generator designs in traditional observer-based fault detection systems. The effectiveness of the proposed approach is verified on two well-known benchmark systems: a direct-current motor and three tank systems. Several types of faults are successfully detected in both applications.

• Ahmad, M., & Mohd-Mokhtar, R. (2021). Fault detection full order filter apply to discrete time-invariant linear system. Journal of Engineering Science and Technology, 16(5), 4221-4234.

• Ahmad, M., & Mohd-Mokhtar, R. (2022). A survey on model based fault detection techniques for linear time invariant systems with numerical analysis. Pertanika Journal of Science & Technology, 30(1), 53-78. https://doi.org/10.47836/pjst.30.1.04

• Ammiche, M., Kouadri, A., Halabi, L. M., Guichi, A., & Mekhilef, S. (2018). Fault detection in a grid-connected photovoltaic system using adaptive thresholding method. Solar Energy, 174, 762-769. https://doi.org/10.1016/j.solener.2018.09.024

• Blanke, M., Kinnaert, M., Lunze, J., & Staroswiecki, M. (2015). Diagnosis and Fault-Tolerant Control (3rd ed.). Springer.

• Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics.

• Chen, J., & Patton, R. J. (2012). Robust Model-Based Fault Diagnosis for Dynamic Systems. Springer Science & Business Media.

• Ding, S. X. (2013). Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools. Springer Science & Business Media.

• Ding, S. X. (2014). Data-Driven Design of Fault Diagnosis and Fault-Tolerant Control Systems. Springer Science & Business Media.

• Gertler, J. J. (2017). Fault Detection and Diagnosis in Engineering Systems. CRC Press.

• Isermann, R. (2006). Fault Diagnosis Systems. Springer.

• Montes de Oca, S., Puig, V., & Blesa, J. (2012). Robust fault detection based on adaptive threshold generation using interval LPV observers. International Journal of Adaptive Control and Signal Processing, 26(3), 258-283. https://doi.org/10.1002/acs.1263

• Na, Y., & Ahmad, M. (2019). A fault detection scheme for switched systems with noise under asynchronous switching. In 9th International Conference on Information Science and Technology (pp. 258-262). IEEE Publishing. https://doi.org/10.1109/ICIST.2019.8836838

• Rahnavard, M., Ayati, M., Yazdi, M. R. H., & Mousavi, M. (2019). Finite time estimation of actuator faults, states, and aerodynamic load of a realistic wind turbine. Renewable Energy, 130, 256-267. https://doi.org/10.1016/j.renene.2018.06.053

• Puig, V., Montes de Oca, S., & Blesa, J. (2013). Adaptive threshold generation in robust fault detection using interval models: Time‐domain and frequency‐domain approaches. International Journal of Adaptive Control and Signal Processing, 27(10), 873-901. https://doi.org/10.1002/acs.2362

• Raka, S. A., & Combastel, C. (2013). Fault detection based on robust adaptive thresholds: A dynamic interval approach. Annual Reviews in Control, 37(1), 119-128. https://doi.org/10.1016/j.arcontrol.2013.04.001

• Salimi, A., Batmani, Y., & Bevrani, H. (2019). Model-based fault detection in DC microgrids. In 2019 Smart Grid Conference (SGC) (pp. 1-6). IEEE Publishing. https://doi.org/10.1109/SGC49328.2019.9056589