Fault detection for linear discrete time-varying systems with multiplicative noise based on parity space method

Area of Science:

• Control Systems Engineering
• Signal Processing
• Stochastic Systems

Background:

• Fault diagnosis is critical for system reliability in linear discrete time-varying systems.
• Multiplicative noise presents significant challenges in accurately detecting system faults.
• Existing methods may lack robustness or computational efficiency.

Purpose of the Study:

• To develop a robust fault diagnosis scheme for linear discrete time-varying systems with multiplicative noise.
• To propose a novel fault detection performance index based on stochastic robustness/sensitivity ratio.
• To provide computationally efficient algorithms for fault diagnosis and threshold setting.

Main Methods:

• Utilizing the parity space method for residual generation.
• Developing a recursive algorithm for computing a complex matrix related to the performance index.
• Applying random matrix analysis and multi-objective optimization for analytical solutions.
• Implementing Randomized Algorithms for fault detection threshold setting.

Main Results:

• A novel fault detection performance index is proposed, enhancing stochastic robustness.
• A computationally efficient recursive algorithm is derived for key matrix computations.
• Analytical solutions are obtained through multi-objective optimization and random matrix theory.
• Two threshold setting algorithms are presented, balancing fault detection and false alarm rates.

Conclusions:

• The proposed parity space-based fault diagnosis scheme effectively addresses robust fault detection in systems with multiplicative noise.
• The novel performance index and efficient algorithms contribute to improved fault detection performance and reliability.
• The developed threshold setting algorithms provide a probabilistic framework for residual performance assessment.