Chapter 9
Neural Network-Based Robust Fault
Detection for Nonlinear Multi-model
Jumping System
In this chapter, we investigate the robust fault detection (RFD) design scheme for
LDI-based multi-model jumping system. Primarily, we build a multi-layer neural
networks (MNN) [263, 264] to approach the nonlinearities. Then, the linear difference inclusion (LDI) representation is constructed for approximating the MNN.
Subsequently, we devote to establishing a residual generator that is dependent on an
observer. Moreover, considering the robustness against disturbances and sensitivity
to faults, the H ∞ filtering issue is introduced to minimize the influences of unknown
inputs and a new performance index is adopted to improve the sensitivity to faults.
According to these factors, the RFD observer design scheme can come down to a
two-objective optimization. Finally, the correctness of the proposed RFD observer
which can detect the faults after the occurrences without any false alarm is effectively
demonstrated by an illustrated example.
9.1 System Description
Consider the following nonlinear multi-model jumping system defined on the probability space ((, F, P):
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
˙
x(t) = A (r t ) x(t) + A h (r t ) x(t − h) + B d (r t ) ω(t) + B f (r t ) f (t)
+F (x(t), r t ) + g (x(t), x(t − h), ω(t), f (t), r t ) ,
y(t) = C (r t ) x(t) + C h (r t ) x(t − h) + D d (r t ) ω(t) + D f (r t ) f (t)
+h (x(t), x(t − h), ω(t), f (t), r t ) ,
x(t) = x 0 , r t = r 0 , t ∈ [−h 0],
(9.1)
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5_9
159
Neural Network-Based Robust Fault
Detection for Nonlinear Multi-model
Jumping System
In this chapter, we investigate the robust fault detection (RFD) design scheme for
LDI-based multi-model jumping system. Primarily, we build a multi-layer neural
networks (MNN) [263, 264] to approach the nonlinearities. Then, the linear difference inclusion (LDI) representation is constructed for approximating the MNN.
Subsequently, we devote to establishing a residual generator that is dependent on an
observer. Moreover, considering the robustness against disturbances and sensitivity
to faults, the H ∞ filtering issue is introduced to minimize the influences of unknown
inputs and a new performance index is adopted to improve the sensitivity to faults.
According to these factors, the RFD observer design scheme can come down to a
two-objective optimization. Finally, the correctness of the proposed RFD observer
which can detect the faults after the occurrences without any false alarm is effectively
demonstrated by an illustrated example.
9.1 System Description
Consider the following nonlinear multi-model jumping system defined on the probability space ((, F, P):
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
˙
x(t) = A (r t ) x(t) + A h (r t ) x(t − h) + B d (r t ) ω(t) + B f (r t ) f (t)
+F (x(t), r t ) + g (x(t), x(t − h), ω(t), f (t), r t ) ,
y(t) = C (r t ) x(t) + C h (r t ) x(t − h) + D d (r t ) ω(t) + D f (r t ) f (t)
+h (x(t), x(t − h), ω(t), f (t), r t ) ,
x(t) = x 0 , r t = r 0 , t ∈ [−h 0],
(9.1)
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5_9
159