EventTriggered Fault Estimation for Stochastic Systems over MultiHop Relay Networks with Randomly Occurring Sensor Nonlinearities and Packet Dropouts
Abstract
:1. Introduction
 (1)
 A codesign algorithm of eventtriggered state and fault estimator is presented for a class of linear stochastic system, for the first time, to deal with the phenomena of simultaneous randomly occurring nonlinearity and randomly occurring packet dropouts, which reflects the reality closely. An upper bound of state and fault error covariances is minimized by appropriately designing the desired estimator gain.
 (2)
 A Sufficient condition and a dataforwarding scheme are given such that the error covariance is meansquare bounded in the multihop relay links with random packet dropouts. Such dataforwarding scheme enables each relay node to forward the estimated values to the remote estimator.
 (3)
 Implementation issues of the theoretical results are discussed. A new dataforwarding communication protocol that could be applied to our addressed topology is designed; this involves hardware design and the corresponding procedure implementation. The proposed communication protocol and theoretical results are verified in a classical industrylike process.
2. Problem Statement
3. Main Results
3.1. A CoDesign Algorithm of EventTriggered State and Fault Estimator
 (a)
 For the phenomenon of packet loss and randomly occurring sensor nonlinearities, an upper bound of the error covariance ${P}_{k}^{0}$ is derived, i.e., there exists a sequence of positivedefinite matrices ${\overline{P}}_{k}^{0}\left(0\le k\le L\right)$ that satisfies$$\mathbb{E}\left[\left({x}_{k}{\widehat{x}}_{k}^{0}\right){\left({x}_{k}{\widehat{x}}_{k}^{0}\right)}^{T}\right]\le {\overline{P}}_{k}^{0}$$
 (b)
 The sequence of upper bound ${\overline{P}}_{k}^{0}$ is minimized by the designed estimator gain ${K}_{k}$ through a recursive scheme.
3.2. Data Forwarding with Packet Dropouts
Algorithm 1 Eventtriggered dataforwarding scheme 
At each time instant k, the relay node i executes: initialization ${\widehat{x}}_{0}^{i}$ and ${\overline{P}}_{0}^{i}={P}_{0}^{0}$;

4. Experimental Verification
4.1. A New Transmission Protocol for Data Forwarding Scheme
Algorithm 2 The implementation steps for the new transmission protocol 
When the data packet is requested to be sent from the relay node i to the relay node $i+1$, the following steps are performed: Step 1: For relay node i, the computation module sends a specified digital signal to the transmitter through I/O ports. Step 2: For relay node i, the switching module turns on the power of WTM. Step 3: The transmitter of relay node i sends a signal to the receiver of relay node $i+1$. Step 4: For relay node $i+1$, the receiver sends a specified digital signal to wake up the computation module by I/O ports. Step 5: For relay node $i+1$, the computation module requires switching module to power on the WTM. Step 6: The WTM of relay node i forwards data packets to the WTM of relay node $i+1$. Step 7: For relay node i, the switching module turns off the power of WTM after the end of transmission. end 
4.1.1. Hardware Design for the Experiment
4.1.2. Implementation of the Experiment
Algorithm 3 The active mode for Node i 
When Node i sends the data packet to Node $i+1$, the following steps will be performed: Step 1: For Node i: STM32 sends a signal to 315M transmitter and activates HC11. Step 2: For Node $i+1$: 315M receiver activates STM32 then activates HC11. Step 3: Node i forwards data packets to Node $i+1$. Step 4: For Node i: turns off HC11. end 
Algorithm 4 The sleep mode for Node i 
When Node i is not allowed to send the data packet to Node $i+1$, the following steps will be performed: Step 1: For Node i: STM32 and 315M transmitters enter an idle state and the HC11 is not turned on. Step 2: For Node $i+1$: STM32 calculates the corresponding decision to determine whether or not sending data packets based on the proposed dataforwarding scheme. The 315M receiver enters an idle state then HC11 is not turned on. end 
Algorithm 5 Data validation 
When sending the data packets from Node 1 to Node 2 (or from Node 2 to Node 3), the following procedures will be executed: initialization $flag1=flag2=failure$;

4.2. System Description and Modeling of the Twin WaterTank System
4.3. Assessment of Effectiveness of the Theoretical Results
5. Conclusions and Further Work
Acknowledgments
Author Contributions
Conflicts of Interest
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An upper bound of error covariance  0.231  0.24  0.373  0.381  0.396  0.412  0.438  0.466 
$\mathbf{1}\mathbf{}{\mathit{\beta}}^{\mathit{i}}$ (i = 1 and 2)  0.12  0.16  0.22  0.26  0.32  0.36  0.42  0.46 
An upper bound of error covariance  0.315  0.362  0.397  0.416  0.478  0.503  0.612  0.681 
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Share and Cite
Li, Y.; Peng, L. EventTriggered Fault Estimation for Stochastic Systems over MultiHop Relay Networks with Randomly Occurring Sensor Nonlinearities and Packet Dropouts. Sensors 2018, 18, 731. https://doi.org/10.3390/s18030731
Li Y, Peng L. EventTriggered Fault Estimation for Stochastic Systems over MultiHop Relay Networks with Randomly Occurring Sensor Nonlinearities and Packet Dropouts. Sensors. 2018; 18(3):731. https://doi.org/10.3390/s18030731
Chicago/Turabian StyleLi, Yunji, and Li Peng. 2018. "EventTriggered Fault Estimation for Stochastic Systems over MultiHop Relay Networks with Randomly Occurring Sensor Nonlinearities and Packet Dropouts" Sensors 18, no. 3: 731. https://doi.org/10.3390/s18030731