[Paper Review] Efficient Sensor Fault Detection Using Group Testing

Chun Lo, Yechao Bai+2 more|arXiv (Cornell University)|Jan 17, 2015

SARS-CoV-2 detection and testing32 references3 citations

TL;DR

This paper proposes a novel group testing approach using Kalman filtering to detect rare faulty sensors in wireless sensor networks with significantly fewer tests than traditional methods. By testing groups of sensors and leveraging Kalman filter-based fault detection, the method reduces computational complexity and improves accuracy, especially under noisy conditions, outperforming non-adaptive and existing adaptive group testing techniques in real-world vibration data from the New Carquinez Bridge.

ABSTRACT

When faulty sensors are rare in a network, diagnosing sensors individually is inefficient. This study introduces a novel use of concepts from group testing and Kalman filtering in detecting these rare faulty sensors with significantly fewer number of tests. By assigning sensors to groups and performing Kalman filter-based fault detection over these groups, we obtain binary detection outcomes, which can then be used to recover the fault state of all sensors. We first present this method using combinatorial group testing. We then present a novel adaptive group testing method based on Bayesian inference. This adaptive method further reduces the number of required tests and is suitable for noisy group test systems. Compared to non-group testing methods, our algorithm achieves similar detection accuracy with fewer tests and thus lower computational complexity. Compared to other adaptive group testing methods, the proposed method achieves higher accuracy when test results are noisy. We perform extensive numerical analysis using a set of real vibration data collected from the New Carquinez Bridge in California using an 18-sensor network mounted on the bridge. We also discuss how the features of the Kalman filter-based group test can be exploited in forming groups and further improving the detection accuracy.

Motivation & Objective

• To address the inefficiency of individual sensor fault detection in large-scale sensor networks where faulty sensors are rare.
• To reduce the number of required tests below O(N) by leveraging group testing principles in sensor networks.
• To improve fault detection accuracy and robustness in noisy test environments, especially when system models are imperfect.
• To integrate Kalman filtering with group testing to exploit dynamic system behavior for better subgroup formation and detection.
• To develop a scalable, adaptive method that uses prior test results to minimize tests while maintaining high detection accuracy.

Proposed method

• The method uses combinatorial group testing (CGT) to test random groups of sensors and determine if any faulty sensor is present, based on binary outcomes from Kalman filter-based fault detection.
• An adaptive Bayesian group testing (BGT) method is proposed that uses previous test results to sequentially refine group selection, reducing the number of required tests.
• Kalman filtering is applied to estimate system states within each group, and discrepancies between state estimates with and without faulty sensors are used to detect faults.
• A novel enhancement, KF-BGT, improves BGT by dividing test groups into subgroups with balanced faulty sensor distribution and adding high-confidence normal sensors to subgroups to stabilize estimation.
• The system model order (state size) is tuned to balance estimation accuracy and computational cost, with results showing sensitivity to model quality.
• A detection threshold is selected based on group size to maintain consistent error probability across different group sizes.

Experimental results

Research questions

• RQ1 Can group testing reduce the number of required tests for sensor fault detection in large networks with rare faulty sensors?
• RQ2 How does Kalman filtering enhance group testing performance when test results are noisy?
• RQ3 To what extent does adaptive Bayesian group testing (BGT) outperform non-adaptive combinatorial group testing (CGT) in terms of test efficiency and accuracy?
• RQ4 How does the distribution of faulty sensors between subgroups affect detection accuracy in Kalman filter-based group testing?
• RQ5 Can KF-BGT maintain high detection accuracy even when the system model is of low order or inaccurate?

Key findings

• The proposed KF-BGT method reduces test count significantly compared to non-group testing methods while maintaining high detection accuracy, especially under noisy conditions.
• BGT outperforms CGT by using adaptive test selection, reducing the number of tests required due to sequential use of prior results.
• When the system model order is reduced from 162 to 90, BGT performance degrades significantly, but KF-BGT shows only a slight decline, demonstrating robustness to model inaccuracy.
• The discrepancy in state estimates between normal and faulty conditions increases with group size, indicating that uniform group sizes are essential for consistent detection error probability.
• Evenly distributing faulty sensors across subgroups (e.g., one per group) leads to higher state estimate discrepancies than concentrating them, improving detection accuracy.
• Adding high-confidence normal sensors to small subgroups improves detection stability and reduces variance in state estimate discrepancies.