A Neural-symbolic Network for Interpretable Fault Diagnosis of Rolling Element Bearings Based on Temporal Logic
Ruoyao Tian, Mengqian Cui, Gang Chen*
IEEE Transactions on Instrumentation and Measurement,2024
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This study examines the issue of interpretability in fault diagnosis for rolling bearings using a symbolic learning technique. We propose the adoption of weighted signal temporal logic (wSTL) as a formal language and introduce the temporal logic network (TLN) as a neural-symbolic learning architecture capable of encoding symbolic wSTL representations for input signals. TLN comprises three subnetworks: a basic predicate network for abstracting features and generating predicates from vibration signals, an autoencoder for identifying significant signal components, and a logic network for constructing a formal language that aids in fault classification and model interpretation. To improve comprehensibility, timed failure propagation graphs (TFPGs) are used to visually represent the logical relationships and propagation of fault events. Experimental results demonstrate TLN’s ability to extract impulse fault patterns from signals, accurately describe fault events through learned wSTL formulas, and enhance understanding of fault events for nonexpert individuals through TFPGs. These findings contribute to the field of fault diagnosis in rolling bearings by incorporating symbolic learning techniques, using formal language representation and TFPG for improved interpretability.

          @article{tian2024neural,
            title={A Neural-symbolic Network for Interpretable Fault Diagnosis of Rolling Element Bearings Based on Temporal Logic},
            author={Tian, Ruoyao and Cui, Mengqian and Chen, Gang},
            journal={IEEE Transactions on Instrumentation and Measurement},
            year={2024},
            publisher={IEEE}
          }
        

Interpretable fault diagnosis with shapelet temporal logic: Theory and application
Gang Chen*, Yu Lu, Rong Su
Automatica, 2022
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Shapelets are discriminative subsequences of sequential data that best predict the target variable and are directly interpretable, which have attracted considerable interest within the interpretable fault diagnosis community. Despite their immense potential as a data mining primitive, currently, shapelet-based methods ignore the temporal properties of shapelets. This paper presents a shapelet temporal logic, which is an expressive formal language to describe the temporal properties of shapelets. Moreover, an incremental algorithm is proposed to find the optimal logic expression with formal and theoretical guarantees, and the obtained logic expression can be used for fault diagnosis. Additionally, a case study on rolling element bearing fault diagnosis shows the proposed method can diagnose and interpret faults with high accuracy. Comparison experiments with other logic-based and shapelet-based methods illustrate the proposed method has better interpretability at the cost of computation efficiency.

          @article{chen2022interpretable,
            title={Interpretable fault diagnosis with shapelet temporal logic: Theory and application},
            author={Chen, Gang and Lu, Yu and Su, Rong},
            journal={Automatica},
            volume={142},
            pages={110350},
            year={2022},
            publisher={Elsevier}
          }
        

Formal language generation for fault diagnosis with spectral logic via adversarial training
Gang Chen et al.
IEEE Transactions on Industrial Informatics, 2020
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Fault diagnosis with formal languages can be performed in an interpretable way. However, the traditional formal languages cannot deal with noisy environments. Additionally, finding the optimal formal language for fault diagnosis is still a challenge due to the sparse reward issue. This article presents a novel method to find formal languages, written with signal spectral logic (SSL), to describe the fault behaviors among frequency domain for fault diagnosis. The formal language defined by SSL is robust to noise, acts as the fault diagnoser, and provides interpretabilities for human operators. Moreover, the fault diagnoser construction procedure has been formulated as a language generation process and an adversarial training technique is used to find the optimal formal language and avoid sparse reward issue existing in language generation problems. Some experiments with real rolling element bearing data and simulated signals demonstrate that our method is able to find formal languages to diagnose faults efficiently and accurately under noisy environments.

       
        
              @article{chen2020formal,
                title={Formal language generation for fault diagnosis with spectral logic via adversarial training},
                author={Chen, Gang  et al.},
                journal={IEEE Transactions on Industrial Informatics},
                volume={18},
                number={1},
                pages={119--129},
                year={2020},
                publisher={IEEE}
              }
              

Frequency-temporal-logic-based bearing fault diagnosis and fault interpretation using Bayesian optimization with Bayesian neural networks
Gang Chen et al.
Mechanical Systems and Signal Processing, 2020
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Rolling element bearings are widely used components in modern rotary machines, and accurate diagnosis and interpretation for faults of bearings are significant for equipment maintenance. This paper introduces a fault diagnosis method with a formal specification language, which overcomes the difficulty of understanding the decision process of fault diagnosis. The formal specification is written with a novel formal language, called frequency-temporal-logic, defining the time-frequency properties of time series signals, which not only is a classifier to diagnose the faults but also gives interpretations for the fault signals with its semantics. To find an optimal description for the fault signals, the Bayesian optimization with Bayesian neural networks has been utilized to infer the structure and parameters of the formal specification. The semantics of frequency-temporal-logic then gives the fault interpretation. Moreover, the quantitative semantics for the formal language is defined based on a novel satisfaction metric, which has a noise resistance property. Analysis of the proposed method shows that the formal description can deal with noisy signals and variable speed operations of the bearings. Finally, comparison experimental results indicate the proposed method can obtain high fault diagnosis accuracy.

       
      
            @article{chen2020frequency,
              title={Frequency-temporal-logic-based bearing fault diagnosis and fault interpretation using Bayesian optimization with Bayesian neural networks},
              author={Chen, Gang et al.},
              journal={Mechanical Systems and Signal Processing},
              volume={145},
              pages={106951},
              year={2020},
              publisher={Elsevier}
            }
            

Temporal-logic-based semantic fault diagnosis with time-series data from industrial internet of things
Gang Chen, et al.
IEEE Transactions on Industrial Electronics, 2020
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The maturity of sensor network technologies has facilitated the emergence of an industrial Internet of Things (IIoT), which has collected an increasing volume of data. Converting these data into actionable intelligence for fault diagnosis is key to reducing unscheduled downtime and performance degradation, among other examples. This article formalizes a problem called semantic fault diagnosis- to construct the formal specifications of faults directly from data collected from IIoT-enabled systems. The specifications are written as signal temporal logic formulas, which can be easily interpreted by humans. To tackle the issue of the combinatorial explosion that arises, we propose an algorithm that combines ideas from agenda-based searching and imitation learning to train a policy that searches formulas in a strategic order. Specifically, we formulate the problem as a Markov decision process, which is further solved with a reinforcement learning algorithm. Our algorithm is applied to time-series data collected from an IIoT-enabled iron-making factory. The results show empirically that our proposed algorithm is both scalable to the size of the data set and interpretable, therefore allowing human users to take actions, for example, predictive maintenance.

       
      
            @article{chen2020temporal,
              title={Temporal-logic-based semantic fault diagnosis with time-series data from industrial internet of things},
              author={Chen, Gang  et al.},
              journal={IEEE Transactions on Industrial Electronics},
              volume={68},
              number={5},
              pages={4393--4403},
              year={2020},
              publisher={IEEE}
            }