Anuradha Kodali

Dynamic Multiple Fault Diagnosis: Mathematical Formulations and Solution Techniques

Imperfect test outcomes, due to factors such as unreliable sensors, electromagnetic interference, and environmental conditions, manifest themselves as missed detections and false alarms. This paper develops near-optimal algorithms for dynamic multiple fault diagnosis (DMFD) problems in the presence of imperfect test outcomes. The DMFD problem is to determine the most likely evolution of component states, the one that best explains the observed test outcomes. Here, we discuss four formulations of the DMFD problem. These include the deterministic situation corresponding to perfectly observed coupled Markov decision processes to several partially observed factorial hidden Markov models ranging from the case where the imperfect test outcomes are functions of tests only to the case where the test outcomes are functions of faults and tests, as well as the case where the false alarms are associated with the nominal (fault free) case only. All these formulations are intractable NP-hard combinatorial optimization problems. Our solution scheme can be viewed as a two-level coordinated solution framework for the DMFD problem. At the top (coordination) level, we update the Lagrange multipliers (coordination variables, dual variables) using the subgradient method. At the bottom level, we use a dynamic programming technique (specifically, the Viterbi decoding or Max-sum algorithm) to solve each of the subproblems, one for each component state sequence. The key advantage of our approach is that it provides an approximate duality gap, which is a measure of the suboptimality of the DMFD solution. Computational results on real-world problems are presented. A detailed performance analysis of the proposed algorithm is also discussed.

Novel Classifier Fusion Approaches for Fault Diagnosis in Automotive Systems

Faulty automotive systems significantly degrade the performance and efficiency of vehicles, and oftentimes are the major contributors of vehicle breakdown; they result in large expenditures for repair and maintenance. Therefore, intelligent vehicle health-monitoring schemes are needed for effective fault diagnosis in automotive systems. Previously, we developed a data-driven approach using a data reduction technique, coupled with a variety of classifiers, for fault diagnosis in automotive systems. In this paper, we consider the problem of fusing classifier decisions to reduce diagnostic errors. Specifically, we develop three novel classifier fusion approaches: class-specific Bayesian fusion, joint optimization of fusion center and of individual classifiers, and dynamic fusion. We evaluate the efficacies of these fusion approaches on an automotive engine data. The results demonstrate that dynamic fusion and joint optimization, and class-specific Bayesian fusion outperform traditional fusion approaches. We also show that learning the parameters of individual classifiers as part of the fusion architecture can provide better classification performance.

An integrated health management process for automotive cyber-physical systems

Automobile is one of the most widely distributed cyber-physical systems. Over the last few years, the electronic explosion in automotive vehicles has significantly increased the complexity, heterogeneity and interconnectedness of embedded systems. Although designed to sustain long life, systems degrade in performance due to gradual development of anomalies eventually leading to faults. In addition, system usage and operating conditions (e.g., weather, road surfaces, and environment) may lead to different failure modes that can affect the performance of vehicles. Advanced diagnosis and prognosis technologies are needed to quickly detect and isolate faults in network-embedded automotive systems so that proactive corrective maintenance actions can be taken to avoid failures and improve vehicle availability. This paper discusses an integrated diagnostic and prognostic framework, and applies it to two automotive systems, viz., a Regenerative Braking System (RBS) in hybrid electric vehicles and an Electric Power Generation and Storage (EPGS) system.

Dynamic Set-Covering for Real-Time Multiple Fault Diagnosis With Delayed Test Outcomes

The set-covering problem is widely used to model many real-world applications. In this paper, we formulate a generalization of set-covering, termed dynamic set-covering (DSC), which involves a series of coupled set-covering problems over time. We motivate the DSC problem from the viewpoint of a dynamic multiple fault diagnosis problem, wherein faults, possibly intermittent, evolve over time; the fault-test dependencies are deterministic (components associated with passed tests cannot be suspected to be faulty and at least one of the components associated with failed tests is faulty), and the test outcomes may be observed with delay. The objective of the DSC problem is to infer the most probable time sequence of a parsimonious set of failure sources that explains the observed test outcomes over time. The DSC problem is NP-hard and intractable due to the fault-test dependency matrix that couples the failed tests and faults via the constraint matrix, and the temporal dependence of failure sources over time. By relaxing the coupling constraints using Lagrange multipliers, the DSC problem can be decoupled into independent subproblems, one for each fault. Each subproblem is solved using the Viterbi decoding algorithm, and a primal feasible solution is constructed by modifying the Viterbi solutions via a heuristic. The Lagrange multipliers are updated using a subgradient method. The proposed Viterbi-Lagrangian relaxation algorithm provides a measure of suboptimality via an approximate duality gap. As a major practical extension of the above problem, we also consider the problem of diagnosing faults with delayed test outcomes, termed delay DSC. A detailed experimental evaluation of the algorithms is provided using real-world problems that exhibit masking faults.

A prognostic framework for health management of coupled systems

This paper describes a unified data-driven prognostic framework that combines failure time data, static parameter data and dynamic (time-series) data. The approach employs Cox proportional hazards model (Cox PHM) and soft dynamic multiple fault diagnosis algorithm (DMFD) for inferring the degraded state trajectories of components and to estimate their remaining useful life (RUL). This framework takes into account the cross-subsystem fault propagation, a case prevalent in any networked and embedded system. The key idea is to use Cox proportional hazards model to estimate the survival functions of error codes and symptoms (soft test outcomes/prognostic indicators) from failure time data and static parameter data, and use them to infer the survival functions of components via a soft DMFD algorithm. The average remaining useful life and its higher-order central moments (e.g., variance, skewness, kurtosis) can be estimated from these component survival functions. The proposed prognostic framework has the potential to be applicable to a wide variety of systems, ranging from automobiles to aerospace systems.

A factorial hidden markov model (FHMM)-based reasoner for diagnosing multiple intermittent faults

This paper presents a factorial hidden Markov model (FHMM)-based diagnostic reasoner to handle multiple intermittent faults. The dynamic multiple fault diagnosis (DMFD) problem is to determine the most likely evolution of fault states, the one that best explains the observed test outcomes over time. In our previous research work [1], we have shown that the problem of diagnosing dynamic multiple faults in the presence of imperfect test outcomes, is an NP-hard problem. Here, we combine a Gauss-Seidel coordinate ascent optimization method with a Soft Viterbi decoding algorithm for solving the DMFD problem. We demonstrated the algorithm on small-scale and medium-scale systems and the simulation results shows that this approach improves primal function value (1.4%∼8.3%) and correct isolation rate (1.7%∼11.4%) as compared to a Lagrangian relaxation method discussed in our previous work [1].

Dynamic fusion of classifiers for fault diagnosis

This paper considers the problem of temporally fusing classifier outputs to improve the overall diagnostic classification accuracy in safety-critical systems. Here, we discuss dynamic fusion of classifiers which is a special case of the dynamic multiple fault diagnosis (DMFD) problem [1]-[3]. The DMFD problem is formulated as a maximum a posteriori (MAP) configuration problem in tri-partite graphical models, which is NP-hard. A primal-dual optimization framework is applied to solve the MAP problem. Our process for dynamic fusion consists of four key steps: (1) data preprocessing such as noise suppression, data reduction and feature selection using data-driven techniques, (2) error correcting codes to transform the multiclass data into binary classification, (3) fault detection using pattern recognition techniques (support vector machines in this paper), and (4) dynamic fusion of classifiers output labels over time using the DMFD algorithm. An automobile engine data set, simulated under various fault conditions [4], was used to illustrate the fusion process. The results demonstrate that an ensemble of classifiers, when fused over time, reduces the classification error as compared to a single classifier and static fusion of classifiers trained over the entire batch of data. The results for sliding window dynamic fusion are also provided.

Incremental Classifiers for Data-Driven Fault Diagnosis Applied to Automotive Systems

One of the common ways to perform data-driven fault diagnosis is to employ statistical models, which can classify the data into nominal (healthy) and a fault class or distinguish among different fault classes. The former is termed fault (anomaly) detection, and the latter is termed fault isolation (classification, diagnosis). Traditionally, statistical classifiers are trained using data from faulty and nominal behaviors in a batch mode. However, it is difficult to anticipate, a priori, all the possible ways in which failures can occur, especially when a new vehicle model is introduced. Therefore, it is imperative that diagnostic algorithms adapt to new cases on an ongoing basis. In this paper, a unified methodology to incrementally learn new information from evolving databases is presented. The performance of adaptive (or incremental learning) classification techniques is discussed when: 1) the new data has the same fault classes and same features and 2) the new data has new fault classes, but with the same set of observed features. The proposed methodology is demonstrated on data sets derived from an automotive electronic throttle control subsystem.

Coupled Factorial Hidden Markov Models (CFHMM) for Diagnosing Multiple and Coupled Faults

In this paper, we formulate a coupled factorial hidden Markov model-based (CFHMM) framework to diagnose dependent faults occurring over time (dynamic case). In our previous research, the problem of diagnosing multiple faults over time (dynamic multiple fault diagnosis (DMFD)) is solved based on a sequence of test outcomes by assuming that the faults and their time evolution are independent. This problem is NP-hard, and, consequently, we developed a polynomial approximation algorithm using Lagrangian relaxation within a FHMM framework. Here, we extend this formulation to a mixed memory Markov coupling model, termed dynamic coupled fault diagnosis (DCFD) problem, to determine the most likely sequence of (dependent) fault states, the one that best explains the observed test outcomes over time. An iterative Gauss-Seidel coordinate ascent optimization method is proposed for solving the DCFD problem. A soft Viterbi algorithm is also implemented within the framework for decoding-dependent fault states over time. We demonstrate the algorithm on simulated systems with coupled faults and the results show that this approach improves the correct isolation rate (CI) as compared to the formulation where independent fault states (DMFD) are assumed. As a by-product, we show empirically that, while diagnosing for independent faults, the DMFD algorithm based on block coordinate ascent method, although it does not provide a measure of suboptimality, provides better primal cost and higher CI than the Lagrangian relaxation method for independent fault case. Two real-world examples (a hybrid electric vehicle, and a mobile autonomous robot) with coupled faults are also used to evaluate the proposed framework.

Fault Diagnosis in the Automotive Electric Power Generation and Storage System (EPGS)

In this paper, we present an initial study to develop fault detection and isolation techniques for the vehicle systems that are controlled by a network of electronic control units (ECUs). The root causes of the faults include hardware components such as actuators, software within the controllers (ECUs), or the interactions between hardware and software, i.e., between controllers and plants. These faults, originating from various interactions and especially between hardware and software, are particularly challenging to address. Our basic strategy is to divide the fault universe of the cyber-physical system in a hierarchical manner, and monitor the critical variables/signals that have impact at different levels of interactions. Diagnostic matrix is established to represent the relationship between the faults and the test outcomes (also known as fault signatures). A factorial hidden Markov model-based inference algorithm, termed dynamic multiple fault diagnosis, is used to infer the root causes based on the observed test outcomes. The proposed diagnostic strategy is validated on an electrical power generation and storage system controlled by two ECUs in an environment with CANoe/MATLAB co-simulation. Eleven faults are injected with the failures originating in actuator hardware, sensor, controller hardware, and software components (sensor faults are not considered in this paper). The simulation results show that the proposed diagnostic strategy is effective in addressing the interaction-caused faults.