Diagnostic Bond Graph Research Articles

Fault diagnosis of landing gear retraction system with bond graph under uncertain conditions.

Given the lack of sufficient historical data for aircraft landing gear retractor systems, a model-based fault diagnosis approach is needed to overcome this data deficiency. Meanwhile, inherent uncertainties are inevitable in engineering practice, and it is a great challenge to construct a model that accurately reflects the complexity of the actual system under uncertain conditions. Due to the urgent need for reliable model-based diagnostic methods and the need to cope with inherent uncertainties, this paper proposes an improved fault diagnostic method aimed at increasing the diagnostic efficiency of the landing gear retractor system, a critical component in aircraft take-off and landing operations. Due to a lack of historical data, the model-based fault diagnosis method can solve the problem of lack of data. The proposed uncertainty method addresses the challenge of multiple sources of uncertainty by using subsystems to reduce complexity. Fault diagnosis is achieved by comparing residuals with thresholds derived from a diagnostic bond graph (DBG) model. To address the problem of limited fault data, we modeled and simulated the landing gear retractor system using AMESim®. In addition, the linear fractional transform (LFT) approach has been used to resolve parametric uncertainties, but is unable to resolve system structural uncertainties. Therefore, we also analyzed the comparative fault diagnosis results derived from the linear fractional transformation-DBG (LFT-DBG) and the subsystem-DBG approaches. The experimental results support the effectiveness of the subsystem approach in improving fault diagnosis accuracy and reliability, highlighting its potential as a viable diagnostic strategy in aerospace engineering applications.

Fault Detection of Landing Gear Retraction/Extension Hydraulic System Based on Bond Graph-Linear Fractional Transformation Technique and Interval Analytic Redundancy Relations

Fault detection in the landing gear retraction/extension hydraulic system is difficult due to uncertainties in component parameters and sensor measurement values. This work lies in the introduction of linear fractional transformation technology and uncertainty analysis theory for the construction of the diagnostic bond graph of the landing gear retraction/extension hydraulic system. Thus, interval analytical redundancy relations can be derived as well as fault signature matrices. By using the fault signature matrix, existing faults can be detected and isolated preliminary. Furthermore, interval analytical redundancy relations can be used to detect system faults in detail. The analysis results of the failure cases of the internal and external leakage of the actuator and landing gear selector valve reversing stuck show that compared to the traditional analytical redundancy relations, this method takes into account the negative factors of uncertainty, so it can effectively reduce missed diagnosis and misdiagnosis; compared to the traditional absolute diagnostic threshold, the interval diagnostic threshold is more accurate and sensitive.

Compound Fault Diagnosis and Sequential Prognosis for Electric Scooter with Uncertainties

This paper addresses diagnosis and prognosis problems for an electric scooter subjected to parameter uncertainties and compound faults (i.e., permanent fault and intermittent fault with non-monotonic degradation). First, the diagnostic bond graph in linear fractional transformation form is used to model the uncertain electric scooter and derive the analytical redundancy relations incorporating the nominal part and uncertain part, based on which the adaptive thresholds for robust fault detection and the fault signature matrix for fault isolation can be obtained. Second, an adaptive enhanced unscented Kalman filter is proposed to identify the fault magnitudes and distinguish the fault types where an auxiliary detector is introduced to capture the appearing and disappearing moments of intermittent fault. Third, a dynamic model with usage dependent degradation coefficient is developed to describe the degradation process of intermittent fault under various usage conditions. Due to the variation of degradation coefficient and the presence of non-monotonic degradation characteristic under some usage conditions, a sequential prognosis method is proposed where the reactivation of the prognoser is governed by the reactivation events. Finally, the proposed methods are validated by experiment results.

A Hybrid Bond Graph Model-based - Data Driven Method for Failure Prognostic

Failure prognostic builds up on constant data acquisition and processing and fault diagnosis and is an essential part of predictive maintenance of smart manufacturing systems enabling condition based maintenance, optimised use of plant equipment, improved uptime and yield and to prevent safety problems. Given known control inputs into a plant and real sensor outputs or simulated measurements, the model-based part of the proposed hybrid method provides numerical values of unknown parameter degradation functions at sampling time points by the evaluation of equations that have been derived offline from a bicausal diagnostic bond graph. These numerical values are computed concurrently to the constant monitoring of a system and are stored in a buffer of fixed length. The data-driven part of the method provides a sequence of remaining useful life estimates by repeated projection of the parameter degradation into the future based on the use of values in a sliding time window. Existing software can be used to determine the best fitting function and can account for its random parameters. The continuous parameter estimation and their projection into the future can be performed in parallel for multiple isolated simultaneous parametric faults on a multicore, multiprocessor computer.The proposed hybrid bond graph model-based, data-driven method is verified by an offline simulation case study of a typical power electronic circuit. It can be used to implement embedded systems that enable cooperating machines in smart manufacturing to perform prognostic themselves.

Decentralized fault detection and isolation using bond graph and PCA methods

This paper proposes a new method for fault detection and isolation of a large-scale system by the bond graph (BG) model and the principal component analysis (PCA) technique in a decentralized architecture. The proposed method is entitled the BG-PCA technique. The main objective is to address the problem of monitoring large-scale system components by fault detection and isolation (FDI) methods. In the modeling framework, the BG model is presented by exploiting its structural and causal properties and the diagnostic bond graph (DBG). In measurement noise and perturbation conditions, the probability density function takes place to generate a clear decision procedure to detect the operating mode. In our approach, we firstly generate the structured residues. Furthermore, with a decentralized architecture, we can locate in what subsystem a fault is first detected. Finally, for isolation, the generation of the structured residues method from PCA is exploited to ensure localization. To validate the suggested BG-PCA algorithm, simulations are computed on a three-tank system to show the efficiency of the proposed FDI method, and satisfactory results are found.

Fault indicators and unique mode-dependent state equations from a fixed-causality diagnostic bond graph of linear models with ideal switches

Analytical redundancy relations are fundamental in model-based fault detection and isolation. Their numerical evaluation yields a residual that may serve as a fault indicator. Considering switching linear time-invariant system models that use ideal switches, it is shown that analytical redundancy relations can be systematically deduced from a diagnostic bond graph with fixed causalities that hold for all modes of operation. Moreover, as to a faultless system, the presented bond graph–based approach enables to deduce a unique implicit state equation with coefficients that are functions of the discrete switch states. Devices or phenomena with fast state transitions, for example, electronic diodes and transistors, clutches, or hard mechanical stops are often represented by ideal switches which give rise to variable causalities. However, in the presented approach, fixed causalities are assigned only once to a diagnostic bond graph. That is, causal strokes at switch ports in the diagnostic bond graph reflect only the switch-state configuration in a specific system mode. The actual discrete switch states are implicitly taken into account by the discrete values of the switch moduli. The presented approach starts from a diagnostic bond graph with fixed causalities and from a partitioning of the bond graph junction structure and systematically deduces a set of equations that determines the wanted residuals. Elimination steps result in analytical redundancy relations in which the states of the storage elements and the outputs of the ideal switches are unknowns. For the later two unknowns, the approach produces an implicit differential algebraic equations system. For illustration of the general matrix-based approach, an electromechanical system and two small electronic circuits are considered. Their equations are directly derived from a diagnostic bond graph by following causal paths and are reformulated so that they conform with the matrix equations obtained by the formal approach based on a partitioning of the bond graph junction structure. For one of the three mode-switching examples, a fault scenario has been simulated.

Determination of a Function for a Degradation Process by Means of Two Diagnostic Bond Graphs

This paper proposes a novel approach to a bond graph model-based failure prognosis for systems represented by a mode switching linear time-invariant model. A function for a degradation process is numerically determined by using a first stage and a second stage diagnostic bond graph model (DBG). Evaluation of the Analytical Redundancy Relations (ARRs) from the first stage DBG provides residuals that enable to detect the onset of incipient faults. The second stage DBG model accounts for parametric degradation by means of an unknown function. ARRs derived from the second stage DBG make use of the residuals of the first stage ARRs and constitute an implicit relation for the unknown degradation function. The computation takes place online concurrently to the monitoring of a real system and the measurement of its output signals. Once the time evolution of a degradation process has been computed up to some time instant, the time evolution of an ARR residual using it can be projected into the future in order to estimate the Remaining Useful Life (RUL) of a system. With progress of time the computation of a degradation process can be repeated and estimations of a RUL can be improved.

Robust fault detection and isolation in bond graph modelled processes with Bayesian networks

The main objective of this paper is to present a new method for Fault Detection and Isolation (FDI) of non-linear uncertain parameters systems modelled by bond graphs (BGs) with Bayesian networks (BN). From the BG model of a process, residuals, which are fault detectors, are determined directly from the Diagnostic Bond Graph (DBG). In ideal conditions, those residuals are equal to zero. But in practice, owing to uncertainties, perturbations and measurement noises, residuals are different from zero. Classical approaches used thresholds to deduce whether a process is in normal operating mode or in faulty mode. In our approach, we generate a statistical decision procedure to detect the operating mode. For isolation, a Bayesian network is generated by covering the causal paths of the DBG, and the method proposed by Weber et al. is exploited. A simulation example on a three tanks system is provided to show the efficiency of the proposed FDI procedure.

Robust fault detection and isolation in bond graph modelled processes with Bayesian networks

The main objective of this paper is to present a new method for Fault Detection and Isolation (FDI) of non-linear uncertain parameters systems modelled by bond graphs (BGs) with Bayesian networks (BN). From the BG model of a process, residuals, which are fault detectors, are determined directly from the Diagnostic Bond Graph (DBG). In ideal conditions, those residuals are equal to zero. But in practice, owing to uncertainties, perturbations and measurement noises, residuals are different from zero. Classical approaches used thresholds to deduce whether a process is in normal operating mode or in faulty mode. In our approach, we generate a statistical decision procedure to detect the operating mode. For isolation, a Bayesian network is generated by covering the causal paths of the DBG, and the method proposed by Weber et al. is exploited. A simulation example on a three tanks system is provided to show the efficiency of the proposed FDI procedure.

Hybrid bond graph model based for robust fault detection and isolation

The article deals with the robust fault detection and isolation based on linear fractional transformation hybrid bond graph. The main objective is to improve the robustness of fault detection step in the presence of parametric uncertainties in hybrid models in order to minimize the false alarms. The scientific interest of the proposed method is the use of only one tool – the bond graph not only for dynamic modelling of uncertain hybrid system but also for generation of adaptive thresholds needed in residual evaluation step. For this task, hybrid bond graph uncertain model approach with controlled junctions in linear fractional transformation form (allowing to represent graphically the parametric uncertainties) is first proposed to represent all the modes of the hybrid system. Second, based on causal and structural properties of the hybrid bond graph, analytical redundancy relations (with nominal and uncertain part) valid for all the modes are then derived systematically from the diagnostic hybrid bond graph. An application to a hydraulic system is used to illustrate this method.

Sequential fault diagnosis for mechatronics system using diagnostic hybrid bond graph and composite harmony search

This article proposes a sequential fault diagnosis method to handle asynchronous distinct faults using diagnostic hybrid bond graph and composite harmony search. The faults under consideration include fault mode, abrupt fault, and intermittent fault. The faults can occur in different time instances, which add to the difficulty of decision making for fault diagnosis. This is because the earlier occurred fault can exhibit fault symptom which masks the fault symptom of latter occurred fault. In order to solve this problem, a sequential identification algorithm is developed in which the identification task is reactivated based on two conditions. The first condition is that the latter occurred fault has at least one inconsistent coherence vector element which is consistent in coherence vector of the earlier occurred fault, and the second condition is that the existing fault coherence vector has the ability to hide other faults and the second-level residual exceeds the threshold. A new composite harmony search which is capable of handling continuous variables and binary variables simultaneously is proposed for identification purpose. Experiments on a mobile robot system are conducted to assess the proposed sequential fault diagnosis algorithm.

A Fault Isolation Method Based on Analytical Redundancy Relations for Spacecraft Propulsion System

Based on time-varying characters of spacecraft propulsion system, which generates tremendous difficulty to establish diagnostic criteria artificially, the fault isolation method based on Analytical Redundancy Relations (ARRs) generating from Diagnostic Bond Graph (DBG) has been proposed. The ARRs for Spacecraft Propulsion System are built on time-invariant structural characters, which can overcome the challenges from artificially establishing time-varying diagnostic criteria beforehand. By the tendency analysis of the residuals of ARRs, the fault signature matrix can be established. Then faults are isolated by comparison of observed signature and fault signature. Through the analysis of isolation results of a spacecraft propulsion system, it shows that ARRs is valid and practicable at fault isolation with rapid rates.

Robust fault detection and isolation of hybrid systems with uncertain parameters

This article addresses a robust fault detection and isolation procedure which is applicable for a hybrid system undergoing discrete mode changes. Global analytical redundancy relations, which may undergo change in their structure depending on the switched mode, are derived from the diagnostic hybrid bond graph model of the system. For fault detection and isolation analysis, the residuals, evaluated at every instant from the global analytical redundancy relations, are tested against adaptive thresholds which are changed with mode shift and variation of states, but not changed due to any fault. The parametric uncertainties are included in the diagnostic hybrid bond graph through the linear fractional transformation approach and the adaptive thresholds are obtained from the modified diagnostic hybrid bond graph model. The residuals are made robust in a sense that these would always remain within the upper and lower threshold bound for any perturbation except fault occurrence. For application of the robust fault detection and isolation analysis, a hybrid thermo-fluid system is selected whose behavioural evolution combines both discrete as well as continuous changes of states. It is shown through simulation that with parameter uncertainties in a hybrid system subject to frequent mode shift, robust fault detection and isolation is successfully achieved using the passive approach. The novelty of this work lies in the integration of the model-based diagnosis principle for hybrid systems with the approach for robust residual threshold generation for systems having uncertain parameters.

Sensitivity bond graph approach to multiple fault isolation through parameter estimation

In model-based quantitative multiple fault detection and isolation (FDI), fault disambiguation is based on parameter estimation. In this paper, the fault hypothesis is generated by evaluating a set of analytical redundancy relations (ARRs) and parameter values corresponding to the unstructured part of the fault subspace are estimated by minimizing a function of the ARRs. Process and measurement uncertainties are handled by using a passive approach for robust FDI. Bond graph modelling is used to describe process models and to derive the ARRs. The bond graph model of the process is differentially causalled and it is then converted into a diagnostic bond graph form. The diagnostic bond graph is further converted into its corresponding sensitivity bond graph form, which gives the residual sensitivity to parametric changes. The developed algorithm provides quicker fault isolation because only a few parameters are estimated and it does not need several model simulations, thereby making it suitable for real-time process supervision.

Diagnostic bond graphs for online fault detection and isolation

Analytical redundancy relations (ARR) are symbolic equations representing constraints between different known process variables (parameters, measurements and sources). ARR are obtained from the behavioural model of the system through different procedures of elimination of unknown variables. Numerical evaluation of each ARR is called a residual, which is used in model based fault detection and isolation (FDI) algorithms. For processes and systems with complex non-linearity, eliminating all unknown variables is not trivial, e.g. in the presence of algebraic loops, implicit equations, non-invertible functions, etc. However, most symbolically non-resolvable relationships can be numerically solved; and then, it becomes possible to maximise the number of structurally independent residuals. Bond graph modelling is used in this paper to derive ARR and to obtain the computational model in the case of non-resolvability of equations. A set of sub-graph substitutions in the bond graph model are developed. These substitutions directly lead to a form, where known variables (measurements, sources and parameters) are the inputs and the residuals are the outputs. Such a model is then called a diagnostic bond graph (DBG) model. It is shown that DBG models can be used for online residual computation as well as for offline verification using process data from a database. A method for the coupling of the bond graph model, used to generate the residuals, with a bond graph model, used to describe the process behaviour, is presented. The coupled model allows simulation of process behaviour both in the presence and in the absence of the faults, which is consequently used to obtain residual responses and validate the fault signatures.