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This study presents a FDI strategy for nonlinear dynamic systems. It shows a methodology of tackling the fault detection and isolation issue by combining a technique based on the residuals signal and a technique using the multiple Kalman filters. The usefulness of this combination is the on-line implementation of the set of models, which represents...
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... threshold depends on the probability of false alarms. Threshold limits can be defined for innovations for a normal behavior. Threshold limit selection, in most cases, is dependent on the process at hand (Himmelblau, 1978). The threshold hypothesis accounts for innovation changes due to noise and some process-model mismatch. In other words, threshold limits can be defined and based on minimum process deviations that are not acceptable. The standard multiple filters method is based on all the models (normal and faulty) of the mathematical library of faults (or bank of filters). The on-line implementation of all the models is carried out upon starting the process. Another inconvenience of the EKF compared to the linear filter is the high time required for processing; the Kalman gain is related to the Jacobian matrices of the model based on the estimated state. In fact, the extended Kalman filter is based on a linearization, enabling the state estimation of the nonlinear system. Consequently, it cannot be guaranteed that the estimation will converge. If the filter converges, the precision of the estimation depends on the system’s trajectory. In order to avoid this numerical issue, this study proposes an algorithm which scrutinizes the state of the standardized innovation i.e. the use of only one extended Kalman filter. During a normal functioning, this filter allows estimation of the measurable and non-measurable states of the process (moles number, concentrations, or others) and could be even used for the development of the control laws based on the process predictions. In other cases when the statistical threshold for the standardized innovation exceeds a fixed level of significance (15 %), including the measurement noises and the modelling errors, the fault isolation module is engaged. The usefulness of this combination is to avoid the matrix inversions and numerical integrations when the process is functioning near to the normal mode. This combination is described by the diagram in Fig. 2. The chemical reactor represented in Fig. 3 works under atmospheric pressure. It is a glass-jacketed reactor with a tangential input for heat transfer fluid. The capacity of the reactor is two liters. It is equipped with an electrical calibration heating, a stirring system (anchor) and an input system (two dosing pumps and two scales, with temperature measurement at input). It is also equipped with Pt100 temperature probes. Five probes are inserted through the chemical reactor in the reaction mass, in the cooling, in the condenser and in the flow rate introduction. The heating-cooling system, which uses a single heat transfer fluid, works within a temperature range from -15 to +200 °C. Supervision software allows the fitting of the parameters and their instruction value. The parameters introduced in the supervision system are the control modes of the reaction mass temperature (isothermal or slope of the temperature) and of the jacket fluid (constant or slope of the temperature). The distillation mode (the difference between the reaction mass temperature and the fluid jacket temperature is maintained constant) can also be introduced. Supervision software also allows the regulation of the flow rate introduction and the stirring rate of the reactor. It displays and stores data during the experiment for further exploitation. In order to illustrate the proposed FDI approach, a chemical synthesis in a laboratory-size reactor was carried-out. The reaction chosen is a very exothermic oxido-reduction one (Aime, 1991), the oxidation of sodium thiosulfate by hydrogen peroxide. This reaction can be expressed by the following ...
Citations
... It is design with large number of sensors and actuators to monitor and control the process. With a complex build and a nonlinear characteristic these system is susceptible to faults [1][2][3]. ...
Continuous Stirred Tank Reactor (CSTR) plays a major role in chemical industries, it ensures the process of mixing reactants according to the attended specification to produce a specific output. It is a complex process that usually represent with nonlinear model for benchmarking. Any abnormality, disturbance and unusual condition can easily interrupt the operations, especially fault. And this problem need to detect and rectify as soon as possible. A good knowledge based fault detection using available model require a good error residual between the measurement and the estimated state. Kalman filter is an example of a good estimator, and has been exploited in many researches to detect fault. In this paper, Higher degree Cubature Kalman Filter (HDCKF) is proposed as a method for fault detection by estimation the current state. Cubature Kalman filter (CKF) is an extension of the Kalman filter with the main purpose is to estimate process and measurement state with high nonlinearities. It is based on spherical radial integration to estimate current state by generating cubature points with specific value. Conventional CKF use 3rd degree spherical and 3rd degree radial, here we implement Higher Degree CKF (HDCKF) to have better accuracy as compared to conventional CKF. High accuracy is required to ensure no false alarm is detected and furthermore good computational cost will improve its detection. Finally, a numerical example of CSTR fault detection using HDCKF is presented. Implementation of HDCKF for fault detection is compared with other filter to show effective results.
... MM-based FDI algorithm has been widely used in different applications such as jet engine [23][24][25][26] and chemical reactors. 27 The model corresponding to m i is given as where X(k) 2 R n , u(k) 2 R p , and z(k) 2 R q , k ø 0, denote the state, the input, and the output of the system, respectively, and w i (k) and v i (k) are the process and observation noises which are assumed to be mutually independent zero mean white Gaussian stochastic process with covariance matrices Q i and R i , respectively. The fault parameter vector m i may represent actuator or system faults. ...
In this article, an actuator fault-tolerant control scheme is proposed for differential-drive mobile robots based on the concept of multiple-model approach. The nonlinear kinematic model of the differential-drive mobile robot is discretized and a bank of extended Kalman filters is designed to detect, isolate, and identify actuator faults. A fault-tolerant controller is then developed based on the detected fault to accommodate its effect on the trajectory-tracking performance of the mobile robot. Extensive experimental results are presented to demonstrate the efficacy of the proposed fault-tolerant control approach.
... 10 MM methods offer the advantage of low computational cost while still providing diagnostic information; however, there are only limited examples of their use in chemical systems. 16,17 Furthermore, these works focus on unbiased output estimation and control, which does not necessarily guarantee unbiased state estimation. The design of an appropriate model set to use with MM methods is also challenging, because there needs to be enough separation between models based on output residuals 15 and enough models to capture the range of system dynamics; however, using too many models will decrease performance. ...
Accurate state estimates are important for the success of MPC. State estimates are obtained using a model but in real plants there will always be model plant mismatch (MPM) which affects these estimates. In this work, we present a multiple model based approach to obtain unbiased state estimates in the presence of MPM. Necessary assumptions on the source of mismatch and models used are presented. It is shown that unbiased output estimates do not guarantee unbiased state estimates. Our approach is shown to provide unbiased state estimates when all the assumptions are met using a froth flotation system. A model identification based control approach using our multiple model estimation approach with a conventional MPC was tested on the froth flotation system and was found to successfully provide offset free reference tracking when all the necessary assumptions for unbiased state estimation were met. A nonlinear offset free MPC was also tested on the froth flotation system but was not able to provide offset free reference tracking as some necessary conditions were not met.
... Reliable availability of the process variables and signals is essential for the design and maintenance of waste-heat recovery systems, which is often not the case in real-case scenarios due to incomplete models or lack of sensors. The Extended Kalman Filter is a well-known observer providing state and parameter estimates of unmeasured signals in many industrial applications such as in chemical P reactors, biochemical, food industry and turbo-charged diesel engine in automotive applications, [5], [6], [7], [8]. As long as the models are deterministic -as in the aforementioned work -proper estimates are obtained. ...
... Reliable availability of the process variables and signals is essential for the design and maintenance of waste-heat recovery systems, which is often not the case in real-case scenarios due to incomplete models or lack of sensors. The Extended Kalman Filter is a well-known observer providing state and parameter estimates of unmeasured signals in many industrial applications such as in chemical reactors, biochemical, food industry and turbo-charged diesel engine in automotive applications, [5], [6], [7], [8]. As long as the models are deterministic -as in the aforementioned work -proper estimates are obtained. ...
This paper presents the waste-heat energy recovery estimation of a cooling network on cruising ships. Based on first principle modelling and a known circuit layout the waste-heat recovery system is presented as a partially-observed system, whose unknown states and parameters can be estimated online by application of Conditionally Gaussian filtering. Accurate estimates and input-output behaviour of the circuit are obtained, which has been validated against a set of real data provided by the ship operator confirming the efficiency of the algorithm.
... In this context, diverse model-based observers for fault diagnosis have been applied to chemical processes for instance: the Luenberger observer [19] [20], the Kalman filter [21] [22], the sliding mode observer [23], the H 1 based observer [24], the adaptive observer [4], high-gain observer based on Fliess's generalized observability canonical form [25] and unknown input observer [26] [27], just to cite some of them. Better methods for fault diagnosis have become necessary to accomplish the scientific and industrial development of modern processes. ...
Under the vast variety of fuzzy model-based observers reported in the literature, what would be the proper one to be used for fault detection in a class of chemical reactor? In this study four fuzzy model-based observers for sensor fault detection of a Continuous Stirred Tank Reactor were designed and
compared. The designs include (i) a Luenberger fuzzy observer, (ii) a Luenberger fuzzy observer with sliding modes,(iii) a Walcott–Zak fuzzy observer, and (iv) an Utkin fuzzy observer. A negative, an oscillating fault signal, and a bounded random noise signal with a maximum value of +-0.4 were used to evaluate and compare the performance of the fuzzy observers.The Utkin fuzzy observer showed the best performance under the tested conditions.
... An industrial chemical process plant is often subjected to low productivity caused by abnormal operating conditions as a result of faulty operations, equipment degradation, and external disturbances. The ever-increasing demands on safety and environmental protection, and the economic concerns have forced the industries to search for newer and more effective techniques to diagnose process malfunctions [1]. Fault diagnosis in large-scale and complex industrial plants is particularly difficult because of the high degree of interconnection among various plant components. ...
... In fact, most of the reported actuator faults are due to the stickiness and corrosiveness of the materials that circulate in the chemical processes [4]. Early Fault Detection and Isolation (FDI) in industrial plants is crucially required to prevent product damage, severe machine failure, production deterioration, quality degradation, profit loss, environmental pollution and threats to human health [1]. ...
... The main sources of process disturbances include nonlinear effects like saturation, dead zone or hysteresis in the control valves, sensors or the process, local instability due to control loops interactions, structural disturbances arising from mass or energy transfer between different process units especially with recycle streams, disturbances in the process boundaries and weakly-tuned controllers. A major part of these disturbances is oscillatory in nature [1]. ...
Complexity of industrial plants and their stringent environmental and safety regulations have necessitated early detection and isolation of process faults. All the existing fault isolation methods can be categorized into two general groups: model-based and data-based. Transfer entropy is a data-based method for measuring propagation direction of disturbance and finding its root cause. In this paper, a new transfer entropy-based method is proposed to isolate different process faults. The novelty of this paper lies in using the transfer entropy idea to generate distinct patterns of information flow among process variables, recognize their correlations in the context of the transferred information in any abnormal condition, and finally isolate different process faults. The experimental results clearly demonstrate the superiority of the proposed method to the conventional methods.
... Hybrid systems modeling and supervision have been used extensively in automation, and manufacturing applications that includes such faults [1]. Different frameworks for dynamic supervisory controllers are used in flexible manufacturing systems and automated batch processes [2][3]. The high-level system changes in hybrid systems are modeled as discrete event dynamic systems, while the low-level systems changes are modeled as continuous variable dynamic systems. ...
... Researches have been conducted for this issue; however, they are computationally demand. Chetouani presented a FDI strategy for nonlinear dynamic systems [2]. It shows a methodology of tackling the fault detection and isolation issue by combining a technique based on the residuals signal and a technique using the multiple Kalman filters. ...
Fault diagnosis plays a vital role in ensuring safe and efficient operation of modern process plants. Despite the encouraging progress in its research, developing a reliable and interpretable diagnostic system remains a challenge. There is a consensus among many researchers that an appropriate modelling, representation and use of fundamental process knowledge might be the key to addressing this problem. Over the past four decades, different techniques have been proposed for this purpose. They use process knowledge from different sources, in different forms and on different details, and are also named model-based methods in some literature. This paper first briefly introduces the problem of fault detection and diagnosis, its research status and challenges. It then gives a review of widely used model- and knowledge-based diagnostic methods, including their general ideas, properties, and important developments. Afterwards, it summarises studies that evaluate their performance in real processes in process industry, including the process types, scales, considered faults, and performance. Finally, perspectives on challenges and potential opportunities are highlighted for future work.
This paper deals with the problem of simultaneous concentration and faults estimations of a continuous stirred tank reactor (CSTR) subject to unknown inputs. We propose a combination of two robust nonlinear observers for state estimation and fault reconstruction without any use of a linear approximation of the CSTR dynamic model. Based on the high-gain observer, the proposed scheme can guarantee the asymptotic estimation of the concentration inside the reactor, while, a robust term is added to the nominal plant on the basis of the super-twisting algorithm for fault reconstruction. The stability analysis is proved mathematically using the Lyapunov theory. The effectiveness and robustness of the proposed scheme are illustrated via simulations.
This paper presents a fault detection and isolation (FDI) approach for actuator faults of complex thermal management systems. In the case of safety critical systems, early fault diagnosis not only improves system reliability, but can also help prevent complete system failure (i.e., aircraft system). In this work, a robust unknown input observer (UIO)-based actuator FDI approach is applied on an example aircraft fluid thermal management system (FTMS). Robustness is achieved by decoupling the effect of unknown inputs modeled as additive disturbances (i.e., modeling errors, linearization errors, parameter variations, or model order reduction errors) from the residuals generated from a bank of UIOs. Robustness is central to avoid false alarms without reducing residual sensitivity to actual faults in the system. System dynamics are modeled using a graph-based approach. A structure preserving aggregation-based model-order reduction technique is used to reduce the complexity of the dynamic model. A reduced-order linearized state space model is then used in a bank of UIOs to generate a set of structured robust (in the sense of disturbance decoupling) residuals. Simulation and experimental results show successful (i.e., no false alarms) actuator FDI in the presence of unknown inputs.
