Sensor Fault Diagnosis

As previously stated, two observers are adopted for sensor fault diagnosis  

Both the observers have the following form (hereafter i = 1, 2)  

The state estimation error xsMi = x — jcsm can be analyzed by considering the estimation error dynamics, derived from (6.5) and (6.10), 

Convergence properties of jEsm are established by the following result. 

Theorem 6.1 In the absence of faults, uncertainties, and sensor noise (i.e., fs = 0, i) = 0, and rii = 0), if the rate constants are bounded as in (2.32) and (2.33), there exists a set of observer gains such that the state estimation error sm of the observer (6.10) is globally uniformly convergent to 0 as t 00. Moreover, the convergence is exponential. 

---

D.L. Yu, J.B. Gomm, and D. Williams. Sensor fault diagnosis in a chemical process via RBF neural networks. Control Engineering Practice, 7 49-55, 1999. 

System diagnosis frequently lies on a model that represents the normal behavior of a particular process to be supervised. The fundamental problem comes then from the inaccuracies associated with the model, either related to the ignorance of the kinetics or its parameters, or related to the ignorance of its inputs. Within the framework of this chapter, the interest is focused on the detection and location of sensor faults in the presence of unknown inputs. Among the existing solutions based on observers, one can distinguish the approaches based on non-linear unknown inputs observers (see for example, [21],... 

A traditional approach to fault diagnosis in the wider application context is based on hardware i.e. physical) redundancy methods which use multiple lines of sensors, actuators, computers and software to measure and/or control a particular variable. Typically, a voting scheme is applied to the hardware redundant system to decide if and when a fault has occurred and its likely location amongst redundant system components. The use of multiple redundancy in this way is common, for example with digital fly-by-wire flight control... 

The previous section concentrated on the management of a hard and soft sensors network. This is an important step since the information sources must be carefully checked before being further used. This section will be devoted to the diagnosis of the overall biological state of the process. In particular, it will illustrate that the use of the Evidence theory approach improves the fault diagnosis system in terms of modularity and d3mamical adaptation. 

Dunia R, Qin SJ. Joint diagnosis of process and sensor faults using principal component analysis. Control Engineering Practice 1998, 6, 457 169. 

Early approaches to fault diagnosis were often based on the so-called physical redundancy [11], i.e., the duplication of sensors, actuators, computers, and softwares to measure and/or control a variable. Typically, a voting scheme is applied to the redundant system to detect and isolate a fault. The physical redundant methods are very reliable, but they need extra equipment and extra maintenance costs. Thus, in the last years, researchers focused their attention on techniques not requiring extra equipment. These techniques can be classified into two general categories, model-free data-driven approaches and model-based approaches. 

The literature focused on model-based FD presents a few applications of observers to chemical plants. In [10] an unknown input observer is adopted for a CSTR, while in [7] and [21] an Extended Kalman Filter is used in [9] and [28] Extended Kalman Filters are used for a distillation column and a CSTR, respectively in [45] a generalized Luenberger observer is presented in [24] a geometric approach for a class of nonlinear systems is presented and applied to a polymerization process in [38] a robust observer is used for sensor faults detection and isolation in chemical batch reactors, while in [37] the robust approach is compared with an adaptive observer for actuator fault diagnosis. 

In this chapter, an FD framework for batch chemical processes is developed, where diagnosis of sensor, actuator, and process faults can be achieved via an integrated approach. The proposed approach is based on physical redundancy for detection of sensor faults [38], while an analytical redundancy method, based on a bank of diagnostic observers, is adopted to perform process/actuator fault detection, isolation, and identification [4],... 

In the fifth chapter, a general overview of temperature control for batch reactors is presented the focus is on model-based control approaches, with a special emphasis on adaptive control techniques. Finally, the sixth chapter provides the reader with an overview of the fundamental problems of fault diagnosis for dynamical systems, with a special emphasis on model-based techniques (i.e., based on the so-called analytical redundancy approach) for nonlinear systems then, a model-based approach to fault diagnosis for chemical batch reactors is derived in detail, where both sensors and actuators failures are taken into account. 

Fault detection and isolation are a prerequisite of fault diagnosis necessitating system observability and proper signal measurement and processing in the presence of noise. The thus obtained information then is to be processed in real time by a decision support software system that takes into account that sensors themselves can be faulty. According to Venkatasubramanian et al. [14-16], fault detection and diagnosis methods may be classified into... 

Isermann, R. (2011). Fault diagnosis applications - model-based condition monitoring actuators, drives, machinery, plants, sensors, and fault-tolerant systems. Springer. 

Adaptive thresholds are designed to achieve robustness in fault diagnosis. The robustness is particularly required with respect to parameter and measurement uncertainties (sensor noise) so that misdetections and false alarms are both minimized. The active approach to robustness is based on generating residuals that are insensitive to uncertainties, but sensitive to faults. The passive approach tries to accomplish robustness in the decision-making stage. Adaptive threshold is a passive approach. 

The importance of this case study is three-fold (1) to explain simple concepts, (2) comparison with the results discussed in the literature and, (3) to emphasize the ability to perform multiple fault diagnosis. The controlled tank and its SDG under the perfect control scenario are given in Figure 2 (a) and (b), respectively. fi and / are the inlet and outlet flowrates, respectively. L is the level of the liquid in the tank, kc is negative. The measurements are f , and CS. Diagnosis for two fault scenarios is discussed below. Positive sensor bias The observed pattern is [/<, Xm G5] = [0 0 +). Any fault in /< or set point is ruled out. The candidate faults are VPuas = (= X= 0 ) or Xm,bias = + (= X = - ). Further resolution cannot be achieved. 

Zug, S., Dietrich, A., Kaiser, J. Fault-handling in networked sensor systems. In Fault Diagnosis in Robotic and Industrial Systems (2012)... 

Repetition of this measurement step each time a new campaign is initiated is tracked and assessed for variance in the distribution, trends, and outliers in the data measurement and risk (continuous fault) analysis on the sensors or analyzers and CPUs. All or part of the measurement and sensor data may become part of a database constructed from past validation and historical data that have been previously shown through root cause analysis to be the result of known material, process, or sensor variation that has exceeded the specifications. Each manufacturing campaign becomes a potential well for new data, which in turn becomes fodder for a dynamic database for which variable data can be assessed against nominal and expected process and sensor performance, diagnosis made, and remedial action instituted, all occurring perhaps in a millisecond to a second timescale. 

A fault can be regarded as a not allowed deviation of at least one property or one characteristic parameter of the system compared to the normal operating conditions. The occurrence of a fault may have serious consequences in the process and may cause the facilities standstill, even to damage them. Several examples illustrating the gravity of the occurrence of sensor or actuators faults are reported in [25], [26], [62]. The fault detection refers to the determination of the presence of faults as well as their occurrence moment while the diagnosis is the determination of its amplitude and its behavior. 

Related studies to the diagnosis of bioprocess have been limited and have used mainly heuristic approaches. Moreover, they have been concerned with the detection of a disfunction of the bioprocess (detection of a desestabiliza-tion, state of the biomass, etc.) rather than the detection and the location of sensor and/or actuators faults. The interested reader will be able to refer to the following references [4], [5], [12], [14], [27], [28], [43], [45], [47], [52], [59], [60], [61], [63], [64], [71]. 

In the following, the diagnosis method has been validated using a data set of 2 weeks, with a serie of on-line measurements every 30 minutes (see Figure 10). During this period, dynamical changes were imposed on the process through Qin, the feed flow rate, while the input concentrations i.e., CODin and Zin) were supposed to be constant. However, no on-line measurements were performed on these variables so only intervals for the values of CODin and Zin are known. Moreover, several faults occurred on different on-line sensors ... 

---