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Several papers presents fault detection and isolation techniques for fault in only one sensor; in this paper we will present a technique for multiples faults detection and isolation in sensors of dynamic systems. Multiples faults have less probability to occur but it is not null. So in critical applications the system needs to be operational even in this situation. In this paper we will present a design for a Multiples Faults Detection and Isolation (MFDI) system, an example to illustrate this technique and its respective results. INTRODUCTION In critical applications, the fault in a component can be catastrophic if the control does not have any degree of redundancy, physical or analytical. Therefore, it is important to implement a control system with redundancy and capability to detect and isolate faults in components as fast as possible, such a way, that it can be able to reconfigure the use of the remaining components or even the control law with faults to an alternative control law. In this paper we will only consider sensor faults. To test a sensor we need to have its respective redundant signal. Redundant signals can be supplied by a redundant sensor, physical redundancy, or by a mathematical procedure, analytical redundancy. Our technique is to be employed in situations where it is not possible to use physical redundancy or to improve a voting system performance. Multiples Faults Detection and Isolation (MFDI) technique, presented in this paper, makes use of analytical redundancy approach. To do so we will employ observers to generate redundant signals [1, 3-8, 13]. These redundant signals and the real sensor signal will be processed by a decision function to generate fault signatures called residues. These fault signatures will be processed by a logic function which will allow detecting and isolating the faults. This technique can be applied in any dynamic system that can be represented by a linear time invariant state model. The main steps of this technique are: 1) design the observer for the desired dynamic; 2) design the decision functions to generate the faults signatures; 3) design the logic functions, and 4) evaluate the MFDI system performance in detection and isolation of faulty sensors. BASIC CONCEPTS A fault detection and isolation technique is an algorithm to detect and isolate (locate) faulty components in a dynamic process, such as sensor biases, actuator malfunctions, leaks and equipment deterioration. Fault detection is the first step to achieve fault tolerance, but for this the redundancy has to be included in the system. The redundancy can be either by hardware (physical redundancy) or by software (analytical redundancy). Hardware redundancy, e.g., an extra sensor or extra actuator, can produce several problems associated with: cost, space, weight and complexity of the system. Besides, it has been observed that redundant components tend to have similar functioning expectancies; so the event that causes one component to fail probably could cause its redundant components to fail soon. Analytical redundancy is a mathematical procedure that uses the system mathematical model; therefore this approach only needs some system computational resources to be implemented. In this paper we will use the word fault instead of failure because strictly speaking the term failure suggests complete breakdown while fault may connote something tolerable. FAULT – Fault can be defined as a malfunction of any component of a system, causing since a loss of performance up to a total stop of its functions. According to [1] the faults can be divided in: • Abrupt Fault: fault that suddenly occurs and persists in a component. • Incipient Fault: fault that develops slowly at a component. The early detection of an incipient fault can help to avoid a total breakdown of the system or even catastrophes that could result in loss of significant amount of material or serious personal injury. So, it is desired to have a fault tolerant system, that is, a system that can continue to do its tasks, even when there are hardware faults or software errors. But the implementation of such system is not easy to do. According to the terminology used in [2], the fault detection and diagnosis consist of the following tasks: • Fault Detection: detection that something is wrong in the system. Special emphasis is laid upon incipient faults rather than abrupt faults because incipient faults are harder to detect. • Fault Isolation: determination of the fault origin. • Fault Identification: determination of the gravity of the fault. Other relevant aspects, in fault detection and isolation, are the problems relative to false alarm and alarm loss. False Alarm is the indication of the occurrence of a fault when the system is operating at its normal state. Alarm Loss, on the other hand, is the indication that the system is operating normally, when it is at a faulty state. The decision threshold between the fault state and normal state of operation should be chosen in such a way to minimize these wrong and conflicting indications. REDUNDANCY – A wide class of fault detection and isolation methods makes explicit use of the system mathematical model, such as the model-based methods, which are based on the idea of the analytical redundancy [3]. In contrast with the physical redundancy, where measurements of different sensors are compared, in the analytical redundancy the measurements supplied by a sensor are compared with the respective variable value obtained through a mathematical model. Such value is obtained through calculations that use current and/or previous measurements of another variable and the mathematical model that describes their relationships. The idea can still be extended only for the comparison of the values generated analytically, each of them being obtained through different calculations. In both cases, the resultant differences are called residues. RESIDUES – The residues have zero value in ideal situations but in practice this rarely happens. The deviations of this value are a combined result of the noise, parameters change and/or faults. If the deviations due noise and parameters are negligible, the residues can be analyzed directly for a decision threshold. If the residue is greater then the decision threshold we can declare that a fault occurred. For multiple fault detection and isolation approaching the residues must be processed to indicate the fault conditions. Based on definitions given in [4], for multiple fault detection and isolation in sensors we can define: a residue vector r(t) is a vector that its elements have null or very small values, in the faults absence, and they have values different from zero when a fault occurs. This definition implies that a residue vector r(t) has to be independent of or, at least, insensitive to system states, control input and unmeasured disturbances. In case of linear systems, a general structure of a linear residue generator can be described as in the Figure 1. Figure 1 – General structure of a linear residue generator. The transfer function from the fault f(t) to the residue r(t) is given by: r(s) = Hy(s) Gf(s) f(s) (1) Note: for easy identification, we will use bold italic letters to represent matrix and vectors and regular italic letters for scalar variables. DETECTABILITY – The condition, for the system to be able to detect a fault is based on the detectability definition [4]. Detectability is the capability to detect a fault at the vector r(s) when its elements have values different from zero. However, this condition is not sufficient in some practical situations. Assume that we have two residue generators as presented in the Figure 1. And in fault occurrence the residues behave as in Figure 2. Here we see that we have a fundamentally different behavior between r1(t) and r2(t), because r1(t) only reflects transitions on the faulty signal while r2(t) has approximately the same shape of the faulty signal. Thus, r1(t) can not be used in a reliable MIFD application even though it is clear that r1(s) ≠ 0. Figure 2 – Residue vector examples. The difference between these two residues in this example is the values of r(s = 0). Clearly we can see that the residue 1 has r1(s = 0) = 0 while the residual 2 has r2(s = 0) ≠ 0. This leads to the definition of strong detectability. The fault is said to have strong detectability if and only if: ri(s = 0) ≠ 0 (2) DETECTION AND ISOLATION STRATEGIES To design residues strongly detectable, we can base on the structured residue methods described in [1] to develop the residues vector generator. ANALITYCAL REDUNDANT SIGNALS GENERATOR – The conception of the Analytical Redundant Signals Generator (ARSG) can be based on a bank of Reduced Order Observers (ROO) similar to the Dedicated Observer Scheme (DOS), described in [1]. As in DOS structure, only the system control signal of and one of the measures are used as input signal for each ROO. The i ROO is, therefore, sensitive only to the i sensor fault. An ARSG block diagram for p sensors is presented in Figure 3. Figure 3 – Analytical Redundant Signal Generator. DECISION FUNCTIONS – The decision functions are used to generate the fault signatures, i. e., they process the residue vectors. For this MFDI technique, the decision functions are developed considering the module of the error between the sensor output and the equivalent values obtained by the ROO output. The dimension of these residues vectors are (p – 1) where p is the number of sensors. To easy determine the decision threshold, the sensor signals output and respective estimated signals are submitted to a scale factor conversion, such a way that all signals output will operate at the same range. Range from -10uni to +10uni is a good choice. So the elements of the i decision function vector are formed by:    ≠ = = ⇒ − = i j p j p i S Obs y i j i i i j ; ..., , 1 ..., , 1 , , η (3) where p is the number of sensors, yi is the output of the i sen

Multiples Faults Detection and Isolation in Sensors of Dynamic Systems