ON FAULT ISOLATION BY FUNCTIONAL AND HARDWARE REDUNDANCY Ferreiro García R, Universidade da Coruña (UDC), España.
[email protected] Pérez Castelo J., UDC, España.
[email protected] Piñón Pazos A, UDC, España.
[email protected] Calvo Rolle J.L., UDC, España
[email protected]
ABSTRACT The aim of the work is to exploit some aspects of the functional and hardware redundancy in fault detection and isolation tasks using back-propagation neural networks as functional approximation devices to be used as residuals generators which will evaluated by means of rule based strategies. Implementation procedure is carried out with the facilities supplied by a FOUNDATION™ Fieldbus compliant tool, which manage databases, neural network structures and training algorithms under mentioned standard. KEYWORDS: g, Computed variable control, Functional approximation, Feedforward neural networks, Conjugate gradient algorithm
1. INTRODUCTION Most of the supervisors design methods are based on the plant models. Model based strategies are effective for making local process changes within a specific range of operation [2]. However, the existence of highly non-linear relationships between process input/output variables have bogged down all efforts to come up with reliable mathematical models mainly for large scale plants. These methods do not depend on the analytical plant model and utilise I/O data only. Therefore, they are inherently robust against plant model uncertainty, and sometimes give us systematic approach to steady state prediction response. Additionally, the implementation of intelligent control technology based on soft computing methodologies such as neural networks (NN) and genetic algorithms (GA) can remarkably enhance the supervision and advanced control capabilities of many industrial processes such as oil refineries or chemical engineering processes [3],[4]. The implementation of massive neural network based models using back propagation algorithm [1], [7] based on collection of real-time data for a steady state operation condition is presented. The main relevant topic of the contribution in this work is the utilisation of artificial neural networks technology for the inferential analysis of performance in a wide range of instrumentation of controlled plants. The proposed neural networks architectures can accurately predict various properties associated with plant performance behaviour. The back-propagation network is the most popular feedforward predictive network deployed in process industries The back-propagation network assumes that all processing elements and connections are somewhat responsible for the difference of expected output and the actual output [6].. The training algorithm is an iterative gradient descent algorithm designed to minimise the mean square error (RMS) between the actual output and the desired output. It requires a continuous differentiable non-linear search space 1.2. Neural Network based models Causal processes can be modelled by means of universal functional approximation devices. A modelling property of causality is used in this work to predict steady state process input output relationships.
In order to exploit the concept of neural network based modelling (NNBM), let us consider a causal process where V1 is the output variable and V2, V3, …VN are input variables. Under such structure, the following steady state inputs/output relationship may be expressed: (1) V1 = f (V2 ,V3 ,LV N ) Given a database containing steady state data supplied from the process defined by expression (1), following relationships can be stated as output predictions according the following expressions: V1 = f (V2 ,V3 , LV N ),
V2 = f (V1 ,V3 , LV N ), V3 = f (V1 , V2 , LV N ),
(2)
V N = f (V1 , V2 , LV N −1 ) where V1 =f(V2, V3, VN) is a direct model predictor (DMP), while V2=f(V1, V3, VN), V3=f(V1, V2,…VN) and VN .= f(V1, V2, VN-1) are inverse model predictors (IMP). Fault detection and isolation strategy Proposed strategy concerns to two aspects of redundancy combined between them as required: functional or analytical redundancy and hardware redundancy [8], [9], [10]. Functional redundancy deals with two or more functions describing the same process, while hardware redundancy is referred to more than one hardware device applied in measuring the same variable. Supervision task is being carried out in two phases: fault detection and fault isolation. Fault detection is inferred by evaluating functions achieved by functional redundancy with parity relations [11], [12]. Fault isolation is inferred by logic evaluation of hardware redundancy with parity relations on pairs of devices, which means that fault isolation concerns to discrimination of a faulty sensor. Given a process defined by means of functional approximation procedures under NNBM1, NNBM2 and a redundant group of devices under NNBM3 as DMP1 : Y1 = f ( X 1 , X 2 ,... X N ) (3) DMP 2 : Y2 = f ( Z 1 , Z 2 ,...Z N ) ′ ′ ′ DMP3 : Y3 = f ( Z 1 , Z 2 ,...Z N )
where X1, X2,..XN, are inputs to DMP1, Z1, Z2,..ZN are inputs to DMP2, Z1’, Z2’,..ZN’ are redundant inputs from hardware devices to DMP3, Y1 Y2 and Y3 are DMP1, DMP2 and DMP3 outputs respectively. From expression (3) it follows that residuals can be achieved by parity relations expressed by R12 = Y2 − Y1 = f ( Z 1 , Z 2 ,...Z N ) − f ( X 1 , X 2 ,... X N ) ′ ′ ′ R13 = Y3 − Y1 = f ( Z 1 , Z 2 ,...Z N ) − f ( X 1 , X 2 ,... X N ) ′ ′ ′ R23 = Y3 − Y2 = f ( Z 1 , Z 2 ,...Z N ) − f ( Z 1 , Z 2 ,...Z N )
(4)
where R12, R13, and R23 are the residuals achieved by parity relations applied by means of functional redundancy. Applying logical evaluation of achieved residuals, faults detection and isolation at groups level is being carried out according the following rules FD & FI at group level: IF R12 AND R13 AND NOT R23 THEN Fault in group of devices 1 (G1) IF R12 AND NOT R13 AND R23 THEN Fault in group of devices 2 (G2) IF NOT R12 AND R13 AND R23 THEN Fault in group of devices 3 (G3) A block diagram of the partial supervision scheme (b) is shown in figure 1, where a rule base is used to evaluate residuals generated by neural networks technology where fault isolation al groups level is carried out.
G G
X1 X2 XN Z1 Z2 ZN Z1 ’ Z2
DMP Y 1
R1
DMP 2
R1
DMP 2
Rulebase
G
Y R23 Y
Fig. 1. Supervision scheme (b): Fault detection and isolation between groups of devices The complete decision making procedure using is carried out by a true table, which is to be included into a rulebase, and . is depicted in table 1. Table 1. Decision making using a true table R12 R13 R23 Decision making 0 0 0 OK 0 0 1 software error 0 1 0 software error 0 1 1 G3 fails 1 0 0 software error 1 0 1 G2 fails 1 1 0 G1 fails 1 1 1 at least two fails Nevertheless, fault isolation at device level requires to add a step more which consists in exploit the concept of hardware redundancy such as it is depicted in figure 2, where the device that fails is isolated by the following inferential procedure: Z 3 ⇐ G 2 ∧ R3 , Z 2 ⇐ G 2 ∧ R 2 , Z 1 ⇐ G 2 ∧ R1 ′ ′ ′ Z 3 ⇐ G3 ∧ R3 , Z 2 ⇐ G3 ∧ R 2 , Z 1 ⇐ G3 ∧ 1 R1
DMP 2 DMP 2 + + + -
R1 R13
Y2 R23 Y3
G
Rulebase1
DMP Y 1
G3
R R
Rulebase2
X1 X2 XN Z1 Z2 ZN Z1 ’ Z2
R
Fig. 2. Supervision scheme (b): Fault detection and isolation at device level
(5)
2. IMPLEMENTATION PROCEDURES Heat exchanger supervision.-Given a pilot plant consisting in a heating process defined by means of functional approximation procedures under NNBM1, NNBM2 and a redundant group of devices under NNBM3, as shown in figure 3, by applying expression (3) yields
DMP1 : qe1 = f (U , ∆p, ∆T ) DMP 2 : qe 2 = f ( qi, Ti , T ) DMP3 : qe3 = f ( qi ′, Ti ′, T ′)
(6)
where U, ∆p,.. ∆T, are inputs to DMP1,q, T1,.T are inputs to DMP2, q’, T1’,.T’ are redundant inputs from hardware devices to DMP3, qe1, qe2 and qe3 are DMP1, DMP2 and DMP3 outputs respectively. From expression (4) it follows that residuals can be achieved by parity relations as shown in figure 1, where R12, R13, and R23 are the residuals achieved by parity relations applied by means of functional redundancy. Applying logical evaluation of achieved residuals, faults detection and isolation at groups level is being carried out according the following rules
q’
q
T
Ti’
U T’ T ∆P
∆T
Fig. 3. Heating processq´under hardware redundancy FD & FI at group level: Rulebase 1 IF R12 AND R13 AND NOT R23 THEN Fault in the group of devices 1 (G1=∆p, ∆T) IF R12 AND NOT R13 AND R23 THEN Fault in the group of devices 2 (G2=qi, Ti, T) IF NOT R12 AND R13 AND R23 THEN Fault in the group of devices 3 (G3=qi’,Ti’, T’)
U ∆p ∆T qi Ti T qi’ Ti’ T’
DMP qe1 1
R1
DMP 2
R1
qe
DMP 2 qe
Rulebase1
A block diagram of the partial supervision scheme (b) is shown in figure 8, where a rule base is used to evaluate residuals generated by neural networks technology, and fault isolation al groups level is carried out. Nevertheless, fault isolation at device level requires a step more, which consists in exploit the concept of hardware redundancy such as it is depicted in figure 5 and shown by means of an additional rule base, the rulebase 2.
R23
Fig. 4. Supervision scheme (b): FD & FI between groups of devices in the heater example.
Rulebase 2
DMP qe1 1
R1
DMP 2
R1
qe
DMP 3 qe + + + -
R23
G G
R R R
Rulebase2
U ∆p ∆T qi Ti T qi’ Ti’ T’
Rulebase1
IF G2 AND R3 THEN Fault in T IF G2 AND R2 THEN Fault in Ti IF G2 AND R1 THEN Fault in qi IF G3 AND R3 THEN Fault in T’ IF G3 AND R2 THEN Fault in Ti’ IF G3 AND R1 THEN Fault in qi’ In this section it has been shown that combining hardware redundancy with functional redundancy, ambiguity is avoided and the FD & FI problem is deterministically solved under some constraints such as: Residuals evaluation must be performed only under steady state dynamics Determinism under normal process operation exists only under a unique fault and not more than one at a time.
Fig. 5. Supervision scheme (b): FD & FI at device level on groups of devices G2 and G3
2.1 Implementation issues Experiments were carried out on a pilot plant where a heat exchanger is being controlled by a closed loop PID controller and supervised for checking instrumentation status. Figure 6 shows the results of a supervision session in which some transient states and steady states are represented. In transient states fault finding and isolation results are not valid. In steady states the detection and isolation of any kind of device fault if one and only one device fails, is successfully carried out. In the case of simultaneous faults where more than a device fails then the detection is deterministic and the isolation is ambiguous. Decision-making based on reconfiguration of controlled systems requires strongly to substitute or change the service of a faulty device by the stand-by or redundant one. Such task is successfully carried out by adding more knowledge to the actual rulebase with the addition of only two rules per device under the status condition achieved before. So that, decision making on system reconfiguration is carried out by means of the following rules under the assumption of correct control algorithm: IF steady state error > error_limit AND actuator is not saturated, THEN Process variable fails. IF Process variable fails, THEN “SWAP” sensor service by its redundant sensor and acknowledge.
System response qi’ Ti’ T’ qi Ti T 1000
time sec.
4000
Fig. 6. Layout of a display of instruments supervision of the heater SCADA The layout of a small SCADA for the pilot plant shown in figure 6 include the heater response, the time domain status of all sensors of group 2 and group 3 as well as alerts of groups of devices and sensors faults including an alert for task validation. Consequently, to admit that a sensor is in a fault status it is necessary that the supervision status alert be “Valid” state. For instance, in the case of figure 6, that status is in state “no valid” because system is not in steady state. In order to check the performance of supervision task, sensors were manipulated alternatively in sequential order to generate, detect and isolate faults. After switching off the power supply of sensor Ti of group 2, the layout depicted by figure 6 shows that the first sensor that fails is Ti of group 2, which indicates a fault by changing the status value from “0” to “1” during a time close to 4 minutes. Consequently, an indication of the group of sensors and the sensor that fails appear in the pilot lamps of right hand of display. All sensors were checked for running properly. When the output of T’ fails, it can be seen at heater response but such variable is not on line with process variable because it is in stand-by. Nevertheless when the sensor T fails, then process variable generate the reason and the symptom to change this sensor T by the standby sensor T’. Nevertheless, in the actual status supervision status alert result is “not valid” because of transient state. After steady state is established then results are completely satisfactory.
3. CONCLUSION A systematic methodology to implement the supervision task of process instrumentation applied on industrial processes has been developed and presented. The approach combines functional approximation implemented on the basis of massive back-propagation NN [5], with rule based strategies, both implemented with the facilities of an object oriented programming tool: the DeltaV Neural. Failure analysis has been carried out to detect and isolate potential faults due to measuring instrumentation under the following constraints: • any fault belongs to a single device • process operation is correct. • system dynamics remain at steady state The availability of used advanced FOUNDATION™Fieldbus based tools brings the gap between the proposed methodology and its implementation procedure.
4. ACKNOWLEDGMENT The authors wishes to acknowledge the financial support of the Spanish MICYT and FEDER Founding at DPI2003-00512 project
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