The optimal design and upgrade of sensor networks (SN) have been receiving an increase in attention for the last few years. A wide-ranging variety of approaches relying on exhaustive enumeration, algorithmic procedures, rigorous mathematical models and meta-heuristic techniques were developed to address the complexity of the sensor network placement problem, usually assuming a steady-state system at the nominal operating conditions. Within this context, the sensor placement can be regarded as a highly combinatorial optimization problem where the main goal is to find the optimal balance between the performance indicators and the cost of the data acquisition system [1, 2].

On the other hand, in most of the articles dealing with fault diagnosis it is assumed that the SN is already in place and the relationship between sensor location and the FDS performance is rarely discussed. In this work, both issues are considered and a methodology to optimally design a SN which on-line supplies reliable data to a fault diagnosis system (FDS) is presented. In that sense, sensors are placed to minimize the sum of investment costs while keeping the original FDS performance when all measured variables were originally considered.

The way in which the investment cost is minimized, is based on the selection of just some process key variables that allows maintaining the FDS performance. These variables will gather the essential information given at each moment by the process from the fault diagnosis point of view. Then a methodology that assures the observability of the process as well as the minimum, imposed as input, of the reliability of such process key variables estimation is applied in order to allocate the required instrumentation. In order to check the methodology, a data based FDS and a challenging diagnosis problem such as the Tennessee Eastman benchmark [3] is considered. The FDS is based on a PCA detection module integrated with a rules based fuzzy logic system that on-line interpret the statistics calculated from PCA [4]. In order to estimate its performance, the accuracy, defined as the rate of right diagnosis and the total diagnosis responses, is evaluated.

Firstly, the variables set is minimized whereas keeping the FDS performance. Because of this is a highly non linear problem and is based on a difficult modeling fuzzy logic inference procedure, a genetic algorithm was selected to search the key variables set. The objective function consists of a sum of the FDS accuracy and a weighting index that is proportionally higher with regard to the number of removed variables in the diagnostic procedure. Besides that, the optimization is subject to a constraint which, weighting negatively those individuals that reduce the initial FDS accuracy more than 1 %, prevents reductions in the set of variables at the expense of FDS performance.

After such procedure a methodology [5, 6] for evaluating the reliability of the FDS resulting key variables as well as to warranty the observability of the process is applied. Such method takes into account all the redundancies offered by the system in terms of functional and hardware as well. In this evaluation, both quantitative process knowledge and fault tree analysis are considered and combined, which leads to a more suitable and practical evaluation of reliability. The formulated sensor placement optimization problem is also solved using genetic algorithms.

To sum up, a reduction in measured process variables allows a sensible diminution in the instrumentation investment cost whereas the FDS performance and the system observability is maintained. All the work proposed is integrated in an easily usable software developed in Matlab 6.5©.

Acknowledgments

Financial support received from the European Community (PRISM project MRTN-CT-2004-512233) is fully appreciated.

References

[1] Ali, Y. & Narasimahan, S. “Sensor network design for maximizing reliability of linear processes”, AIChe Journal, 39, pp. 820-826 (1993).

[2] Madron, F. & Veverka, V. “Optimal selection of measuring points in complex plants by linear models”, AIChE Journal, 38, pp. 227-236 (1992).

[3] Downs, J.J and Vogel, E.F. “A plant-wide industrial process control problem”, Comput. Chem. Eng., 17, pp. 245-255 (1993).

[4] Musulin, E., Yélamos, I., Puigjaner, L. “Integration of Principal Component Analysis and Fuzzy Logic System for comprehensive fault diagnosis”, ”, Ind. Eng. Chem., Res, 45, 1739-1750.

[5] Angelini, R., Méndez, C.A., Musulin E., Puigjaner, L. “An optimization framework to computer-aided design and upgrade of measurement systems”, To be presented at ESCAPE 16 – PSE 2006, Paper 1464, Garmisch-partenkirchen, Germany, July 9 – 13 (2006)

[6] Benquilou, C., Graells, M., Musulin, E., Puigjaner, L. “Design and Retrofit of Reliable Sensor Networks”, Ind. Eng. Chem., Res, 43, pp. 8026-8036 (2004).