* Correspondence to: Mehmet Sunar, Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. Email: mehmets@kfupm.edu.sa CCC 0363} 907X/99/131123} 09$17.50 Received 1 February 1999 Copyright  1999 John Wiley & Sons, Ltd. Accepted 24 March 1999 INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. 23: 1123 } 1131 (1999) ARTIFICIAL NEURAL NETWORKS FOR THERMOPIEZOELECTRIC SYSTEMS MEHMET SUNAR* Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia SUMMARY A radial basis function}arti"cial neural network modelling of thermopiezoelectric systems is presented. The neural network model can emulate the electrical response of two thermopiezoelectric layers bonded on a cantilever beam structure. The electrical outputs of thermopiezoelectric layers are due to sudden changes in temperature of thermo piezoelectric/beam system and vertical step force at the free end of the beam. The neural network is trained so that it mimics the electrical response of the system for di!erent thermopiezoelectric layer locations. The test results of neural network are shown together with the actual system results to illustrate the accuracy of the network in predicting the thermopiezoelectric system behaviour to temperature and force e!ects. Copyright  1999 John Wiley & Sons, Ltd. KEY WORDS: arti"cial neural network; radial basis function; thermopiezoelectric; energy functional; generalized heat conduction; "nite element method 1. INTRODUCTION Owing to their ability to emulate various systems, arti"cial neural networks (ANNs) have gained much popularity in recent years. After su$cient training, ANNs can predict the output of energy processes. Among their applications are prediction of mean daily values of solar radiation (Mohandes et al, 1999), forecasting of energy in electric utilities (Al-Shehri, 1999; McMenamin and Monforte, 1998), prediction of annual heating energy demand for residential buildings (Olofsson et al., 1998), and measurement of retro"t energy savings for heating, ventilating and air-conditioning systems (Jang et al., 1996). Frequently, physical phenomena occur in coupled forms in nature. Coupled system equations may include the e!ects of mechanical, thermal, electrical and/or magnetic "elds. Such coupled system behaviour is di$cult to capture due to complex interactions among various "elds. The medium in which mechanical, thermal and electrical "elds are coupled is named as thermopiezoelectric (Mindlin, 1974). Thermopiezo- electric equations can be used to study thermal e!ects on a piezoelectric material used as a sensor and/or actuator (Rao and Sunar, 1993). Various forms of solutions are obtained by researchers for the responses of these media (Tauchert, 1997; Bao et al., 1998). In this paper, the linear equations governing the quasi-static behaviour of thermopiezoelectric media are used to obtain the system equations through the generalized heat conduction equation and Hamilton's principle applied over an energy functional. Finite element method is applied as the numerical technique for discretization of these equations. The resultant "nite element equations are employed to a system composed of a cantilever beam and two thermopiezoelectric layers bonded to the upper and lower surfaces of the beam. A radial basis function (RBF) ANN is trained so that it is able to track the electrical response of thermo- piezoelectric layers when the system is subjected to sudden (step) changes in temperature and vertical step