Automatic modeling of physical phenomena: Application to ultrasonic data
Igor Grabec, Wolfgang H. Sachse · Journal of Applied Physics · 1991
The physical modeling of natural phenomena is treated in this paper as an information transforming process which can be performed by a general modeler composed of an array of sensors, a central processing unit, a memory, and an array of actuators. The most characteristic property of such a system is its capability of predicting some properties of observed phenomena from partial perception and past experience. This property is realized if the central processing unit is acting as an estimator of a conditional average. As the condition, the partial set of signals from the sensor array is employed, while the complementary set is estimated from it. In the estimation the smoothed empirical probability distribution is employed. It is constructed from the empirical samples obtained by a set of prototype experiments and stored as a data base in the memory. The proposed modeler was simulated on a laboratory minicomputer which was part of a general data acquisition system. It was applied to the modeling of acoustic emission and ultrasonic scattering phenomena. It is shown experimentally that forward and inverse acoustic emission problems can be solved and a simple characterization of material inhomogeneities can be performed by the modeler. A mutual mapping of conditional data to estimated ones and the reverse is the basis of an iteration procedure which corresponds to a discrete dynamical process in the multidimensional data space. Numerical examples show that attractors of this process are the vectors of the data base. Therefore, the iteration can be efficiently applied for noise reduction. The operation of this dynamical system is comparable to the operation of neural networks in which the memory corresponds to the data base.