Comparison of some non-adaptive deconvolution techniques for resolution enhancement of ultrasonic data

We present a computation technique for one-dimensional piezoelectric transducers, resonators, or interferometers having an arbitrary number of layers and piezoelectric elements electrically in parallel. Explicit and exact expressions are derived for the electric impedance and acoustic velocities. This method is based upon a systematic use of the electrical transmission line analogy, each passive or active medium being represented by a line. It has successfully been applied to various structures, particularly a symmetrical resonator with an intermediate liquid medium and a total of 29 media.

Exact one-dimensional computation of ultrasonic transducers with several piezoelectric elements and passive layers using the transmission line analogy

A comparison between simulation- and measurement-based characterization is provided for the design of one-dimensional, nonadaptive, inverse filters for ultrasonic applications. Both prefiltering and postfiltering are considered by means of two different filtering strategies performed in the time and frequency domains. The results clearly indicate that theoretical methods can be used successfully, provided that the physical limitations of the simulation process are fully appreciated. In some instances, the simulation-based approach is shown to provide superior results, and the reasons for this are explained. >

A theoretical approach for inverse filter design in ultrasonic applications

Publisher Summary This chapter introduces nondestructive testing of materials with ultrasound. It is concerned with excitation, propagation, scattering, reception, data, and imaging. The physics of elastodynamic waves is the basis for NDT with ultrasound, and the pertinent mathematical formulation must help to design transmitting/receiving devices and to understand the signals obtained in a real-life testing situation as well as to invent appropriate signal processing tools like imaging algorithms. To model excitation, propagation, and scattering of ultrasound in solids, the governing equations for elastic waves are needed. They allow for fundamental analytic solutions accounting on one hand, for the justification of the “ultrasonic language” spoken in the NDT community and, on the other hand, for some canonical modeling concepts. They are the basis to formulate inverse scattering algorithms for imaging purposes.

Applications to Nondestructive Testing with Ultrasound

Multilayer ultrasonic transducers with layers of uniform design are in common use. It is also possible to devise such transducers in which the layer design is nonuniform. However, this adds many degrees of freedom to the transducer design, and conventional design techniques are inadequate to realize desired behavior or even to assess potential benefits. In this paper, a theoretical investigation of multilayer piezoelectric structures with nonuniform layers is reported. Results are presented from a study using computer code to solve the one-dimensional wave equation. It is first shown how multilayer structures with nonuniform layer thicknesses generate even and odd harmonics in their frequency response, suggesting that frequency response can be controlled by choice of layer thickness. However, this choice is complicated and it is impossible to analyze all possible combinations of layer thicknesses. Hence, use of the stochastic optimization technique of simulated annealing is reported. Two optimized transducer designs illustrate this. The first design maximizes uniformity of the fundamental, second, and third harmonics of pressure output, achieved to approximately plusmn3%. The results suggest additional bandwidth can be achieved for practical applications, as the presence of a finite response at the second harmonic frequency avoids the null usually associated with this frequency. This is further illustrated with the second optimized transducer design in the form of a three-layer 1-3 connectivity piezo- composite transducer for underwater operation.

Mathematical Optimization of Multilayer Piezoelectric Devices with Nonuniform Layers by Simulated Annealing

Abstmct-The development of a new three-port model of the thickness-mode piezoelectric transducer, employing linear systems theory, is presented. A discrete bidirectional lattice is used to describe mechanical wave propagation and continuous transfer functions to represent the electrical parameters. When presented in block-diagram format, an extremely valuable insight is gained into the nature of piezoelectric interaction. The lattice concept is extended to the analysis of multilayered structures and, when implemented in the discrete time domain, close agreement with experimental data is obtained. A number of experimental and simulation results are included for comparison. I. INTRODUCTION ONVENTIONAL models of the thickness-mode piezoelectric transducer invariably utilize transmissionline analogs in which the electromechanical properties of the system are evaluated by means of electrical network concepts. Examples of this include the equivalent circuits of Mason [l] and the more recent KLM [2] model, which uses a center-tapped transmission line to model acoustic wave propagation. In this form both models are also readily adapted for the analysis of multilayered transducer structures. However, electrical analogs possess some disadvantages which limit their flexibility when applied to piezoelectric transducer modelling [3]. Physical insight into the nature of the transduction process is often masked, and as a'result the influence of external electrical and mechanical load conditions on transducer behaviour is difficult to determine. To overcome this, an alternative strategy has been proposed by Hayward [3] who adopted a systems feedback approach to

M.N. Jackson

Papers

A lattice model of the thickness-mode piezoelectric transducer