Structural Health Monitoring of Composite Materials Using the Two Dimensional Fast Fourier Transform

Abstract. This work is part of an effort to develop smart composite materials that monitor their own health using embedded micro-sensors and network communication nodes. Here we address the issue of data management through the development of localized processing algorithms. We demonstrate that the two-dimensional Fast Fourier Transform (FFT) is a useful algorithm due to its hierarchical structure and ability to determine the relative magnitudes of different spatial wavelengths in a material. This may be applied, for example, to determine the global components of a strain field or temperature distribution. We develop two methods for implementing the distributed 2D FFT developed based on the radix-2 (Row-Column) and radix-2×2 (Vector Radix) structures, and compare them in terms of computational requirements within a lowpower, low-bandwidth network of microprocessors. Our results show that the VectorRadix algorithm requires 50% fewer multiplications than the Row-Column algorithm when performed in a distributed manner. Since the most important information of the 2D FFT can often be found in the lowest frequency components, we develop pruning methods for the Row-Column and Vector-Radix algorithms that reduce communication requirements by 50% in both cases. We conclude that the pruned Vector-Radix 2D FFT is an efficient and useful algorithm for rapidly assessing the health of composite materials.