Abstract
This paper presents a new method for the design of Walsh to Fourier Transform (WFT), and discusses its application to vibration diagnosis of rotating machinery.
W-FT is faster than the Cooley-Tukey FFT when the number 2n of sampled data is small or when the number of Fourier components is relativery small compared with 2n. However as the number 2n increases, the W-FT program size expands rapidly, because the program requires 2n×2n matrix Ci, k to convert Walsh components to Fourier components. Thus the implementation of the program into a micro computer is impractical when 2n is large.
To solve the above problem, a simplified algorithm of W-FT is derived. Namely, its linear conversion matrix Ci, k is expressed by Walsh matrix and Fourier matrix. First, WFT algorithm is improved, by using orthogonal relations between sinusoids and Walsh functions. And 2n×2n matrix is reduced by dividing the matrix into 2p-2×2p-2 submatrices C(p)s(i), s(k) which are independent each others, and by deleting zero submatrices among them. Next, when p is large, the elements whose values are small are deleted. As the result, the number of elements of C(p)s(i), s(k) are reduced by 2/3 and the time to calculate is shortened so as to meet for practical use.
From the simulation results of vibration diagnosis for turbine and generator, it was shown that the improved W-FT, presented in this paper, was faster than FFT by 3/4.
