Efficient computation of spectral moments for determination of random response statistics

This paper will first review the use of temporal spectral moments, and then propose an efficient running sum technique to determine the spectral moments frequency by frequency. Combining this summation process with modal superposition techniques allow a significant reduction in input and output file sizes and computational time.The proposed technique uses finite element analysis (FEA) to generate modal vectors that are post processed using mode superposition techniques to calculate the power spectral density (PSD) moments, eliminating the need to form PSD response functions. This requires storage of only the modal response and force vectors and the running sum of the PSD moments. Once the moments of the PSD are determined, the random response statistic calculations are a straightforward problem. Two example problems are given: a simple cantilever beam and a detailed optical telescope. These examples show how different problems can be solved using the proposed technique