Efficient Calculation of Statistical Moments for Structural Health Monitoring

Wireless networks of smart sensors with computations distributed over multiple sensor packages have shown considerable promise in providing low-cost structural health monitoring. In these networks, microprocessors are typically embedded in individual smart sensor packages. The efficiency of embedded computational algorithms is of critical importance because the size, cost, and power requirements of the sensor arrays are central concerns. Here, very efficient methodologies are presented to compute statistical moments of a measured response time-history. These moments: the mean, standard deviation, skewness, and kurtosis are often used to characterize a measured irregular response. Two alternative approaches are presented, each of which can save substantial computer memory requirements and CPU time in certain applications. The first approach reconsiders the computational benefits of computing statistical moments by separating the data into bins and then computing the moments from the geometry of the resulting histogram, which effectively becomes a one-pass algorithm for higher moments. One benefit is that the statistical moment calculations can be carried out to arbitrary accuracy such that the computations can be tuned to the precision of the sensor hardware. The second approach is a new analytical methodology to combine statistical moments from individual segments of a time-history such that the resulting overall moments are those of the complete time-history. This methodology could be used to allow for parallel computation of statistical moments with subsequent combination of those moments, or for combination of statistical moments computed at sequential times. A worked example is presented comparing two implementations of the new methodologies with conventional calculations in monitoring the global performance of an offshore tension leg platform. Accuracy, efficiency, and storage requirements of the calculation methods are compared with those of conventional methods. The results show that substantial CPU and memory savings can be attained with no loss in accuracy and that more dramatic savings can be attained if a slight reduction in accuracy is acceptable.