Regularization Strategies for Contiguous and Noncontiguous Damage Detection of Structures

Regularization strategies have attracted attention in the structural damage detection (SDD) field. However, there is lack of studies on regularization strategies for damage patterns in the existing methods. This paper proposes regularization strategies for contiguous and noncontiguous damages of structures and performs comparative studies. The objective functions are first defined to consider effects of strategies on SDD by adding distinct norm penalties, and then are solved by the particle swarm optimization (PSO). Three numerical simulation models are employed to assess the applicability of three strategies. The results show that the [Formula: see text] norm regularization is suitable for detecting multiple damages, the [Formula: see text] norm regularization performs well in contiguous damages, and the sparsest solutions can be obtained by the [Formula: see text] norm regularization.

Linear Program Relaxation of Sparse Nonnegative Recovery in Compressive Sensing Microarrays

Compressive sensing microarrays (CSM) are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR) which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss thel1relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and thel1relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set.