Damage Detection in Bridge Structures through Compressed Sensing of Crowdsourced Smartphone Data

Algorithm 2

Numerical investigation procedure.

	Input: Acceleration signals for the baseline and an unknown case
	Output: Damage index for the unknown case
	Data Compression: Acquire and compress the acceleration signals of vehicles passing over the bridge, considering a specified compression level for both cases.
	Reconstruction of Original Signals: Reconstruct all original signals using the CS theory.
	for each run (Run number 30) do
	Signal Selection: Randomly select 50% of the baseline signals as a baseline set. Use the remaining signals as a validation set. Similarly, select only 50% of the recorded signals for the unknown case.
	Feature Extraction: Extract feature matrices using MFCC analysis from the selected signals in both cases separately.
	PCA: Apply PCA to reduce dimensionality and obtain principal components of the feature matrices separately.
	Probability Distribution Functions: Calculate the multivariate probability distribution of the projected features for both cases.
	Dissimilarity Measure between the PDFs: Calculate the Wasserstein distance between the probability distribution of the baseline and the unknown case.
	end
	Average Wasserstein distance: Calculate the average Wasserstein distance over the 30 runs.
	Damage Index: Normalize the average Wasserstein distance value with respect to the average from the validation set.
	Output: Output the normalized damage index for the unknown case.