Sparse Structural System Identification & Low Rank Methods




Damage Detection

Dynamic imaging of concrete structures

This method provides the dynamic process of local structural damage detection. The multiple temporal frames are represented by a superposition of a low-rank background component and a sparse innovation (dynamic) component. The low-rank component represents the irrelevant temporally-correlated background, whereas the sparse innovation component indicates the evolutionary damage-induced information.Reference: Yang, Y. and Nagarajaiah, S. (2015). Real-time structural damage detection by dynamic imaging with blind separation of low-rank background and sparse innovation. ASCE Journal of Structural Engineering.

Sparse representation classification of structural damage

This classification method for damage identification expresses the test damage feature with a sparse representation in terms of a large reference damage feature dictionary. The non-zero entry in the sparse representation, which is recovered by L1-minimization, directly assigns the damage class which the test structure (feature) belongs to.Reference: Yang, Y. and Nagarajaiah, S. (2014). Structural damage identification via a combination of blind feature extraction and sparse representation classification. Mechanical Systems and Signal Processing 45(1): 1-23.

Unsupervised learning of sparse damage signature

This method uses the multivariate machine learning theory to directly extract the spike-like sparse damage signature from the noisy multi-channel structural vibration responses, simultaneously detecting damage instants and damage locations.

Reference: Yang, Y. and Nagarajaiah, S. (2014). Blind identification of damage in time-varying system using independent component analysis with wavelet transform. Mechanical Systems and Signal Processing 47(1): 3-20.

System identification

Sparse clustering of vibration modes

This method reveals the essence of modal expansion: the monotone modal responses with disjoint sparsest representations in frequency domain naturally cluster in the directions of the mode matrix�s columns (modeshapes), which are readily extracted from the measured system responses using a simple clustering algorithm. Direct decoupling can then be performed in determined case, or L1 sparse recovery can be performed in underdeterined case with limited sensors.

Reference: Yang, Y. and Nagarajaiah, S. (2013). Output-only modal identification with limited sensors using sparse component analysis. Journal of Sound and Vibration 332(19): 4741-4765.

Real-time Identification of Time-varying Cable Tension Time History from Accelerations

(Winner of the ASCE Reese Research Prize 2017).

This study develops a new data-driven framework to identify the time-varying stay cable tension time history via an unsupervised machine learning algorithm complexity pursuit (CP), using as little information as the measured cable accelerations from only two accelerometers.

Reference: Yang, Y., Li, S., Nagarajaiah, S., Li, H., and Zhou, P. (2015). Real-time output-only identification of time-varying cable tension from accelerations via complexity pursuit. ASCE Journal of Structural Engineering, accepted for publication.

Yang, Y. and Nagarajaiah, S. (2013). Blind modal identification of output-only structures in time-domain based on complexity pursuit. Earthquake Engineering and Structural Dynamics 42 (13): 1885-1905.

Data compression of very large-scale structural vibration responses

This method exploits the intrinsic low-dimensional structure, which is implicit in the large-scale data sets of structural seismic and typhoon responses, for efficient data compression. Such a low-dimensional structure, empirically, stems from that few modes are active in the structural dynamic responses. Originally, limited to the sensor and time-history dimension, the structural seismic and typhoon response data set generally doesn�t have an explicit low-rank representation (e.g., by singular value decomposition or principal component analysis). By the proposed matrix reshape scheme, the low-rank structure of the large-scale data set stands out, regardless of the original data dimension.

Reference: Yang, Y. and Nagarajaiah, S. (2014). Data compression of very large-scale structural seismic and typhoon responses by low-rank representation with matrix reshape. Structural Control and Health Monitoring, tentatively accepted for publication.

Yang, Y. and Nagarajaiah, S. (2014). Data compression of structural seismic responses using principled independent component analysis. ASCE Journal of Structural Engineering 140(7): 04014032.

Data cleansing of very large-scale structural vibration responses

This method simultaneously de-noises both gross errors (outliers) and dense noise that are not uncommon in the data acquisition of structural health monitoring systems. This is enabled by explicitly taking advantage of the fact that typically only few modes are active in the vibration responses; as such, re-stacking the response data matrix guarantees a most low-rank representation for the underlying clean structural vibration responses, removing both the outliers and dense noise.

Reference: Yang, Y. and Nagarajaiah, S. (2014). Blind denoising of structural responses with outliers via principal component pursuit. Structural Control and Health Monitoring 21(6): 962-978.