| Structural damage detection has always been a research hotspot,many damage detection methods have been proposed.The majority of these methods are based on modal analysis,but due to noise,structural complexity and human factors,the use of test data for modal analysis will produce bigger fitting errors,and then affects the efficiency of damage detection.Structural frequency response function contains all the information of structural modal parameters and is easy to be measured.Therefore some scholars have put forward Frequency Response Function(FRF)Curvature method for structural damage detection along the line of modal curvature,this method only uses FRF and is no longer dependent on structural dynamical model parameters identification.Its main idea is that the absolute difference of FRF Curvatures between the damaged and undamaged structure will have mutation in the damage region.In this paper,the rationality of the above detection method have been derived,and the theoretical basis and physical interpretation of Frequency Response Function Curvature for damage detection have been proven.In order to break through the frequency band limit of Frequency Response Function Curvature method , an improved frequency response function curvature (Im_FRFC) method is proposed.In the case of a wide frequency range,the improved method can still give satisfactory results.As the increasing complexity of system structure,its nature of the mechanism is difficult to understand.Through the system identification method,the equivalent model of the system can be modeled using response signals.In this paper,time series models (AR model) are established using only the response signal of structure.It is found that AR model coefficients are very sensitive to the changes of structural characteristics.Since there is no corresponding relationship between changes in the AR model coefficients and local changes in system structure ,it is not suitable for damage localization.Before and after structural damage,AR model coefficients have changed significantly and the absolute difference of Im_FRFC have mutation in the damage region,the quantitative analysis of above changes and mutations can provide a "threshold" for structural damage identification and structural damage localization.In addition,in order to get more information from the system structure,researchers tend to install multiple sensors in different parts and different directions of the system structure,this makes the dimension of response data growing.Dimensionality reduction method(PCA) can be properly achieve dimension reduction,compression and reconstruction of the original data matrix.In order to achieve dimensionality reduction of data and quantitative analysis,AR model coefficients and the absolute difference of Im_FRFC between the damaged and undamaged structure were established damage identification matrix respectively.It is found that the first several order principal component represents the most information contained in the original data through PCA. Subsequently,the use of multivariate control charts can separate'Outlier Data',achieve the quantitative analysis of the above changes and mutations and complete damage identification and location of cantilever. SPE statistic depicts the degree of the data under test deviated from principal component models.The degrees of SPE statistics exceeded the control limits between two detection are different ,the greater degree corresponds the larger damage.Overall,in this paper,the idea of dimensionality reduction and the basic theory of Multivariate Statistical Analysis are applied for damage detection of cantilever. The feasibility and effectiveness of the proposed method are analysed through theoretical analysis and experimental validation. |
