Improved minimum variance distortionless response spectrum method for efficient and robust non-uniform undersampled frequency identification in blade tip timing

The noncontact blade tip timing(BTT)measurement has been an attractive technology for blade health monitoring(BHM).However,the severe undersampled BTT signal causes a significant challenge for blade vibration parameter identification and fault feature extraction.This study proposes a novel method based on the minimum variance distortionless response(MVDR)of the direction of arrival(DoA)estimation for blade natural frequency estimation from the non-uniformly undersampled BTT signals.First,based on the similarity between the general data acquisition model for BTT and the antenna array model in DoA estimation,the circumferentially arranged probes on the casing can be regarded as a non-uniform linear array.Thus,BTT signal reconstruction is converted into the DoA estimation problem of the non-uniform linear array signal.Second,MVDR is employed to address the severe undersampling issue and recover the BTT undersampled signal.In particular,spatial smoothing is innovatively utilized to enhance the estimation of covariance matrix of the BTT signal to avoid ill-condition or singularity,while improving efficiency and robustness.Lastly,numerical simulation and experimental testing are employed to verify the validity of the proposed method.Monte Carlo simulation results suggest that the proposed method behaves better than conventional methods,especially under a lower signal-to-noise ratio condition.Experimental results indicate that the proposed method can effectively overcome the severe undersampling problem of BTT signal induced by physical limitations,and has a strong potential in the field of BHM.

Non-convex sparse optimization-based impact force identification with limited vibration measurements

Impact force identification is important for structure health monitoring especially in applications involving composite structures.Different from the traditional direct measurement method,the impact force identification technique is more cost effective and feasible because it only requires a few sensors to capture the system response and infer the information about the applied forces.This technique enables the acquisition of impact locations and time histories of forces,aiding in the rapid assessment of potentially damaged areas and the extent of the damage.As a typical inverse problem,impact force reconstruction and localization is a challenging task,which has led to the development of numerous methods aimed at obtaining stable solutions.The classicalℓ2 regularization method often struggles to generate sparse solutions.When solving the under-determined problem,ℓ2 regularization often identifies false forces in non-loaded regions,interfering with the accurate identification of the true impact locations.The popularℓ1 sparse regularization,while promoting sparsity,underestimates the amplitude of impact forces,resulting in biased estimations.To alleviate such limitations,a novel non-convex sparse regularization method that uses the non-convexℓ1-2 penalty,which is the difference of theℓ1 andℓ2 norms,as a regularizer,is proposed in this paper.The principle of alternating direction method of multipliers(ADMM)is introduced to tackle the non-convex model by facilitating the decomposition of the complex original problem into easily solvable subproblems.The proposed method namedℓ1-2-ADMM is applied to solve the impact force identification problem with unknown force locations,which can realize simultaneous impact localization and time history reconstruction with an under-determined,sparse sensor configuration.Simulations and experiments are performed on a composite plate to verify the identification accuracy and robustness with respect to the noise of theℓ1-2-ADMM method.Results indicate that compared with other existing regularization methods,theℓ1-2-ADMM method can simultaneously reconstruct and localize impact forces more accurately,facilitating sparser solutions,and yielding more accurate results.