Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Time-Varying Mesh Stiffness Calculation and Dynamic Modeling of Spiral Bevel Gear with Spalling Defects

Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.

Time analysis for aero-engine acoustic modes exploiting block sparsity

Acoustic Mode Analysis(AMA)for aero-engines can offer valuable insights for the design of silent engines as well as for fault diagnosis.Commonly,this is done in the(spatial)Fourier domain,necessitating the use of multiple uniformly spaced microphones to ensure adequate resolution.Recent works show that sub-Nyquist estimation is feasible using sparse reconstruction frameworks,although such modelling generally introduces an estimation bias that has to be compensated for.Moreover,there is a growing interest in monitoring mode amplitude over continuous time,as it can offer crucial insights for diagnosing operational conditions.In this work,we introduce a Block Orthogonal Matching Pursuit(BOMP)method for continuous time mode analysis,exploiting the underlying structural sparsity of the signal model.Specifically,the(pseudo)‘0ànorm penalty is employed to induce sparsity in the wavenumber domain,whereas a block structure is imposed as a constraint to monitor the amplitude variation in the time domain.The effectiveness of the BOMP is evaluated using both numerical simulations and experimental measurements,indicating the proposed method's preferable performance as compared to the classic Least Absolute Shrinkage and Selection Operator(LASSO)and Orthogonal Matching Pursuit(OMP)methods.

基于声模态分解的风扇叶盘同步振动辨识

采用非接触式非侵入式的测量方法实现航空发动机叶盘振动测量,对发动机研制、试验、运行安全具有重要意义。提出基于声模态分解的叶盘同步振动辨识方法,在某三级风扇试验器的进气道布置环形声阵列,作为参照并在动叶布置若干应变片,开展升降速试验。分析声压信号的叶片通过频率随转速的变化规律,对动叶一阶通过频率下的声阵列信号进行声模态分解,结合应变片实测的动叶坎贝尔图,建立主导声模态数与叶盘节径数的映射关系。声场和动应力测试结果表明:当主导声模态数与叶盘节径相等时,动叶发生共振现象,此时可有效地对风扇叶盘同步振动进行辨识;动叶与前后叶排静叶都存在转静干涉现象,声压信号呈现为窄带宽频,形成声模态离散,造成动叶表现为多模态振动;声压信号是叶片不同振动模态的气动载荷分布的综合反映,具有好的灵敏性和完备性,可实现航空发动机动叶非接触式非侵入式振动测量。

Basic research on machinery fault diagnostics： Past, present, and future trends

Machinery fault diagnosis has progressed over the past decades with the evolution of machineries in terms of complexity and scale. High-value machineries require condition monitoring and fault diagnosis to guarantee their designed functions and performance throughout their lifetime. Research on machinery Fault diagnostics has grown rapidly in recent years. This paper attempts to summarize and review the recent R＆D trends in the basic research field of machinery fault diagnosis in terms of four main aspects： Fault mechanism, sensor technique and signal acquisition, signal processing, and intelligent diagnostics. The review discusses the special contributions of Chinese scholars to machinery fault diagnostics. On the basis of the review of basic theory of machinery fault diagnosis and its practical applications in engineering, the paper concludes with a brief discussion on the future trends and challenges in machinery fault diagnosis.

Mesh relationship modeling and dynamic characteristic analysis of external spur gears with gear wear

Gear wear is one of the most common gear failures,which changes the mesh relationship of normal gear.A new mesh relationship caused by gear wear affects meshing excitations,such as mesh stiffness and transmission error,and further increases vibration and noise level.This paper aims to establish the model of mesh relationship and reveal the vibration characteristics of external spur gears with gear wear.A geometric model for a new mesh relationship with gear wear is proposed,which is utilized to evaluate the influence of gear wear on mesh stiffness and unloaded static transmission error(USTE).Based on the mesh stiffness and USTE considering gear wear,a gear dynamic model is established,and the vibration characteristics of gear wear are numerically studied.Comparison with the experimental results verifies the proposed dynamic model based on the new mesh relationship.The numerical and experimental results indicate that gear wear does not change the structure of the spectrum,but it alters the amplitude of the meshing frequencies and their sidebands.Several condition indicators,such as root-mean-square,kurtosis,and first-order meshing frequency amplitude,can be regarded as important bases for judging gear wear state.

Full-field dynamic strain reconstruction of an aero-engine blade from limited displacement responses

Blade strain distribution and its change with time are crucial for reliability analysis and residual life evaluation in blade vibration tests.Traditional strain measurements are achieved by strain gauges(SGs)in a contact manner at discrete positions on the blades.This study proposes a method of full-field and real-time strain reconstruction of an aero-engine blade based on limited displacement responses.Limited optical measured displacement responses are utilized to reconstruct the full-field strain.The full-field strain distribution is in-time visualized.A displacement-to-strain transformation matrix is derived on the basis of the blade mode shapes in the modal coordinate.The proposed method is validated on an aero-engine blade in numerical and experimental cases.Three discrete vibrational displacement responses measured by laser triangulation sensors are used to reconstruct the full-field strain over the whole operating time.The reconstructed strain responses are compared with the results measured by SGs and numerical simulation.The high consistency between the reconstructed and measured results demonstrates the accurate strain reconstructed by the method.This paper provides a low-cost,real-time,and visualized measurement of blade full-field dynamic strain using displacement response,where the traditional SGs would fail.

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.