Analysis of precision and error of cable force identification of cable-stayed bridge

In this paper,in order to improve the precision of cable force identification of a practical cable-stayed bridge and consider some precision problems of vibration method in surveying the cable force in the engineering application,firstly,three calculation methods for the cable force measurement are analyzed and contrasted;secondly,using the method of finite element numerical simulation and the theory of the error analysis,the effect of both bending rigidity and constraint conditions on simple formula of vibration method is investigated;and the dependence of the precision of cable frequency identification on spectrum resolution,sampling time,and the number of sampling points is studied;Finally,fundamental frequency method,frequency difference method,and peak value method are applied to the cable force calculation of a practical project;and their computational precision and error are contrasted and analyzed.It is observed that it is essential to take into account the effect of every factor on the precision of the cable force identification and make it possible to identify the cable force more accurate by vibration method;and that it simultaneously provides an effective basis for the development of a high-precision equipment.

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.

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 handlingl_(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 vial_(p) regularization is conducted.It turns out that?_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classicl_(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.

Impact Force Magnitude and Location Recognition of Composite Materials

In order to identify the location and magnitude of the impact force accurately,determine the damage range of the structure and accelerate the health monitoring of key components of the composite,this paper studies the location and magnitude of the impact force of composite plates by an inverse method.Firstly,a PZT sensor mounted on the material plate is used to collect the response signal generated by the impact force,which is from several impact locations,and establish transfer functions between the impact location and the PZT sensor.Secondly,this paper applies several forces to any location on the material plate,and collects the corresponding response signals,and reconstructs the impact force of several locations in turn.Finally,according to the reconstruction result of each location,the correct impact location is identified.Then,an improved regularization method is used to optimize the reconstructed impact force and accurate the magnitude of the impact force.The comparison experiments prove that the recognition error of this method is smaller.

Analysis of Key Factors in Cable Force Calculation for Cable-Stayed Bridges

Three methods for calculating cable force （analytic method, fitting method and finite element method） are analyzed and compared. The effects of boundary condition, spectrum resolution, sampling time, and number of sampling points on the precision of cable force identification are discussed, and error analysis is conducted. The results of three methods applied to a practical project are significantly less than the design value. Comparatively, the result of finite element method is the closest to the design value. Moreover, their computational precision and error are compared and analyzed. The precision of frequency identification of cables, long cables in particular, is strongly affected by frequency resolution. If the frequency resolution is included in calculating the cable force, the identification error can be reduced greatly.

Identification of Forcing Mechanisms of Convective Initiation over Mountains through High-Resolution Numerical Simulations

Convection and its ensuing severe weather, such as heavy rainfall, hail, tornado, and high wind, have significant im- pacts on our society and economy （e.g., Cao et al., 2004; Fritsch and Carbone, 2004; Verbout et al., 2006; Ashley and Black, 2008; Cao, 2008; Cao and Ma, 2009; Zhang et al., 2014）. Due to its localized and transient nature, the initiation of convection or convective initiation remains one of the least understood aspects of convection in the scientific communi- ties, and it is a significant challenge to accurately predict the exact timing and location of convective initiation （e.g., Cai et al., 2006; Wilson and Roberts, 2006; Xue and Martin, 2006; Cao and Zhang, 2016）.

Approximation of structural damping and input excitation force

Structural dynamic characteristics are the most significant parameters that play a decisive role in structural damage assessment. The more sensitive parameter to the damage is the damping behavior of the structure. The complexity of structural damping mechanisms has made this parameter to be one of the ongoing research topics. Despite all the difficulties in the modeling of damping, there are some approaches like as linear and nonlinear models which are described as the energy dissipation throughout viscous, material or structural hysteretic and frictional damping mechanisms. In the presence of a mathematical model of the damping mechanisms, it is possible to estimate the damping ratio from the theoretical comparison of the damped and un-damped systems. On the other hand, solving the inverse problem of the input force estimation and its distribution to each SDOFs, from the measured structural responses plays an important role in structural identification process. In this paper model-based damping approximation method and a modelless structural input estimation are considered. The effectiveness of proposed methods has been carded out through analytical and numerical simulation of the lumped mass system and the results are compared with reference data. Consequently, high convergence of the comparison results illustrates the satisfactory of proposed approximation methods.