| Large-aperture,lightweight and high-frequency have become the development trend of radio telescope.The high-frequency asks for the high pointing accuracy.However,the inherent frequency is in decreased with the aperture increasing,which would lead to the relative position and orientation of sub-reflector deviated under the affection of the environment loadings,such as the temperature,the winding disturb and its own gravity.In the result,the observation performance index of telescope is affected seriously.Adjusting the position and orientation of sub-reflector with active adjusting instrument is an effective method to ensure the observation performance of the radio telescope,but this method requires that the position and orientation deviation information of sub-reflector is accurately obtained.The existing photo-electricity measuring schemes,such as photogrammetry,Position Sensing Device(PSD),et.al are limited to the disturbances of the measuring environment and the requirement of the measuring device,it is difficult to track and measure the position and orientation of sub-reflector in real-time.In order to figure the above problem out,a new measurement scheme based on reconstructing the structural deformation with strain measurements by using the inverse Finite Element Method(i FEM)is proposed to real-time measuring position and orientation of sub-reflector in this paper.The research content includes the following aspects:1.Description of the innovative measuring scheme.In order to real-time monitor the position and orientation of sub-reflector,the strain measurement is used to reconstruct the frame deformation of the sub-reflector supporting legs,and then the position and orientation of sub-reflector is estimated in the new measurement scheme.It means that the relationship model between structural deformation and the measured strain is applied to reconstruct the structure by using the real-time strain information obtained with the fiber Bragg grating(FBG)strain sensor attached to the supporting leg truss of sub-reflector.After that,the position and orientation of sub-reflector is obtained by using the forward kinematics when the lengths of the adjusting device supporting legs are known.Compared to the existing photo-electricity measuring schemes,such as photogrammetry,the proposed measurement scheme in the paper is able to measure position and orientation of sub-reflector in real-time.2.The criterion of the relationship between the minimum section number and the section strain order is established to avoid the singularity of reconstruction model of the beam element.Reconstructing the structural deformation with using the strain measurements is an inverse problem in engineering.The improper combination of the boundary conditions and the measured strain can cause the singularity of the deformation reconstruction model,which results in that the correct structural deformation solution of the reconstruction model cannot be obtained.Therefore,the criterion of the relationship between the minimum section number and the section strain order is proposed in order to avoid the singularity of reconstruction model.The strain order of each section is obtained through analysis of the loads exerting on the beam element;then,based on the analysis of the number of cross-section strains required to solve the unknown parameters of the cross-section strain expression,it is concluded that the minimum cross-section number should be one order higher than the maximum order of cross-section strains.The finite element simulation and the cantilever model loading experiments have shown that the singularity of the reconstruction model of the inverse finite beam element deformation is effectively avoided by applying this criterion.3.The optimal placement model of sensors is established to avoid the ill-condition of the reconstruction model of beam element.When the inverse finite beam element is used to reconstruct the structural deformation of the beam,the placement of the sensors will affect the reconstruction accuracy of the model on the one hand,and may cause the ill-condition of the reconstruction model on the other hand.In this paper,according to the fact that the good coefficient matrix has a "good" eigenvalue distribution,that is,the obvious differences exist among the eigenvalues,the optimal placement model of sensors is established to avoid the ill-condition of the reconstruction model from the perspective of the observability of linear system.The finite element simulation and the truss model loading experiment have demonstrated that the optimal placement model of sensors can precisely reconstruct the beam/truss structural deformation through the inverse finite beam element model;also,the measurement system error interference caused by the sensors-stuck-error and the sensors-own measurement-error is robust.4.The interpolation shape function of the beam element is selected to accurately estimate the deformation of any node in beam element of the support truss.For the frame of the sub-reflector supporting leg of a radio telescope,the force exerting on each beam element is complex,and the interpolation precision of the deformation of any structure in the element is different for the different order shape functions.Therefore,0-order,1-order and the interpolation shape function,which is appropriate for the inverse finite beam element for the supporting truss structure of the sub-reflector,are derived according to the different cross-section strain orders.Also,the inverse finite beam element for the truss structure is established.Taking the frame of the sub-reflector support leg of the 25-meter radio telescope as an example.The shape function established in this paper can accurately calculate the deformation of each node in the beam element of the support leg,whose results are consistent with the ANSYS simulation analysis.In addition,the reconstruction precision for the deformation of cantilever beam under the mixed loads is obviously improved by using the new inverse finite beam element.5.Estimating the morbidity of the reconstructing model of the supporting fram structure.The improper placement of sensors will not only affect the reconstruction accuracy for the deformation of the beam element,but also affect the reconstruction results of supporting fram structre.Thus,the beam element positioning method for the improper placement of sensors is proposed in addition to that the ill-posed degree of the overall reconstruction model can be judged.At last,the experiment is conducted on the simple finite element model of the support structure of sub-reflector,the simple physical model and the full-size finite element model of the supporting truss to verify the proposed scheme.The experiment on the simple finite element model demonstrates that the measurement scheme method can reconstruct the deformation of the supporting leg end with high precision.Whereas,the experiments on the physical model and the full-size finite element model show that the estimation accuracy of the contact measurement scheme proposed in this paper decreases slightly because of the existence of the modeling error and the sensor-stuck-error. |
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