基于应变的空间桁架系统热变形重构方法研究OA

Objective On-orbit deformation monitoring of large-scale space truss structures is crucial for ensuring the stable operation of space science pay-loads and enabling the on-orbit assembly and expansion of space structures.Currently,deformation monitoring of these structures faces two chal-lenges:deformation reconstruction of complex assembled structures under thermo-mechanical loads and discontinuous deflection curves caused by hinges.A method integrating Ko displacement theory with least-squares optimization is proposed to address the difficulty in solving deflection curves caused by special assemblies,thereby expanding the application scope of Ko displacement theory.By introducing combined measurement methods,a thermal deformation reconstruction strategy for space truss systems that considers hinge effects is developed. Methods First,the deformation reconstruction of the space truss system was decomposed into two parts:the main truss structure and the solar panel.For the main truss structure,functions for the deformation deflection curves of each main beam were established using Ko displacement theory.Integral functions were solved using deformation strain data and boundary conditions to achieve deformation reconstruction of the main truss structure.Then,displacements,w1 and w2,at two connection points between the main truss and solar panels were adopted as inputs for solar panel deformation reconstruction.For solar panel A,its deflection curve function was established using Ko displacement theory.With the deflec-tion at the starting point set as w1,candidate curves were generated within the feasible range of[-π/2,π/2]due to the unknown rotation angle.Deri-vations showed that the deflection curve function is a monotonic function of the unknown rotation angle.Therefore,by introducing the hinge dis-placement(wmid)captured via photogrammetry and combining it with the least-squares optimization algorithm,the optimal deformation deflec-tion curve of solar panel A was determined within the feasible range.For solar panel B,its deflection curve function was also established using Ko displacement theory;with the deflection at the endpoint set as w2,a series of feasible solutions for deflection curves was obtained.Based on the hinge displacement(wmid),the optimal solution was identified using the least-squares optimization algorithm.Deformation reconstruction of the solar panel structure,accounting for hinge effects,was achieved by splicing the optimal deflection curves of solar panels A and B at the hinge. Results and Discussions The research object was a 2 500 mm-long space truss system comprising a carbon fiber main truss and honeycomb sand-wich solar panels.Deformations of the structure under three typical temperature conditions(maximum temperature gradient,high temperature,and low temperature)was investigated.A reconstruction accuracy function was defined as the root mean square(RMS)error between the recon-structed displacement response and the theoretical response.Under the maximum temperature gradient condition,the reconstruction error of truss A for bending deformation in one primary deformation direction was 0.16 mm(accounting for approximately 1%of its maximum displacement),and 0.02 mm in the other direction.For truss B,the errors in the two primary deformation directions were 0.10 mm and 0.02 mm,respectively.For truss C(connected to the solar panel structure),the RMS errors of the deformation reconstruction results in the two primary deformation di-rections were 0.06 mm and 0.02 mm,respectively.Similar reconstruction accuracy was observed under high and low temperature conditions.In addition,an analysis of factors influencing the reconstruction accuracy of the algorithm was conducted;the effects of errors caused by random noise,manufacturing,sensor bonding position,and sensor configuration on the accuracy was examined.Results showed that when the measure-ment response contained±5%random noise,the reconstruction errors of the proposed method were mainly distributed within £0.35 mm,with the maximum RMS error accounting for approximately 2.8%of the peak value of the deflection curve.When a maximum 5%thickness error was considered,reconstruction errors of the proposed algorithm were less than 0.1 mm.When a maximum 10 mm sensor bonding position error ex-isted,the reconstruction errors were less than 0.11 mm.Sensor configuration optimization was conducted using a genetic algorithm.Results indi-cated that the fitness function was positively correlated with the number of sensors involved in deformation inversion.As the number of sensors increased,the strain distribution function became more accurate,and the reconstruction accuracy of the inversion algorithm improved.When the total number of sensors in the main truss structure was 28,the fitness of the deformation reconstruction results was 537.13.The fitness function reached approximately 547.40 when the number of sensors was further increased to 39.Thus,for the case studied in this work,the optimal sensor configuration was determined as follows:9 strain monitoring points were arranged on both Truss A and Truss B,and 10 strain monitoring points on Truss C. Conclusions To address the demand for on-orbit deformation monitoring of large space truss systems,a deformation reconstruction strategy suit-able for complex assembled structures under thermo-mechanical load conditions is developed by integrating Ko displacement theory with least-squares optimization.This strategy addresses the challenges of deformation reconstruction caused by special boundary conditions and abrupt changes in hinge angles,providing a feasible approach for on-orbit deformation monitoring of large spatial truss systems.