基于仿射内点信赖域算法的遥测数据建模预测

Modeling and predicting telemetric data based on trust-region interior reflective algorithm

许多大型航天电子设备的遥测数据表现为不规则周期状,对其进行建模并进行长期预测可以在早期及时发现设备性能异常。研究利用仿射内点信赖域算法(TIR)解决数学模型参数有界约束,结合非线性最小二乘求解和仿射内点方法的特点,用预条件共轭梯度算法求解下降方向,和最速下降方向一起构造二维子空间,通过正交化二维子空间方法将待求解信赖域子问题降至二维,用特征值分解算法求解参数。给出了对某遥测数据建模的Fourier级数模型,先用快速傅里叶变换(FFT)分析求模型参数初始点,然后用上述算法求解出模型精确参数,数值实验结果表明了算法的快速有效性。

The telemetric data of large-scale spaceflight electronic equipments usually appears the irregular period,and the performance abnormity would be discovered early through modeling and prediction on these data. The Trust-region Interior Reflective（ TIR） approach was used to solve the bound-constraint on the model parameters. Combined with the characteristics of non-linear least squares and TIR, the preconditioning matrix was computed by the Cholesky decomposition. The preconditioned conjugate gradient was used to compute one of the descend direction,which with the steepest descent direction forms the two-dimensional subspace. The Schmidt orthogonal two-dimensional subspace approach was adopted to get twodimensional trust region subprobem,which was solute by the eigenvalue decomposition approach. The Fourier model was used in the paper to model telemetric data,and the initial model parameters were calculated through the Fast Fourier Transform（ FFT）,then the above method was used to solve the precise parameters. The results of some numerical experiments show the validity of this trust-region algorithm.