In this paper, we investigate the feasibility of using subspace system identification techniques for estimating transient Structural-Thermal-Optical Performance (STOP) models of reflective optics. As a test case, we use a Newtonian telescope structure. This work is motivated by the need for the development of model-based datadriven techniques for prediction, estimation, and control of thermal effects and thermally-induced wavefront aberrations in optical systems, such as ground and space telescopes, optical instruments operating in harsh environments, optical lithography machines, and optical components of high-power laser systems. We estimate and validate a state-space model of a transient STOP dynamics. First, we model the system in COMSOL Multiphysics. Then, we use LiveLink for MATLAB software module to export the wavefront aberrations data from COMSOL to MATLAB. This data is used to test the subspace identification method that is implemented in Python. One of the main challenges in modeling and estimation of STOP models is that they are inherently large-dimensional. The large-scale nature of STOP models originates from the coupling of optical, thermal, and structural phenomena and physical processes. Our results show that large-dimensional STOP dynamics of the considered optical system can be accurately estimated by low-dimensional state-space models. Due to their lowdimensional nature and state-space forms, these models can effectively be used for the prediction, estimation, and control of thermally-induced wavefront aberrations. The developed MATLAB, COMSOL, and Python codes are available online.
In this paper, we investigate the feasibility of using machine learning methods for the estimation of StructuralThermal-Optical-Performance (STOP) models of reflective optics. We use a model of a Newtonian telescope system to test machine learning methods. To generate the estimation data, we model and simulate a transient finite-element STOP model of the Newtonian telescope by using COMSOL Multiphysics and LiveLink for MATLAB software module. We use a feedforward neural network structure to estimate the STOP model. The inputs and outputs of the neural network correspond to the inputs and outputs of a Vector AutoRegressive eXogenous (VARX) model. Our results show that large-scale STOP dynamics can be effectively approximated by a loworder neural network model. Consequently, low-order VARX or state-space models can be reconstructed from the parameters of the estimated feedforward neural network, and used for the prediction, state estimation, and design of model-based controllers. We use the TensorFlow and Keras machine learning libraries and Python to estimate the feedforward neural network model. The developed COMSOL, MATLAB, and Python codes are available online.
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