Intelligent Optimization Strategy Based on Statistical Machine Learning for Spacecraft Thermal Design

The thermal design of spacecraft becomes increasingly complicated as various advanced technologies are continuously introduced to the spacecraft. Determining and optimizing the uncertainties of a spacecraft thermal control system through global sensitivity analysis has long been an essential task for thermal engineers. It is a difficult task that relies heavily on engineering experience and is a time-intensive, trial-and-error endeavor that may not even lead to global optimization. Hence, an intelligent optimization strategy based on statistical machine learning for spacecraft thermal design, called IOSML, is proposed. An intelligent batch processing system (IBPS) based on MATLAB, Python, and NX/TMG real-time data interaction is designed. The IBPS uses a surrogate model to reduce the computational cost of global sensitivity analysis while using a detailed thermal mathematical model to maintain accuracy. We combine a Bayesian inference framework with a neural network surrogate spacecraft-thermophysical model that is $100\times $ faster than numerical solvers. This article first reports on a density-based global sensitivity analysis that evaluates the effect of design parameters on the temperature difference between the complementary metal–oxide–semiconductor and cold screen of the Lehman Alpha Solar Space Telescope detector. From 42 design parameters, the most sensitive four are selected for optimization, and the temperature difference and the boundary temperature are used as the objective function. Adopting IOSML, under no supervision, four design parameters are optimized through the IBPS, and the effectiveness of the algorithm is verified by comparison with traditional methods. Additionally, IOSML is versatile and can be used in various complex engineering applications to provide guidance for the better selection of appropriate parameters and optimization.


I. INTRODUCTION
Temperature is a major factor affecting the performance of space telescopes [1]. The uniformity of the space temperature and the control of the rate of the temperature change critically affect the quality of space telescope imaging. Thermal design is particularly important to the temperature control of space telescopes, as many parameters of the thermal design affect performance. The optimization of thermal design is thus essential for the accurate and stable imaging of space telescopes [2]- [4]. Typically, black-box optimization methods (adopting, for example, experimental design, a genetic The associate editor coordinating the review of this manuscript and approving it for publication was Weipeng Jing . algorithm [5]- [8], a particle swarm algorithm [9], or the non-dominated sorting genetic algorithm II [10]) are used in the optimization of thermal design. Selected variables are systematically modified within a certain range and the response surface of the system is mapped [11], [12] to reach an optimal design. These methods have great potential for the thermal design of spacecraft, are highly cost effective, and are generally speculated to be the ideal choice for the thermal design parameter optimization of spacecraft to be developed for future deep-space exploration. However, the conventional black-box optimization approach has limitations in that the thermal design engineer's choice of variables and their range artificially limits the parameter space and the maximum performance improvement that can be achieved. Furthermore, insights into the root causes of poor performance have been severely limited.
Optimization of the spacecraft thermal design first requires a global sensitivity analysis (GSA) [13], [14] to define uncertainties in the spacecraft thermal control system. This requires many space thermal analyses to be performed to achieve appropriate thermal control. These analyses are time-consuming finite element analyses [15]- [17] that solve partial differential equations. Several meta-modeling approaches that replace the original model with approximate or surrogate models can be adopted to improve the computational efficiency. These approaches include support vector regression [18] and the use of artificial neural networks and have been adopted in the optimization of the thermal design of spacecraft. However, these methodologies require a detailed thermal mathematical model (DTMM) [19]- [21] to guarantee adequate accuracy of the metamodel and are time consuming to employ [22], [23]. Stout [24] proposed a Bayesian-based thermal modeling approach to optimize the thermal design of spacecraft, but the computational efficiency of their approach struggles to satisfy engineering requirements.
Conversely, Bayesian optimization [25]- [27] has recently been combined with physics-based forward models. Fast, simple, and temperature-dependent current-voltage measurements allow the statistically rigorous optimization of the thermal control of early stages of spacecraft, providing new insight for further improvements in methods of optimizing the thermal design of spacecraft. In the present paper, an intelligent optimization strategy based on statistical machine learning for spacecraft thermal design, called IOSML, is proposed to improve on traditional methods of optimizing the thermal design of spacecraft [28], [29]. This is the first time that Bayesian optimization algorithms have been applied to the optimization of spacecraft thermal design. Additionally, IOSML differs from traditional methods of optimizing spacecraft thermal design that adopt time-consuming Monte Carlo estimation. IOSML involves an intelligent batch processing system based on MATLAB, Python, and NX/TMG [30] real-time data interaction (IBPS), whereby the cost of GSA is reduced using a surrogate model [31] while a DTMM is used to maintain accuracy. The system automatically evaluates the model within its variation space according to sampling inputs without supervision, and it is at least 5 times faster than traditional artificial Monte Carlo estimation. In particular, we combine the Bayesian inference framework with a neural network surrogate model [32]. This is a novel approach based on the hybrid strategy of using artificial neural networks in approximating nonlinear systems, which has been applied to approximate the computation of spacecraft thermophysical models and is 10 times faster than a numerical solver. The present paper first evaluates the effect of a temperature difference between the complementary metaloxide-semiconductor (CMOS) and the cold screen of the SCI121.6 detector (TD_CS) onboard the Lehman Alpha Solar Space Telescope (LST) via a density-based GSA of the thermal design parameters. From 42 thermal design parameters, four parameters are selected as optimization parameters, and the TD_CS and boundary temperature are then employed to construct the target function. The automatic optimization of the optimization parameters is performed without supervision via the IBPS using IOSML.
The remainder of the paper is organized as follows. Section II presents the background and motivation of the study. Section III presents details of the IOSML design methodology. Section IV presents the application of IOSML to the optimization of the thermal design parameters of the LST, and compares the performance of IOSML with that of three classical optimization methods. Finally, conclusions of the study are presented in Section V.

II. BACKGROUND AND MOTIVATION
A. SURROGATE MODEL Surrogate models are used in engineering when quantities of interest are not easily and directly measurable [33]. This approach has the potential to speed up complex modeling without sacrificing accuracy or detail and can reduce numerical instability, thereby facilitating calibration and uncertainty analysis.
A growing number of scholars are investigating surrogate models. We typically group agent modeling techniques into three categories: data-driven, projection, and hierarchy-based approaches [34]. In particular, the data-driven surrogate model approximates the thermophysical model via an empirical model that captures the original model's input-output mapping. Projection-based models reduce the dimensionality of the parameter space by projecting governing equations onto the basis of a normal vector. Conversely, hierarchical or multi-fidelity methods create surrogate models by simplifying the physical system; e.g., by ignoring certain processes or by reducing the accuracy of numerical calculations.
In this article, we propose a novel surrogate model approach by combining the advantages of the above three types of surrogate model to improve the efficiency of thermal design optimization and to guarantee the accuracy of thermal analysis.

B. BAYESIAN OPTIMIZATION
Bayesian optimization is a powerful strategy for discovering the optimal value of an objective function that has high evaluation costs [35], [36]. It is applicable in cases that one does not have a closed-form expression of the objective function but can make observations of that function at the sampled value.
In general, Bayesian optimization is a typical example of model-based sequential optimization [37]- [40]. The Bayesian optimization framework has two components: a Bayesian surrogate model for modelling the objective function and an acquisition function for deciding where to sample next. The surrogate models are frequently in the form of Gaussian Processes (GPs) [41], which provide efficient representations of complex functions and characterize model uncertainty in probabilistic frameworks, consequently also called a probabilistic surrogate model. The search for the optimum is guided by an acquisition function that is defined on the statistical surrogate and defines a metric for evaluating the next point to sample through a continuous trade-off between a global exploration and a local exploitation of the surrogate.
Initial sampling strategies are often an important consideration in sequential model-based optimization. Available approaches mainly include random, quasi-random, and Latin hypercube sampling (LHS) of the domain [42].
Specifically, we consider the problem of finding the maximum value of an expensive function f : A → R, where the input x is in R d for a value of d that is typically small. It is noted that d ≤ 20 in most cases of the successful application of Bayesian optimization. The feasible set A is a simple set for which it is easy to evaluate membership. We consider a dataset of n paired input/output observations , with x i ∈ R d and y(x i ) ∈ R, generated by the unknown mapping function y(x) = f (x) + ε, where ε ∼ N (µ ε , σ ε ). GP regression defines a supervised problem in which we associate to the function f a GP prior having mean function m and covariance function κ : We denote the kernel matrix by K ∈ R n×n , such that K (i, j) = κ(x i , x j ). κ n (x) . = (κ(x, x 1 ), . . . , κ(x, x n )), the predictive distribution of the GP, is defined by the mean function µ(x) and the variance function σ (x): where y . = (y(x 1 ), . . . , y(x n )) T denotes the set of hyperparameters and I is the n-dimensional identity matrix.
Once we have a statistical model that reflects our beliefs about the unknown function f given D n , we need a sampling strategy or policy to select new query points x n+1 . Available approaches mainly include random sampling, quasi-random sampling, and LHS of the domain. In this article, we adopt a novel LHS-optimized strategy proposed by Huntington and Lyrintzis [43]. The acquisition function used in this article is the expected improvement, which can be evaluated analytically: where φ(·) and (·) are respectively the probability density function and cumulative distribution function of a standard normal distribution. f (x + ) denotes the maximum value and x + is the corresponding sample location. µ is the mean of all observations while σ is the standard deviation of all observations. EI (·) seeks the expectation that the unknown point function value is greater than f (x + ), while Z the standardized improvement where the parameter ζ allows adjustment of the tradeoff between exploration and exploitation, determining the relative importance of the posterior mean µ(x) versus the potential improvement in the region with high uncertainty; i.e., large σ (x).

III. INTELLIGENT OPTIMIZATION STRATEGY
This section presents an intelligent optimization strategy based on statistical machine learning. A method of surrogate modelling based on the artificial neural network is first introduced. Important parameters are then obtained through GSA of the thermal design parameters. Next, the setting of the objective function and other important parameters required for Bayesian optimization according to the optimization goal are presented. Finally, the practical workflow of IOSML is presented in detail.

A. INTELLIGENT BATCH PROCESSING SYSTEM FOR THE THERMAL ANALYSIS OF A SPACE TELESCOPE
Thermophysical models of space telescopes have many parameters, and traditional methods of spacecraft thermal control require thermal engineers to manually import these parameters into thermal analysis software. In finding the best solution for the thermal design of space telescopes, thermal engineers need to obtain and analyze a large amount of data from thermal analysis results for different modeling parameters. This requires much repetitive work and is time consuming and error prone. An intelligent batch system for thermal analysis based on machine learning is therefore proposed in this article. The system automatically creates a sample input space and conducts batch thermal analysis and the extraction of generated data without supervision. This reduces the effort and time required and improves the efficiency of thermal analysis. The IBPS has multiple functional modules, such as modules for the sampling of the thermal design parameters, the loading of parameters, and the extraction of results of space thermal analysis (see Fig. 1). Additionally, the IBPS realizes the unsupervised automatic construction of datasets of the space thermal analysis results, which effectively reduces the effort and time required and improves the efficiency of space thermal analysis.

B. REPLACEMENT OF THE THERMOPHYSICAL MODEL WITH A SURROGATE MODEL
Thermal radiation is the main mode of heat transfer in the thermal analysis of spacecraft, and Monte Carlo ray tracing [44] is the method most widely adopted in the analysis of 204270 VOLUME 8, 2020 thermal radiation. However, Monte Carlo ray tracing has an extremely long calculation time and requires a great computational resource; i.e., it demands exceptionally high performance of a computer's graphics card. Therefore, to improve the efficiency of thermal analysis, a simplified model (surrogate model) of the spacecraft thermal analysis model must be constructed without reducing the overall computational accuracy.
There are also many methods for formulating surrogate models, such as the Response Surface Method (RSM) [45], Radical basic function (RBF) [46], Support Vector Regression (SVR) [47], Kriging [48], Sparse Polynomial Chaos Expansions (SPCE) [49], etc. . . RSM is one of the widely available surrogate models. For problems with N input variables, there are (N +1)(N +2) 2 coefficients required to be determined; the third-order and higher-order models are intolerable with an increase in the number of variables. In general, RSM is only applicable to the approximation of low nonlinear models. RBF does not require the specification of an objective function expression or derivative information, which requires only the selection of a radial basis function to efficiently construct a relatively accurate surrogate model with a small amount of input data. The support vector machine [50] is one of the most widely used machine learning algorithms for applying kernel tricks to solve pattern recognition problems and was first introduced by Cortes and Vapnik [51]. And it was extended to a nonlinear regression based on the support vector machine framework, called SVR. However, when solving the models with large sample sets, high input dimensions, and strong nonlinearities, the SVR must spend a significant amount of computational time solving the quadratic planning which is the core process of the SVR [52]. The Kriging model has high approximation accuracy for various nonlinear functions, which has been widely used in the field of optimization. However, the construction of the Kriging model is too slow and there are some problems such as premature convergence for certain objective functions with a wide range of response values. SPCE is a popular surrogate modeling approach, which exploits polynomial chaos expansion [53], the sparse effects principle, and a powerful sparse regression solver to approximate a nonlinear model with many input parameters, while relying on very little model evaluation. However, as the number of model inputs M increases, the number of polynomials in the expansion will grow rapidly, and the number of samples must be larger than the number of polynomials to guarantee accuracy, so an excessive number of input parameters will cause dimensional catastrophe problems.
On the other hand, heuristic intelligent optimization algorithms, such as genetic algorithms (GA) [54] and particle swarm optimization (PSO) [55] algorithms, have gradually become a research hotspot in recent years. This provides new ideas and means for solving complex problems. The combination of artificial neural networks and heuristic optimization algorithms can significantly improve the accuracy of models. Although classical evolutionary algorithms such as GA and PSO have been successfully applied in various fields with outstanding achievements, their shortcomings cannot be ignored [56]. For example, they cannot utilize feedback from the network in a timely manner, resulting in a slow algorithmic search speed. Additional training time is required to obtain more accurate solutions, and the potential advantages of the algorithm's parallel mechanism is underutilized. In order to overcome the shortcomings of GA and PSO, the Mind Evolution Algorithm (MEA) was first proposed by Sun in 1998 [57], which was inspired by the activity of human mind. Compared with GA and PSO, the MEA converges much faster. After several rounds of comprehensive comparative analysis of the above various methods, the RBF neural network (RBF NN) surrogate model based on the improved mind evolution algorithm is employed in this article to develop the surrogate model of the thermophysical model of the spacecraft, called RBF-IMEA [58]. Here, the RBF is a Gaussian function, for which the activation function is and the output of the network is where x q represents the q th input vector of the n dimensional vector x, c i is the center of the Gaussian function, and ω ij is the weight of connection between the hidden and input layers. The proposed RBF-IMEA (Fig. 2) includes the following optimization steps: Step 1: According to the topology of the RBF NN, mapping from the decoding space to the coding space is implemented, and the length of the IMEA code is where L 1 , L 2 , and L 3 are respectively the number of nodes in the input, hidden, and output layers.
Step 2: The reciprocal of the mean squared error of the training set is chosen as the reward function F for each VOLUME 8, 2020 individual and group and expressed as where x obs,i is the true value of the i th sample and x pre,i the predicted value of the i th sample.
Step 3: Initialize the group to obtain an excellent subgroup and a temporary subgroup. After convergence and mutation operations are performed, the global optimal individual and its score are obtained.
Step 4: The optimized parameters obtained from the IMEA are input into the RBF NN for further training.

C. DENSITY-BASED GSA OF THERMAL DESIGN PARAMETERS FOR THE LST
Variance-based GSA methods are widely employed in the thermal design of spacecraft and are usually calculated adopting Monte Carlo estimation. However, such estimation requires many samples to ensure sufficient accuracy, and when modeling is difficult, these analyses are costly to perform and the convergence of GSA is slow. Therefore, an intelligent density-based GSA method based on RBF-IMEA neural networks is proposed. This method adopts a DTMM to maintain accuracy and then adopts an RBF-IMEA neural network trained with data from thermal analysis results under many different thermal modeling parameters to reduce the cost of GSA, which contributes to a more comprehensive understanding of the impact of all model parameters on model performance and can greatly speed up thermal design optimization of spacecraft.
Density-based GSA has long been studied by many authors [59], [60] and gives consideration to the probability distribution of the output rather than just the output at a particular moment in time. Specifically, the sensitivity to x i is determined by the distance measured between the unconditional probability distribution of y obtained when all inputs change at the same time and the conditional distribution obtained when all inputs except x i change.
For simplicity, we describe the conditional and unconditional probability distributions in terms of the cumulative distribution function rather than probability distribution functions, as the cumulative distribution function is easier to compute. A time-independent GSA is defined as Suppose that F Y (y) and F Y |X i (y) intersect at m points, where y = a 1 , a 2 Here, δ i is the sensitivity index of input X i to Y , s(X i ) the separation of the output density F Y (y) and the conditional accounts for the average shift in the decision-maker's view of the output provoked by Xi.

D. PRACTICAL WORKFLOW OF IOSML
IOSML proposed in this article has three phases and six steps. Full use is made of three programming languages and space thermal analysis software (Fig. 3). Stage 1: A thermophysical model of the spacecraft is first established using the node network method (NNM) [61]. Sampling in the range of thermal modeling parameters is then conducted to create a sample input space based on the LHS method, which is imported by the IBPS into the DTMM for batch space thermal analysis to maintain the accuracy of the model output in an unsupervised manner. The spacecraft thermophysical model computed by the IBPS is then approximated using the RBF-IMEA neural network as a function of the tracking GSA, while the surrogate model based on a neural network can greatly accelerate post-processing. Finally, convergence analysis is conducted to evaluate the fitting performance of the RBF-IMEA neural network and to decide whether to extend the sampling space further.
Stage 2: An LHS-based sampling space is first generated for the GSA. Density-based GSA is then performed for the thermal modeling parameters, and the effect of each thermal modeling parameter on the telescope CMOS temperature and TD_CS is evaluated according to the GSA results. Here RBF-IMEA neural network surrogate model is adopted in the GSA process instead of the space thermal analysis model to accelerate the thermal analysis. Several groups of key parameters are selected for post-optimization according to the degree of influence.

Stage 3:
The optimal objective function is first determined according to thermal control requirements. The thermal design parameters of the space telescope are then optimized by the Bayesian optimization algorithm through the IBPS without supervision.

IV. EXAMPLE APPLICATIONS AND RESULTS
To verify its performance, IOSML was applied to the optimization of the thermal design parameters of the Extreme Ultraviolet (EUV) detector of the space-based LST, which was designed and manufactured in China, and its performance compared with that of a genetic algorithm (GA), particle swarm optimization algorithm (PSO), and Powell algorithm (POW) [62]- [65].
This section describes the application of IOSML to the LST in depth. The background of the LST is first provided. A thermophysical model of the LST is then described. Furthermore, intelligent optimization of the thermal design parameters of the LST under high-temperature conditions is carried out using IOSML proposed in this article. Finally, the performance of IOSML is compared with that of the GA, PSO, and POW.

A. BACKGROUND OF THE LST
To allow astronomers to observe and study various solar activities, such as coronal mass ejections, solar flares, and sunspots, the Chinese Academy of Sciences designed a novel space-based Lyman alpha and visible dual-band internally buried coronagraph that satisfies the requirements of simultaneous high-resolution imaging and observation of the corona at wavelengths of 121.6 and 700 nm. The overall structure of the LST is shown in Fig. 4A. The barrel of the primary mirror permanently faces the sun. The SCI 121.6 detector and SCI 700 detector are two core detectors of the LST and are essential for observing and studying the internal activity and dynamics of the solar interior in the 121.6-nm and 700-nm bands. The parameters and settings of the orbital environment are given in Table 1, showing that the LST operates in a solar-synchronous orbit at an altitude of 720 km and is exposed to a complex thermal environment, including direct sunlight, infrared radiation from the Earth, and sunlight reflected from the Earth (see Fig. 5). Additionally, there is a large difference in heat flux between the sunny side and shaded side, which may result in an uneven temperature distribution between the primary mirror and detector, thus affecting the imaging quality of the LST. Consequently, there is a strong desire to design a reliable, efficient, and accurate thermal control system for the LST, especially for the detector.   be maintained between 50 and 20 • C. The CMOS within the SCI121.6 detector has aluminum ammonia heat pipes for cooling (see Fig. 4C) but the pipes will fail when their temperature falls below 70 • C, and it is thus essential to control the temperature of the CMOS in the range of 30 to 25 • C, which poses a great challenge in the thermal design of the SCI121.6 detector. Figure 4B illustrates the structure of the well-designed SCI 121.6 detector. The cold plate utilizes electron convection generated by the temperature difference between the cold plate and CMOS to achieve a controlled flow of micro-dust and other pollutants to decontaminate and ensure the imaging quality of the CMOS. This requires that the temperature of the cold plate be lower than that of the CMOS, and the temperature difference (TD_CS) should be maintained above 5 • C. Table 2 specifies the materials used in the detector and their physical properties, which are affected by manufacturing and processing (see Table 3). In particular, in terms of ensuring the accuracy of temperature control of important components such as the CMOS and heat pipes and ensuring that the temperature difference between the CMOS and cold plate is always greater than 5 • C, relying on the experience of thermal design engineers would be time consuming and make it almost impossible to optimize a large number of thermal design parameters.  Bayesian optimization is a powerful strategy for obtaining optimal values of objective functions with high evaluation costs. To validate its performance in the optimization of the thermal design of space telescopes, IOSML is applied to the optimization of thermal design parameters that affect the COMS temperature of the space-based EUV radiation detector of the LST, called the SCI121.6 detector. Figure 4C shows the structure of the SCI121.6 detector.

B. THERMOPHYSICAL MODEL OF THE LST
The thermophysical model of the spacecraft must be analyzed before IOSML can be applied to the thermal analysis of the LST. The node network methodology is a simplified finite difference method and the most commonly employed methodology for the thermo-physical modelling of spacecraft. In the thermal analysis of a spacecraft adopting node network methodology, the actual physical model of the spacecraft is divided into modules (i.e., nodes) of a certain size, and various thermal parameters in the modules are represented by centralized parameters represented by the nodes. The radiative, conductive, and convective heat transfer processes between nodes are respectively summarized as radiation network branches, conduction network branches, and convective network branches that connect the heat flow among nodes. According to its properties, the LST can be decomposed into several special finite units, each of which is considered an isothermal object. The thermophysical model is shown in Fig. 6. Following the 3D model and thermal control scheme of the LST, the thermophysical model of the LST was built using NX TMG Thermal Analysis software, as shown in Fig. 6. The model has 53,970 cells, 55,874 nodes, and 236 thermal couplings and is referred to as a DTMM.

C. APPLICATION OF IOSML 1) SURROGATE MODEL BASED ON THE RBF-IMEA
In creating the training dataset for the surrogate model, we first sampled 5000 samples adopting LHS for 42 sets of parameters within their value ranges. The description and range of thermal design parameters are given in Table 4. We then input 80% of the samples into the IBPS as the training dataset for batch thermal analysis, 10% to verify the generality of the network, and the remaining 10% for testing. After all thermal analyses are complete, the IBPS stores all result data, especially the TD_CS and CMOS temperatures, in text format in the same Excel file in the specified path for training the surrogate model.  The RBF NN toolbox in MATLAB is used in this article, where the command 'newrbe' provides an automatic search for the optimal structure of the RBF NN. The specific node number and learning rate of the implicit layer are respectively taken as 71 and 0.1. After 474 iterations, the mean square error in training the RBF NN surrogate model is 5.9306, which is greater than the pre-defined training target of 1e-2 and does not meet the convergence requirement. As shown in the regression analysis of Figs. 7 and 8, the computational error between the RBF NN surrogate model and the traditional thermophysical model is still less than 85%, so the hyperparameters of the RBF NN must be optimized. VOLUME 8, 2020    and optimization, an RBF-IMEA neural network surrogate model with a structure of 42-71-1 was obtained, and its mean square error was reduced to 3.56e-3. Regression analysis of 204276 VOLUME 8, 2020 the proposed RBF-IMEA surrogate model in both hot and cold cases shows that the model accurately reflects the functional relationship between the TD_CS and 42 parameters (see Figs. 9 and 10). Additionally, the RBF-IMEA surrogate model has a computational speed 100+ times faster than that of the traditional thermophysical model and a high computational accuracy of 95%+.

2) GSA OF THERMAL DESIGN PARAMETERS OF THE LST
Once the RBF-IMEA neural network surrogate model is obtained, the second stage begins (see Section 3.4). Table 5 shows that the difference between the maximum and minimum values of the density-based GSA for the effects of 42 thermal design parameters of the SCI121.6 detector on the CMOS temperature in the hot case does not exceed 0.05 when the computational cost reaches 5000, satisfying the accuracy requirements of the GSA for the initial thermal design parameters of the LST. Additionally, the density-based GSA for the effect of 42 thermal design parameters of the SCI121.6 detector on the CMOS temperature in the cold case, shown in Table 6, satisfies the accuracy requirements of the GSA for the initial thermal design parameters of the LST.
The main effect refers to each input factor's main contribution to the output variance. The total effect explains the total contribution of all higher-order effects to the output variance due to the main effect and interactions between different inputs. It is clear from  and can thus be ignored when optimizing the thermal design parameters of the LST.
Comparing the effects of each thermal design parameter on the CMOS temperature in the hot and cold cases(see Table 6), the trends are similar, and only a few individual parameters have conflicting results. Additionally, the degree of the effect on the CMOS temperature is relatively similar. As an example, the main effect and total effect of Parameters 23 and 38 on the CMOS temperature are respectively 0.4026, 0.6313 and 0.7908, 0.8654 in the hot case and 0.5316, 0.6927 and 0.8694, 0.9041 in the cold case. The main reason for the similar trends with little difference in GSA is that there is little difference in the beta angle between hot and cold cases. The beta angle is the angle between the sunlight and orbital plane, which greatly affects the solar radiation received by the space telescope and thus the overall temperature distribution of the space telescope. The above analysis clearly shows that Parameters 23, 34, 38, and 41 are the four parameters that strongly affect the CMOS temperature and require attention in the optimization of LST thermal design parameters.

3) BAYESIAN OPTIMIZATION OF THERMAL DESIGN PARAMETERS OF THE LST
Once the four important parameters that appreciably affect the CMOS temperature are acquired through the GSA of the LST thermal design parameters, the last but critical step of the second phase begins-the optimization of the LST thermal design parameters adopting the Bayesian optimization algorithm. Table 7 presents the numbers of optimized iterations and results of IOSML in the hot case with no supervision. As the number of optimized iterations increases, the CMOS temperature remains within the range of 30 to 25 • C, and the TD_CS value has an increasing trend. After nine iterations, the TD_CS is greater than 5 • C, meeting the requirements of LST thermal control.
Similarly, as shown in Table 8, the TD_CS can exceed 5 • C after nine optimization iterations, and the CMOS temperature meets the thermal control specifications.

D. RESULITS
To compare the optimization performance of GA, PSO, and POW with that of IOSML proposed in this article, four major factors are selected as the main optimization parameters from the density-based GSA (Parameter 23: thermal resistance between the cold cover and double-layer insulating board; Parameter 34: thermal resistance between the CMOS and printed circuit board (PCB); Parameter 38: coefficient of heat transfer between the multiple layers and wrapped area; and Parameter 41: thermal conductivity of the cold cover), and the remaining parameters are used as supplementary optimization parameters. One-hundred unsupervised iterations of optimization are then performed using each algorithm separately through the IBPS. Detailed information of the parameters for the four algorithms are given in Table 9. Figure 11 shows that, after nine optimized iterations of IOSML in the hot case, the TD_CS of the SCI121.6 detector onboard the LST meets the requirement of thermal control (i.e., the TD_CS temperature always exceeds 5 • C when the CMOS temperature is precisely controlled from 30 to 25 • C), which is better than the performance of the GA, PSO, and POW. Indeed, after nine iterations, the GA, PSO and POW only control the temperature of the CMOS within the temperature range required for thermal control, while the TD_CS temperature is still far from standard. Only after at least 60 optimization iterations do the latter three algorithms meet VOLUME 8, 2020   the requirements of thermal control. IOSML is thus at least twice as efficient as the other methods. Figure 12 shows that, similar to the optimization procedure in the cold case, after nine iterations based on IOSML, the TD_CS of the SCI121.6 detector onboard the LST also meets the requirements of thermal control. However, the convergences of the GA, PSO, and POW are slow. It is clear that IOSML not only greatly improves the efficiency of optimization of thermal design parameters but also ensures that the CMOS temperature is unaffected by the optimization process, allowing unsupervised multi-objective optimization.
The efficiency of the optimization of thermal design parameters based on statistical machine learning proposed in this article is limited by the computational resources used (Intel Core i9-9900X CPU, 64GB RAM, GeForce RTX 2080 Ti), which directly affects the time required for model calculation. With the further improvement of computational resources, the calculation time of the model evaluation and GSA will be shortened, further promoting the application of IOSML in the thermal design parameter optimization task of a space telescope.

V. CONCLUSION
An intelligent optimization strategy based on statistical machine learning for spacecraft thermal design was proposed. The strategy uses an RBF-IMEA neural network surrogate model to reduce the computational cost of model evaluation, while accuracy is maintained by constructing a training dataset for the RBF-IMEA neural network surrogate model with a DTMM. Additionally, an intelligent batch thermal analysis system was designed specifically for the present study, allowing the unsupervised transfer of textual command data and analysis result data between the various software programs through real-time data interaction between MAT-LAB and NX TMG Thermal Analysis software.
In the specific application process, the RBF-IMEA neural network surrogate model was first applied to approximate the thermophysical model of the space telescope; the important factors affecting the CMOS temperature of the SCI121.6 detector onboard the LST were then identified adopting density-based GSA via the IBPS. Optimization adopting the Bayesian optimization algorithm was finally carried out.
Both theoretical and experimental results show that the optimization of thermal design parameters based on IOSML is better than optimization adopting traditional methods such as the use of a GA, PSO, or POW, achieving better model evaluation accuracy and higher calculation efficiency. It is crucial that the entire process be automated to help avoid human errors and thus improve the efficiency of the thermal design optimization for space telescopes. Moreover, it is obvious that the intelligent optimization strategy proposed in this article is applicable not only to the optimization of thermal design parameters of space telescopes but also to post-processing and design optimization in other fields.
Additionally, the convergence of IOSML is not particularly stable and there is random fluctuation because the process involved in engineering applications is complex. To further improve the thermal design of space telescopes, it is essential to further improve the convergence effect and simplify the implementation process of IOSML.
YAN XIONG received the B.S. degree in mechanical design, manufacturing and automation from the School of Engineering, Shenyang Agricultural University, China, in 2015. He is currently pursuing the Ph.D. degree in mechanical manufacturing and automation with the Department of Space Robot Engineering, CIOMP, University of Chinese Academy of Sciences, China. His research interests include intelligent control, spacecraft thermal control, reinforcement learning, and application of machine learning in engineering.