Small-thrust trajectory optimization method and system based on structural adaptive neural network

Abstract

The application provides a small-thrust trajectory optimization method and system based on a structure adaptive neural network, and relates to the technical field of spacecraft trajectory optimization. The application trains and verifies a structure adaptive neural network based on a small-thrust trajectory data set of a spacecraft, and obtains a dynamic neural network model. The structure adaptive neural network comprises an initial neural network, a performance stagnation monitor and a deep neural network capacity heuristic adjustment module. The deep neural network capacity heuristic adjustment module is used for hierarchical regulation and control of the capacity of the structure adaptive neural network. When trajectory data with new features are accumulated, the application adaptively adjusts the network structure, can absorb new knowledge through incremental evolution of the network structure, and does not need to retrain from the beginning. On the basis of fully trained knowledge, the model can accommodate and learn new small-thrust trajectory optimization rules through structure growth, and can effectively solve the fundamental problem that the learning potential of a fixed structure model is limited when facing new data.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of spacecraft trajectory optimization, and in particular to a small-thrust trajectory optimization method and system based on a structure-adaptive neural network. BACKGROUND

[0002] One of the core challenges of small-thrust spacecraft complex mission planning (such as interplanetary exploration, constellation deployment and maintenance) is trajectory optimization. Traditional numerical optimization methods, whether indirect methods based on the variational principle or direct methods based on nonlinear programming, are essentially a process of solving an optimal control problem under complex differential equation constraints. Although such methods can theoretically guarantee the optimality or near-optimality of the solution, they face the bottleneck of huge computational resource consumption in engineering practice. A high-precision trajectory optimization calculation may require several hours of iterative solution, and this time cost makes it difficult for traditional methods to handle such scenarios in large-scale mission screening, sudden mission re-planning, or extensive exploration of the mission design space.

[0003] To break through this efficiency bottleneck, academia and industry have begun to explore the use of deep neural networks (DNNs). The basic idea is to use a traditional optimizer to generate a large-scale, diverse small-thrust trajectory database offline, and then train a DNN to learn the complex mapping relationships contained in this database. The workflow mainly includes:

[0004] Data-driven offline training: Through a high-precision numerical optimizer, simulate trajectory tasks for a large number of different boundary conditions and constraints to solve and build a large training dataset. Each data sample contains the input features of the task (such as spacecraft initial and final orbit states, flight time window, etc.) and the corresponding output label (such as the minimum fuel consumption calculated by the traditional optimizer).

[0005] Design of fixed topology network: Researchers design and determine a deep neural network with a fixed topology structure based on experience or through optimization means. This structure, including the total number of layers (depth), the number of neurons in each layer (width), and the type of activation function, is once selected in the design stage and will not be changed.

[0006] Model training and updating: Train the network with a fixed structure using a large-scale dataset. Through algorithms such as backpropagation and gradient descent, iteratively adjust the network parameters to minimize the prediction error of the network on the training data.

[0007] However, the topology structure and weight parameters of the model trained by the prior art are optimized for a generated training data set. In the long-term practice of space engineering, as new types of tasks appear, the trajectory database is continuously evolved and expanded, and when the feature distribution of the new data sample is significantly different from the original data set, the generalization ability of the original fixed structure model will decrease sharply. That is, the fixed model trained by the prior art lacks the adaptive evolution ability of new knowledge. SUMMARY

[0008] (I) Technical problems solved

[0009] In view of the deficiencies of the prior art, the present application provides a small-thrust trajectory optimization method and system based on a structure adaptive neural network, which solves the technical problem that the fixed model trained by the prior art lacks the adaptive evolution ability of new knowledge.

[0010] (II) Technical solutions

[0011] To achieve the above object, the present application is implemented by the following technical solutions:

[0012] In a first aspect, the present application provides a small-thrust trajectory optimization method based on a structure adaptive neural network, comprising:

[0013] obtaining a small-thrust trajectory initial set of a spacecraft; extracting trajectory features in the small-thrust trajectory initial set of the spacecraft to obtain a small-thrust trajectory data set of the spacecraft;

[0014] training and verifying a structure adaptive neural network based on the small-thrust trajectory data set of the spacecraft to obtain a dynamic neural network model, wherein the dynamic neural network model is used to predict an optimal small-thrust orbit trajectory and a transfer cost according to input small-thrust orbit maneuver features; and the structure adaptive neural network comprises an initial neural network, a performance stagnation monitor and a deep neural network capacity heuristic adjustment module.

[0015] The performance stagnation monitor is used to monitor the performance of the structure adaptive neural network and determine whether the deep neural network capacity heuristic adjustment module needs to be triggered to adjust the network capacity.

[0016] The deep neural network capacity heuristic adjustment module is used to adjust the capacity of the structure adaptive neural network in stages.

[0017] Preferably, the initial neural network comprises a fully connected network, each layer containing neurons.

[0018] Preferably, the working process of the performance stagnation monitor comprises:

[0019] The firstz one training cycle After the end, the structure adaptive neural network is tested by the validation set, and the validation set loss of the structure adaptive neural network in the current training cycle is calculated ;

[0020] Read the total of loss values of the network tested on the validation set in training cycles, and take the minimum or average value thereof as the loss bottleneck value as required , and calculate the loss drop rate :

[0021]

[0022] If the maximum drop percentage is lower than the expected , i.e. , it is determined that the training performance of the structure adaptive neural network is stagnant, and the deep neural network capacity heuristic adjustment module is driven to adaptively adjust the capacity of the structure adaptive neural network; wherein is a percentage threshold.

[0023] Preferably, the deep neural network capacity heuristic adjustment module adaptively adjusts the capacity of the structure adaptive neural network, comprising:

[0024] After the training starts, the performance stagnation monitor counter is initialized: , ; and represent the number of width and depth adjustment triggers in this round of adjustment, respectively;

[0025] After entering the training, the network reads the batch data, calculates the loss, updates the network weights, and monitors the network performance according to the designed performance stagnation monitor. In the training cycle where the performance detector is not triggered, the network snapshot is saved for later execution of network structure and weight rollback operation;

[0026] After determining the performance stagnation, the performance stagnation detector is triggered and the network width adjustment counter is initialized =1; perform width adjustment based on neuron splitting, and continue training;

[0027] If the training is successful, the counter is reset to zero , , and the current network snapshot is saved; if the performance is still stagnant in the next training cycle, the monitor is triggered again and the counter is counted =2, width adjustment is performed again; when ​​The number of performance stalls exceeded the limit. If the width adjustment strategy fails, the network structure is rolled back to the network snapshot at the time of the last effective network width adjustment, and depth adjustment is triggered.

[0028] Enter depth adjustment and initialize the depth adjustment technology. After performing deep tuning, continue training for several more epochs. If training is successful, the counter is reset to zero. , It saves the current network snapshot; if performance remains stagnant in the following training cycles, the monitor is triggered again and counts. =2; Perform depth adjustment again until... .

[0029] Preferably, the width adjustment includes:

[0030] During the training period, targeting... The first of the validation set samples For each sample, calculate the loss function. Perform a backpropagation and calculate the loss function for the first... Layer network layer The output of each activated neuron The average absolute value of the gradient is used as the importance score of the neuron. :

[0031]

[0032] in, It is the first Loss per sample;

[0033] Based on neuron importance score Select the neurons to perform the fission operation;

[0034] A fission operation is performed on the selected neurons to increase the network capacity, wherein the fission operation is performed as follows:

[0035] Original neuron output Represented as:

[0036]

[0037] in, The weights are the connections between neurons in the current network layer and the previous network layer. To increase the bias, the width of the current network layer is increased by splitting a neuron into two neurons, thereby increasing the network capacity. After the split, the node output is... and :

[0038]

[0039]

[0040] wherein, is a perturbation factor for neuron splitting, for splitting neurons, or takes a value close to zero, then the split neuron instantaneously outputs approximately equal to the output when the neuron is not split, realizing the preservation of the original network function after splitting:

[0041]

[0042] wherein, is the node's instantaneous output value of the network splitting.

[0043] Preferably, the depth adjustment comprises:

[0044] After the depth adaptive adjustment is triggered to meet the triggering condition, two network layers are randomly selected and An identity mapping layer is inserted between them; The weight matrix of the newly inserted layer is , and the bias is

[0045] The original network update process is:

[0046]

[0047] After inserting the new layer, the network updates as follows:

[0048]

[0049] After inserting the new layer, the input of the subsequent network layer becomes:

[0050]

[0051] If the weight matrix is initialized as the identity matrix , the bias is set to ; for the activation function Relu, for non-negative input, the output of the new layer is .

[0052] Preferably, when updating the network after inserting the new layer, the active gradient injection and learning rate local scaling mechanism are used to update and , including:

[0053]

[0054] wherein, is a unit matrix I of the same dimension, with mean 0 and variance of a Gaussian distribution noise with bias set to ;

[0055] weight matrix and bias update rule is:

[0056]

[0057]

[0058] wherein,

[0059]

[0060] wherein, denotes the maximum decay period, denotes the learning rate temporary scaling factor at the th period, is the initial value of the scaling factor, denotes the learning rate.

[0061] In a second aspect, the present application provides a small thrust trajectory optimization system based on a structure adaptive neural network, comprising:

[0062] a data set generation module, configured to obtain a spacecraft small thrust trajectory initial set; extract trajectory features in the spacecraft small thrust trajectory initial set to obtain a spacecraft small thrust trajectory data set;

[0063] a model training and adaptive adjustment module, configured to train and verify a structure adaptive neural network based on the spacecraft small thrust trajectory data set to obtain a dynamic neural network model, wherein the dynamic neural network model is used to predict an optimal small thrust orbit maneuvering trajectory and a transfer cost according to input small thrust orbit maneuvering features; and the structure adaptive neural network comprises an initial neural network, a performance stagnation monitor and a deep neural network capacity heuristic adjustment module.

[0064] The performance stagnation monitor is configured to monitor the performance of the structure adaptive neural network and determine whether the deep neural network capacity heuristic adjustment module needs to be triggered to adjust the network capacity.

[0065] The deep neural network capacity heuristic adjustment module is configured to adjust the capacity of the structure adaptive neural network in stages.

[0066] In a third aspect, the present application provides a computer readable storage medium storing a computer program for small-thrust trajectory optimization based on a structure adaptive neural network, wherein the computer program causes a computer to perform the small-thrust trajectory optimization based on a structure adaptive neural network as described above.

[0067] In a third aspect, the present application provides an electronic device comprising:

[0068] one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs comprise a program for performing the small-thrust trajectory optimization based on a structure adaptive neural network as described above.

[0069] (Three) beneficial effects

[0070] The present application provides a small-thrust trajectory optimization method and system based on a structure adaptive neural network. Compared with the prior art, the present application has the following beneficial effects:

[0071] When trajectory data with new features are accumulated, the adaptive mechanism of the present application enables the network to absorb new knowledge through incremental evolution of the network structure. The model does not need to be retrained from scratch, but can accommodate and learn new small-thrust trajectory optimization rules through structure growth based on fully trained knowledge, effectively solving the fundamental problem of limited learning potential of fixed structure models when facing new data. The sustainable online evolution capability of the present application is completely not possessed by static networks, laying a solid technical foundation for building a small-thrust trajectory intelligent optimization system that can be iterated and self-improved for a long time, greatly enhancing the life cycle value and sustainability of the technical solution. BRIEF DESCRIPTION OF DRAWINGS

[0072] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0073] Figure 1 A flowchart of the small-thrust trajectory optimization method and system based on a structure adaptive neural network of the embodiments of the present application;

[0074] Figure 2 A schematic diagram of the capacity heuristic adjustment of the dynamic neural network model. DETAILED DESCRIPTION

[0075] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application are described clearly and completely. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0076] The embodiments of the present application provide a small-thrust trajectory optimization method and system based on a structure adaptive neural network, and solve the technical problem that a fixed model obtained by training in the prior art lacks adaptive evolution capability of new knowledge. The network can absorb new knowledge through incremental evolution of the network structure through an adaptive mechanism.

[0077] To solve the above technical problems, the technical solutions in the embodiments of the present application have the following general ideas:

[0078] In addition to the above-mentioned fixed model lacking adaptive evolution capability of new knowledge, there is a lack of an effective incremental learning mechanism to adapt the model to such changes. When new data samples appear, only the complete process of high-cost calculation including structure redesign and full data retraining can be selected to completely discard the existing model and recompute. This makes the life cycle cost of the model high, and the knowledge cannot be effectively inherited. The existing fixed model also has the following defects:

[0079] Over-reliance of network structure design on prior knowledge and computing resources: the selection of the topology structure (depth, width) and hyperparameters of a fixed structure network with excellent performance itself is a difficult optimization problem. The prior art mainly relies on two ways to solve it: one is based on the prior knowledge of R&D personnel and a large number of manual experiments, which is highly subjective, has poor reproducibility and low efficiency; the other is to use grid search or Bayesian optimization and other automatic hyperparameter search technologies. However, such automatic methods need to perform hundreds or even thousands of complete training evaluations, which is a high-cost training, and it is difficult to extend the DNN to multiple types of task scenarios.

[0080] Mismatch between model capacity and task complexity: the nonlinearity degree and solution difficulty of the small-thrust trajectory optimization task will change with the changes of the orbit type, transfer target and dynamics environment. The prior art uses a fixed-capacity network to fit complex small-thrust scenarios, which inevitably leads to performance bottlenecks. For a relatively simple task subset, a complex network will increase the risk of overfitting due to capacity redundancy, and waste computing resources; while for a highly complex task subset (such as transfer in a multi-body gravitational environment), a network with insufficient capacity will be significantly underfitted due to the limitation of model expression capability, and cannot achieve the required prediction accuracy. This inherent capacity mismatch limits the performance upper limit that a single fixed structure network can achieve.

[0081] To solve the above problems of the fixed model, the embodiment of the application provides a novel small-thrust trajectory optimization method based on a structure adaptive neural network, which enables the neural network to get rid of the fixed capacity constraint, gives it the ability to dynamically adjust its model capacity according to the inherent complexity of the small-thrust trajectory optimization scene and the learning process in the training process, finally realizes the balance of model performance, training efficiency and computing resource utilization, and enables the model to have long-term online evolution ability.

[0082] In order to better understand the above technical solutions, the above technical solutions will be described in detail below in combination with the drawings of the specification and specific embodiments.

[0083] The embodiment of the application provides a small-thrust trajectory optimization method based on a structure adaptive neural network, as shown in Figure 1 The embodiment of the application provides a small-thrust trajectory optimization method based on a structure adaptive neural network, as shown in

[0084] S1, obtaining a spacecraft small-thrust trajectory initial set; extracting trajectory features in the spacecraft small-thrust trajectory initial set to obtain a spacecraft small-thrust trajectory data set;

[0085] S2, training and verifying a structure adaptive neural network based on the spacecraft small-thrust trajectory data set to obtain a dynamic neural network model, wherein the dynamic neural network model is used to predict an optimal small-thrust orbit trajectory and a transfer cost according to input small-thrust orbit maneuver features; the structure adaptive neural network includes an initial neural network, a performance stagnation monitor and a deep neural network capacity heuristic adjustment module.

[0086] The performance stagnation monitor is used to monitor the performance of the structure adaptive neural network and determine whether the deep neural network capacity heuristic adjustment module needs to be triggered to adjust the network capacity.

[0087] The deep neural network capacity heuristic adjustment module is used to regulate the structure adaptive neural network capacity in stages.

[0088] In an embodiment, S1, a spacecraft small-thrust trajectory initial set is obtained; trajectory features in the spacecraft small-thrust trajectory initial set are extracted to obtain a spacecraft small-thrust trajectory data set. The specific implementation process is as follows:

[0089] It should be noted that in the specific implementation process, the spacecraft small-thrust trajectory initial set can be solved by various algorithms. A large amount of feasible trajectory data and label data are obtained as the spacecraft small-thrust trajectory initial set by generating random tasks and solving. A way to solve the spacecraft small-thrust trajectory initial set is described in detail as follows:

[0090] S101. Construct a task scenario, randomly generate and select targets based on the task scenario, and construct a small-thrust trajectory optimization model including constraints and objective functions. Specifically, this includes:

[0091] In this embodiment of the invention, a spatial target rendezvous task scenario is constructed, in a spatial target dataset. Two targets are randomly selected from the middle. , Randomly select the initial moment of the low-thrust transfer mission. Set flight time According to search time step The scan is complete, and the task ends at [time]. For each group , and The velocity increment under the double-pulse orbit assumption was calculated by applying the Lambert equation. Select the smallest and the corresponding transfer time Generate low-thrust trajectory transfer time. Thus, the initial spatial target position and velocity vector are obtained. The spatial target position and velocity vector at the end time .

[0092] The trajectory optimization problem is transformed into an optimal control problem, which is then discretized and rearranged into a nonlinear programming (NLP) problem. The specific steps are as follows:

[0093] Discretize the small thrust trajectory to form If there are discrete units, then the discretized spacecraft state variables can be expressed as:

[0094]

[0095] in, The position after discretization. The velocity is the discretized value. The mass of the spacecraft decreases as it travels along its trajectory.

[0096] The engine in The maximum velocity increment that can be generated at each discrete moment is calculated as follows:

[0097]

[0098] in, It is the number of effective thrusters. The duty cycle of the thruster ignition time. , where is the discretized time step. For the first The spacecraft mass of a discrete point, For the maximum thrust of the thruster, assume the maximum power allocated to the thruster Fixed, can be calculated as:

[0099]

[0100] Where, is the standard gravity acceleration, is the engine efficiency, is the specific impulse of the thruster.

[0101] The spacecraft state recursion equation is as follows:

[0102]

[0103]

[0104] Where, is the to-be-solved thruster control variable at time , which determines the propulsion direction of the thruster, is the maximum mass change at time due to fuel consumption, calculated as . Where, is the mass flow rate of the fuel, which can be calculated by the rocket equation or other modeling methods.

[0105] The spacecraft state bidirectional recursion is adopted to establish the constraint condition:

[0106]

[0107]

[0108]

[0109] Where, is the dry weight of the spacecraft structure, , , respectively, the state difference of the forward and backward state geopush at the same intermediate matching point, that is, the forward and backward must ensure the continuity of the spacecraft state quantity on the trajectory.

[0110] The objective function is established:

[0111]

[0112] S102, substitute the selected target into the low-thrust trajectory optimization model, configure the solver to solve the low-thrust trajectory, and obtain a plurality of trajectory data as an initial set. Specifically, it includes:

[0113] According to the above steps, the small thrust trajectory optimization model is established, the solver parameters are configured, and the decision variables are solved. The above process is relatively independent, so the parallel computing automation computing framework is adopted. The workflow of each thread is as follows:

[0114] The small thrust task initialization process is automatically completed, the small thrust trajectory to be solved is obtained, and the NLP problem modeling is performed according to the above steps.

[0115] It should be noted that in the solving stage, the small-scale NLP problem is first solved, The smaller value is taken, the decision variable is initially taken as a random number, and the above process is solved. If the small thrust trajectory has no feasible solution, the decision variable is randomly initialized again until times still fail to solve, it is considered that the trajectory has no feasible solution, the target selection and trajectory initialization process are performed again, and the solving is attempted. If there is a solution, the existence of a feasible solution identifier is set to 1.

[0116] After the solution existence identifier is obtained, The larger value is taken, the large-scale NLP problem is constructed, the solving speed is reduced but the more accurate optimal solution can be obtained, the decision variable and task data are stored, the existence of a feasible solution identifier is set to 0, and the trajectory initialization process is repeated.

[0117] The above process is automatically and parallelly computed according to the computing resource condition, greatly improving the data generation efficiency.

[0118] S103, extracting trajectory features in the trajectory data to obtain a spacecraft small thrust trajectory data set. Specifically, it includes:

[0119] The trajectory features include basic features and high-dimensional features.

[0120] According to the trajectory data that has been solved, the task start time , flight time , task end time , initial mass of the spacecraft , mass at arrival and other basic features are extracted, and a small thrust trajectory high-dimensional feature data set is constructed according to the basic features.

[0121] The positions and velocities of the two targets in the Cartesian inertial coordinate system are read , the positions and velocities in the cylindrical coordinate system are calculated , the positions and velocities in the spherical coordinate system are calculated , the classical orbit elements of the two targets are calculated , the improved equinox orbit elements are calculated , and the corresponding ephemeris changes are calculated , , , 、 。

[0122] Continue to artificially construct high-dimensional features of low-thrust trajectories and calculate the low-thrust flight time. Below Speed ​​increment The orbital energy change is as follows: ( The change in angular momentum is: ( The angle between the angular momentum vectors is the initial orbital angular momentum. With the angular momentum of the arriving orbit dot product: .

[0123] The characteristics of any trajectory can be described as follows:

[0124]

[0125] In practice, the basic features included in the trajectory features can be adjusted according to the actual situation; for example, three or four features can be selected. You can also choose not to select it. .

[0126] In this embodiment of the invention, the final mass of the spacecraft in the trajectory features is used as the reference. This data serves as label data during model training. Alternatively, in practice, time optimization can be considered, with the shortest flight time as the optimization objective, and correspondingly, the shortest flight time used as the label data.

[0127] The spacecraft low-thrust trajectory dataset is divided into a training set and a validation set.

[0128] In one embodiment, S2, a structure-adaptive neural network is trained and validated based on a spacecraft low-thrust trajectory dataset to obtain a dynamic neural network model. The structure-adaptive neural network includes an initial neural network, a performance stagnation monitor, and a deep neural network capacity heuristic adjustment module. The specific implementation process is as follows:

[0129] The initial neural network can predict the optimal low-thrust trajectory and transfer costs (e.g., time, fuel, energy) based on the input low-thrust trajectory maneuvering characteristics. Depending on the complexity of the scenario and the complexity of the dynamic constraints, the network dynamically adjusts its structure, evolving into adaptive neural networks with different structures.

[0130] The initial neural network of the structurally adaptive neural network is constructed from a fully connected network, which contains... Layers, each layer contains The activation function of the neuron is . , The initial value is selected empirically, and the simplest network structure that ensures effective network growth should be selected as much as possible.

[0131] The performance stagnation monitor is constructed to monitor the network capacity when the network capacity is insufficient, and the deep neural network capacity heuristic adjustment module is used to adjust the structure adaptive neural network capacity.

[0132] The working process of the performance stagnation monitor is as follows:

[0133] After the first z training cycle , the structure adaptive neural network is tested on the validation set, and the loss of the structure adaptive neural network is calculated.

[0134] The loss value of the structure adaptive neural network is read on the validation set in a total of training (evaluation) cycles from to , the set loss bottleneck value is calculated, and the loss drop rate is calculated:

[0135]

[0136] Among them, is the current training cycle number, if the maximum drop percentage (the is the percentage threshold), it is determined that the network training performance is stagnant, and the deep neural network capacity heuristic adjustment module is driven to adaptively adjust the capacity of the structure adaptive neural network. Among them according to the actual situation, the maximum value, the minimum value or the average value in periods can be taken. Taking the minimum value means strict strategy, which ensures that each structure adjustment ensures loss reduction; taking the maximum value means loose strategy, that is, as long as the new loss is improved compared to the worst case of the previous period, it is considered effective; taking the average value means robust strategy, which requires the new loss to be better than the average performance level of the previous period.

[0137] The process of the deep neural network capacity heuristic adjustment module for network capacity adaptive adjustment is as follows:

[0138] After the training starts, the performance stagnation monitor counter is initialized: , . and respectively represent the width and depth adjustment trigger times in this round of adjustment. After entering the training, the network reads the batch data, updates the network weights, and monitors the network performance according to the designed performance stagnation monitor. In the training period when the performance detector is not triggered, the network snapshot is saved for later network structure and weight rollback operation.

[0139] After determining the performance stagnation, the performance stagnation detector is triggered and the network width adjustment counter is initialized = 1. Since the network capacity is usually increased with higher benefits and lower training divergence risk through width adjustment, the neural network width adjustment based on neuron splitting is preferentially performed, and the training is continued.

[0140] If the training is successful, the counter is reset to zero , , and the current network snapshot is saved. If the performance is still stagnant in the next training period, the monitor is triggered again and the counter is counted = 2, and the system performs width adjustment again. When , the performance stagnation times exceed the limit value , it is considered that the width adjustment strategy fails, and it is determined that the structure adaptive neural network does not have the problem of insufficient expression capacity, and the problem of insufficient feature abstraction level needs to be solved. At this time, the network structure is rolled back to the network snapshot at the last effective network width adjustment, and depth adjustment is triggered to increase the feature abstraction level.

[0141] Enter the depth adjustment, and initialize the depth adjustment detector . After performing the depth adjustment, set the learning rate scaling rate and other key parameters, and continue training for several periods. If the training is successful, the counter is reset to zero , , and the current network snapshot is saved. If the performance is still stagnant in the next training period, the monitor is triggered again and the counter is counted = 2, and the system performs depth adjustment again. Until , if the depth adjustment reaches the upper limit and there is still no obvious progress, it is considered that the network capacity has been expanded to the maximum limit, and the structure adaptive neural network has reached the upper limit of the small thrust trajectory optimization representation ability for the scene. The generalization ability of the structure adaptive neural network will not be substantially improved, and the training ends here.

[0142] The width and depth adjustment of the deep neural network of the application follows the function preservation principle, so the adjustment process is smooth and orderly. The overall process of the heuristic adjustment framework is shown in Figure 2 .

[0143] The specific process of network width adaptive adjustment is as follows:

[0144] First, identify the key neurons of the network layer for width expansion. During the training period, for the i-th sample in the validation set containing N samples, calculate the loss function L(i), perform one back propagation (without network weight update), calculate the average absolute value of the gradient of the loss function with respect to the output of the j-th neuron of the i-th layer after activation, as the importance score of the neuron:

[0145]

[0146]

[0147] According to the importance score of the neuron, select the neurons for performing the fission operation, such as setting an importance score threshold T, taking the neurons with importance score greater than T to perform the fission operation, or taking the neurons with importance score less than T to perform the fission operation. top-n

[0148] Perform the fission operation on the selected neurons to increase the network capacity, and the process of the fission operation is as follows:

[0149] The overall idea of fission is to keep the value received by the next layer of network neurons equal or approximately equal before and after the fission of the neurons, and the output of the original neuron can be represented as:

[0150]

[0151]

[0152]

[0153]

[0154] wherein, is the weight of the neuron of the current fully connected layer connected to the previous layer, is the bias, then by splitting the current neuron into two neurons, the width of the current fully connected layer is increased, the network capacity is increased, and the outputs of the nodes after fission are and

[0152]

[0153]

[0154] wherein, is the perturbation factor for splitting the neuron, is close to zero, then the instantaneous output of the split neuron is approximately equal to the output of the unsplit neuron, and the original network function is maintained after splitting:​​​​​​​​​​

[0155]

[0156] where, is the instantaneous output value of the node.

[0157] In this process, although the nonlinearity of the activation function will cause the input received by the next layer of neurons before and after the split to be not strictly equal, but since is small, the amount of deviation introduced by the split moment is very small, which can be ignored in the robust training process. Therefore, this design ensures the smooth updating of the deep neural network, and does not cause violent shock in the width adaptive adjustment process. In the subsequent training process, the weights of the new neurons will be updated step by step according to the loss function.

[0158] The specific process of depth adaptive adjustment of the network is as follows:

[0159] The depth adjustment of the deep neural network is realized by inserting a new fully connected layer, and the core mechanism needs to ensure that there is no gradient disappearance or gradient explosion after inserting a new network layer, that is, the function of the network should be maintained after depth adjustment.

[0160] After the depth adaptive adjustment is triggered to meet the triggering condition, two fully connected layers and are randomly selected, and an identity mapping layer is inserted. The weight matrix of the newly inserted layer is , and the bias is .

[0161] The original network update process is:

[0162]

[0163] After inserting the new layer, the network update is as follows:

[0164]

[0165] After inserting the new layer, the input of the subsequent network layer becomes:

[0166]

[0167] If the weight matrix is initialized as the identity matrix , and the bias is , the output of the new layer is . For the activation function Relu, for non-negative input, the output of the new layer is . Therefore, the neural network smoothly transitions at the moment of depth expansion, and does not change violently.

[0168] However, the newly inserted layer has no functional purpose. When backpropagating through this layer, its own weight gradient will be very small, and it will receive almost no effective learning signal in the initial stage. This may cause the weights of this layer to remain in a near-identical mapping state for a long time, thus losing the purpose of increasing the network depth. Therefore, this embodiment of the invention adopts an active gradient injection and local learning rate scaling mechanism. Structured perturbation noise is injected during the initialization stage.

[0169]

[0170] in, For the identity matrix I For elements with the same dimensions, the mean is 0 and the variance is... Gaussian distributed noise, biased as Set as Because the variance of the perturbation noise is extremely small, the newly inserted layer functionally approximates an identity mapping, ensuring a smooth transition in network performance without drastic oscillations. However, this tiny random noise perturbs the identity mapping structure, causing the new layer weights to receive non-zero gradient signals during the first backpropagation. Simultaneously, a temporary learning rate scaling is performed on the newly inserted layer, within the learning rate set by the optimizer. Based on this, set a temporary scaling factor for the learning rate. ( ), and set a decay period for the learning rate scaling factor, in During the period, the learning rate decays to the global learning rate. The cosine annealing update method is used:

[0171]

[0172] Then the weight matrix and bias The update rule has changed to:

[0173]

[0174]

[0175] in, Indicates the maximum decay period. Indicates the first The temporary scaling factor for the learning rate at each cycle, This is the initial value for the scaling factor. This represents the learning rate.

[0176] The deep adjustment mechanism based on the identity mapping designed in the embodiment of the application promotes the instantaneous function retention of the newly inserted network layer; the active gradient injection mechanism designed promotes the identity mapping layer to enter the iterative update state, reduces the risk of training stagnation of the newly inserted layer; the learning rate scaling factor is designed to enable the newly inserted layer to faster perform weight iteration and adjustment; the learning rate scaling factor decay mechanism is designed to enable the learning rate of the new layer to gradually and globally adjust the learning rate, so that the new layer gradually switches from the fast update state to the global update state. The network depth adjustment process designed in the application effectively converts the increase of the network depth each time into the improvement of the model performance.

[0177] The effectiveness of the embodiment of the application is verified by specific data as follows:

[0178] 1. Small-thrust trajectory data generation. The latest near-Earth asteroid ephemeris and epoch are obtained from the NASA small celestial body database, and the target is randomly selected according to step S1 to search for mission opportunities. The semi-major axis of the small celestial body is in the range of , the orbital inclination is in the range of 0-60°. The central celestial body is the sun, the gravitational constant is , the gravitational acceleration constant is , the dry mass of the spacecraft is , the initial mass is , the small-thrust mode is adopted, the specific impulse of the engine is , the maximum power is , the engine efficiency is 0.6, and the duty cycle is 0.9. The flight time is randomly selected in the range of [30, 6 365] days.

[0179] 2. After obtaining the mission opportunity, the small-thrust trajectory is optimized. The dynamics modeling is performed according to step S1, the corresponding constraints and optimization objectives are constructed, and the optimization objective is fuel optimization. The fmincon function in Matlab is used for solving, and the SQP algorithm is selected. If there is a convergent solution, the mission start time , the flight time , the mission end time , the initial mass of the spacecraft , the mass at arrival and other basic characteristics are saved, and at least 50,000 groups of feasible trajectory data are saved as the initial set of small-thrust trajectories of the spacecraft.

[0180] 4. Small-thrust trajectory features are constructed. They include position and velocity in the Cartesian inertial coordinate system , position and velocity in the cylindrical coordinate system , position and velocity in the spherical coordinate system , classical orbital elements , and improved equinox elements , , , 、 、 。 Artificially constructed high-dimensional features of small-thrust trajectories: Speed ​​increment orbital energy change angular momentum change The angle between the angular momentum vectors High-dimensional features and basic features are used as the dataset.

[0181] 5. Design the initial neural network structure. The initial network is constructed from a fully connected network, consisting of fully connected layers and two hidden layers. There are neurons, and the activation function is... The above network structure is derived from experience. While ensuring convergence, a simple structure should be chosen as much as possible to enable the network to adaptively expand and grow.

[0182] 6. Construct a network width adjustment model: In the width adaptive model, for a given layer, calculate the importance score of the neurons in that layer. Importance score The first 5% (less than 20) of neurons are selected for batch splitting. The weight of each neuron is extracted, and a neuron splitting factor is set. After splitting, the neuron is biased to Then, the neurons after splitting:

[0183]

[0184]

[0185] but Function is preserved instantly upon splitting, and the new neurons will gradually update the weights. and bias.

[0186] 7. Constructing a network depth adjustment model: In depth adaptation, two fully connected layers are randomly selected. Layers and Layers, with fully connected layers inserted in between, where the newly inserted fully connected layers have a multiplication matrix. Initialize to identity matrix , bias is Set as Set the gradient injection parameters, with noise distributed Gaussianly, mean 0, and variance . The activation function is Then, after inserting a new layer, it becomes an identity mapping instantly, thus preserving functionality during depth expansion.

[0187] Set the learning rate scaling factor The scaling factor decay period is set to 20 rounds. time, That is, at the initial moment, the new layer is updated according to the set maximum learning rate. .along with Depend on Increase to , The value gradually decreases from 1 to -1. time, That is, the learning rate of the new layer is smoothly aligned with the global learning rate. .

[0188] 8. Training of Dynamically Structured Neural Networks. The training parameters use... Optimizer, Learning Rate for The exponential decay rate estimated by the first moment The exponential decay rate estimated by the second moment The training batch size is .

[0189] 9. Dynamic adjustment driving technology for deep neural network structure in low-thrust trajectory optimization. The deep network capacity adjustment adopts a heuristic driving mechanism, using a closed-loop adjustment strategy of performance monitoring, priority width adjustment, bottleneck depth adjustment, and rollback readjustment to adjust the neural network capacity in stages.

[0190] (1) Set a performance stagnation monitor. After the current training cycle ends, test and record the loss of the neural network on the validation set during this training cycle. In this use case, the following is set: Read the loss set from the past 5 training (evaluation) cycles. For example: calculating the bottleneck value of the loss function. And calculate the rate of decrease in loss. :

[0191]

[0192] Set a threshold for the rate of decrease in loss. The percentage was 1%, representing the largest rate of loss reduction over the past five training cycles. (In this use case) If the network reaches a plateau, it is considered that the model training has reached a bottleneck and the network capacity needs to be expanded to obtain better representation. At this point, a performance stagnation counter is initialized. That is, when the performance stagnation monitor first detects that the model's performance on the validation set has not improved significantly, it triggers network width adjustment.

[0193] (2) Select the current network's widest layer, and perform network width expansion according to step 6, and continue training. Before performing adjustment, the system will save the current network state (weights and structure) snapshot, marked as Snapshot_W1.

[0194] (3) Post-adjustment evaluation window. The network needs several cycles to adjust the new neurons' weights, at this time, the performance monitor will trigger again. 。 After width adjustment, the system will continue training cycles. During this window, the performance monitor is working continuously, observing whether the performance has improved.

[0195] (4) Determine whether the width adjustment is successful. If successful: within cycles, , it is considered that the updated loss has successfully decreased and broken through the previous bottleneck. At this time, the performance stagnation counter is cleared, i.e. , the update , and then continue normal training until the next performance stagnation. If failed: after cycles, the loss has not improved. The monitor will trigger again, and the performance stagnation counter will be updated to .

[0196] (5) Width adjustment cycle and failure determination. The zero-width adjustment performance stagnation counter limit is: , when , repeat steps (2) (3) (4) to try network width adjustment; width adjustment fails, and it is determined that the width adjustment strategy has completely failed.

[0197] (6) Network rollback and network depth adjustment trigger. , it is determined that the width adjustment has failed, and the system reads the network snapshot to perform network rollback: discard all 5 failed width adjustments, and restore the network to the last network snapshot where the loss has decreased to meet the requirements. The system triggers a depth adjustment (network layer insertion) and saves the snapshot before depth adjustment. Initialize , the depth adjustment is consistent with the width adjustment strategy, and the depth adjustment is performed according to the performance monitoring results, and the network snapshot is saved. Set . If the depth adjustment fails for 3 times, the depth adjustment is over.

[0198] After the depth adjustment is completed, the performance monitoring counter , is set to 0, obtaining a capacity adaptive neural network. The network has the advantage that as new training data arrives, the network structure can continue to evolve without having to be retrained. For the scenario of the embodiment, the network depth is gradually adjusted from 2 layers to 5 layers, and the number of neurons in each hidden layer is gradually expanded from 64 to 150-200, and finally the average relative error of the small thrust trajectory prediction is reduced from 40% to 5.2%.

[0199] The embodiment of the present application also provides a small thrust trajectory optimization system based on a structure adaptive neural network, comprising:

[0200] A data set generation module is configured to obtain a small thrust trajectory initial set of a spacecraft; and extract trajectory features in the small thrust trajectory initial set of the spacecraft to obtain a small thrust trajectory data set of the spacecraft.

[0201] A model training and adaptive adjustment module is configured to train and verify a structure adaptive neural network based on the small thrust trajectory data set of the spacecraft to obtain a dynamic neural network model, wherein the dynamic neural network model is configured to predict an optimal small thrust orbit trajectory and a transfer cost according to input small thrust orbit maneuver features; and the structure adaptive neural network comprises an initial neural network, a performance stagnation monitor and a deep neural network capacity heuristic adjustment module.

[0202] The performance stagnation monitor is configured to monitor the performance of the structure adaptive neural network and determine whether the deep neural network capacity heuristic adjustment module needs to be triggered to adjust the network capacity.

[0203] The deep neural network capacity heuristic adjustment module is configured to adjust the capacity of the structure adaptive neural network in stages.

[0204] The embodiment of the present application also provides a computer readable storage medium storing a computer program for small thrust trajectory optimization based on a structure adaptive neural network, wherein the computer program causes a computer to execute the small thrust trajectory optimization method based on a structure adaptive neural network as described above.

[0205] The embodiment of the present application also provides an electronic device comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the program comprises a program for executing the small thrust trajectory optimization method based on a structure adaptive neural network as described above.

[0206] It can be understood that the small-thrust trajectory optimization system based on the structure adaptive neural network, the storage medium and the electronic device provided by the embodiment of the application correspond to the task scheduling and energy consumption adaptive optimization method in the emergency scenario of multiple data centers provided by the embodiment of the application, and the explanation, examples and beneficial effects of the related contents can refer to the corresponding parts in the task scheduling and energy consumption adaptive optimization method in the emergency scenario of multiple data centers. Here, it will not be repeated.

[0207] In summary, compared with the prior art, the following beneficial effects are achieved:

[0208] 1. When the trajectory data with new features is accumulated, the adaptive mechanism of the embodiment of the application enables the network to absorb new knowledge through incremental evolution of the network structure. The model does not need to be retrained from scratch, but can accommodate and learn new small-thrust trajectory optimization rules through structure growth on the basis of fully trained knowledge, effectively solving the problem of limited learning potential of fixed structure models when facing new data. The sustainable online evolution capability of the embodiment of the application is completely not possessed by the static network, which lays a solid technical foundation for constructing a small-thrust trajectory intelligent optimization system that can be long-term iterated and self-improved, greatly enhancing the life cycle value and sustainability of the technical scheme.

[0209] 2. The capacity adaptive mechanism proposed in the embodiment of the application enables the structure size of the neural network to be no longer a hyperparameter that needs to be pre-solidified, but can be dynamically evolved according to the inherent complexity of the data during the training process. The network starts from a simple initial structure, and only increases its depth or width when the performance bottleneck is monitored. This enables the final network capacity to be highly matched with the true intrinsic complexity of the task. The embodiment of the application solves the overfitting problem caused by capacity redundancy of the existing fixed structure network, or the underfitting problem caused by insufficient capacity. When processing small-thrust trajectory data with different complexities, the method of the embodiment of the application can obtain lower average prediction error and stronger generalization performance than any single fixed capacity network.

[0210] 3. By introducing a dynamically adjustable adaptive network structure, the automation of model design and the significant improvement of efficiency are realized. The structure adaptive neural network designed in the embodiment of the application can automatically perform the adjustment of width (neuron fission) and depth (layer insertion) according to objective indexes such as performance feedback of a validation set and internal gradient flow state in a training process. The mechanism ensures that the network structure for processing simple trajectory tasks remains simple and efficient, and the network structure for processing complex tasks is deepened or widened accordingly. This process endows the network with an approximately optimal model capacity without the need for a large amount of manual parameter adjustment or time-consuming offline search. It automatically and intelligently integrates the most time-consuming and experience-dependent network structure design link in the traditional technology into the training process itself, reduces the threshold and comprehensive research and development cost of deep learning application in the field of spacecraft small thrust trajectory optimization, and significantly improves the efficiency of model construction.

[0211] It should be noted that the relational terms herein such as first and second, and the like, are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any such actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element preceded by "comprises... a" does not, without more constraints, foreclose the existence of additional identical elements in the process, method, article, or apparatus that comprises the recited element.

[0212] The above embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the foregoing embodiments of the present application have been described in detail, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A small-thrust trajectory optimization method based on a structure-adaptive neural network, characterized in that, The method comprises the following steps: An initial set of small-thrust trajectories of a spacecraft is acquired; and trajectory features in the initial set of small-thrust trajectories of the spacecraft are extracted to obtain a small-thrust trajectory dataset of the spacecraft; A dynamic neural network model is obtained by training and verifying a structure-adaptive neural network based on the small-thrust trajectory dataset of the spacecraft, wherein the dynamic neural network model is used to predict an optimal small-thrust orbit trajectory and a transfer cost according to input small-thrust orbit maneuver features; and the structure-adaptive neural network comprises an initial neural network, a performance stagnation monitor and a deep neural network capacity heuristic adjustment module. The performance stagnation monitor is used to monitor the performance of the structure-adaptive neural network and determine whether the deep neural network capacity heuristic adjustment module needs to be triggered to adjust the network capacity. The deep neural network capacity heuristic adjustment module is used to adjust the capacity of the structure-adaptive neural network in stages; specifically comprising: After the training starts, the performance stagnation monitor counter is initialized: , ; and represent the number of width and depth adjustment triggers in this round of adjustment, respectively. After entering the training, the network reads batch data, calculates loss, updates network weights, and monitors network performance according to the designed performance stagnation monitor; in the training period when the performance detector is not triggered, the network snapshot is saved for later execution of network structure and weight rollback operation. Upon determining performance stagnation, triggering the performance stagnation detector and initializing the network width adjustment counter = 1; performing width adjustment based on neuron splitting, and continuing training; If training is successful, the counter is reset to zero , , and the current network snapshot is saved; if the performance stagnates in the next training period, the monitor triggers again and counts = 2, the width adjustment is performed again; when , the number of performance stagnation exceeds the limit value , the width adjustment strategy is considered to be invalid; at this time, the network structure is rolled back to the network snapshot at the last valid network width adjustment, and the depth adjustment is triggered; Enter depth adjustment and initialize depth adjustment counter ; continue training for several cycles after depth adjustment, if training is successful, the counter is reset to zero , , and save the current network snapshot; if the performance is still stagnant in the next training cycle, the monitor triggers again and counts =2; depth adjustment is performed again until , represents the upper limit value of depth adjustment.

2. The small-thrust trajectory optimization method based on structure adaptive neural network according to claim 1, wherein, The initial neural network comprises layer fully connected network, each layer containing neurons.

3. The small-thrust trajectory optimization method based on structure adaptive neural network according to claim 1, wherein, The working process of the performance stagnation monitor comprises: The first training cycle z After the first training cycle , the structure adaptive neural network is tested by the validation set, and the validation set loss of the structure adaptive neural network in the current training cycle is calculated ; The reading structure adaptive neural network is in a total of training cycles, the network is tested on the validation set history loss value, take the minimum value or the average value as the loss bottleneck value according to the demand , and calculate the loss drop rate : If the maximum percentage of decrease is lower than expected , i.e. , it is determined that the performance of the structure adaptive neural network stagnates, and the deep neural network capacity heuristic adjustment module is driven to adaptively adjust the capacity of the structure adaptive neural network; wherein, is a percentage threshold value.

4. The small-thrust trajectory optimization method based on structure- adaptive neural network of claim 1, wherein, The width adjustment comprises: During the training period, targeting... The first of the validation set samples For each sample, calculate the loss function. Perform a backpropagation and calculate the loss function for the first... Layer network layer The output of each activated neuron The average absolute value of the gradient is used as the importance score of the neuron. : wherein, is the loss for the th sample. According to the importance score of the neuron selecting a neuron for performing the fission operation; The fission operation is performed on the selected neurons to increase the network capacity, wherein the process of the fission operation is as follows: Raw neuronal output is represented as: wherein, is the weight of the connection of the neuron of the current network layer to the neuron of the previous network layer, is the bias, the current network layer width is increased by splitting the neuron into two neurons in such a way that the network capacity is increased, the output of the node after splitting is and : wherein, is a perturbation factor for neuron division, for dividing neurons, then the output of the divided neuron is equal to the output of the undivided neuron, and the original network function is maintained after division: wherein, the node instant output value for network splitting.

5. The small-thrust trajectory optimization method based on structure- adaptive neural network of claim 1, wherein, The deep adjustment comprises: After the trigger condition is met to trigger the deep adaptive adjustment, two network layers are randomly selected layer and layer, insert an identity mapping layer ; the newly inserted layer The weight matrix is , and the bias is ; The original network update process is as follows: After inserting a new layer, the network update is as follows: After inserting a new layer, the input of the subsequent network layer becomes as follows: If the weight matrix is initialized as the identity matrix , the bias is set as , and the activation function is ReLU, the output of the new layer is for non-negative input. ​ 6. The small-thrust trajectory optimization method based on structure adaptive neural network according to claim 5, wherein, The network is updated after inserting a new layer, and an active gradient injection and learning rate local scaling mechanism is used for updating and comprise: wherein, is a unit matrix I of the same dimension as is a Gaussian distributed noise with mean 0 and variance is set to ; weight matrix and bias The update rule is Wherein, wherein, denotes the maximum decay period, denotes the learning rate temporary scaling factor at the th period, is the scaling factor initial value, denotes the learning rate.

7. A small-thrust trajectory optimization system based on structure adaptive neural network, characterized in that, The small-thrust trajectory optimization system is used to execute the small-thrust trajectory optimization method based on the structure-adaptive neural network according to any one of claims 1-6, comprising: A dataset generation module is used to acquire an initial set of small-thrust trajectories of a spacecraft; and trajectory features in the initial set of small-thrust trajectories of the spacecraft are extracted to obtain a small-thrust trajectory dataset of the spacecraft; A model training and adaptive adjustment module is used to obtain a dynamic neural network model by training and verifying a structure-adaptive neural network based on the small-thrust trajectory dataset of the spacecraft, wherein the dynamic neural network model is used to predict an optimal small-thrust orbit trajectory and a transfer cost according to input small-thrust orbit maneuver features; and the structure-adaptive neural network comprises an initial neural network, a performance stagnation monitor and a deep neural network capacity heuristic adjustment module. The performance stagnation monitor is used to monitor the performance of the structure-adaptive neural network and determine whether the deep neural network capacity heuristic adjustment module needs to be triggered to adjust the network capacity. The deep neural network capacity heuristic adjustment module is used to adjust the capacity of the structure-adaptive neural network in stages.

8. A computer-readable storage medium, characterized in that, The computer program for small-thrust trajectory optimization based on a structure-adaptive neural network is stored, wherein the computer program enables the computer to execute the small-thrust trajectory optimization method based on the structure-adaptive neural network according to any one of claims 1-6.

9. An electronic device, comprising: The method comprises the following steps: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs comprising programs for performing the method for small-thrust trajectory optimization based on a structure-adaptive neural network according to any one of claims 1-6.

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