A target detection performance surface progressive sampling method based on Gaussian process multi-kernel fusion

Abstract

The application is a target detection performance surface gradual sampling method based on Gaussian process multi-kernel fusion. The application relates to the technical field of target detection. In the target detection process, a multi-level search space is constructed to realize efficient kernel function combination and optimization in a complex performance surface scene. A multi-scale collaborative adaptive kernel system gradual sampling optimization strategy is established to gradually optimize the kernel function combination structure and parameters and improve the fitting accuracy of the Gaussian process model on the target detection performance surface. The method is mainly used to solve the model performance evaluation problem under multi-dimensional interference conditions. Through optimization of the kernel function combination and parameter tuning, the performance evaluation efficiency and accuracy of the target detection model in a complex environment are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of target detection, and is a target detection performance surface gradual sampling method based on Gaussian process multi-kernel fusion. BACKGROUND

[0002] Target detection models face various interference factors in practical applications, such as illumination changes, noise, and weather conditions, and the superposition of these factors directly affects the detection performance of the model. When evaluating the performance of the model, existing research usually analyzes the relationship between interference intensity and performance indicators (such as detection accuracy or mAP) by examining the performance of the model under single-dimensional interference. However, most research is limited to single-dimensional interference and cannot fully reflect the actual performance of the model under multi-dimensional interference.

[0003] Existing literature shows that many studies focus on the evaluation of single-dimensional interference. For example, the benchmark test proposed by Michaelis et al. mainly focuses on the performance curve under different interference intensities, while the research by Zhu et al. and This method is insufficient in practical applications because target detection is usually affected by multiple interference factors, such as the simultaneous existence of illumination changes and noise. In addition, there is a lack of effective algorithms and evaluation methods for the construction and optimization of model performance surfaces under multi-dimensional interference, making it difficult to cope with complex multi-dimensional interference environments.

[0004] The current limitations are that single-dimensional interference evaluation cannot meet the deployment needs of models in multi-dimensional interference environments, leading to one-sidedness and incompleteness of the evaluation results. Therefore, there is an urgent need for a new method that can accurately evaluate the performance of models under multiple interference conditions by constructing multi-dimensional performance surfaces.

[0005] To fill this research gap, the present application proposes a target detection performance surface gradual sampling method based on Gaussian process multi-kernel fusion, which aims to accurately fit the model performance surface under multi-dimensional interference with fewer sampling points, thereby improving the performance characterization ability of models in multi-interference environments. SUMMARY

[0006] In view of the deficiencies in the prior art, the present application provides a target detection performance surface gradual sampling method based on Gaussian process multi-kernel fusion, which comprises the following technical solutions:

[0007] A target detection performance surface gradual sampling method based on Gaussian process multi-kernel fusion, the method comprising the following steps:

[0008] Step 1: In the target detection process, a multi-level search space is constructed to realize efficient kernel function combination and optimization in a complex performance surface scenario;

[0009] Step 2: A progressive sampling optimization strategy of a multi-scale cooperative adaptive kernel system is established to gradually optimize the kernel function combination structure and parameters, and improve the fitting accuracy of the Gaussian process model to the target detection performance surface.

[0010] Preferably, the step 1 includes: performing kernel function combination search space and its constraints:

[0011] The search space includes 8 sub-kernel functions and two operators, each combination is constructed by multiple sub-kernel functions and operators to form a diversified kernel structure.

[0012] Preferably, the step 1 further includes: a process of intelligent generation of initial solution driven by reinforcement learning:

[0013] The state is represented as the kernel function combination sequence constructed by the agent and the current position, the length of the sequence S = [s1, s2, …, s L ] is L = 2n-1, the odd position stores the kernel function index, the even position stores the operator index, and the current position p has a value range of p ∈ {1, 2, …, L};

[0014] The action space is defined as: when the odd position, the action set is the sub-kernel function set K = {k1, k2, …, k8}; when the even position, the action set is the operator set O = {+, ×}, according to the ∈-greedy strategy to select the action, which can explore random action or select the action with the maximum Q value;

[0015] The reward function is defined, and the specific reward function expression is:

[0016]

[0017] R train = -E train

[0018]

[0019] Preferably, the step 3 includes: performing multi-scale kernel structure cooperative evolution exploration:

[0020] The basic kernel function set K = {k1, k2, …, k8} is defined, where each k i represents a basic kernel function type, and the operator set is defined as O = {+, ×}, representing the addition and multiplication combination between kernel functions, respectively;

[0021] Each chromosome is encoded as a symbolic expression, representing a specific kernel combination form, the gene sequence of which is composed of kernels and operators alternately, with the following structure:

[0022]

[0023] where k ij ∈K represents a kernel selected from the kernel set, op j ∈O represents an operator selected from the operator set, and n represents the number of kernels.

[0024] Based on the above encoding strategy, the search space S of kernel combination is defined as the set of all kernel and operator sequences:

[0025]

[0026] The size of the search space is determined by the number of kernels n and the number of operators n-1, and its size is:

[0027] |S|=|K| n ×|O| n-1

[0028] where |K| represents the number of kernels and |O| represents the number of operators.

[0029] Preferably, by dynamically adjusting the target threshold, the fitness evaluation is continuously optimized with the iteration of the algorithm, ensuring that the search process always moves towards a better solution set, defined as follows:

[0030] f(C)=T target -E avg

[0031]

[0032] where f(C) represents the fitness value of chromosome C, T target represents the target threshold, and E avg is the average error of the chromosome in K-fold verification. After each iteration, the target threshold T target is dynamically adjusted to the 30th percentile value of the average K-fold training error of all chromosomes in descending order;

[0033] A probability selection strategy based on the fitness ratio is adopted, so that chromosomes with high fitness are selected and passed to the next generation, while maintaining a certain randomness to maintain the diversity of the population,

[0034] By recombining part of the genes of the parent chromosomes, offspring chromosomes with new kernel combinations are generated;

[0035]

[0036] where r is the position of the crossover point, at which the parts of C1 and C2 are exchanged, resulting in new chromosomes C'1 and C'2.

[0037] Preferably, in order to enhance the global search ability of the genetic algorithm in the kernel function combination search, and prevent the population from falling into a local optimal solution, a random change is introduced in the chromosome to break the local pattern in the existing chromosome structure, thereby exploring a wider solution space;

[0038] In order to flexibly adjust the mutation strength at different iteration stages, a dynamic mutation probability with exponential decay is adopted:

[0039] P mutation ((t)=P initial ·exp(-αt)

[0040] where P initial is the initial mutation probability, α is a parameter that controls the rate of decrease of the mutation probability, and t is the number of iterations of the algorithm. The adaptive multi-mode mutation mechanism includes two aspects, namely the multi-mode mutation of the kernel function and the mutation of the operator gene.

[0041] Preferably, the step 2 further comprises: performing progressive weight parameter fine tuning, using a whale optimization algorithm to optimize the combined kernel function, and by fine tuning the weight coefficient of each sub-kernel function, enhancing the model's ability to capture complex nonlinear relationships in the data, thereby improving the model's prediction performance;

[0042] The constructed combined kernel function is composed of n sub-kernel functions k i (x, x'; θ i ), in order to achieve fine fitting of complex nonlinear relationships, a weight coefficient α i is introduced for each sub-kernel function, the introduction of the weight coefficient allows the model to assign different importance to different kernel functions in different regions, thereby better adapting to local changes in the data. The combined kernel function after the introduction of the weight coefficient is defined as follows:

[0043]

[0044] In order to evaluate the performance of the Gaussian process model in the parameter optimization process, a combined kernel function fitness evaluation objective function based on K-fold cross-validation error is used, and the objective function is defined as the average of the validation errors of all folds:

[0045]

[0046] where α = {α1, α2,..., α ndenote the weight coefficients of each sub-kernel function, and θ = {θ1, θ2,..., θ n denote the parameter set of each sub-kernel function, and E k denote the error of the combined kernel function C(x, x'; a, θ) on the k-fold validation set.

[0047] In the bubble-net attack phase, the weight coefficients a i and the kernel function parameters θ i are updated as follows:

[0048]

[0049] A = 2a · r - a

[0050] where a i (t) and θ i (t) represent the weight coefficients and the kernel function parameters of the current iteration number t, respectively, and the weight coefficients and the kernel function parameters of the optimal solution of the current iteration number t, a is a factor that linearly decays with the iteration number, and r is a random number between 0 and 1. The parameter updating strategy in the exploration and development phase is as follows:

[0051]

[0052] where a rand，i and θ rand，i are the weight coefficients and the kernel function parameters randomly selected from the population, respectively.

[0053] A target detection performance surface progressive sampling system based on Gaussian process multi-kernel fusion, comprising:

[0054] A space construction module that, in a target detection process, performs multi-level search space construction to achieve efficient kernel function combination and optimization in a complex performance surface scenario;

[0055] An optimization sampling module that establishes a multi-scale collaborative adaptive kernel system progressive sampling optimization strategy to gradually optimize the kernel function combination structure and parameters and improve the fitting accuracy of the Gaussian process model to the target detection performance surface.

[0056] A computer-readable storage medium having stored thereon a computer program that is executed by a processor to implement a target detection performance surface progressive sampling method based on Gaussian process multi-kernel fusion.

[0057] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a target detection performance surface progressive sampling method based on Gaussian process multi-kernel fusion is implemented.

[0058] The present invention has the following beneficial effects:

[0059] Compared with the prior art, the present invention has the following advantages:

[0060] This paper constructs a Gaussian process model that integrates multiple kernel functions for the first time, significantly enhancing the model's expressive power and uncertainty inference capabilities. This innovation enables the model to more accurately fit complex performance surfaces and improves the accuracy of target detection performance prediction under dual interference dimensions.

[0061] This paper proposes a search space construction method using a combination of multi-level kernel functions and introduces constraints to effectively reduce the search dimension. Combined with a reinforcement learning-driven intelligent initial solution generation strategy, this method significantly improves search efficiency. The innovation of this method lies in its ability to more efficiently explore the optimization space and reduce the waste of computing resources.

[0062] This paper designs a progressive sampling optimization strategy that combines multiscale coevolution with progressive weight tuning. Through the coevolution of multiscale kernel structures, it effectively integrates features at different scales. Meanwhile, progressive weight tuning ensures optimal synergy between the combined kernel functions at each stage. This strategy improves the accuracy of performance surface construction and enhances the model's ability to characterize performance in complex, multi-interference environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0064] Figure 1 Shown is a schematic diagram of chromosome crossover for combined nuclear function;

[0065] Figure 2 Schematic diagram of the mutation pattern shown as a kernel function;

[0066] Figure 3 Shown as operator mutation;

[0067] Figure 4 Displayed as three error line graphs;

[0068] Figure 5 The distribution of sampling points is displayed as a heat map;

[0069] Figure 6 Displayed as three error line graphs;

[0070] Figure 7 The display shows the distribution when the sampling point is 30;

[0071] Figure 8 Displayed as three error line graphs;

[0072] Figure 9 Displayed as a distribution diagram of 90 sampling points;

[0073] Figure 10 Displayed as three error line graphs;

[0074] Figure 11 Displayed as a distribution diagram of 20 sampling points. DETAILED DESCRIPTION

[0075] The present invention is described in detail below with reference to specific embodiments. Specific embodiment one:

[0077] according to Figures 1 to 11 As shown, the specific optimization technical solution adopted by the present invention to solve the above technical problems is: the present invention relates to a target detection performance surface progressive sampling method based on Gaussian process multi-kernel fusion.

[0078] A method for progressive sampling of target detection performance surfaces based on Gaussian process multi-kernel fusion, the method comprising the following steps:

[0079] Step 1: During the target detection process, a multi-level search space is constructed to achieve efficient kernel function combination and optimization in complex performance surface scenarios;

[0080] Step 2: Establish a progressive sampling optimization strategy for the multi-scale collaborative adaptive kernel system, gradually optimize the kernel function combination structure and parameters, and improve the fitting accuracy of the Gaussian process model to the target detection performance surface. Specific embodiment two:

[0082] The difference between the second embodiment of the present application and the first embodiment is that:

[0083] The step 1 includes: performing a kernel function combination search space and its constraints:

[0084] The search space includes 8 sub-kernel functions and two operators. Each combination is constructed through multiple sub-kernel functions and operators to form a diverse kernel structure. Specific embodiment three:

[0086] The only difference between the third embodiment of the present application and the second embodiment is that:

[0087] The step 1 further includes a process of reinforcement learning driven initial solution intelligent generation:

[0088] The state is represented as a kernel function combination sequence constructed by the agent and the current position, the length of the sequence S=[s1, s2,..., s L L=2n-1, the odd positions store kernel function indexes, the even positions store operator indexes, and the current position p has a value range of p∈{1, 2,..., L};

[0089] The action space is defined as follows: when in the odd position, the action set is the sub-kernel function set K={k1, k2,..., k8}; when in the even position, the action set is the operator set O={+, ×}, and the action is selected according to the ∈-greedy strategy, that is, a random action can be explored, or an action with the maximum Q value can be selected;

[0090] The reward function is defined, and the specific reward function expression is as follows:

[0091]

[0092] R train =-E train

[0093] Specific embodiment four:

[0095] The difference between the fourth embodiment of the application and the third embodiment is only:

[0096] The step 3 includes: performing multi-scale kernel structure co-evolution exploration:

[0097] The basic kernel function set K={k1, k2,..., k8} is defined, where each k i represents a basic kernel function type, and the operator set is defined as O={+, ×}, representing the addition and multiplication combination between kernel functions, respectively;

[0098] Each chromosome is encoded as a symbolic expression, representing a specific kernel function combination form, and the gene sequence of the chromosome is composed of kernel functions and operators alternately, and the structure is as follows:

[0099]

[0100] Wherein, k ij ∈K represents a kernel function selected from the basic kernel function set, and op j ∈O represents an operator selected from the operator set, and n represents the number of kernel functions;

[0101] Based on the above encoding strategy, the search space S of kernel function combinations is defined as the set of all kernel functions and operator sequences:

[0102]

[0103] The size of the search space is determined by the number of kernel functions n and the number of operators n-1, and its size is:

[0104] |S|=|K| n ×|O| n-1

[0105] Here, |K| represents the number of kernel functions, and |O| represents the number of operators. Specific embodiment five:

[0107] The only difference between the fifth embodiment of the present invention and the fourth embodiment is that:

[0108] By dynamically adjusting the target threshold, the fitness evaluation is continuously optimized with the iteration of the algorithm, ensuring that the search process always moves towards a better solution set, which is defined as follows:

[0109] f(C)=T target -E avg

[0110]

[0111] Among them, f(C) represents the fitness value of chromosome C, T target It represents the target threshold, E avg is the average error of the chromosome in K-fold validation. After each iteration, the target threshold T target It will be dynamically adjusted to the 30% quantile value of the average K-fold training error of all chromosomes in descending order;

[0112] A probability selection strategy based on fitness ratio is adopted, so that chromosomes with high fitness are selected and passed to the next generation, while retaining a certain degree of randomness to maintain the diversity of the population.

[0113] By recombining some genes of the parent chromosome, offspring chromosomes with new nuclear function combinations are generated;

[0114]

[0115] Among them, r is the position of the crossover point. At the crossover point r, parts of C1 and C2 are exchanged to produce new chromosomes C′1 and C′2. Specific embodiment six:

[0117] The only difference between the sixth embodiment of the present invention and the fifth embodiment is that:

[0118] In order to enhance the global search ability of the genetic algorithm in the kernel function combination search, and prevent the population from falling into a local optimal solution, the diversity of random change is introduced in the chromosome, the local mode in the existing chromosome structure is broken, and a wider solution space is explored;

[0119] In order to flexibly adjust the mutation strength at different iteration stages, an exponential decay dynamic mutation probability is adopted:

[0120] P mutation (t)=P initial ·exp(-αt)

[0121] Wherein, P initial is the initial mutation probability, alpha is the parameter for controlling the decreasing speed of mutation probability, t is the number of algorithm iterations, the adaptive multi-mode mutation mechanism includes two aspects, which are the multi-mode mutation of kernel function and the mutation of operator gene. Specific embodiment seven:

[0123] The difference between the embodiment seven and the embodiment six is only:

[0124] The step 2 further includes: performing progressive weight parameter fine tuning, adopting the whale optimization algorithm to optimize the combined kernel function, enhancing the capturing ability of the model to the complex nonlinear relationship in the data by fine adjusting the weight coefficient of each sub-kernel function, so as to improve the prediction performance of the model;

[0125] The combined kernel function constructed by n sub-kernel functions k i (x, x'; theta i ) is composed of, in order to realize the fine fitting of complex nonlinear relationship, a weight coefficient alpha i is introduced for each sub-kernel function, the introduction of the weight coefficient allows the model to give different importance to different kernel functions in different regions, so as to better adapt to the local change of data, and the combined kernel function after introducing the weight coefficient is defined as follows:

[0126]

[0127] In order to evaluate the performance of the Gaussian process model in the parameter optimization process, the combined kernel function fitness evaluation objective function based on K-fold cross-validation error is adopted, and the objective function is defined as the average value of the validation error of all folds:

[0128]

[0129] Wherein, alpha = {alpha1, alpha2,..., alpha n} represents the weight coefficient of each sub-kernel function, theta = {theta1, theta2,..., theta n} represents the parameter set of each sub-kernel function, Ek (a, theta) represents the error of the combined kernel function C(x, x'; a, theta) on the k-fold validation set;

[0130] In the bubble net attack stage, the weight coefficient a i and the kernel function parameter theta i The update strategy is as follows:

[0131]

[0132] A = 2a * r - a

[0133] Wherein, alpha i (t) and theta i (t) represent the weight coefficient and the kernel function parameter of the current iteration number t respectively, And The weight coefficient and the kernel function parameter of the optimal solution of the current iteration number t, a is a factor that linearly decays with the iteration number, r is a random number between 0 and 1, and the parameter update strategy in the exploration and development stage is as follows:

[0134]

[0135] Wherein, alpha rand，i and theta rand，i are the weight coefficient and the kernel function parameter randomly selected in the population. Specific embodiment eight:

[0137] The difference between the embodiment eight of the application and the embodiment seven is only:

[0138] The application provides a target detection performance surface gradual sampling system based on Gaussian process multi-kernel fusion, which comprises:

[0139] A space construction module, which constructs a multi-level search space during target detection, and realizes efficient kernel function combination and optimization in a complex performance surface scene;

[0140] An optimization sampling module, which establishes a gradual sampling optimization strategy of a multi-scale cooperative adaptive kernel system, gradually optimizes the kernel function combination structure and parameters, and improves the fitting accuracy of the Gaussian process model to the target detection performance surface. Specific embodiment nine:

[0142] The difference between the embodiment nine of the application and the embodiment eight is only:

[0143] The application provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to implement a target detection performance surface gradual sampling method based on Gaussian process multi-kernel fusion. Embodiment ten:

[0145] The difference between the embodiment ten and the embodiment nine is only that:

[0146] The application provides a computer device, including a memory and a processor, the memory stores a computer program, and the processor realizes a target detection performance surface gradual sampling method based on Gaussian process multi-kernel fusion when executing the computer program. Embodiment eleven:

[0148] The difference between the embodiment eleven and the embodiment ten is only that:

[0149] The current limitation is that single-dimensional interference evaluation cannot meet the deployment requirements of the model in a multi-dimensional interference environment, resulting in one-sidedness and incompleteness of the evaluation results. Therefore, there is an urgent need for a new method that can accurately evaluate the performance of the model under multiple interference conditions by constructing a multi-dimensional performance surface.

[0150] To fill this research gap, the application provides a target detection performance surface gradual sampling method based on Gaussian process multi-kernel fusion, aiming to accurately fit the model performance surface under multi-dimensional interference with fewer sampling points, thereby improving the performance description ability of the model in a multi-interference environment.

[0151] Step one: multi-level search space construction

[0152] Multi-level search space construction is to ensure that the Gaussian process model can realize efficient kernel function combination and optimization in a complex performance surface scenario. Through the designed kernel function combination and constraint conditions, as well as the intelligent initial solution generation strategy, the model fitting quality can be effectively improved and the search complexity can be reduced, providing a solid foundation for subsequent gradual sampling.

[0153] (1) Kernel function combination search space and its constraints

[0154] When constructing the kernel function combination of the Gaussian process, the key is to reasonably define the search space to realize the best combination of sub-kernel functions and operators. This section will discuss the combination method and its constraints from the perspective of kernel functions and operators.

[0155] The search space is composed of 8 sub-kernel functions (RBF, linear, polynomial, Sigmoid, exponential, rational quadratic, Matern, and periodic) and two operators (addition and multiplication). Each combination is constructed by multiple sub-kernel functions and operators, forming a diversified kernel structure. To ensure the rationality of the search space, we set combination rules, including avoiding repeated superposition of the same kernel function and balancing the proportion of addition and multiplication. Through these constraints, a kernel function search space is finally constructed, which has rich expression ability and maintains simple structure.

[0156] (2) Intelligent generation of initial solutions driven by reinforcement learning

[0157] To address the exponential expansion of the search space as the number of kernel function combinations increases, traditional random generation methods struggle to fully capture high-quality solutions. To this end, this paper introduces reinforcement learning (RL) technology, using an intelligent agent to learn and generate diverse and high-performance kernel function combinations as the initial solutions for the genetic algorithm.

[0158] First, the state is represented as a sequence of kernel functions constructed by the agent and the current position. Sequence S = [s1, s2, ..., s L ] is of length L = 2n - 1. Odd positions hold kernel function indices, and even positions hold operator indices. The value range of the current position p is p∈{1, 2, ..., L}. The action space is defined as the set of actions for odd positions being the set of kernel functions K = {k1, k2, ..., k8}; and the set of actions for even positions being the set of operators O = {+, ×}. The agent selects actions according to an ∈-greedy strategy, which can either explore random actions or select the action with the maximum Q value.

[0159] The reward function is the core design of reinforcement learning. This paper defines the reward function from four dimensions: training error, entropy, similarity penalty, and rare kernel function reward: rewarding combinations with high-quality training performance, encouraging diverse kernel function combinations, penalizing combinations that are too similar to existing chromosomes, and promoting the use of rare kernel functions. The specific reward function expression is:

[0160]

[0161] R train =-E train

[0162]

[0163] Among them, α, β, γ, and δ are weight parameters that adjust the influence of each part of the reward. train The error of the kernel function combination corresponding to the current chromosome on the training data, that is, the mean square error, R train is the training error reward. p i Represents the probability of an element appearing in the search space, R entropy It represents the entropy bonus that measures the distribution of elements. Sim(C, C j ) indicates the current chromosome C and chromosome C j The similarity, d Hamming (C, C j) represents the Hamming Distance between the two chromosomes. L represents the length of the chromosome, i.e., the total number of kernel functions and operators, and M represents the number of existing chromosomes. k represents the number of times the kernel function k is used in all chromosomes, U max represents the maximum value of the number of times all kernel functions are used, K current represents the set of kernel functions in the current chromosome. The pseudo code is as follows.

[0164]

[0165]

[0166] Step two: Progressive sampling optimization strategy of multi-scale collaborative adaptive kernel system

[0167] The progressive sampling optimization strategy of the multi-scale collaborative adaptive kernel system aims to improve the fitting accuracy of the Gaussian process model to the target detection performance surface by gradually optimizing the kernel function combination structure and parameters. This strategy includes two core stages: first, the collaborative evolution exploration of the multi-scale kernel structure is realized through the genetic algorithm, and then the parameters are fine-tuned through the whale optimization algorithm to ensure the efficient adaptability and generalization ability of the model in complex scenarios.

[0168] (1) Collaborative evolution exploration of multi-scale kernel structure

[0169] In the genetic algorithm, the coding method determines the structure of the search space and the set of solutions that can be explored. In order to effectively represent the complex kernel function combination, the invention proposes a coding method for collaborative representation of multi-scale kernel structure. First, define the basic kernel function set K = {k1, k2,..., k8}, where each k i represents a basic kernel function type, and the operator set is defined as O = {+, ×}, representing the addition and multiplication combination of kernel functions, respectively. Then, each chromosome is encoded as a symbolic expression, representing a specific kernel function combination form. The gene sequence of the chromosome is composed of kernel functions and operators alternately, with the following structure:

[0170]

[0171] where k ij ∈K represents the kernel function selected from the basic kernel function set, op j ∈O represents the operator selected from the operator set, and n represents the number of kernel functions.

[0172] Based on the above coding strategy, the search space S of the kernel function combination is defined as the set of all possible kernel function and operator sequences:

[0173]

[0174] The size of the search space is determined by the number of kernel functions n and the number of operators n-1, and its size is:

[0175] |S|=|K| n ×|O| n-1

[0176] Where |K| represents the number of kernel functions, and |O| represents the number of operators.

[0177] The fitness function is an important tool to guide the search process towards the optimal solution. In order to guide the algorithm to gradually find better kernel function combinations, the present application proposes a dynamic threshold guided fitness evaluation method. This method dynamically adjusts the target threshold, so that the fitness evaluation is continuously optimized with the iteration of the algorithm, ensuring that the search process always moves towards a better solution set. The definition is as follows:

[0178] f(C)=T target -E avg

[0179]

[0180] Where f(C) represents the fitness value of chromosome C, T target represents the target threshold, and E avg is the average error of the chromosome in K-fold verification. After each iteration, the target threshold T target is dynamically adjusted to the 30th percentile value of the average K-fold training error of all chromosomes in descending order.

[0181] The present application adopts a probability selection strategy based on the fitness ratio (also known as roulette wheel selection strategy), aiming to give chromosomes with high fitness a greater chance of being selected and passed on to the next generation, while retaining a certain randomness to maintain the diversity of the population.

[0182] In addition, the present application constructs a chromosome recombination method based on random crossover points, which generates offspring chromosomes with new kernel function combinations by recombining part of the genes of parent chromosomes.

[0183]

[0184] Where r is the position of the crossover point. At the crossover point r, part of C1 and C2 is exchanged, and new chromosomes C′1 and C′2 are generated after the exchange, as shown in Figure 1 .

[0185] Figure 1Schematic diagram of chromosome crossover using a combined kernel function. On the left are the two parent chromosomes before crossover, with the red dashed line indicating the crossover location. On the right are the two chromosomes after crossover. The letters AH represent different kernel functions, and the plus sign and title denote the operational logic between the different kernel functions.

[0186] To enhance the global search capability of the genetic algorithm in kernel function combination search and prevent the population from being trapped in local optimal solutions, this paper proposes an adaptive multi-pattern mutation mechanism. This mechanism introduces diverse random changes in chromosomes, breaking the local patterns in the existing chromosome structure and exploring a wider solution space.

[0187] In order to flexibly adjust the mutation intensity at different iteration stages, the present invention adopts an exponentially decaying dynamic mutation probability:

[0188] P mutation (t) = P initial exp(-αt)

[0189] Among them, P initial is the initial mutation probability, α is the parameter that controls the rate at which the mutation probability decreases, and t is the number of algorithm iterations. The adaptive multi-mode mutation mechanism consists of two aspects: the multi-mode mutation of the kernel function and the mutation of the operator gene.

[0190] There are three types of multi-mode mutations of kernel functions. The first is random replacement. The kernel function k i Can be randomly replaced by the set K\{k i Any other kernel function k′ in i =Random(K\{k i}); The second is the unit kernel function replacement, when the kernel function k i When in a multiplication term, it can be replaced by the unit kernel function The third is the replacement of the zero kernel function. Whether in the addition term or the multiplication term, the kernel function k can be unconditionally replaced. i Replace with zero function like Figure 2 shown.

[0191] In addition, in the mutation of the operator part, the mutation operation is designed to switch between addition and multiplication to change the structure of the kernel function combination. like Figure 3 shown.

[0192] Through the adaptive multi-mode mutation mechanism, the genetic algorithm proposed in the present invention can effectively balance exploration and utilization in the search process of kernel function combinations, enhance the global search capability and convergence efficiency of the algorithm, and thus significantly improve the prediction performance of the Gaussian process model.

[0193] Figure 2 Mutation mode of kernel function. The mutation mode of kernel function is divided into three kinds, which are zero mutation (left), unit function mutation (middle) and other kernel function mutation (right), and when mutation is carried out, the probability of each mutation mode is used for mutation, so that a new kernel function combination is formed.

[0194] (2) Progressive weight parameter fine tuning

[0195] In order to further improve the fitting ability of the Gaussian process model on complex data sets, the application introduces a progressive weight parameter fine tuning method, and adopts a whale optimization algorithm to optimize the combined kernel function. The method fine adjusts the weight coefficient of each sub-kernel function, enhances the capturing ability of the model to the complex nonlinear relationship in the data, and thus improves the prediction performance of the model.

[0196] In the Gaussian process model, the selection of the combined kernel function and the setting of its parameters have a decisive influence on the performance of the model. The combined kernel function constructed by the application is composed of n sub-kernel functions k i (x, x'; θ i ), in order to realize fine fitting of complex nonlinear relationship, the application introduces a weight coefficient α i for each sub-kernel function, the introduction of the weight coefficient allows the model to assign different importance to different kernel functions in different regions, so as to better adapt to the local changes of the data. The combined kernel function after introducing the weight coefficient is defined as follows:

[0197]

[0198] Where S m m represents the index set of the mth multiplication term, and the kernel function k i belongs to S m . M represents the number of addition terms, and each addition term is composed of multiple multiplication terms. α i is the weight coefficient of the kernel function k i . θ i is a set of parameters related to the kernel function k i . The parameter search space of each kernel function k i (x, x'; θ i ) is Where and represent the parameter range of the kernel function, which limits the parameter search of each kernel function within a reasonable upper and lower limit.

[0199] In order to evaluate the performance of the Gaussian process model in the parameter optimization process, the application designs a combined kernel function fitness evaluation objective function based on K-fold cross-validation error. The objective function is The average value of the validation errors of all folds is defined as:

[0200]

[0201] where α = {α1, α2,..., α n} represents the weight coefficients of each sub-kernel function, and θ = {θ1, θ2,..., θ n} represents the parameter set of each sub-kernel function. k E (α, θ) represents the error of the combined kernel function C(x, x'; α, θ) on the kth fold validation set.

[0202] In the bubble-net attack phase, the weight coefficients α i and the kernel function parameters θ i are updated as follows:

[0203]

[0204] A = 2a·r - a

[0205] where α i (t) and θ i (t) represent the weight coefficients and kernel function parameters of the current iteration number t, respectively, and the weight coefficients and kernel function parameters of the optimal solution of the current iteration number t. a is a factor that linearly decays with the iteration number, and r is a random number between 0 and 1. The parameter update strategy in the exploration and development phase is as follows:

[0206]

[0207] where α rand，i and θ rand，i are the randomly selected weight coefficients and kernel function parameters in the population, respectively.

[0208] Experimental setup

[0209] The dataset used in this invention is VOC2007, which contains images of various categories and their corresponding annotation information, suitable for evaluating the performance of the model in natural images. This experiment is conducted on the following hardware platform: the processor is Intel i7-14700H, equipped with NVIDIA RTX 4060 graphics card. This experiment uses Spline Interpolation method to construct a surface model by smoothing the interpolation between the sampled points. In the evaluation of surface fitting, the three commonly used indicators are MSE, RMSE and R 2 .

[0210] MSE is the average value of the square of the error between the predicted value and the actual value. y iis the ith actual value, is the ith predicted value, n is the number of samples.

[0211]

[0212] RMSE is the square root of MSE.

[0213]

[0214] R 2 is a dimensionless index to measure the explanatory power of the model to the data. It represents the correlation between the predicted value and the actual value, the value is between 0 and 1, 1 indicates that the model perfectly fits, 0 indicates that the model cannot explain the change of the data. Where is the average value of the actual value. The closer R2 is to 1, the stronger the explanatory power of the model.

[0215]

[0216] The sampling method compared by the present application is WMVAS [1] and CVAS [2], in addition, spiral sampling, Hilbert curve sampling and cross sampling are also introduced for comparison. The present application designs four groups of two-dimensional interference combinations. The first group is contrast-gaussian blur, which constructs a regular performance degradation surface. The second group is also contrast-gaussian blur, which expands the setting range of contrast, when the contrast is negative, pixel inversion is performed, generating a performance surface with symmetric structure but uneven convex peak height. The third group is light adjustment-gaussian noise, which combines the method of light adjustment to construct a double-convex asymmetric performance surface. The fourth group is contrast-light adjustment, which constructs a performance surface with two interference dimensions having a trough.

[0217] Analysis of experimental results

[0218] Experimental results under contrast-gaussian blur interference

[0219] First, two kinds of interference are constructed, including contrast adjustment and gaussian blur, and the performance comparison results of different sampling point numbers are constructed under the condition of the same initial point, as shown in Tables 1-3. The present application samples 40 points, and the results of each index under an interval of 10 sampling points are shown in the table. From the data comparison in the table, it can be seen that the sampling method proposed by the present application has certain advantages compared with other methods, and can capture points with high value in the surface under the condition of fewer sampling points.

[0220] Table 1, MSE error result

[0221] Number of sampling points Ours WMVAS CVAS Spiral Cross Hilbert 10 0.0093 0.0123 0.01276 0.01219 0.00969 0.0123 20 0.00462 0.00663 0.01273 0.01175 0.00644 0.00709 30 0.00189 0.0066 0.01273 0.01147 0.00413 0.00697 40 0.00175 0.00658 0.01276 0.01376 0.00414 0.00674

[0222] Table 2, R2 Fitting results

[0223] Ours WMVAS CVAS Spiral Cross Hilbert 10 0.72988 0.64271 0.62925 0.6459 0.71848 0.64274 20 0.86576 0.80742 0.63009 0.65864 0.81279 0.79396 30 0.94501 0.80822 0.63009 0.66685 0.87987 0.7975 40 0.94901 0.80889 0.62923 0.60026 0.87969 0.80413

[0224] Table 3, RMSE error results

[0225] Ours WMVAS CVAS Spiral Cross Hilbert 10 0.09642 0.11089 0.11296 0.11039 0.09843 0.11089 20 0.06797 0.08141 0.11283 0.10839 0.08027 0.08421 30 0.0435 0.08124 0.11283 0.10708 0.0643 0.08348 40 0.04189 0.0811 0.11296 0.11729 0.06435 0.0821

[0226] The sampling point data is plotted as a line graph as shown in Figure 4 , which shows the change of three evaluation errors (RMSE, R 2 , MSE) with the increase of the number of sampling points. As can be seen from the error analysis, the sampling method proposed in the present application can fit a surface with lower error in fewer sampling times. The main reason is that the multi-scale cooperative adaptive kernel system progressive sampling optimization strategy designed in the present application can more accurately capture the position information in the three-dimensional space based on the spatial distribution information of the sampled points, so as to more effectively estimate the uncertainty and calculate the position of the next sampling point with the maximum uncertainty. Compared with the uncertainty estimation method based on the single kernel function of the Gaussian process (WMVAS and CVAS), the combined kernel function proposed in the present application has fully demonstrated its advantages in the sampling process. Through the cooperative evolution exploration of the multi-scale kernel structure, the effectiveness and robustness of the combined kernel function in fitting the observation data are ensured. First, the spiral sampling method is characterized by outward diffusion sampling from the central region, but this method is not suitable for the current performance surface, resulting in fluctuations in error with the increase of sampling points. Second, the cross sampling method uses a diagonal line parallel to the coordinate axis sampling method, which makes the sampling points close to the center of the two-dimensional region more dense, while the sampling points away from the center are more sparse, which is easy to ignore the sampling information of the boundary region. If there is a key sampling point at the boundary, it may be missed. The present application also constructs a sampling point distribution diagram as shown in Figure 5 , which shows the comparison of the trajectories of the sampling method proposed in the present application and the Hilbert curve sampling method in the performance surface heat map.

[0227] Figure 5 The sampling point distribution points of the heat map. In the figure, the black points represent the initial sampling points, the red points represent the sampling points of the sampling method proposed in the present application, and the green points represent the sampling points of the Hilbert trajectory. As can be seen from the figure, the sampling method proposed in the present application is more aggressive in exploring the unknown region, and tends to uniform sampling in the region outside the initial sampling points. It can be seen that the sampling points in the unknown region are more dense. It can be seen that part of the sampling points can cover the unknown region and the points with rich sampling information.

[0228] Experimental results under contrast (including pixel inversion) - Gaussian blur interference

[0229] In this experiment, we constructed the contrast-Gaussian blur performance surface and performed 40 samplings. The experimental results are shown in Tables 4-6. As can be seen from the tables, the sampling method proposed in the present application has certain advantages in the calculation of the three errors. It is particularly prominent from the 10th sampling. Compared with the cross-sampling and the trajectory sampling method based on the Hilbert curve, the multi-scale kernel structure co-evolution exploration strategy and the progressive weight parameter fine tuning method proposed in the present application show more obvious advantages and adaptability in the sampling task of complex performance surface, can more accurately capture key points, significantly improve the fitting accuracy of the model and reduce errors.

[0230] Table 4, MSE error

[0231]

[0232]

[0233] Table 5, R 2 error

[0234] Ours WMVAS CVAS Spiral Cross Hilbert 10 0.78694 0.79328 0.768 0.85977 0.78974 0.78894 20 0.86711 0.79924 0.77492 0.85984 0.79052 0.79054 30 0.86478 0.82508 0.81423 0.85957 0.79052 0.79569 40 0.86284 0.82565 0.81485 0.86437 0.79052 0.81933

[0235] Table 6, RMSE error

[0236] Ours WMVAS CVAS Spiral Cross Hilbert 10 0.06799 0.06697 0.07095 0.05516 0.06754 0.06767 20 0.0537 0.066 0.06988 0.05515 0.06742 0.06741 30 0.05417 0.06161 0.06349 0.0552 0.06742 0.06658 40 0.05455 0.06151 0.06338 0.05425 0.06742 0.06261

[0237] As Figure 6 shown, the spiral sampling performs well in the initial stage, and the main reason is that its sampling strategy first covers the key area of the performance surface. The spiral sampling starts from the center area and gradually expands in the counterclockwise direction, and the sampling radius gradually increases, which makes it possible to effectively capture the key feature points of the surface in the initial sampling, which helps the initial fitting of the model. However, as the sampling points gradually move away from the center area, the spiral sampling path becomes more dispersed, and the distribution of sampling points becomes gradually sparse, resulting in a decline in its ability to capture the edge area of the surface and more complex local features, and it cannot further effectively reduce the error. When the sampling number exceeds 11, the method proposed in the present application begins to show significant error reduction ability and is superior to other methods in overall performance. Especially in the complex performance surface constructed in this experiment, due to the difficulty of a single kernel function to effectively fit and capture uncertain points, the sampling methods based on a single kernel function such as WMVAS and CVAS face greater challenges in this scenario. At the same time, the present application also constructs a two-dimensional sampling distribution diagram, as shown in Figure 7 .

[0238] Figure 7Figure is the distribution of sampling points of 30, from the figure, it can be seen that the spiral sampling method is in the middle position at the beginning, and is in the intersection of the performance curve surfaces, so the sampled position captures more sufficient curve information than other methods. As the sampling proceeds, due to the large nonlinearity of the performance curve itself, the sampling method proposed in the application has more boundary exploration.

[0239] Experimental results under the interference of Gaussian noise and light-dark adjustment

[0240] The application constructs a performance curve with Gaussian noise and light-dark adjustment, and the experimental results are shown in Tables 7-9. The experiment was performed 90 times, and from the data in the table, it can be seen that the method proposed in the application has a significant advantage, and after 20 times of sampling points, the key sampling points can be accurately captured, and a more accurate performance curve can be constructed. The final experiment reached an MSE error of 0.00581 and an R 2 Result. This is due to the multi-scale kernel structure co-evolution exploration and progressive weight parameter fine tuning strategy proposed in the application, which can construct a suitable Gaussian process combined kernel function based on the sampled points. Compared with the sampling method based on a single kernel function, the method of the application is more accurate in fitting training data and determining the coordinates of the maximum uncertainty point.

[0241] Table 7, MSE error result

[0242]

[0243]

[0244] Table 8, R 2 Fitting result

[0245] Ours WMVAS CVAS Spiral Cross Hilbert 10 0.55891 0.5593 0.55963 0.56335 0.43226 0.50601 20 0.5596 0.55906 0.55018 0.55221 0.44075 0.38865 30 0.55914 0.55822 0.5496 0.55419 0.44628 0.30378 40 0.65948 0.55755 0.54959 0.32117 0.41221 0.14886 50 0.68254 0.55643 0.54959 0.25303 0.39274 0.14567 60 0.68201 0.49882 0.54959 0.29307 0.3778 0.14645 70 0.68045 0.40804 0.54959 0.29045 0.33858 0.14662 80 0.68088 0.42113 0.54959 0.27598 0.33824 0.14454 90 0.74278 0.42376 0.54953 0.18397 0.33838 0.14403

[0246] Table 9, RMSE error result

[0247] Ours WMVAS CVAS Spiral Cross Hilbert 10 0.09981 0.09976 0.09973 0.0993 0.11323 0.10562 20 0.09973 0.09979 0.10079 0.10056 0.11238 0.1175 30 0.09978 0.09989 0.10086 0.10034 0.11183 0.12539 40 0.08769 0.09996 0.10086 0.12382 0.11522 0.13864 50 0.08467 0.10009 0.10086 0.12988 0.11711 0.1389 60 0.08474 0.10639 0.10086 0.12635 0.11854 0.13884 70 0.08495 0.11562 0.10086 0.12659 0.12222 0.13883 80 0.08489 0.11434 0.10086 0.12787 0.12225 0.139 90 0.07622 0.11408 0.10086 0.13575 0.12224 0.13904

[0248] In Figure 8It can be seen from the broken line graph in the figure that the errors of the surfaces constructed by the sampling methods are basically not much different at the beginning of sampling, but as the number of sampling points increases, the sampling method proposed in the application shows certain advantages. The main problem of the spiral sampling method is that its sampling path is too regular, especially when the performance surface is complex, the spiral sampling often ignores a large number of key sampling points. This method focuses on the central region in the early sampling stage, which leads to insufficient capture of information in the edge region, and important boundary points are easily missed, thereby affecting the overall fitting effect of the model. The limitation of the cross sampling method is that the sampling points are mainly concentrated on the diagonal and the path parallel to the coordinate axis, although the sampling is relatively dense in the central region, but as the distance from the center increases, the distribution of the sampling points gradually becomes sparse, which leads to insufficient capture of complex regions on the performance surface. This uneven sampling strategy easily ignores key sampling points far from the center, thereby affecting the accuracy of the overall model. The disadvantage of the Hilbert curve sampling is that the sampling points are too scattered. Although this method can theoretically cover the entire sampling space, in practical application, especially when facing performance surfaces with complex local features, the over-dispersed sampling points lead to insufficient accurate capture of local information, thereby weakening the fitting ability of the model, resulting in unsatisfactory final effect. Meanwhile, the application also constructs a distribution graph of two-dimensional sampling points, as shown in Figure 9

[0249] Figure 9 Sampling point distribution graph. We show the distribution graph of 90 sampling points, and the selected comparative algorithm is CVAS. Compared with the Gaussian process based on a single kernel function, it can be seen from the graph that the algorithm proposed in the application has certain advantages, and has better surface fitting capability under such a complex surface.

[0250] Experimental results under contrast (including pixel inversion) and light and dark adjustment interference

[0251] In this experiment, the application constructs a performance surface with contrast and light and dark adjustment, and we perform 25 samplings, and the experimental results are shown in Tables 10-12. From the data in the table, it can be seen that the sampling methods based on a single kernel function (WMVAS and CVAS) have very limited performance, which further illustrates the limitations of the single kernel function in data fitting under a complex performance surface. The spiral sampling is not suitable for this performance surface due to its specific trajectory characteristics, resulting in the loss of a large number of key information points. The main disadvantage of the spiral sampling is that its sampling path is concentrated in the central region of rotation, and as the trajectory gradually expands outward, it is easy to ignore the key regions far from the center, especially when the performance surface has complex local features, the information loss is more serious.

[0252] ​The cross sampling method is relatively dense in the sampling points near the center of the region, which is consistent with the characteristics of the performance surface, and thus achieves good results. However, the disadvantage of the method is that the farther the sampling points are from the center, the sparser the distribution, resulting in insufficient ability to capture key information in the boundary region. At the same time, the uniformity of cross sampling is low, and it is difficult to adapt to asymmetric surfaces with high complexity.

[0253] The Hilbert curve sampling method is too dispersed due to its characteristics. Although this method can better cover the entire sampling space, it cannot fully capture local detail information when dealing with complex performance surfaces, resulting in fewer effective information points, and ultimately it is difficult to construct a performance surface with high fitting accuracy. The main disadvantage is that it excessively pursues global coverage, ignoring the capture of local key points, especially in complex surfaces with high-dimensional interference, showing low sampling efficiency.

[0254] In contrast, the multi-scale kernel structure co-evolution method proposed in the present application overcomes the limitations of these sampling methods, can achieve a better balance between local and global, dynamically adjust the sampling strategy, and more accurately capture key sampling points, showing stronger adaptability.

[0255] Table 10, MSE error results

[0256] Ours WMVAS CVAS Spiral Cross Hilbert 5 0.02081 0.02115 0.02097 0.02097 0.0195 0.02103 10 0.01737 0.02076 0.02077 0.02105 0.01922 0.0206 15 0.01322 0.0207 0.02083 0.02102 0.01902 0.02034 20 0.01291 0.01878 0.021 0.02101 0.01727 0.0202 25 0.01295 0.01881 0.01774 0.02081 0.01729 0.02019

[0257] Table 11, R 2 Results

[0258] Ours WMVAS CVAS Spiral Cross Hilbert 5 -0.07936 -0.0968 -0.08784 -0.08775 -0.01153 -0.09057 10 0.09926 -0.07701 -0.07714 -0.09171 0.0031 -0.06852 15 0.31411 -0.07378 -0.08038 -0.09029 0.01359 -0.05501 20 0.33046 0.02602 -0.08897 -0.08973 0.1042 -0.04788 25 0.32813 0.02428 0.07972 -0.07924 0.10331 -0.04739

[0259] Table 12, RMSE error

[0260] Ours WMVAS CVAS Spiral Cross Hilbert 5 0.14426 0.14542 0.14482 0.14482 0.13965 0.145 10 0.13178 0.1441 0.14411 0.14508 0.13864 0.14353 15 0.11499 0.14388 0.14432 0.14498 0.13791 0.14262 20 0.11362 0.13703 0.1449 0.14495 0.13142 0.14214 25 0.11381 0.13716 0.1332 0.14425 0.13148 0.1421

[0261] The curve graph of the number of sampling points and errors constructed in the experiment is shown in Figure 10 Although only 25 samplings are performed in the current performance surface, the effectiveness of the method proposed in the present application is sufficient. In the face of such a complex performance surface, although the final MSE error is 0.01295, the R 2 The result is 0.32813, which has certain gap compared with the previous performance surface experiment, but the surface structure of this experiment is extremely complex, which is sufficient to verify the sampling effect of the multi-scale cooperative adaptive kernel system progressive sampling optimization strategy proposed in the present application in complex scenarios. At the same time, we also constructed the sampling point distribution graph, as shown in Figure 11 .

[0262] Figure 11Sampling point distribution diagram. We show the distribution diagram of 20 sampling points. As can be seen from the sampling point distribution in the figure, the sampling method proposed by the application can distribute more sampling points at positions with large performance changes, and can capture sampling points with high values.

[0263] The above is only a preferred embodiment of the target detection performance surface progressive sampling method based on Gaussian process multi-kernel fusion. The protection scope of the target detection performance surface progressive sampling method based on Gaussian process multi-kernel fusion is not limited to the above-mentioned embodiments. Any technical solution that belongs to the idea is within the protection scope of the application. It should be noted that for those skilled in the art, some improvements and changes without departing from the principles of the application should also be considered as the protection scope of the application.

Claims

1. A target detection performance surface progressive sampling method based on Gaussian process multi-kernel fusion, characterized by: The method comprises the following steps: Step 1: During the target detection process, a multi-level search space is constructed to achieve efficient kernel function combination and optimization in complex performance surface scenarios; Step 2: Establish a progressive sampling optimization strategy for the multi-scale collaborative adaptive kernel system, gradually optimize the kernel function combination structure and parameters, and improve the fitting accuracy of the Gaussian process model to the target detection performance surface; Conduct multi-scale nuclear structure co-evolution exploration: Define the basic kernel function set K = {k1, k2, ..., k8}, where each k i Represents a basic kernel function type, and the operator set is defined as o = {+, ×}, which respectively represent the addition and multiplication combinations between kernel functions; Each chromosome is encoded as a symbolic expression, which represents a specific combination of kernel functions. The gene sequence of the chromosome is composed of kernel functions and operators alternately, with the following structure: Among them, k ij ∈K represents the kernel function selected from the basic kernel function set, op j ∈O represents the operator selected from the operator set, and n represents the number of kernel functions; Based on the above encoding strategy, the search space S of kernel function combinations is defined as the set of all kernel functions and operator sequences: The size of the search space is determined by the number of kernel functions n and the number of operators n-1, and its size is: |S|=|K| n ×|O| n-1 Among them, |K| represents the number of kernel functions, and |O| represents the number of operators; By dynamically adjusting the target threshold, the fitness evaluation is continuously optimized with the iteration of the algorithm, ensuring that the search process always moves towards a better solution set, which is defined as follows: f(C)=T target -E avg Among them, f(C) represents the fitness value of chromosome C, T target It represents the target threshold, E avg is the average error of the chromosome in K'fold validation. After each iteration, the target threshold T target It will be dynamically adjusted to the 30% quantile value of the average K'-fold training error of all chromosomes in descending order; A probability selection strategy based on fitness ratio is adopted, so that chromosomes with high fitness are selected and passed to the next generation, while retaining a certain degree of randomness to maintain the diversity of the population. By recombining some genes of the parent chromosome, offspring chromosomes with new nuclear function combinations are generated; Among them, r is the position of the crossover point. At the crossover point r, parts of C1 and C2 are exchanged to produce new chromosomes C′1 and C′2; Step 2 further includes: performing progressive weight parameter fine tuning, optimizing the combined kernel function using the whale optimization algorithm, and enhancing the model's ability to capture complex nonlinear relationships in the data by fine-tuning the weight coefficient of each sub-kernel function, thereby improving the model's predictive performance; The constructed combined kernel function consists of n sub-kernel functions k i (x, x′; θ i ), in order to achieve a fine fitting of complex nonlinear relationships, a weight coefficient α is introduced for each sub-kernel function i The introduction of weight coefficients allows the model to assign different importance to different kernel functions in different regions, thereby better adapting to local changes in the data. The combined kernel function after the introduction of weight coefficients is defined as follows: In order to evaluate the performance of the Gaussian process model in the parameter optimization process, the objective function is evaluated based on the fitness of the combined kernel function of the K'-fold cross-validation error. It is defined as the average of the validation errors of all folds: Among them, α = {α1, α2, ..., α n } represents the weight coefficient of each sub-kernel function, θ={θ1,θ2,...,θ n } represents the parameter set of each sub-kernel function, E k’ (α,θ) represents the error of the combined kernel function C(x, x′; α, θ) on the k′-th fold validation set; In the bubble network attack phase, the weight coefficient α i and kernel function parameters θ i The update strategy is as follows: A=2a·ra Among them, α i (t) and θ i (t) represents the weight coefficient and kernel function parameter of the current iteration number t, and The weight coefficient and kernel function parameters of the optimal solution at the current iteration number t, a is a factor that decays linearly with the number of iterations, and r is a random number between 0 and 1. The parameter update strategy in the exploration and development phases is as follows: Among them, α rand,i and θ rand,i are the weight coefficients and kernel function parameters randomly selected from the population respectively.

2. The method according to claim 1, wherein: The step 1 includes: performing a kernel function combination search space and its constraints: The search space includes 8 sub-kernel functions and two operators. Each combination is constructed through multiple sub-kernel functions and operators to form a diverse kernel structure.

3. The method according to claim 2, wherein: The step 1 also includes: a process of intelligently generating an initial solution driven by reinforcement learning: The state is represented as a sequence of kernel functions constructed by the agent and the current position, where the sequence S = [s1, s2, ..., s L The length of ] is L=2n-1, the odd positions store kernel function indexes, the even positions store operator indexes, and the value range of the current position p is p∈{1,2,...,L}; The action space is defined as the set of sub-kernel functions K = {k1, k2, ..., k8} at odd positions; the set of operators O = {+, ×} at even positions. Actions are selected according to the ∈-greedy strategy, which can explore random actions or select the action with the maximum Q value. Define the reward function. The specific reward function expression is: R train =-E train Among them, α', β, γ, δ are weight parameters that adjust the influence of each part of the reward, E train The error of the kernel function combination corresponding to the current chromosome on the training data, that is, the mean square error, R train is the training error reward, p i Represents the probability of an element appearing in the search space, R entropy It represents the entropy reward for measuring the element distribution, Sim(C, C j ) indicates the current chromosome C and chromosome C j The similarity, d Hamming (C, C j ) represents the Hamming Distance between the two chromosomes, L represents the length of the chromosome, that is, the total number of kernel functions and operators, M represents the number of existing chromosomes, U k It represents the number of times the kernel function k is used in all chromosomes, U max Indicates the maximum number of times used among all kernel functions, K current Represents the set of kernel functions in the current chromosome.

4. The method according to claim 1, wherein: In order to enhance the global search capability of the genetic algorithm in the kernel function combination search and prevent the population from falling into the local optimal solution, random changes in diversity are introduced into the chromosome to break the local pattern in the existing chromosome structure, thereby exploring a wider solution space; In order to flexibly adjust the mutation intensity at different iteration stages, an exponentially decaying dynamic mutation probability is adopted: P mutation (t)=P initial ·exp( - α”t) Among them, P initial is the initial mutation probability, α' is the parameter that controls the rate of decrease of the mutation probability, and t is the number of algorithm iterations. The adaptive multi-mode mutation mechanism includes two aspects: the multi-mode mutation of the kernel function and the mutation of the operator gene.

5. A system for progressive sampling of target detection performance surfaces based on Gaussian process multi-core fusion, wherein the system operates based on the method for progressive sampling of target detection performance surfaces based on Gaussian process multi-core fusion according to claim 1, and is characterized by: The system comprises: A spatial construction module, which performs multi-level search space construction during target detection and implements efficient kernel function combination and optimization in complex performance surface scenarios; The optimized sampling module establishes a progressive sampling optimization strategy for a multi-scale collaborative adaptive kernel system, gradually optimizes the kernel function combination structure and parameters, and improves the fitting accuracy of the Gaussian process model to the target detection performance surface.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the method according to any one of claims 1 to 4.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 4 is implemented.

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