Target detection performance curved surface progressive sampling method based on Gaussian process multi-core fusion

Abstract

The invention relates to a target detection performance curved surface progressive sampling method based on Gaussian process multi-core fusion. The invention relates to the technical field of target detection, in a target detection process, multi-level search space construction is carried out, and efficient kernel function combination and optimization are realized in a complex performance curved surface scene; a progressive sampling optimization strategy of a multi-scale collaborative adaptive kernel system is established, a kernel function combination structure and parameters are optimized step by step, and the fitting precision of a Gaussian process model to a target detection performance curved surface is improved. The method is mainly used for solving the problem of model performance evaluation under a multi-dimensional interference condition, and the performance evaluation efficiency and accuracy of the target detection model in a complex environment are improved by optimizing kernel function combination and parameter tuning.

Description

Technical Field

[0001] The present invention relates to the field of target detection technology, and is a target detection performance surface progressive sampling method based on Gaussian process multi-kernel fusion. The method of the present invention is mainly used to solve the problem of model performance evaluation under multi-dimensional interference conditions, and improves the performance evaluation efficiency and accuracy of the target detection model in a complex environment by optimizing kernel function combination and parameter tuning. Background Art

[0002] In practical applications, target detection models face a variety of interference factors, such as illumination changes, noise, and weather conditions. The combination of these factors directly affects the detection performance of the model. When evaluating model performance, existing studies usually analyze the relationship between interference intensity and performance indicators (such as detection accuracy or mAP), mainly using two-dimensional curves to show the performance of the model under a single interference condition. However, most studies are limited to single-dimensional interference and cannot fully reflect the actual performance of the model under multi-dimensional interference conditions.

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

[0004] The current limitation is that the single-dimensional interference assessment cannot meet the deployment requirements of the model in a multi-dimensional interference environment, resulting in one-sided and incomplete 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.

[0005] To fill this research gap, the present invention proposes a progressive sampling method for target detection performance surface 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 model's performance characterization capability in a multi-interference environment. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention provides a method for progressive sampling of target detection performance surface based on Gaussian process multi-kernel fusion. The present invention provides the following technical solutions:

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

[0008] 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;

[0009] 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.

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

[0011] The search space includes eight sub-kernel functions and two operators. Each combination is constructed through multiple sub-kernel functions and operators to form a diverse kernel structure.

[0012] Preferably, step 1 further comprises: a process of intelligently generating an initial solution driven by reinforcement learning:

[0013] 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 ] has a length of 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};

[0014] The action space is defined as the action set K = {k1, k2, ..., k8} for odd positions and the operator set O = {+, ×} for even positions. Actions are selected according to the ∈-greedy strategy, which can explore random actions or select actions with the maximum Q value.

[0015] Define the reward function. The specific reward function expression is:

[0016]

[0017] R train =-E train

[0018]

[0019] Preferably, the step 3 comprises: performing multi-scale nuclear structure co-evolution exploration:

[0020] Define a 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;

[0021] 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, and the structure is as follows:

[0022]

[0023] 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;

[0024] 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:

[0025]

[0026] 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:

[0027] |S|=|K| n ×|O| n-1

[0028] Here, |K| represents the number of kernel functions, 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 to ensure that the search process always moves towards a better solution set, which is defined as follows:

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

[0031]

[0032] Among them, f(C) represents the fitness value of chromosome C, T target 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;

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

[0034] By recombining some genes of the parent chromosome, offspring chromosomes with new nuclear function combinations are generated;

[0035]

[0036] Among them, r is the position of the crossover point. At the crossover point r, parts of C1 and C2 are exchanged to generate new chromosomes C′1 and C′2.

[0037] Preferably, 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, by introducing a random change of diversity in the chromosome, the local pattern in the existing chromosome structure is broken, thereby exploring a wider solution space;

[0038] In order to flexibly adjust the mutation intensity at different iteration stages, an exponentially decaying dynamic mutation probability is adopted:

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

[0040] Among them, P initial is the initial mutation probability, α is the parameter that controls the decreasing speed of the mutation probability, t is the number of algorithm iterations, and 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, step 2 further comprises: performing progressive weight parameter fine tuning, optimizing the combined kernel function using a whale optimization algorithm, and enhancing the model's ability to capture complex nonlinear relationships in the data by finely adjusting the weight coefficient of each sub-kernel function, thereby improving the model's prediction performance;

[0042] 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, so as to better adapt to local changes in data. The combined kernel function after the introduction of weight coefficients is defined as follows:

[0043]

[0044] 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 the K-fold cross-validation error is used. Defined as the average of the validation errors of all folds:

[0045]

[0046] 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-fold validation set;

[0047] In the bubble network attack phase, the weight coefficient α i and kernel function parameter θ i The update strategy is as follows:

[0048]

[0049] A=2a·ra

[0050] Among them, α i (t) and θ i (t) represent the weight coefficient and kernel function parameter of the current iteration number t, and The weight coefficient and kernel function parameter of the optimal solution for the current iteration number t, a is a factor that decays linearly with the number of iterations, r is a random number between 0 and 1, and the parameter update strategy in the exploration and development phases is as follows:

[0051]

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

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

[0054] A space construction module, which performs multi-level search space construction during target detection and realizes efficient kernel function combination and optimization in complex performance surface scenarios;

[0055] 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.

[0056] A computer-readable storage medium stores a computer program, which is executed by a processor to implement a target detection performance surface progressive sampling method based on Gaussian process multi-core fusion.

[0057] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a method for progressive sampling of target detection performance surface based on Gaussian process multi-core 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 with multi-kernel function fusion for the first time, integrating multiple kernel functions, significantly enhancing the model's expressive power and uncertainty inference capabilities. This innovation enables the model to fit complex performance surfaces more accurately and improves the prediction accuracy of target detection performance under dual interference dimensions.

[0061] The present invention proposes a search space construction method for multi-level kernel function combinations and introduces constraints to effectively reduce the search dimension. Combined with the intelligent initial solution generation strategy driven by reinforcement learning, the search efficiency is significantly improved. The innovation of this method lies in the ability to more efficiently explore the optimization space and reduce the waste of computing resources.

[0062] The present invention designs a progressive sampling optimization strategy that combines multi-scale co-evolution with progressive weight tuning. Through the co-evolution of multi-scale kernel structures, the effective fusion of features of different scales is achieved. At the same time, progressive weight tuning ensures the optimal coordination of the combined kernel function 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 implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

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

[0065] Figure 2 Schematic representation 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 points of the sampling points are 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] Fig. 9 Displayed as a distribution diagram of 90 sampling points;

[0073] Fig.10 Displayed as three error line graphs;

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

[0075] The present invention is described in detail below in conjunction with 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-core fusion.

[0078] A method for progressive sampling of target detection performance surface 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 2:

[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 eight 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 difference between the third embodiment of the present application and the second embodiment is that:

[0087] The step 1 also includes: a process of intelligently generating an initial solution driven by reinforcement learning:

[0088] 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 ] has a length of 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};

[0089] The action space is defined as the action set K = {k1, k2, ..., k8} for odd positions and the operator set O = {+, ×} for even positions. Actions are selected according to the ∈-greedy strategy, which can explore random actions or select actions with the maximum Q value.

[0090] Define the reward function. The specific reward function expression is:

[0091]

[0092] R train =-E train

[0093] Specific embodiment four:

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

[0096] The step 3 includes: conducting multi-scale nuclear structure co-evolution exploration:

[0097] Define a 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;

[0098] 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, and the structure is as follows:

[0099]

[0100] 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;

[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 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 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 on 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 generate new chromosomes C′1 and C′2. Specific embodiment six:

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

[0118] 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 of diversity are introduced into the chromosome to break the local pattern in the existing chromosome structure, thereby exploring a wider solution space;

[0119] In order to flexibly adjust the mutation intensity at different iteration stages, an exponentially decaying dynamic mutation probability is adopted:

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

[0121] Among them, P initial is the initial mutation probability, α is the parameter that controls the decreasing speed of the mutation probability, t is the number of algorithm iterations, and 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. Specific embodiment seven:

[0123] The difference between the seventh embodiment of the present invention and the sixth embodiment is that:

[0124] The step 2 also 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 finely adjusting the weight coefficient of each sub-kernel function, thereby improving the model's prediction performance;

[0125] 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, so as to better adapt to local changes in data. The combined kernel function after the introduction of weight coefficients 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 the K-fold cross-validation error is used. Defined as the average of the validation errors of all folds:

[0128]

[0129] 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, Ek (α, θ) represents the error of the combined kernel function C(x, x′; α, θ) on the k-fold validation set;

[0130] In the bubble network attack phase, the weight coefficient α i and kernel function parameter θ i The update strategy is as follows:

[0131]

[0132] A=2a·ra

[0133] Among them, α i (t) and θ i (t) represent the weight coefficient and kernel function parameter of the current iteration number t, and The weight coefficient and kernel function parameter of the optimal solution for the current iteration number t, a is a factor that decays linearly with the number of iterations, r is a random number between 0 and 1, and the parameter update strategy in the exploration and development phases is as follows:

[0134]

[0135] Among them, α rand，i and θ rand，i are the weight coefficients and kernel function parameters randomly selected from the population respectively. Specific embodiment eight:

[0137] The difference between the eighth embodiment of the present invention and the seventh embodiment is that:

[0138] The present invention provides a target detection performance surface progressive sampling system based on Gaussian process multi-core fusion, the system comprising:

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

[0140] 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. Specific embodiment nine:

[0142] The difference between the ninth embodiment of the present invention and the eighth embodiment is that:

[0143] The present invention provides a computer-readable storage medium on which a computer program is stored. The program is executed by a processor to implement a target detection performance surface progressive sampling method based on Gaussian process multi-core fusion. Specific embodiment ten:

[0145] The difference between the tenth embodiment of the present invention and the ninth embodiment is that:

[0146] The present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a method for progressive sampling of target detection performance surface based on Gaussian process multi-kernel fusion is implemented. Specific embodiment eleven:

[0148] The difference between the eleventh embodiment of the present invention and the tenth embodiment is that:

[0149] The current limitation is that the single-dimensional interference assessment cannot meet the deployment requirements of the model in a multi-dimensional interference environment, resulting in one-sided and incomplete 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 present invention proposes a progressive sampling method for target detection performance surface 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 model's performance characterization capability in a multi-interference environment.

[0151] Step 1: Multi-level search space construction

[0152] The multi-level search space is constructed to ensure that the Gaussian process model can achieve efficient kernel function combination and optimization in complex performance surface scenarios. 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 progressive sampling.

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

[0154] When constructing a Gaussian process kernel function combination, the key is to reasonably define the search space to achieve 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 consists of 8 sub-kernel functions (RBF, linear, polynomial, sigmoid, exponential, rational quadratic, Matern, periodic) and two operators (addition and multiplication). Each combination is constructed through multiple sub-kernel functions and operators to form a diverse kernel structure. To ensure the rationality of the search space, we set combination rules, including avoiding repeated superposition of similar kernel functions and balancing the ratio of addition and multiplication. Through these constraints, we finally constructed a kernel function search space that has rich expression capabilities and simple structure.

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

[0157] In order to cope with the exponential expansion of the search space caused by the increase in the number of kernel function combinations, the traditional random generation method is difficult to fully cover the high-quality solution set. To this end, the present invention introduces reinforcement learning (RL) technology, and uses intelligent agents to learn and generate diversified and high-performance kernel function combinations as the initial solutions of genetic algorithms.

[0158] First, the state is represented as a sequence of kernel functions constructed by the agent and the current position. The sequence S = [s1, s2, ..., s L ] is of length L = 2n-1, the kernel function index is stored in the odd position, the operator index is stored in the even position, and the value range of the current position p is p∈{1, 2, ..., L}. The action space is defined as the action set is the sub-kernel function set K = {k1, k2, ..., k8} at the odd position; the action set is the operator set O = {+, ×} at the even position. The agent selects actions according to the ∈-greedy strategy, which can either explore random actions or select actions 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 of high-quality training performance, encouraging diverse kernel function combinations, penalizing combinations that are too similar to existing chromosomes, and improving 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, that is, the total number of kernel functions and operators, and M represents the number of existing chromosomes. k It represents the number of times the kernel function k is used in all chromosomes, U max Represents the maximum number of times used among all kernel functions, K current It represents the set of kernel functions in the current chromosome. The pseudo code is as follows.

[0164]

[0165]

[0166] Step 2: Progressive sampling optimization strategy for 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 consists of two core stages: first, the genetic algorithm is used to achieve the collaborative evolutionary exploration of the multi-scale kernel structure, and then the parameters are fine-tuned through the whale optimization algorithm to ensure the model's efficient adaptability and generalization ability in complex scenarios.

[0168] (1) Exploration of multi-scale nuclear structure co-evolution

[0169] In genetic algorithms, the encoding method determines the structure of the search space and the set of solutions that can be explored. In order to effectively represent complex kernel function combinations, this paper proposes an encoding method for collaborative representation of multi-scale kernel structures. 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 = {+, ×}, which represent the addition and multiplication combinations between 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, and the structure is as follows:

[0170]

[0171] 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.

[0172] Based on the above encoding strategy, the search space S of kernel function combinations is defined as the set of all possible kernel functions 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] Here, |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 a better kernel function combination, this paper proposes a fitness evaluation method guided by a dynamic threshold. 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, 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.

[0181] The present invention adopts a probability selection strategy based on fitness ratio (also called roulette selection strategy), which aims to make chromosomes with high fitness have a greater chance of being selected and passed on to the next generation, while retaining a certain degree of randomness to maintain the diversity of the population.

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

[0183]

[0184] Where 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. Figure 1 shown.

[0185] Figure 1Schematic diagram of chromosome crossover with combined kernel function. On the left are the two parent chromosomes before crossover, the red dotted line indicates the position of crossover, and on the right are the two chromosomes after crossover. The letters AH represent different kernel functions, and the plus sign and title represent the operation logic between different kernel functions.

[0186] 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, this paper proposes an adaptive multi-mode mutation mechanism. This mechanism introduces diverse random changes in chromosomes to break the local mode in the existing chromosome structure, thereby 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 decreasing speed of the mutation probability, and t is the number of algorithm iterations. 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.

[0190] There are three types of multi-mode mutations of kernel functions. The first is random replacement. 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, improve 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 modes of kernel functions. There are three types of mutation modes of kernel functions, namely zero mutation (left), unit function mutation (middle) and other kernel function mutation (right). When performing mutation, the probability of each mutation mode is used to perform mutation, thus forming a new kernel function combination.

[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, this paper introduces a progressive weight parameter fine tuning method and uses the whale optimization algorithm to optimize the combined kernel function. This method fine-tunes the weight coefficient of each sub-kernel function to enhance the model's ability to capture complex nonlinear relationships in the data, thereby improving the model's prediction performance.

[0196] In the Gaussian process model, the selection of the combined kernel function and its parameter setting have a decisive influence on the model performance. The combined kernel function constructed in the present invention is composed of n sub-kernel functions k i (x, x′; θ i ), in order to achieve a fine fitting of complex nonlinear relationships, the present invention introduces a weight coefficient α 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 data. The combined kernel function after the introduction of weight coefficients is defined as follows:

[0197]

[0198] Among them, S m Represents the index set of the mth multiplication term, kernel function k i Belongs to S m M represents the number of addition terms, each of which consists of multiple multiplication terms. i is the kernel function k i The weight coefficient of θ. i is the kernel function k i Related parameter set. Each kernel function k i (x, x′; θ i )’s parameter search space is in and Represents the parameter range of the kernel function, which limits the parameter search of each kernel function to a reasonable upper and lower limit.

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

[0200]

[0201] where 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. k (α, θ) represents the error of the combined kernel function C(x, x′; α, θ) on the k-fold validation set.

[0202] In the bubble network attack phase, the weight coefficient α i and kernel function parameter θ i The update strategy is as follows:

[0203]

[0204] A=2a·ra

[0205] where α i (t) and θ i (t) represent the weight coefficient and kernel function parameter of the current iteration number t, and The weight coefficient and kernel function parameter of the optimal solution for 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:

[0206]

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

[0208] Experimental setup

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

[0210] MSE is the average of the squares of the errors between the predicted values ​​and the actual values. iis the ith actual value, is the i-th predicted value and n is the number of samples.

[0211]

[0212] RMSE is the square root of MSE.

[0213]

[0214] R 2 It is a dimensionless indicator used to measure the model's ability to explain the data. It represents the correlation between the predicted value and the actual value, and the value is between 0 and 1, where 1 means the model fits perfectly and 0 means the model cannot explain the changes in the data. is the average of the actual values. The closer R2 is to 1, the stronger the explanatory power of the model.

[0215]

[0216] The sampling methods compared in the present invention are WMVAS[1] and CVAS[2]. In addition, spiral sampling, Hilbert curve sampling and cross sampling are introduced for comparison. The experiment of the present invention designs four groups of two-dimensional interference combinations. The first group is contrast-Gaussian blur, which constructs a conventional 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 to generate a performance surface with a symmetrical structure but uneven peak heights. The third group is brightness adjustment-Gaussian noise, which combines the brightness adjustment method to construct an asymmetric performance surface with double peaks and equal heights. The fourth group is contrast-brightness adjustment, which constructs a performance surface with valleys in two interference dimensions.

[0217] Experimental results analysis

[0218] Experimental results under contrast-Gaussian blur interference

[0219] First, two interferences were constructed, including contrast adjustment and Gaussian blur, and performance comparison results with different numbers of sampling points were constructed based on the same initial point, as shown in Tables 1 to 3. The present invention sampled 40 points, and the table shows the results of various indicators with an interval of 10 sampling points. It can be seen from the data in the table that the sampling method proposed by the present invention has certain advantages over other methods, and can capture points with high-value sampling in the surface with fewer sampling points.

[0220] Table 1. MSE error results

[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] Plot the sampling point data as a line graph such as Figure 4 As shown in the figure, three evaluation errors (RMSE, R 2 , MSE) changes with the increase in the number of sampling points. It can be seen from the error analysis that the sampling method proposed in the present invention can fit a surface with lower error under a smaller number of sampling times. The main reason is that the multi-scale collaborative adaptive kernel system progressive sampling optimization strategy designed by the present invention can capture the position information in three-dimensional space more accurately based on the spatial distribution information of the sampled points through the co-evolutionary exploration of the multi-scale kernel structure and the fine tuning of the progressive weight parameters, so as to more effectively estimate the uncertainty and deduce the position of the next sampling point with the largest uncertainty. Compared with the uncertainty estimation method (WMVAS and CVAS) based on the Gaussian process single kernel function, the advantages of the combined kernel function proposed in the present invention are fully reflected in the sampling process. Through the co-evolutionary exploration of the multi-scale kernel structure, the effectiveness and robustness of the combined kernel function in fitting the observed data are ensured. First, the spiral sampling method is characterized by diffusion sampling from the central area to the outside, but this method is not suitable for the current performance surface, resulting in fluctuations in errors as the sampling points increase. Secondly, the cross sampling method adopts a sampling method in which the diagonal line is parallel to the coordinate axis. This method makes the sampling points near the center of the two-dimensional area denser, while the sampling points far from the center are sparser, which easily ignores the sampling information of the boundary area. If there are key sampling points at the boundary, they may be omitted. The present invention also constructs a sampling point distribution map, such as Figure 5 As shown, the figure shows the comparison of the sampling method proposed by the present invention and the sampling method trajectory of the Hilbert curve in the heat map of the performance surface.

[0227] Figure 5 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 by the present invention, and the green points represent the sampling points of the Hilbert trajectory. It can be seen from the figure that the sampling method proposed by the present invention is more active in exploring the unknown area, and tends to be uniformly sampled in the area outside the initial sampling points. It can be seen that the sampling points performed by the present invention in the unknown area are more dense. It can be seen that the sampling points performed can partially cover the unknown area and points with rich sampling information.

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

[0229] In this experiment, we constructed a contrast-Gaussian blur performance surface and performed 40 samplings. The experimental results are shown in Tables 4 to 6. As can be seen from the table, the sampling method proposed in the present invention shows certain advantages in the calculation of the three errors. The performance has been particularly outstanding since the 10th sampling. Compared with the cross sampling and trajectory sampling methods 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 invention show more obvious advantages and adaptability in the sampling tasks of complex performance surfaces, and can capture key points more accurately, 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] like Figure 6 As shown, spiral sampling performs well in the initial stage, mainly because its sampling strategy first covers the key areas of the performance surface. Spiral sampling starts from the central area and gradually expands in a counterclockwise direction, and the sampling radius gradually increases, which enables the key feature points of the surface to be effectively captured during the initial sampling, which is helpful for the initial fitting of the model. However, as the sampling points gradually move away from the central area, the path of spiral sampling becomes more scattered, and the distribution of sampling points gradually becomes sparse, resulting in a decrease in its ability to capture the edge areas of the surface and more complex local features, and it is unable to further effectively reduce errors. When the number of samplings exceeds the 11th time, the method proposed in the present invention begins to show significant error reduction capabilities and outperforms other methods in overall performance. Especially on the complex performance surface constructed in this experiment, since a single kernel function is difficult to effectively fit and capture uncertainty points, 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 invention also constructs a two-dimensional sampling distribution diagram, such as Figure 7 shown.

[0238] Figure 7The figure shows the distribution when the number of sampling points is 30. It can be seen from the figure that the spiral sampling method captures more surface information than other methods in the initial stage because the initial sampling position is in the middle and at the intersection of the two performance surfaces. As the sampling proceeds, the sampling method proposed in the present invention is more targeted at the exploration of boundaries because the performance surface itself has a large nonlinearity.

[0239] Experimental results under Gaussian noise-brightness adjustment interference

[0240] The present invention constructs the performance surface of Gaussian noise and brightness adjustment. The experimental results are shown in Tables 7-9. A total of 90 samplings were performed in this experiment. From the data in the table, it can be seen that the method proposed by the present invention has significant advantages. After the sampling points reach 20 times, the key sampling points can be accurately captured, and then a more accurate performance surface can be constructed. The final experiment achieved an MSE error of 0.00581 and an R of 0.74278. 2 This is due to the multi-scale kernel structure co-evolutionary exploration and progressive weight parameter fine tuning strategy proposed in the present invention, which can construct a suitable Gaussian process combination kernel function based on the sampled points. Compared with the sampling method based on a single kernel function, the method of the present invention is more accurate in fitting the training data and determining the coordinates of the maximum uncertainty point.

[0241] Table 7. MSE error results

[0242]

[0243]

[0244] Table 8, R 2 Fitting results

[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 results

[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] exist Figure 8It can be seen from the line graph in that in the early stage of sampling, the surface errors constructed by each sampling method are basically the same, but with the increase in the number of sampling points, the sampling method proposed in the present invention shows certain advantages. The main problem with the spiral sampling method is that its sampling path is too regular, especially when the performance surface is complex, spiral sampling often ignores a large number of key sampling points. This method focuses on the central area in the early sampling stage, resulting in insufficient information capture of the edge area, and it is easy to miss important boundary points, which in turn affects the overall fitting effect of the model. The limitation of the cross sampling method is that its sampling points are mainly concentrated on the path parallel to the diagonal and the coordinate axis. Although the sampling is denser in the central area, as it moves away from the center, the distribution of the sampling points gradually becomes sparse, resulting in insufficient capture of complex areas 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 Hilbert curve sampling is that its sampling point distribution is too dispersed. Although this method can theoretically cover the entire sampling space, in practical applications, especially when facing performance surfaces with complex local features, overly dispersed sampling points lead to inaccurate capture of local information, which in turn weakens the model's fitting ability and leads to unsatisfactory final results. At the same time, the present invention also constructs a two-dimensional sampling point distribution map, such as Fig. 9 shown.

[0249] Fig. 9 Sampling point distribution diagram. We show the distribution diagram of 90 sampling points. The selected comparison algorithm is CVAS. Compared with the Gaussian process of a single kernel function, it can be seen from the figure that the algorithm proposed in this invention has certain advantages and has better surface fitting ability under such a complex surface.

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

[0251] In this experiment, the present invention constructed a performance surface for contrast and brightness adjustment. We performed 25 samplings, and the experimental results are shown in Tables 10-12. It can be seen from the data in the table that the performance of the sampling methods based on a single kernel function (WMVAS and CVAS) is very limited, which further illustrates the limitations of a single kernel function in data fitting under a complex performance surface. 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 spiral sampling is that its sampling path is concentrated in the central area of ​​rotation. As the trajectory gradually expands outward, it is easy to ignore the key areas far away from the center, especially when there are complex local features on the performance surface, the information loss is more serious.

[0252] The cross sampling method has a denser distribution of sampling points near the center of the region, which is consistent with the characteristics of the performance surface and thus achieves better results. However, the disadvantage of this 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 area. At the same time, the uniformity of cross sampling is low, making it difficult to adapt to asymmetric surfaces with high complexity.

[0253] Due to its characteristics, the sampling points of the Hilbert curve sampling method are too dispersed. Although this method can cover the entire sampling space well, it cannot fully capture local detail information when dealing with complex performance surfaces, resulting in fewer effective information points and ultimately making it difficult to construct a performance surface with high fitting accuracy. Its main disadvantage is that it over-pursues global coverage and ignores the capture of local key points, especially on complex surfaces with high-dimensional interference, which results in low sampling efficiency.

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

[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 diagram of the number of sampling points and error constructed in the experiment is as follows Fig.10 As shown in the figure, although only 25 samples are taken in the current performance surface, it is enough to demonstrate the effectiveness of the method proposed in the present invention. Faced with such a complex performance surface, although the final MSE error is 0.01295, R 2 The result is 0.32813, which is somewhat different from the previous performance surface experiment. However, the surface structure of this experiment is extremely complex, which is sufficient to verify the sampling effect of the multi-scale collaborative adaptive kernel system progressive sampling optimization strategy proposed in this invention in complex scenarios. At the same time, we also constructed a sampling point distribution map, such as Fig.11 shown.

[0262] Fig.11Sampling point distribution diagram. We show the distribution diagram of 20 sampling points. From the distribution of sampling points in the figure, it can be seen that the sampling method proposed in the present invention can distribute more sampling points at positions with large performance changes, and can capture sampling points with higher values.

[0263] The above is only a preferred implementation of a method for progressive sampling of target detection performance surface based on Gaussian process multi-core fusion. The protection scope of a method for progressive sampling of target detection performance surface based on Gaussian process multi-core fusion is not limited to the above embodiments. All technical solutions under this idea belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, several improvements and changes without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

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.

2. The method according to claim 1, characterized in that: The step 1 includes: performing a kernel function combination search space and its constraints: The search space includes eight 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, characterized in that: 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 ] has a length of 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 action set K = {k1, k2, ..., k8} for odd positions and the operator set O = {+, ×} for even positions. Actions are selected according to the ∈-greedy strategy, which can explore random actions or select actions with the maximum Q value. Define the reward function. The specific reward function expression is: R train =-E train 4. The method according to claim 1, characterized in that: The step 3 includes: conducting multi-scale nuclear structure co-evolution exploration: Define a 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, and the structure is as follows: 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 Here, |K| represents the number of kernel functions, and |O| represents the number of operators.

5. The method according to claim 4, characterized in that: 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 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 on 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 generate new chromosomes C′1 and C′2.

6. The method according to claim 1, characterized in that: 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 of 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(-αt) Among them, P initial is the initial mutation probability, α is the parameter that controls the decreasing speed of the mutation probability, t is the number of algorithm iterations, and 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.

7. The method according to claim 5, characterized in that: The step 2 also 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 finely adjusting the weight coefficient of each sub-kernel function, thereby improving the model's prediction 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, so as to better adapt to local changes in 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 combined kernel function fitness evaluation objective function based on the K-fold cross-validation error is used. 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, 0 = {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-fold validation set; In the bubble network attack phase, the weight coefficient α i and kernel function parameter θ i The update strategy is as follows: A=2a·ra Among them, α i (t) and θ i (t) represent the weight coefficient and kernel function parameter of the current iteration number t, and The weight coefficient and kernel function parameter of the optimal solution for the current iteration number t, a is a factor that decays linearly with the number of iterations, r is a random number between 0 and 1, and 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.

8. A target detection performance surface progressive sampling system based on Gaussian process multi-core fusion, characterized by: The system comprises: A space construction module, which performs multi-level search space construction during target detection and realizes 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.

9. 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 claims 1-7.

10. 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 of claims 1-7 is implemented.

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