Radar interference effect evaluation method based on constraint learning dynamic Bayesian network

Abstract

The invention discloses a radar interference effect evaluation method based on a constraint learning dynamic Bayesian network, is applied to the field of radar interference evaluation, and aims at solving the problem that the accuracy of interference effect evaluation is reduced due to radar detection data missing in a complex electromagnetic environment. Meanwhile, parameter constraints of five types of evaluation indexes and interference effect grades are defined; secondly, constructing a constraint learning dynamic Bayesian network, and learning a conditional probability and a transition probability under a data missing condition; then, proposing a prior constraint expectation maximization algorithm, converting parameter learning into an optimization problem with constraint by combining convex optimization, and overcoming the defects of a traditional expectation maximization algorithm; secondly, a cloud model is introduced to quantify discrete probability distribution into a continuous interference degree value; finally, simulation shows that the method can effectively improve parameter learning stability and evaluation accuracy under the conditions of suppressing and deception jamming and single index deficiency, and provides a reliable scheme for radar jamming effect evaluation in a complex environment.

Description

Technical Field

[0001] This invention belongs to the field of radar electronic warfare and signal processing, and specifically relates to a radar jamming effect evaluation technology for data-deficient scenarios in complex electromagnetic environments. Background Technology

[0002] Radar jamming effectiveness assessment is a core component of electronic warfare, determining jamming effectiveness and optimizing jamming strategies. It quantifies the impact of jamming on radar operational effectiveness by analyzing changes in key parameters of the radar-received signal. Common radar jamming patterns include suppression jamming and deception jamming, with corresponding assessment indicators covering repetition rate fluctuations, average pulse width variation, average bandwidth variation, peak power variation, carrier frequency fluctuations, and beam dwell time increments. In modern complex electromagnetic environments, radar-received signals are susceptible to multi-source noise and transmission loss, leading to data loss phenomena such as pulse leakage, pulse splitting, and measurement errors, thus compromising the completeness of assessment indicators.

[0003] Existing radar jamming effect evaluation methods mainly rely on complete input feature data to establish a mapping relationship between indicators and jamming effects. Typical methods include static model evaluation based on maximum likelihood estimation and traditional dynamic Bayesian network evaluation methods. The literature "Park J, Kim T, Gu C, et al. Dynamic collision estimator for collaborative robots: A dynamic Bayesian network with Markov model for highly reliable collision detection [J]. Robotics and Computer-IntegratedManufacturing, 2024, 86: 102692." proposes a state estimation method based on dynamic Bayesian networks, but it does not consider the parameter learning problem in scenarios with missing data. When the indicator data is incomplete, the model cannot converge effectively. The randomized Monte Carlo parameter expectation maximization algorithm proposed in the paper "Chen R, Schumitzky A, Kryshchenko A, et al. RPEM: randomized Monte Carlo parameter expectation maximization algorithm [J]. CPT: Pharmacometrics & Systems Pharmacology, 2024, 13 (5): 759-780." can handle some missing data problems, but it lacks constraints on the parameter domain, which can easily lead to the learning results deviating from the actual physical meaning and reducing the accuracy of the evaluation.

[0004] With the increasing complexity of electronic warfare environments, data gaps have become a key bottleneck affecting the reliability of jamming effect assessment. Traditional methods suffer from two major drawbacks under data gap conditions: first, the parameter learning algorithm lacks a constraint mechanism, leading to unstable estimation results; second, it cannot effectively establish the correlation between missing indicators and jamming effects, resulting in significant bias in the assessment results. Therefore, developing a radar jamming effect assessment method suitable for data gap scenarios has significant engineering application value. Summary of the Invention

[0005] To address the issue of insufficient accuracy in evaluating interference effects due to missing radar detection data in complex electromagnetic environments, this invention proposes a radar interference effect evaluation method based on a constraint-learning dynamic Bayesian network. This method integrates expert knowledge to construct an initial parameter model of the network, defines parameter constraints for evaluation indicators and interference effect levels, achieves parameter learning under missing data conditions through an improved prior constraint expectation-maximization algorithm, and combines a cloud model to continuously quantify the interference effect, ultimately achieving accurate evaluation in suppressive and deceptive interference scenarios.

[0006] The technical solution adopted in this invention is: a radar jamming effect evaluation method based on constraint learning dynamic Bayesian networks, comprising the following steps:

[0007] S1. Determine the interference assessment index corresponding to different interference patterns, and based on the working parameters of a typical airborne radar system, simulate radar signals under different interference patterns to obtain interference assessment index data, and construct a radar interference assessment index set by simulating data missing scenarios based on the obtained interference assessment index data.

[0008] S2. Construct a dynamic Bayesian network structure based on a hidden Markov model; define the parent node as the interference effect and the child node as the interference evaluation index.

[0009] S3. Constructing initial parameters for a dynamic Bayesian network based on a multi-level information fusion model;

[0010] S4. Define the parameter constraints for interference evaluation indicators and interference effect levels;

[0011] S5. Train the dynamic Bayesian network using the prior-constrained expectation-maximization algorithm.

[0012] S6. Introduce cloud model quantification to determine the level of interference effect based on the output of the trained dynamic Bayesian network.

[0013] The beneficial effects of this invention are as follows: This invention addresses the core pain point of radar jamming effect evaluation in scenarios with missing data. It constructs an initial parameter model through multi-level information fusion, providing reliable prior support when data is missing. Five types of parameter constraints are introduced to ensure the physical rationality of parameter learning, avoiding deviations caused by unconstrained optimization in traditional algorithms. The improved prior-constrained expectation-maximization algorithm achieves constrained parameter learning through convex optimization, enhancing the stability and accuracy of parameter learning under missing data conditions. The application of a cloud model solves the problem that discrete probability distributions are difficult to represent dynamic jamming trends, achieving continuous quantification of jamming effects. This invention maintains high evaluation accuracy even in scenarios involving suppression, deceptive jamming, and missing single indicators. It possesses advantages such as strong robustness, wide applicability, and high evaluation precision, effectively meeting the needs of radar jamming effect evaluation in complex electromagnetic environments. Attached Figure Description

[0014] Figure 1 A flowchart of the constraint learning dynamic Bayesian network interference evaluation scheme provided in an embodiment of the present invention.

[0015] Figure 2 The constraint learning dynamic Bayesian network framework provided in the embodiments of the present invention.

[0016] Figure 3 The KL divergence of the prior-constrained expectation-maximization algorithm under different missing rates;

[0017] Wherein, (a) is a schematic diagram of KL divergence corresponding to conditional probability learning; (b) is a schematic diagram of KL divergence corresponding to transition probability learning.

[0018] Figure 4 A schematic diagram of network evaluation parameter curves for scenarios with missing single indicators;

[0019] Among them, (a) is a schematic diagram of the root mean square error under suppressed interference; (b) is a schematic diagram of the coefficient of determination under suppressed interference; (c) is a schematic diagram of the root mean square error under deceptive interference; and (d) is a schematic diagram of the coefficient of determination under deceptive interference.

[0020] Figure 5 Comparison of predicted values ​​and actual values ​​for different dynamic Bayesian networks;

[0021] Among them, (a) is a suppression interference scenario; (b) is a deception interference scenario. Detailed Implementation

[0022] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0023] like Figure 1 The diagram shown is a flowchart of the constraint learning dynamic Bayesian network interference evaluation scheme of the present invention. The detailed implementation process of the technical solution of the present invention is as follows:

[0024] S1. Construct a set of radar evaluation indicators, simulate radar signals, and simulate scenarios with missing data.

[0025] S11. Based on the differentiated effects of suppression and deception jamming patterns on parameters, differentiated evaluation indicators are designed and a complete indicator system is constructed. Suppression jamming relies on high-power noise or regular pulse signals to submerge radar echoes, prompting the radar to adjust its carrier frequency, bandwidth, and peak power to resist the jamming. Therefore, carrier frequency fluctuation, average bandwidth variation, and peak power variation are selected as core evaluation indicators. Deception jamming, on the other hand, constructs false echo signals to mislead the radar, driving it to adjust its pulse repetition frequency, pulse width, and beam dwell time to verify the target's authenticity. Therefore, repetition frequency fluctuation, average pulse width variation, and beam dwell time increment are determined as core evaluation indicators. The six radar transmitter receptible parameters selected above together constitute the core evaluation indicator set for this scenario, including carrier frequency fluctuation, average bandwidth variation, peak power variation, repetition frequency fluctuation, average pulse width variation, and beam dwell time increment.

[0026] S12. Referring to the operating parameters of a typical airborne radar system, as shown in Table 1, simulations generate radar signal datasets under suppression and deception jamming, including carrier frequency, average bandwidth, peak power, pulse repetition frequency, average pulse width, and beam dwell time. Suppression jamming causes significant changes in radar peak power, bandwidth, and carrier frequency, while deception jamming causes significant changes in radar repetition frequency, pulse width, and beam dwell time. Furthermore, radar parameter configuration must adhere to the physical constraints of the actual application scenario. These parameters are not isolated but rather have close interrelationships and rigid constraints. For example, carrier frequency, as a fundamental constraint, limits the upper limits of average bandwidth and peak power; higher frequency bands are more likely to support large bandwidths, while lower frequency bands are better suited to achieving high peak power, and strict adherence to spectrum allocation rules is required. Pulse repetition frequency and beam dwell time form a time-series closed loop; the beam dwell time must contain a sufficient number of pulse periods to balance range ambiguity and target detection probability.

[0027] Table 1. Operating parameters of a typical airborne radar system

[0028]

[0029] S13. Using the Min-Max normalization method, the dataset generated in S12 is mapped to the [0,1] interval to eliminate the influence of dimensions. The normalization formula is:

[0030] (1)

[0031] in, , , For the first Item Indicators The One data value, This refers to the corresponding standardized data value.

[0032] S14. For the normalized dataset, randomly select a single feature and remove data from 10 consecutive time segments at missing rates of 10%, 20%, 30%, 40%, and 50%. Each missing rate corresponds to the same number of samples, resulting in an evaluation index set containing missing data. The 10 time segments do not have absolute time coordinates; specifically, they refer to 10 consecutive data intervals from the radar continuous time-series signal data generated in S12. The core requirement is to cover the stable operating state of the radar and ensure that the simulation of missing data closely matches the timing characteristics of the radar signal. In practical applications, the time segment division must include a sufficient number of pulses and be suitable for radar operation. For example, based on the parameters in Table 1: Divide the data according to the beam dwell period, taking a typical dwell time of 2 seconds. Divide each of the 5 complete dwell periods into 2 equal-length segments, resulting in segments 1 (0-1s) to 10 (9-10s). In addition, instead of removing data at five different missing rates within each time segment, a complete sample pool of 10 consecutive time segments is used. For a single selected feature, data is removed in batches at missing rates of 10%, 20%, 30%, 40%, and 50%, while strictly ensuring that the number of valid samples corresponding to each missing rate is consistent.

[0033] S2, Constructing based on Hidden Markov Models as follows Figure 2 The dynamic Bayesian network structure shown is shown.

[0034] S21. Divide the network into time slices. Each time slice contains 6 interference assessment indicator nodes. and 1 interference effect level node Define the parent node as the interference effect, and divide the interference effect level nodes into 4 levels ( (The larger the value, the stronger the interference effect). Six indicators are defined as child nodes, and these indicator nodes are divided into low, medium, and high states. A transition relationship, i.e., the transition probability, is established between adjacent time slices for the interference effect level nodes. Establish a causal relationship between indicator nodes and interference effect level nodes within the same time slice, i.e., conditional probability. .

[0035] S22. Based on the Markov assumption and steady-state assumption of the Hidden Markov Model, for the given dynamic Bayesian network above, the joint probability distribution of all disturbance effect levels and all indicators from time slice 1 to 10 can be simplified to the following formula:

[0036] (2)

[0037] in, Indicates the first The interference effect level node for each time slice. Indicates the first The first time slice Each interference assessment index node Indicates the initial probability. Represents the transition probability. This represents the probability of observation. Here, This indicates that the initial interference level for the first time slice is... The probability, This indicates that in the first time slice, the interference effect level is... At that time, the first time slice of that time slice was observed. The observation probability of each interference assessment index.

[0038] S3. Construct initial parameters for a dynamic Bayesian network based on a multi-level information fusion model.

[0039] S31. When the interference effect is at a specific level, determine the possible states (low, medium, high) corresponding to each evaluation index, and form a corresponding evaluation scheme. When the deceptive interference effect level is "1", taking the evaluation index "carrier frequency volatility" as an example, combined with different data and domain expert knowledge, the state scheme for evaluating carrier frequency volatility may be {low}, {medium}, {low, medium}, {medium, high}, {high}, etc. Here, the evaluation scheme should be understood as the range of possible states predicted before evaluation. For example, when the deceptive interference level is 1, expert knowledge predicts that the state of carrier frequency volatility may be in the range of {low, medium, high}, or the approximate range of {low, medium}, {medium, high}. The knowledge matrix is ​​then established to quantify the rationality of this "predicted range" and obtain the initial conditional probabilities corresponding to these three states (low, medium, high) for training the Bayesian network.

[0040] The set of all evaluation schemes is used as the identification framework. , build A knowledge matrix, denoted as The evaluation scheme for each indicator is as follows: Comparing different indicators and and quantification The degree of matching. Assuming... The matching degree is The quantitative criteria for the evaluation scheme are shown in Table 2. Again, taking the evaluation index "carrier frequency volatility" as an example, when the deceptive interference effect level is "1", the identification framework is... The states are {low, medium, {low, medium}, {medium, high}, and {high}}. The overlap degrees of the recognition frames corresponding to the state schemes {low}, {medium}, {low, medium}, {medium, high}, and {high} are 2, 3, 1, 1, and 2, respectively. The matching degree is measured according to the overlap degree value, with the highest overlap degree of 3 corresponding to "very good match", followed by overlap degree of 2 corresponding to "match", and finally overlap degree of 1 corresponding to "moderate match". The quantitative results of all evaluation schemes are combined to construct a knowledge matrix, as shown in Table 3.

[0041] Table 2 Quantitative Criteria for Evaluation Scheme

[0042]

[0043] Table 3 Evaluation Indicators Knowledge Matrix

[0044]

[0045] in, Knowledge Matrix In the evaluation index of interference effect The weighting of the following. For the evaluation plan For the recognition framework The matching degree is 1, which represents a comparison with the solution itself; different solutions are independent of each other and have a matching degree of 0.

[0046] Weight This can be achieved through a combination of subjective and objective weighting methods:

[0047] Step 1: Determine the interference effect level and evaluation scheme set corresponding to each knowledge matrix to ensure that each matrix is ​​strongly associated with a specific interference scenario and scheme.

[0048] Step 2: For each knowledge matrix, according to the quantification criteria in Table 2, calculate the correlation between all evaluation schemes within the matrix and... The sum of matching degrees is used as the initial base score, which is "the sum of matching degrees of a certain matrix / the sum of matching degrees of all matrices".

[0049] Step 3: Assemble 3 radar jamming experts or use relevant expert literature to score each matrix on a scale of 1 to 10, focusing on the fit between the matrix correspondence scheme and the jamming mechanism, and the practicality of matrix engineering. After removing the extreme values ​​of each group of scores, calculate the average score, which is the expert score.

[0050] Step 4: The final weight of a matrix = (base score × 0.3 + expert score × 0.7) / the sum of (base score × 0.3 + expert score × 0.7) of all matrices, ensuring that the sum of the weights of all matrices is 1.

[0051] S32. Find the largest eigenvalue of the knowledge matrix. The corresponding normalized feature vector is Then we have:

[0052] (3)

[0053] Where n corresponds to the number of evaluation schemes, and the final result is... It can be understood as corresponding The probability (weight). The next step is to use the DS matrix to fuse different knowledge matrices. This yields the initial conditional probabilities for the different final states.

[0054] Equation (3) is the basic probability distribution of the interference effect evaluation index in each state when the interference effect is in a certain state under each evaluation scheme.

[0055] S33. Based on the DS evidence theory, information from a multi-source knowledge matrix is ​​fused to obtain a relatively objective and reliable initial conditional probability. Assume... and For evaluation indicators In the identification scheme, two independent probability allocation functions are combined as evidence. Then we have:

[0056] (4)

[0057] in, It is the first knowledge matrix The set of evaluation schemes in the middle, yes The initial probability set of the corresponding evaluation scheme set, which is the feature vector value obtained by the S32 method. It is the collection of all evaluation schemes; It is a symbol of fusion.

[0058] When there are multiple independent probability assignment functions, such as Similarly to equation (4), the composition rules can be applied. Perform synthesis.

[0059] S4. Define the parameter constraints for evaluation metrics and interference effect levels. The prior constraints of network parameters are categorized based on the parent node state and child node state, into five classes. Network parameter constraints are established for frequency repetition rate fluctuation, average pulse width variation, average bandwidth variation, peak power variation, carrier frequency fluctuation, and beam dwell time increment, in relation to the interference effect level. In the following constraints, Indicates the first The state of each node is: At that time, its parent node state is The probability of; Indicates the first The number of states of each node. The initial value is obtained based on step S3. Sure.

[0060] S41. Introduce Type I constraints: Parameters whose parent nodes and states are the same, and whose child nodes are the same but have different states, are subject to a constraint that their sum is 1. Type I constraints are probability normalization constraints, ensuring that under the same parent node state, the sum of the probabilities of all possible child node states is 1, and each probability is within the interval [0,1]. This is a basic requirement of probability theory, ensuring the logical consistency of the model. Type I constraints are as follows:

[0061] (5)

[0062] S42. Introduce Type II constraints: Parameters with the same parent node and state, and the same child nodes but different states, are subject to size and difference constraints between states of different parameters. Type II constraints reflect the rule that "the stronger the interference effect, the more significant the indicator state," requiring that the probability of the indicator being in a high state increases with the increase of the interference level, while limiting the magnitude of probability change to avoid abrupt changes, which conforms to the gradual influence of interference on indicators in reality. There is no fixed value; it is usually chosen between 0.1 and 0.3 based on the gradual changes in the actual interference. A commonly used moderate value is 0.2. Taking the interference assessment indicator "peak power change" as an example: when the interference level is weak, the probability of this indicator being in a high state is low, for example, 0.2; when the interference level rises to medium-weak interference, the probability of this indicator being in a high state increases to 0.35, and the difference from the probability of weak interference is 0.15, which does not exceed 0.2; then to medium-strong interference level, the probability increases to 0.5, and the difference from the previous level is still 0.15. If the difference exceeds... The probability value of the indicator being in a high state needs to be adjusted to match the actual changes in radar parameter states. Type II constraints are as follows:

[0063] (6)

[0064] S43. Introduce Type III constraints: For parameters with the same parent node but different states, and child nodes and parameters with the same state, the constraints are based on magnitude and difference. Type III constraints ensure that the impact of parent node state differences on the same indicator is reasonable, requiring that the state probability of the same indicator under different interference levels changes in an orderly manner according to the strength of the level, and that the change amplitude is smooth, conforming to the continuous transmission logic of interference effects. Type III constraints are as follows:

[0065] (7)

[0066] S44. Introducing Type IV constraints: Parameters with the same parent node and state, and different child nodes but the same state, are subject to size relationship constraints. Type IV constraints reflect the sensitivity differences of different indicators, distinguishing the degree of response of different indicators to the same level of disturbance through probability relationships. For example, sensitive indicators are more likely to exhibit a high state under the same disturbance. Type IV constraints are as follows:

[0067] (8)

[0068] S45. Introduce Type V constraints: Individual parameters are subject to upper and lower bound constraints. Type V constraints limit extreme probabilities, preventing probabilities from approaching 0 or 1, and preventing the model from being affected by the probabilistic influence of absolute probabilities that contradict actual disturbances, thereby improving the model's robustness. and There is no fixed standard value; the core principle is to avoid probabilities approaching 0 or 1, thus preventing the model from making absolute probability judgments. Values ​​are typically chosen between 0.1 and 0.2, and between 0.8 and 0.9. Class V constraints are as follows:

[0069] (9)

[0070] S5. The dynamic Bayesian network is trained using the prior constraint expectation maximization algorithm.

[0071] S51. In scenarios with sufficient and complete sample data, Maximum Likelihood Estimation (MLE) is a typical method for learning Bayesian network parameters. However, in practice, radar data is often missing due to multi-source noise interference, causing the assumptions of MLE to fail and resulting in errors. For scenarios with sufficient samples but missing data, the Expectation Maximization (EM) algorithm can be used. Based on MLE, it iteratively optimizes to achieve dynamic Bayesian network parameter learning when data is missing.

[0072] Assume the set of evaluation metrics for the interference effect used in network training is as follows: Any sample is evaluated based on the indicator that the data is not missing. and data missing assessment indicators Composition, at this point, the log-likelihood function:

[0073] (10)

[0074] S52. Evaluation indicators due to missing data Because of the existence of , the above formula cannot directly solve for the maximum value of the likelihood function. This is achieved by introducing . The distribution function is The derivation of Jensen's inequality. If we can maximize this lower bound, we are also maximizing the log-likelihood function, that is, maximizing the following expression:

[0075] (11)

[0076] S53. Based on the above analysis, the process of learning dynamic Bayesian network parameters under missing data conditions using the EM algorithm is summarized as follows:

[0077] (1) Randomly initialize or manually set network parameters initial value .

[0078] (2) Set the maximum number of iterations Starting from the first iteration:

[0079] Step E: Based on the initial values ​​of the network parameters Or the result of the previous iteration Calculate data missing assessment indicators The posterior probability, as Current estimated value:

[0080] (12)

[0081] (13)

[0082] M-step: Maximization To obtain new parameter values :

[0083] (14)

[0084] S54. Based on the five types of constraints mentioned in S4 above, this step adopts a convex optimization method to introduce constraints into the likelihood function maximization process of the M-step in the expectation maximization algorithm, thereby realizing the constrained optimization search of parameters, and finally obtaining the prior-constrained expectation maximization algorithm, as shown below:

[0085] (15)

[0086] S6. Introducing a cloud model to quantify the interference effect level. Since the discrete probability distribution output by a dynamic Bayesian network is difficult to characterize the dynamic trend over time, this invention introduces a cloud model to map the discrete distribution to continuous interference level values. The cloud model describes the central value, fuzziness, and uncertainty of the interference effect level through three numerical features: expectation, entropy, and hyperentropy. This invention uses a normal cloud model and constructs a four-level interference effect level based on the golden section method; the larger the value, the stronger the interference effect.

[0087] By employing a cloud merging method, the probabilities of each level are fused with the corresponding cloud model features to generate a comprehensive cloud model. The expected value of the comprehensive cloud model is... , where represents the interference level of the target radar:

[0088] (16)

[0089] in, The number of cloud models participating in the merger, For the target radar to be in the first The probability of each level of interference effect.

[0090] The Zhengtai cloud model and its process of quantizing discrete probability distributions are existing known technologies, and will not be described in detail here.

[0091] Finally, the present invention also includes:

[0092] (1) Simulation experiment on parameter learning performance analysis of the prior constraint expectation maximization algorithm. KL divergence is used to measure the difference between the parameter estimates and the true values.

[0093] (17)

[0094] in, and These represent the actual value and the estimated value of the parameter, respectively.

[0095] Based on the constructed dataset, under the conditions of fixed network structure and error-free sample data, the missing data rates were set to 10%, 20%, and 50%, and 50 Monte Carlo simulations were performed to observe the KL divergence of the prior-constrained expectation-maximization algorithm under different missing data rates. Analysis Figure 3 It can be seen that, when sample data is missing, the KL divergence of the conditional probability and transition probability learned by the prior-constrained Expectation-Maximization algorithm at different missing data rates decreases continuously with the increase of the dataset. Furthermore, the lower the missing data rate, the smaller the dataset size required for KL divergence convergence, and at different missing data rates, the KL divergence only exhibits a certain bias when the dataset is small; the bias gradually decreases as the dataset increases. These experiments further verify the effectiveness of the prior-constrained Expectation-Maximization algorithm for learning dynamic Bayesian network parameters under missing data conditions.

[0096] (2) Further experiments were conducted to evaluate the interference effect of the dynamic Bayesian network based on the parameter learning algorithm of this invention under the condition of missing data. In both suppressive and deceptive interference scenarios, this invention simulated and generated 2000 sets of sample data for each type of interference. The dataset was divided into training and test sets in an 8:2 ratio. The experiment also constructed a reference network and a test network, where the reference network was trained on the complete dataset, and the test network was trained on samples containing missing data. The interference severity value of the test set after inference through the reference network and merging through the cloud model was used as the true interference severity value. The root mean square error and coefficient of determination were used to measure the accuracy and effectiveness of the evaluation results.

[0097] Root mean square error This is used to measure the average deviation between the predicted value and the actual value, and the calculation formula is as follows:

[0098] (18)

[0099] Coefficient of determination , used to characterize the goodness of fit between the predicted value and the true value, is calculated using the following formula:

[0100] (19)

[0101] in, For the sample size, For the first The degree of interference predicted by the tested network when there are missing sample data. For the first The true interference level value output by the reference network when there are no missing sample data.

[0102] In scenarios where interfering metrics are missing, a metric is randomly selected from the training set samples, and data is removed across 10 time segments at missing rates ranging from 10%, 20%, to 50%, with the same number of samples corresponding to each missing rate. These samples are then fed into the network for training. After training, a metric is randomly selected from the test set samples using a uniform missing rate for data removal.

[0103] The test set is input into the trained network to predict the probability that the radar is in each level of interference in the last time segment. The probability value is then converted into an interference level value using equation (16). The root mean square error of the network prediction under different missing rates is calculated. With the coefficient of determination like Figure 4 As shown in the figure above, analysis reveals that under both interference scenarios, when data is missing for any indicator, the determination coefficient of the network prediction decreases as the missing rate increases. Gradually decrease, root mean square error The impact of these parameters on the evaluation parameters is gradually increasing. Specifically, the carrier frequency fluctuation, average bandwidth change, and peak power change indicators under suppressive interference, and the repetition rate fluctuation, average pulse width change, and beam dwell time increment indicators under deceptive interference, have a more significant impact. This is directly related to the mechanisms of these two types of interference. Furthermore, even with a data missing rate of 50%, the network's coefficient of determination remains above 68%, indicating good overall prediction accuracy. Simulation results verify the effectiveness of the constrained learning dynamic Bayesian network in evaluating interference effects under conditions of missing single-indicator data.

[0104] (3) To further verify the performance of the constrained learning dynamic Bayesian network in evaluating interference effects in continuous time segments, the original data without missing samples were input into the reference network, and the corresponding missing sample data were input into the unconstrained learning dynamic Bayesian network. The outputs of the two networks were then merged using a cloud model to obtain the interference level value, such as... Figure 5 As shown. By Figure 5 The experimental results in (a) and (b) show that, in both suppressive and deceptive interference scenarios, when the data is complete in time segments 5-7, the predicted interference levels of the constrained learning dynamic Bayesian network are closer to the true values ​​than those of the unconstrained learning network. When the data for a single indicator is missing in time segments 8-10, the predicted values ​​of the unconstrained learning network fluctuate more drastically, with an average deviation of 32.20% for the suppressive interference scenario and 21.97% for the deceptive interference scenario, while the corresponding deviations for the constrained learning network are only 9.32% and 6.70%, respectively. From the overall time segment perspective, the difference between the predicted and true values ​​of the constrained learning network is consistently significantly smaller than that of the unconstrained learning network, verifying that its evaluation results for both types of interference scenarios are closer to the true values ​​under conditions of missing data.

[0105] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A radar jamming effect evaluation method based on constraint learning dynamic Bayesian network, characterized in that, The method comprises the following steps: S1, determining each type of jamming evaluation index corresponding to different jamming patterns, and based on the typical airborne radar system operating parameter value range, simulating radar signals under different jamming patterns to obtain a plurality of jamming evaluation index data, and constructing a radar jamming evaluation index set by simulating data missing scenarios of the plurality of each type of jamming evaluation index data; S2, constructing a dynamic Bayesian network structure based on a hidden Markov model; defining the parent node as the jamming effect level and the child node as each type of jamming evaluation index; S3, constructing the initial parameters of the dynamic Bayesian network based on a multi-level information fusion model; S4, defining the dynamic Bayesian network parameter constraints of the jamming evaluation index and the jamming effect level; S5, training the dynamic Bayesian network by using a prior constraint expectation maximization algorithm; S6, introducing a cloud model to quantify the jamming effect level output by the trained dynamic Bayesian network.

2. The radar jamming effect evaluation method based on constraint learning dynamic Bayesian network according to claim 1, characterized in that, In step S1, the radar jamming evaluation index set is constructed by simulating data missing scenarios of the plurality of jamming evaluation index data, specifically: , the Min-Max normalization method is used to map the obtained index data to the interval [0, 1]; A2, dividing the normalized index data into time segments; A3, removing part of the data in each time segment according to the set different missing rates to obtain the radar jamming evaluation index set containing missing data.

3. The radar jamming effect evaluation method based on constraint learning dynamic Bayesian network according to claim 2, characterized in that, In step S1, the different jamming patterns include suppression jamming and deception jamming.

4. The radar jamming effect evaluation method based on constraint learning dynamic Bayesian network according to claim 3, characterized in that, Step S2 is specifically: Divide the network into an equal number of sub-networks according to the number of time segments of the index data in step S1, each sub-network including all types of jamming index nodes corresponding to all jamming patterns and a jamming effect level node; the jamming effect level node is taken as the parent node, and each type of jamming index node is taken as the child node; The child nodes are divided into three states: low, medium and high; The transition relationship, i.e. transition probability, of the jamming effect level node between adjacent sub-networks is established; The causal relationship, i.e. conditional probability, between the child nodes and the parent node in the same sub-network is established; Based on the Markov assumption and steady-state assumption of the hidden Markov model, the joint probability distribution of all parent nodes and all child nodes in all sub-networks in the network is established.

5. The radar jamming effect evaluation method based on constraint learning dynamic Bayesian network according to claim 4, characterized in that, Step S3 specifically includes the following steps: S31. Use the collection of all evaluation schemes as an identification framework. The evaluation schemes for each type of evaluation indicator data are denoted as follows: Comparing different types of evaluation indicator data and and quantification The matching degree; and a knowledge matrix is ​​constructed based on the matching metric results of all evaluation schemes; constructing A knowledge matrix, denoted as ; S32, obtaining the maximum eigenvalue of the knowledge matrix and the corresponding normalized eigenvector; thereby constructing the probability distribution function of each type of evaluation index; S33, performing DS evidence theory fusion on the probability distribution function of each type of evaluation index.

6. The radar jamming effect evaluation method based on constraint learning dynamic Bayesian network according to claim 5, characterized in that, Step S4 includes: Class I constraint: the parameters of the parent node and its state are the same, the child node is the same but the state is different, and the parameters are subject to the constraint that the sum is 1; Class II constraint: the parameters of the parent node and its state are the same, the child node is the same but the state is different, and the parameters are subject to size relationship constraint and difference constraint between different states; Class III constraint: the parent node is the same but the state is different, the child node and its state are the same, and the parameters are subject to size relationship and difference constraint; Class IV constraint: the parent node and its state are the same, the child node is different but the state is the same, and the parameters are subject to size relationship constraint; Class V constraint: a single parameter is subject to upper and lower limit constraints. Class V constraint limits extreme values of probability, and avoids probability close to 0 or 1 by upper and lower limits.

7. The radar jamming effect evaluation method based on constraint learning dynamic Bayesian network according to claim 6, characterized in that, The normal cloud model is adopted and several interference effect levels are constructed based on the golden section method. The larger the value is, the stronger the interference effect is.

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