Radar detection function boundary design method and system based on critical envelope clipping

Abstract

The application discloses a radar detection function boundary design method and system based on critical envelope surface cutting, relates to radar and radar performance optimization technology, and adopts an active learning strategy based on Gaussian process classification to screen critical sample points, uses a support vector machine to fit an implicit surface and is constructed into a signed distance function form with physical dimensions, so as to define a function existing area and a failure area. Different from traditional mechanical processing cutting, the application establishes a linear sensitivity mapping relationship between a radar physical design parameter variation and an envelope surface normal displacement based on an implicit function theorem, converts a design parameter reverse calculation problem into a quadratic programming model with constraints, and solves minimum parameter adjustment quantity under the performance keeping constraint of a non-target area. The application is verified through iteration to ensure convergence, realizes directional and quantitative expansion of the radar detection boundary, and solves the problems of low efficiency and easy damage to the performance of the non-target area in the traditional trial and error method.

Description

Technical Field

[0001] This application relates to the fields of radar and radar performance optimization technology, and in particular to a radar detection functional boundary design method and system based on critical envelope surface trimming. Background Technology

[0002] The core function of a radar system is to detect targets in complex environments. The functional boundary is defined as the boundary between when the radar detection probability meets or does not meet the requirements in the condition space (such as target range, clutter intensity, interference power, etc.). During the radar design phase, engineers often need to adjust design parameters (transmit power, pulse width, antenna gain, etc.) to expand the functional boundary, enabling the radar to adapt to harsher environments (such as longer distances and stronger clutter).

[0003] Traditional design methods rely heavily on trial and error: engineers guess which parameters need adjustment based on preliminary simulation results, then re-simulate to verify. If the boundary expansion is insufficient or excessive, adjustments are made again, iterating repeatedly. This method lacks quantitative guidance and cannot directly establish a mapping relationship between changes in design parameters and the movement of functional boundaries, resulting in inefficient boundary expansion design.

[0004] In recent years, some researchers have used evolutionary optimization methods such as genetic algorithms to directly optimize design parameters using boundary volume as the objective. These methods suffer from two major drawbacks: First, the computational complexity is disastrous—each individual evaluation requires resampling and fitting a complete critical envelope surface in a multidimensional condition space (requiring hundreds of radar simulations). Evolving through hundreds of generations means tens of thousands of simulations, taking dozens of days, making it completely unusable in engineering design. Second, and more seriously, its "black box" nature is problematic—genetic algorithms use boundary volume as a scalar objective function, essentially compressing the multidimensional condition space into a one-dimensional index. This means that while the optimization result may be better "overall," it cannot guarantee that performance in specific regions (such as near-range low-clutter areas) will not deteriorate. This inability to directionally control the boundary shape means that radar performance in certain critical operational areas may unexpectedly fail after "optimization," posing a serious security risk. Summary of the Invention

[0005] This application provides a radar detection functional boundary design method and system based on critical envelope surface trimming, which realizes the directional and quantitative expansion of the radar functional boundary while strictly ensuring that the boundary of the non-target area does not shrink.

[0006] This application provides a radar detection functional boundary design method based on critical envelope surface trimming, including: Acquire radar detection performance data in a multi-dimensional condition space, which includes environmental clutter intensity, target radar cross-section, and target distance; Critical sample points are selected using an adaptive sampling strategy, and an implicit surface is fitted using a support vector machine to construct a critical envelope surface. The implicit surface is then normalized to a signed distance function, where regions with function values ​​less than 0 are defined as functional regions and regions with function values ​​greater than 0 are defined as functional failure regions. The signed range function is differentiated based on the implicit function theorem to establish a linear sensitivity mapping relationship between the changes in radar physical design parameters and the normal displacement of the critical envelope surface. Based on the expected functional boundary expansion requirements, the linear sensitivity mapping relationship is substituted into a constrained quadratic programming model to solve for the minimum design parameter adjustment amount that satisfies the performance preservation constraint in the non-target region. The radar hardware configuration is adjusted based on the minimum design parameters.

[0007] This application provides a radar detection functional boundary design system based on critical envelope surface trimming, including a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the radar detection functional boundary design method based on critical envelope surface trimming as described above.

[0008] This application's embodiments establish a linear mapping between boundary normal movement and design parameters, transforming the problem into a single quadratic programming solution. Under the premise of strictly ensuring that the boundary of the non-target area does not shrink, it achieves quantitative, directional, and efficient expansion of the radar functional boundary.

[0009] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0010] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a flowchart illustrating the radar detection functional boundary design method based on critical envelope surface trimming, as described in an embodiment of this application. Figure 2 This is a schematic diagram of the critical envelope surface trimming in an embodiment of this application; Figure 3 This is a schematic diagram illustrating the calculation of the normal displacement of the boundary point in an embodiment of this application. Figure 4 This is a schematic diagram illustrating the principle of local sensitivity analysis in an embodiment of this application; Figure 5 This is a schematic diagram of the reverse mapping solution process in an embodiment of this application; Figure 6 This is a schematic diagram illustrating the comparison and verification of the boundaries before and after trimming in an embodiment of this application. Detailed Implementation

[0011] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0012] This application provides a method for designing the functional boundary of radar detection based on critical envelope surface trimming, such as... Figure 1 As shown, it includes the following steps: In step S101, the radar's detection performance data in a multidimensional conditional space x is acquired, where the multidimensional conditional space includes, for example, the target range. Clutter intensity Interference power Target radar cross-section wait.

[0013] In step S102, an adaptive sampling strategy is used to screen critical sample points, and an implicit surface is fitted by a support vector machine to construct a critical envelope surface. The implicit surface is then normalized to a signed distance function, where the region with a function value less than 0 is defined as the functional existence region, and the region with a function value greater than 0 is defined as the functional failure region.

[0014] In step S103, the signed range function is differentiated based on the implicit function theorem to establish a linear sensitivity mapping relationship between the change in radar physical design parameters and the normal displacement of the critical envelope surface.

[0015] In step S104, based on the desired functional boundary expansion requirements, the linear sensitivity mapping relationship is substituted into a constrained quadratic programming model to solve for the minimum design parameter adjustment amount that satisfies the performance maintenance constraint in the non-target region.

[0016] In step S105, the radar hardware configuration is corrected according to the minimum design parameter adjustment amount, and the corrected envelope surface can be iteratively verified.

[0017] In some embodiments, using an adaptive sampling strategy to screen critical sample points includes: An active learning algorithm based on Gaussian process classification (such as active learning based on Gaussian process classification) is used to evaluate the detection performance data in terms of detection probability. Non-uniform sampling is performed near the transition boundary to reduce the number of simulation samples. In a specific example, the detection probability of each condition point under the existing design is obtained through simulation or experimentation. .

[0018] To construct the critical envelope surface, implicit surfaces are fitted using support vector machines, including: Using support vector machines to fit the critical envelope surface And construct it as a signed distance function, for Perform gradient normalization to make it satisfy ,in Indicates the area where the function exists. Indicates the area where the function is disabled.

[0019] In specific examples, the steps also include setting the desired target boundaries and selecting key points. The target boundaries are set according to design requirements and include the following forms: Region-extended: Specifies a conditional subspace All must fall within the functional area. Identify the critical expansion point on the boundary—the point on the current boundary closest to the target expansion area—and assign it a positive expected normal movement. .

[0020] Volume expansion type: Sets the volume of the area where the desired function exists from... Upgraded to This type of objective can be indirectly achieved by transforming it into a region-expanding objective—by increasing the desired volume increment. The expected movement of each boundary point is derived by uniformly distributing the normal directions of the current boundary surface. .

[0021] Boundary offset type: Directly specifies the boundary movement distance in a specific direction.

[0022] Simultaneously, determine the boundary preservation points—points in the non-target region on the current boundary—and assign them a zero-expectation normal movement. .

[0023] Calculate the boundary difference; for key expansion points, calculate the expected normal movement distance from the point along the outward normal direction to the target boundary. For the held point, the expected movement is... .like Figure 2 As shown, the two-dimensional distance R-clutter C conditional plane has the current envelope (dashed line) and the target envelope (solid line), with the normal movement direction along the local outward normal; the key expansion point (solid circle) and its expected normal movement direction and distance δ=0.12. The boundary preservation point (hollow box) and its expected movement amount δ=0. Figure 3 A schematic diagram illustrating the calculation of the normal displacement at the boundary point is shown. Figure 3The geometric meaning of normal movement is illustrated using a magnified view.

[0024] In some embodiments, establishing a linear sensitivity mapping relationship between changes in radar physical design parameters and the normal displacement of the critical envelope surface includes: Define radar main performance function For the detection statistic, where For condition variables, For design parameters; At any point on the critical envelope surface At the place, through the Perform a Taylor expansion on the condition = 0, for example, a first-order Taylor expansion ignoring higher-order terms, to derive the design parameters. Sensitivity coefficient to boundary normal movement The sensitivity coefficient The geometric distance by which the envelope expands outward or contracts inward due to unit parameter adjustment.

[0025] At the boundary point Considering design parameters How do changes affect the boundary position? Figure 4 Display design parameter changes (Δ) How does a change in performance metrics (ΔSNR) ultimately lead to a shift in the boundary normal (ΔSNR)? Using implicit function differentiation formulas, calculate various design parameters. A sensitivity coefficient to changes in the boundary normal. In some embodiments, the sensitivity coefficient... The calculation process includes: Through radar performance function For design parameters partial derivatives , and radar performance function condition variables gradient norm The ratio between them is used to obtain the normalized sensitivity coefficient. for: in, Boundary point The sensitivity coefficient at that location. This application adds design parameters. Make performance indicators The sensitivity coefficient is positive as the boundary extends towards the failure zone (outer normal). Partial derivatives can be calculated using the analytical gradient or finite difference method from the radar performance model.

[0026] The effectiveness of the linearization approximation in the method of this application relies on the following engineering assumptions: (1) The boundary movement caused by the adjustment of design parameters is within the effective range of linear approximation (this range can be calibrated by offline numerical experiments: under typical boundary curvature, apply parameter perturbations of different magnitudes and compare the linear prediction with the actual movement to determine the maximum allowable relative movement that meets the engineering accuracy requirements); (2) The radar performance model has continuous first-order partial derivatives with respect to design parameters and condition variables near the boundary point; (3) The local curvature of the boundary does not change much, and the sensitivity coefficient is approximately constant within the adjustment range. For large-scale expansion requirements, the iterative strategy of this application decomposes a single large displacement into multiple small displacements to ensure that each adjustment is within the local linear effective range.

[0027] In some embodiments, it also includes collecting key extension points on the boundary. and its expected movement amount and sensitivity vector and maintain point and its sensitivity vector Construct a constrained quadratic programming model: The objective function is to minimize the squared L2 norm of the design parameter adjustment vector. Set constraints for key expansion points It forces the envelope to expand into the target region in a specific direction; Set constraints for boundary preservation points. Limit the performance fluctuation range in non-target areas, where To reduce tolerance, To avoid over-expanding the tolerance; Add physical realizable constraints The physical realizable constraints include the upper limit of transmitter saturation power, the upper limit of ADC sampling rate, and the upper limit of filter bandwidth.

[0028] In some embodiments, such as Figure 5 As shown, the iterative solution steps also include the following: When a quadratic programming model solved in a single iteration has no feasible solution (e.g., the expected movement of key points is too large, causing parameter adjustments to exceed the physical upper limit), the shrinkage tolerance is relaxed. Or reduce the desired normal movement proportionally. Continue until a feasible solution is found. If it is still not feasible, output the maximum achievable expansion and prompt for manual intervention.

[0029] Based on the adjusted parameters, local resampling verification is performed. If the actual movement does not reach the preset proportion of the expected value, the current envelope surface is used as the new initial surface, and sensitivity mapping is repeated until convergence.

[0030] In some embodiments, the design parameter p includes: RF link parameters, including low-noise amplifier bias voltage, transmitter peak power, and phase shifter phase weights; Signal processing parameters include the number of pulse accumulations, the constant false alarm rate detection threshold factor, and the Doppler filter order; Beam scanning parameters include the excitation amplitude of the phased array antenna elements and the scanning angle grid density.

[0031] like Figure 6 As shown, the solution obtained from the above method... Modify design parameters and perform adaptive sampling verification in critical regions of boundary changes (requiring only a small number of simulations and no need for global envelope reconstruction). An exemplary convergence criterion is: the actual normal movement of all critical expansion points reaches more than 80% of the expected value, and the movement of all hold-point points is not less than... It usually converges in 1-2 iterations, and the maximum number of iterations is bounded.

[0032] This application also proposes an implementation example of a radar detection functional boundary design method based on critical envelope surface trimming, applied to the functional boundary extension design of a C-band air search radar, including: 1. Existing design description Radar parameters: Transmit power Pulse width Antenna gain Operating frequency Receiver noise figure System losses Testing requirements: For RCS=2m 2 Detection probability of drone targets (false alarm rate) ).

[0033] Select target distance in conditional space (10~100 km) and clutter intensity (0~30dB). The existing design envelope is in The detection probability is exactly 0.8. At that location, the detection probability has dropped to 0.65.

[0034] Design goal: To expand the functional boundaries, so that in It can also be achieved in various places. At the same time, the boundaries of other areas are kept from shrinking.

[0035] 2. Construct the existing critical envelope surface Normalized coordinates were obtained by using active learning sampling (30 sample points) and SVM fitting. , The equation of the envelope surface below: Functional area is Verification: When hour, The system determined it to be safe.

[0036] 3. Set target boundaries and select key points Target point Corresponding normalized coordinates Calculate the point on the current boundary that is closest to this point. The point is expected to move along the normal direction. Select two more boundary points. and As a holding point, the expected movement is 0.

[0037] 4. Local sensitivity analysis exist The sensitivity coefficient is calculated at the boundary point. The relationship between the signal-to-noise ratio (SNR) and the design parameters is determined by the radar equations. At the boundary point, SNR ≈ 10 dB (linear value 10). ,have to: Sensitivity coefficient: Physical meaning: For every 1W increase in transmit power, the boundary expands outward by approximately 0.0048 normalized units; for every 1μs increase in pulse width, the boundary expands outward by approximately 2.38 normalized units.

[0038] 5. Solving by inverse mapping Constructing a quadratic programming problem: minimizing Satisfying key point constraints Maintain point constraints Parameter range Solving for the given information yields... (Pulse width adjustment affects power consumption; after comprehensive optimization, only power is adjusted).

[0039] 6. Verification and Iteration Will Substitute the data into the simulation and verify the results: Key points (85km, 10dB): The value meets the requirement of ≥0.8, and the normal movement is about 0.11, which reaches 92% of the expected value (0.12) and exceeds the 80% convergence threshold.

[0040] Keep point 1 (0.5, 0.2): original ,new (Slight positive shift, no contraction).

[0041] Keep point 2 (0.2, 0.5): original ,new (Not shrunken).

[0042] All key points met the criteria, all hold points did not shrink, and the convergence condition was satisfied, resulting in success in a single iteration. The deviation between the boundary movement predicted by the linear approximation and the actual simulation results was approximately 8%, which is within an acceptable range for engineering applications.

[0043] The method in this application transforms the problem into a single quadratic programming solution through linearization mapping. Under the same simulation accuracy, traditional genetic algorithms require 200 generations × 50 individuals = 10,000 complete simulations, each taking approximately 5 minutes, totaling about 35 days. This invention requires only about 30 active learning samples to construct the initial envelope surface. Each pruning iteration includes one QP solution (millisecond-level) and a small number of verification simulations (usually less than 10), with a total time consumption of about 3 hours, resulting in an overall efficiency improvement of approximately 280 times. In a two-dimensional conditional space, approximately 30 active learning samples are sufficient to construct an envelope surface that meets the accuracy requirements; for higher-dimensional conditional spaces, the number of active learning samples increases accordingly. increase( (in terms of dimensions), it is still far below the exponential growth required by genetic algorithms ( , (where the sampling resolution is per dimension), the efficiency advantage of this method becomes more significant as the dimension expands.

[0044] This application achieves, for the first time, directional expansion of functional boundaries through an explicit inequality constraint mechanism. Ten sets of comparative experiments show that traditional genetic algorithms cause unexpected shrinkage of non-target region boundaries in three sets (shrinkage range of 5%-15%), while the method in this application strictly maintains no shrinkage of non-target region boundaries in all cases (shrinkage range <1%), achieving a zero-shrinkage guarantee that is unattainable by existing technologies.

[0045] This application's sensitivity coefficient directly quantifies "how much the boundary moves with each unit change in parameter," making design adjustments transparent and traceable. The iterative strategy automatically decomposes significantly expanded requirements into multiple small adjustments that satisfy linear approximation conditions.

[0046] This application also proposes a radar detection functional boundary design system based on critical envelope surface trimming, including a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the radar detection functional boundary design method based on critical envelope surface trimming as described above.

[0047] It should be noted that, in the embodiments of this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0048] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0049] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0050] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims. All of these forms are within the protection scope of this application.

Claims

1. A radar detection functional boundary design method based on critical envelope surface trimming, characterized in that, include: Acquire radar detection performance data in a multi-dimensional condition space, which includes environmental clutter intensity, target radar cross-section, and target distance; Critical sample points are selected using an adaptive sampling strategy, and an implicit surface is fitted using a support vector machine to construct a critical envelope surface. The implicit surface is then normalized to a signed distance function, where regions with function values ​​less than 0 are defined as functional regions and regions with function values ​​greater than 0 are defined as functional failure regions. The signed range function is differentiated based on the implicit function theorem to establish a linear sensitivity mapping relationship between the changes in radar physical design parameters and the normal displacement of the critical envelope surface. Based on the expected functional boundary expansion requirements, the linear sensitivity mapping relationship is substituted into a constrained quadratic programming model to solve for the minimum design parameter adjustment amount that satisfies the performance preservation constraint in the non-target region. The radar hardware configuration is adjusted based on the minimum design parameters.

2. The radar detection functional boundary design method based on critical envelope surface trimming as described in claim 1, characterized in that, Using adaptive sampling strategies to select critical sample points includes: An active learning algorithm based on Gaussian process classification is used to analyze the detection performance data in terms of detection probability. Non-uniform sampling is performed near the transition boundary to reduce the number of simulation samples; To construct the critical envelope surface, implicit surfaces are fitted using support vector machines, including: Using support vector machines to fit the critical envelope surface And construct it as a signed distance function, for Perform gradient normalization to make it satisfy ,in Indicates the area where the function exists. Indicates the area where the function is disabled.

3. The radar detection functional boundary design method based on critical envelope surface trimming as described in claim 1, characterized in that, Establishing a linear sensitivity mapping relationship between changes in radar physical design parameters and the normal displacement of the critical envelope surface includes: Define radar main performance function For the detection statistic, where For condition variables, For design parameters; At any point on the critical envelope surface At the place, through the Perform a Taylor expansion on the result of 0 to derive the design parameters. Sensitivity coefficient to boundary normal movement The sensitivity coefficient The geometric distance by which the envelope expands outward or contracts inward due to unit parameter adjustment.

4. The radar detection functional boundary design method based on critical envelope surface trimming as described in claim 3, characterized in that, The sensitivity coefficient The calculation process includes: Through radar performance function For design parameters partial derivatives , and radar performance function condition variables gradient norm The ratio between them is used to obtain the normalized sensitivity coefficient. for: in, Boundary point The sensitivity coefficient at that location.

5. The radar detection functional boundary design method based on critical envelope surface trimming as described in claim 4, characterized in that, This also includes constructing constrained quadratic programming models: The objective function is to minimize the squared L2 norm of the design parameter adjustment vector. Set constraints for key expansion points It forces the envelope to expand into the target region in a specific direction; Set constraints for boundary preservation points. Limit the performance fluctuation range in non-target areas, where To reduce tolerance, To avoid over-expanding the tolerance; Add physical realizable constraints The physical realizable constraints include the upper limit of transmitter saturation power, the upper limit of ADC sampling rate, and the upper limit of filter bandwidth.

6. The radar detection functional boundary design method based on critical envelope surface trimming as described in claim 5, characterized in that, It also includes the following iterative solution steps: When the quadratic programming model solved in a single iteration has no feasible solution, the shrinkage tolerance is relaxed. Or reduce the desired normal movement proportionally. Continue until a feasible solution is found; Based on the adjusted parameters, local resampling verification is performed. If the actual movement does not reach the preset proportion of the expected value, the current envelope surface is used as the new initial surface, and sensitivity mapping is repeated until convergence.

7. The radar detection functional boundary design method based on critical envelope surface trimming as described in claim 3, characterized in that, The design parameter p includes: RF link parameters, including low-noise amplifier bias voltage, transmitter peak power, and phase shifter phase weights; Signal processing parameters include the number of pulse accumulations, the constant false alarm rate detection threshold factor, and the Doppler filter order; Beam scanning parameters include the excitation amplitude of the phased array antenna elements and the scanning angle grid density.

8. A radar detection functional boundary design system based on critical envelope surface trimming, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, which, when executed by the processor, implements the steps of the radar detection functional boundary design method based on critical envelope surface trimming as described in any one of claims 1 to 7.

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