Ultrasonic phased array sparse arrangement method

Abstract

The invention relates to the technical field of ultrasound, in particular to an ultrasonic phased array sparse arraying method. Comprising the following steps: firstly, constructing a planar rectangular ultrasonic array model and determining basic parameters; setting a fitness function by taking a minimum maximum sidelobe level (MSLL) as an optimization criterion; secondly, introducing a tent chaotic mapping-good point set mixing method to obtain a classical solution population; a quantum bit coding strategy is introduced in the coding stage, individuals in the population are expressed as quantum bits, a standard NOA strategy is executed on the classical solution population to update the population, then the update quantity is synchronized to the quantum bits, and finally a new generation of classical solution population is generated through quantum rotation and collapse operation and the fitness is evaluated; integrating a covariance matrix adaptive evolution strategy (CMA-ES) in the optimization iteration process, and dynamically adjusting the shape, direction and step length of search distribution; and finally updating the global optimum. According to the method, the array element distribution of the sparse array is optimized through the multi-strategy fusion ENOA algorithm, the peak side lobe level of the array can be remarkably reduced, the anti-interference capability and precision of target detection are improved, and meanwhile, the hardware cost of the array is reduced.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic technology, and specifically to a method for sparse arraying of ultrasonic phased arrays. Background Technology

[0002] Detection of low-slow-small (LSS) targets is a core challenge in national defense and urban security. In military applications, these targets (such as micro-aircraft and balloons) possess ultra-low-altitude penetration characteristics, limiting traditional radar systems due to the Earth's curvature blind zone and complex multipath effects. Furthermore, their active electromagnetic radiation easily reveals the location of the radar array. In the civilian security field, sensitive facilities (airports, nuclear power plants, urban core areas, etc.) face the threat of LSS target intrusion. However, optoelectronic monitoring is constrained by lighting and weather conditions, and existing acoustic arrays are difficult to scale up due to the high cost of high-density deployment and the deterioration of sidelobe performance.

[0003] Existing detection technologies face significant bottlenecks when dealing with LSS targets. While lidar boasts high precision, it suffers from inherent blind spots at close range, and complex multipath interference in low-altitude environments further exacerbates its positioning errors. Optical detection methods are highly dependent on ambient light; their performance drops sharply or even fails under adverse weather conditions such as nighttime or fog. Among acoustic detection methods, ultrasonic sparse arrays, as a radar-assisted means, offer advantages such as strong passive detection concealment, sensitivity to non-metallic targets, and coverage of radar blind spots. However, existing sparse array schemes often sacrifice array performance to reduce costs, leading to a significant increase in peak sidelobe level (PSLL) and a surge in false alarm rates under battlefield wind noise, mechanical vibration, and other interference.

[0004] Existing technologies employ classical mathematical methods, intelligent optimization algorithms, and hybrid optimization strategies to suppress the rise in sidelobe levels. The document CN116796640B discloses an "Improved Snake Optimization Algorithm for Suppressing Sidelobe Level Rise," whose core scheme includes: using a Sobol sequence to generate a uniform initial population instead of random initialization to improve solution space coverage; introducing a Cauchy mutation strategy to actively escape local optima; designing a nonlinear update function to dynamically balance global exploration and local exploitation; and optimizing element distribution using the minimization of the maximum sidelobe level (MSLL) as the fitness function. However, this method has significant drawbacks: the convergence speed fluctuates severely, being 145.23% slower than Particle Swarm Optimization (PSO) in cylindrical array optimization and even 500% slower in ring arrays; it relies on unquantized environmental temperature parameters to determine snake behavior patterns (fighting / mating), resulting in insufficient engineering robustness; the actual sidelobe suppression effect is limited (azimuth angle -14.6dB, an improvement of less than 2dB compared to PSO), and it fails to overcome the performance bottleneck of traditional methods. Summary of the Invention

[0005] This invention provides a sparse array method for ultrasonic phased arrays to solve the problem of array performance degradation that occurs in the process of reducing costs of traditional ultrasonic arrays, especially the problem of a significant increase in peak sidelobe level.

[0006] To achieve the above objectives, the technical solution of the present invention is: a method for sparse arraying of ultrasonic phased arrays, comprising the following steps:

[0007] Step 1: Construct a rectangular planar ultrasound array and determine the basic parameters of the array;

[0008] Step 2: Using minimizing the maximum sidelobe level as the optimization criterion, set the fitness function and establish a mathematical model for the optimization function;

[0009] Step 3: In the initialization phase of the NOA algorithm, the tent chaotic mapping-optimal point set hybrid method is introduced to obtain the classical solution population;

[0010] Step 4: In the encoding stage, a qubit encoding strategy is introduced to represent individuals in the population as qubits; the standard NOA strategy is applied to the classical solution population to update the population, and the update is then synchronized to the qubits. Finally, a new generation of classical solution population is generated through quantum rotation and collapse operations, and its fitness is evaluated.

[0011] Step 5: In the iteration phase, an adaptive mechanism for the covariance matrix is ​​introduced to calculate the fitness of the new classical solution population, select the individual with the smallest fitness, and dynamically adjust the shape, direction, and step size of the search distribution.

[0012] Step 6: Finally, update the global optimum to obtain a low sidelobe, high gain radiation pattern and array element position pattern.

[0013] Furthermore, the specific method of the tent chaotic mapping-optimal point set hybrid approach in step three above is as follows:

[0014] 3.1 First, a chaotic sequence with a population size of N is generated using the Tent chaotic map, where each component is between [0,1]. The expression is as follows:

[0015]

[0016] Where, x i It is the value of the i-th iteration, a represents the shape of the control mapping, ξ ~ U(0,10) -4 ) represents a small perturbation;

[0017] Then, a sequence with a population size of N is generated using the optimal point set, where each component is between [0,1]. In d-dimensional space, the coordinates of the k-th point in the optimal point set are:

[0018]

[0019] Where, p j Let j be the j-th prime number, and {·} denote taking the fractional part;

[0020] 3.2 By mixing the Tent chaotic map with the sequence of optimal point sets and mapping it to the search space, we obtain the classical solution population, expressed as follows:

[0021]

[0022] Where β is the mixture weight, taking a value between 0 and 1, U j ,L j This represents the boundary of the search space.

[0023] Furthermore, the specific steps of step four above include:

[0024] 4.1 Introduce a qubit encoding strategy during the encoding stage to represent individuals in the population as qubits:

[0025] The classical solution space is linearly mapped to the qubit angle space, such that each classical solution corresponds to a quantum state. Let the classical population be P = {X1, X2, ..., X}. N}, where X i ={x i1 ,x i2 ,…,x id}and x ij ∈[L j U j ]; Each individual Q in the quantum bit population Q i Represented by a set of qubit angles:

[0026]

[0027] 4.2 Update the four strategies (foraging strategy, storage strategy, cache search strategy, and recovery strategy) of the standard NOA for the current classical solution population P to obtain a new classical solution population P. new ,Right now

[0028] P new =S_NOA(P,t)

[0029] Where t is the current iteration number;

[0030] Calculate the update amount for each individual in the classical solution space:

[0031] ΔX i =P new,i -X i

[0032] Among them, X i It's the classic solution before the update, P new,i It is the updated classic solution;

[0033] The updates of NOA in the classical solution space are synchronized to the qubit population, causing the quantum states to move in the search direction of NOA; the update amounts are mapped proportionally to the qubit angle space.

[0034]

[0035] Updated from a quantum bit perspective:

[0036]

[0037] Where η is the learning rate, used to control the update magnitude;

[0038] 4.3 The quantum rotation gate operation rotates the qubits towards the global optimum by adjusting their angles. First, the rotation angle is calculated:

[0039]

[0040] Where, θ best,j γ is the qubit angle corresponding to the global optimal solution, γ is the perturbation coefficient, and N(0,1) is a random number from the standard normal distribution.

[0041] Update the qubit angle and crop it to the range [0, π / 2].

[0042]

[0043] The collapse process of the quantum state transforms the probability amplitude represented by the qubit into a deterministic classical solution in order to evaluate fitness (minimize the maximum sidelobe); observing the qubit population yields a new classical solution population:

[0044]

[0045] Furthermore, step five above introduces an adaptive covariance matrix mechanism in the standard NOA recovery strategy phase:

[0046] 5.1 Calculate the fitness f(X) for the current classical solution population P. i By selecting the μ individuals with the smallest fitness, elite selection ensures that subsequent operations are based on high-quality solutions, thus improving search efficiency.

[0047] P elite ={X (1) ,X (2) ,…,X (μ)}, where f(X) (1) )≤f(X (2) )≤…≤f(X (μ) );

[0048] 5.2 Calculate the mean vector, which represents the distribution center of the elite population and serves as a reference point for generating new solutions:

[0049]

[0050] 5.3 Calculate the covariance matrix. The covariance matrix describes the variance and covariance of the elite population across various dimensions, reflects the spatial distribution shape of the solutions, and guides the direction of new individual generation.

[0051]

[0052] 5.4 Generate λ new individuals based on the distribution information of the elite population, and conduct a directed search around the elite solutions to balance exploration and exploitation:

[0053] X new,k =m+σ·N(0,C),k=1,...,λ

[0054] Where N(0,C) represents a multidimensional normal distribution with a mean of 0 and a covariance matrix of C, and σ is the step size.

[0055] Furthermore, step six above updates the global optimum by comparing it with the current optimal solution X. best And the current population's optimal solution, record the best solution found during the search process as the output result:

[0056]

[0057] Furthermore, the above-mentioned planar rectangular array has M·N elements, a wavelength of λ, an element spacing of λ / 2, and elements with equal amplitude and direction. Its radiation pattern function is expressed as:

[0058]

[0059] Where, d m d represents the distance between the (m,n)th array element and the (0,0)th reference array element in the direction position. n The elevation distance between the (m,n)th array element and the (0,0)th reference array element. (φ0,θ0) represents the direction of the maximum value of the array's main beam, α mn Let Δφ represent the phase of the (m,n)th element. mn This represents the phase difference between the (m,n)th array element and the (0,0)th reference array element.

[0060] Furthermore, the fitness function in step two above is expressed as:

[0061]

[0062] Where max represents the function for finding the maximum value, S1 represents the side lobe interval of the azimuth pattern when θ = θ0, and S2 represents the side lobe interval of the pitch pattern when φ = φ0.

[0063] Furthermore, the optimization function for minimizing the maximum sidelobe level in step two above is:

[0064]

[0065] Here, min represents the minimum value function. By optimizing the value of f, the position of the array elements is optimized so that the sum of the maximum sidelobe level of the azimuth pattern and the maximum sidelobe level of the pitch pattern of the planar rectangular array is minimized.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] 1. At the algorithm architecture level of this invention, the hybrid initialization strategy of Tent chaotic mapping and optimal point set breaks through the limitations of traditional random initialization, generates a highly diverse population, and avoids premature convergence from the root. The quantum-classical dual-space collaborative mechanism combines collapse observation and NOA strategy to balance the breadth of global exploration and the depth of local development. This architecture significantly improves the robustness of the algorithm, ensures efficient and stable convergence characteristics in complex solution spaces, and greatly optimizes the solution efficiency.

[0068] 2. This invention reduces the maximum sidelobe level of an ultrasonic phased array by coupling a qubit encoding strategy with a covariance matrix adaptive evolution strategy (CMA-ES), solving the problem of sidelobe performance degradation in traditional sparse arrays. Quantum rotating gate operation guides intelligent jumps in the solution space, and combined with CMA-ES to dynamically adjust the search step size and distribution direction, it enhances sidelobe suppression capabilities to a new level while ensuring main lobe gain, significantly improving the recognition accuracy and anti-interference capability for low, slow, and small targets in complex noise environments.

[0069] 3. This scheme, based on standard NOA, combines chaotic initialization, quantum jumps, and CMA-ES adaptive optimization. It is entirely based on mathematical and algorithmic principles, without relying on difficult-to-quantify or volatile external environmental parameters (such as temperature), significantly improving the algorithm's engineering applicability and deployment robustness. A qubit encoding strategy is introduced in the encoding stage, utilizing quantum rotation gate operations to adjust individual states, effectively balancing local fine-grained search with global broad exploration, avoiding premature convergence. During the optimization iteration process, a covariance matrix adaptive evolution strategy (CMA-ES) is integrated to dynamically adjust the search direction, step size, and distribution shape, significantly improving the algorithm's optimization efficiency and stability in complex solution spaces, achieving a dynamic balance between global exploration and local development.

[0070] 4. The present invention innovatively achieves synergistic optimization of hardware cost and performance. The sparse array design significantly reduces the number of physical array elements, and reduces material costs while maintaining array aperture and beamwidth, providing technical support for the application of ultrasonic phased arrays in low-cost scenarios such as large-scale security deployment and UAV-borne equipment.

[0071] 5. This invention leverages the advantages of acoustic detection. Compared to radar that relies on active electromagnetic radiation or optical detection technologies that are limited by illumination, acoustic arrays possess unique sensitivity to non-metallic targets and completely avoid the risk of electromagnetic exposure. Its environmental robustness is outstanding, exhibiting minimal performance fluctuations under extreme conditions such as rain, fog, and darkness, effectively covering the blind spots of traditional detection methods and providing an all-weather solution for urban security and military defense. Attached Figure Description

[0072] Figure 1 This is a comparison chart of the convergence performance of the algorithm of this invention;

[0073] Figure 2 A comparison diagram of the elevation orientation of array elements with a sparsity of 36%;

[0074] Figure 3 Comparison diagram of the orientation positions of array elements with a sparsity of 36%;

[0075] Figure 4 This is a diagram showing the position distribution of array elements with a sparsity of 36% according to the present invention. Detailed Implementation

[0076] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0077] Example: A method for sparse arraying of ultrasonic phased arrays, the specific steps of which are as follows:

[0078] Step 1: Construct a rectangular planar ultrasound array and determine the basic parameters of the array:

[0079] The rectangular planar ultrasonic array in this embodiment is an array with uniformly spaced elements. The basic parameters of the array include the number of elements, the element spacing, and the array aperture. Specifically, in this embodiment, the radiation pattern function of the planar rectangular array is set with 10*10 elements, wavelength λ, element spacing λ / 2, and elements of equal amplitude and direction. The radiation pattern function of the planar rectangular array can be expressed as:

[0080]

[0081] Where, d m d represents the distance between the (m,n)th array element and the (0,0)th reference array element in the direction position.n The elevation distance between the (m,n)th array element and the (0,0)th reference array element. (φ0,θ0) represents the direction of the maximum value of the array's main beam, α mn Let Δφ represent the phase of the (m,n)th element. mn This represents the phase difference between the (m,n)th array element and the (0,0)th reference array element.

[0082] Step 2: Using minimizing the maximum sidelobe level as the optimization criterion, set the fitness function and establish a mathematical model for the optimization function;

[0083] Based on the definition of maximum sidelobe level, the fitness function is taken as the sum of the maximum sidelobe level in the azimuth pattern and the maximum sidelobe level in the pitch pattern:

[0084]

[0085] Where max represents the function for finding the maximum value, S1 represents the sidelobe interval of the azimuth pattern when θ = θ0, and S2 represents the sidelobe interval of the pitch pattern when φ = φ0.

[0086] To minimize the maximum sidelobe level, the mathematical model of the optimization function is:

[0087]

[0088] Here, min represents the minimum value function. By optimizing the value of f, the position of the array elements is optimized so that the sum of the maximum sidelobe level of the azimuth pattern and the maximum sidelobe level of the pitch pattern of the planar rectangular array is minimized.

[0089] Step 3: In the initialization phase of the NOA algorithm, the tent chaotic mapping-optimal point set hybrid method is introduced to obtain the classical solution population;

[0090] 3.1tent Chaotic Mapping - Best Point Set Hybridization Method:

[0091] First, a chaotic sequence with a population size of 100 is generated using the Tent chaotic map, where each component is between [0,1]. The expression is as follows:

[0092]

[0093] Where, x i It is the value of the i-th iteration, a represents the shape of the control mapping, ξ ~ U(0,10) -4 () represents a small perturbation.

[0094] Then, a sequence with a population size of 100 is generated using the optimal point set, where each component is between [0,1]. In d-dimensional space, the coordinates of the k-th point in the optimal point set are:

[0095]

[0096] Where, p j Let j be the j-th prime number, and {·} denote taking the fractional part.

[0097] 3.2 By mixing the Tent chaotic map with the sequence of optimal point sets and mapping it to the search space, we obtain the classical solution population, expressed as follows:

[0098]

[0099] Where β = 0.6 is the mixed weight, U j ,L j This represents the boundary of the search space.

[0100] Step 4: In the encoding stage, a qubit encoding strategy is introduced to represent individuals in the population as qubits; the standard NOA strategy is applied to the classical solution population to update the population, and the update is then synchronized to the qubits. Finally, a new generation of classical solution population is generated through quantum rotation and collapse operations, and its fitness is evaluated.

[0101] 4.1 Introduce a qubit encoding strategy during the encoding stage to represent individuals in the population as qubits:

[0102] The classical solution space is linearly mapped to the qubit angle space, such that each classical solution corresponds to a quantum state. Let the classical population be P = {X1, X2, ..., X}. N}, where X i ={x i1 ,x i2 ,…,x id}and x ij ∈[L j U j ]. Each individual Q in the quantum bit population Q. i Represented by a set of qubit angles:

[0103]

[0104] 4.2 Update the four strategies (foraging strategy, storage strategy, cache search strategy, and recovery strategy) of the standard NOA for the current classical solution population P to obtain a new classical solution population P. new ,Right now

[0105] P new =S_NOA(P,t)

[0106] Where t is the current iteration number.

[0107] Calculate the update amount for each individual in the classical solution space:

[0108] ΔXi =P new,i -X i

[0109] Among them, X i It's the classic solution before the update, P new,i It is the updated classic solution.

[0110] The updates of NOA in the classical solution space are synchronized to the qubit population, causing the quantum states to move in the search direction of NOA. The update amounts are then mapped proportionally to the qubit angle space.

[0111]

[0112] Updated from a quantum bit perspective:

[0113]

[0114] Where η is the learning rate, used to control the update magnitude.

[0115] 4.3 The quantum rotation gate operation rotates the qubits towards the global optimum by adjusting their angles. First, the rotation angle is calculated:

[0116]

[0117] Where, θ best,j γ is the qubit angle corresponding to the global optimal solution, γ is the perturbation coefficient, and N(0,1) is a random number from a standard normal distribution.

[0118] Update the qubit angle and crop it to the range [0, π / 2].

[0119]

[0120] The collapse process of the quantum state transforms the probability amplitude represented by the qubit into a deterministic classical solution for evaluating fitness (minimizing the maximum sidelobe). Observing the qubit population yields a new classical solution population:

[0121]

[0122] Step 5: In the standard NOA recovery strategy stage, an adaptive mechanism based on the covariance matrix is ​​introduced to calculate the fitness of the new classical solution population, select the individual with the smallest fitness, and achieve efficient balance between global exploration and local exploitation in the complex solution space by dynamically adjusting the shape, direction, and step size of the search distribution.

[0123] 5.1 Calculate the fitness f(X) for the current classical solution population P. i By selecting the μ individuals with the smallest fitness, elite selection ensures that subsequent operations are based on high-quality solutions, thus improving search efficiency.

[0124] P elite ={X (1) ,X (2) ,…,X (μ)}, where f(X) (1) )≤f(X (2) )≤…≤f(X (μ) )

[0125] 5.2 Calculate the mean vector, which represents the distribution center of the elite population and serves as a reference point for generating new solutions:

[0126]

[0127] 5.3 Calculate the covariance matrix. The covariance matrix describes the variance and covariance of the elite population across various dimensions, reflects the spatial distribution shape of the solutions, and guides the direction of new individual generation.

[0128]

[0129] 5.4 Generate λ new individuals based on the distribution information of the elite population, and conduct a directed search around the elite solutions to balance exploration and exploitation:

[0130] X new,k =m+σ·N(0,C),k=1,…,λ

[0131] Where N(0,C) represents a multidimensional normal distribution with a mean of 0 and a covariance matrix of C, and σ is the step size.

[0132] Step 6: Update the global optimum and compare it with the current optimal solution X. best And the current population's optimal solution, record the best solution found during the search process as the output result:

[0133]

[0134] The effects of this invention are further illustrated by the following simulation experiments:

[0135] This invention employs a hybrid initialization strategy combining Tent chaotic mapping and optimal point sets to generate a highly diverse initial population. During the encoding phase, a qubit encoding strategy is introduced, utilizing quantum rotation gate operations to adjust individual states, effectively balancing local fine-grained search with global broad exploration, thus preventing premature convergence. In the optimization iteration process, a covariance matrix adaptive evolution strategy (CMA-ES) is integrated to dynamically control the search direction, step size, and distribution shape, significantly improving the algorithm's optimization efficiency and stability in complex solution spaces, achieving a dynamic balance between global exploration and local exploitation. This invention optimizes the element distribution of sparse arrays using the ENOA algorithm fused with the above multi-strategy approach, significantly reducing the array's peak sidelobe level, improving the anti-interference capability and accuracy of target detection, while simultaneously reducing array hardware costs.

[0136] 1) To verify the optimization performance of ENOA, Particle Swarm Optimization (PSO) and NOA algorithms were used as benchmarks for comparison. To ensure the rigor of the test, all parameters were set uniformly: population size 80, number of iterations 300. Figure 1 As shown in the convergence curves of different algorithms, ENOA has significantly improved in convergence speed and solution accuracy compared to PSO and NOA.

[0137] 2) Simulation content

[0138] Simulation parameter settings: the number of uniform planar rectangular array elements is 10*10, the minimum array element spacing is half a wavelength, the elevation and azimuth angle scanning range is ±180°, the population size is 100, and the maximum number of iterations is 500.

[0139] Based on the parameter settings, construct the objective function and constraints of the planar rectangular array according to step two.

[0140] According to the method of the present invention, the array element coordinates are dynamically adjusted through 500 iterations (the quantum rotation gate jump solution space and covariance matrix adaptively control the search step size), and the array element position distribution map that minimizes the sum of the maximum sidelobe levels in the azimuth and elevation directions is output.

[0141] Figure 2 In the directional dimension, the performance of full array gain, NOA sparse gain, and ENOA sparse gain at ±180° scan angles was compared after removing 36 elements from a 100-element array (retaining 64). It can be clearly seen that, while keeping the main lobe width unchanged, the ENOA sparse array has the lowest sidelobes.

[0142] Figure 3 In the pitch dimension, the performance of full array gain, NOA sparse gain, and ENOA sparse gain at ±45° scan angles was compared after removing 36 array elements from a 100-element array (retaining 64). With a 36% reduction in array elements, the main lobe width sacrificed less than 20% (2.1° vs 1.8°), and the sidelobe suppression of -22.6dB met the requirements of most scenarios.

[0143] Figure 4 The optimized sparse array position distribution diagram of the method of the present invention is given. It can be seen that the number of active array elements is 64.

[0144] The above results demonstrate the advantages of the method of the present invention in sparsely adjusting the array element positions, achieving better sidelobe suppression effect while significantly reducing the number of array elements.

[0145] The above description is a specific illustration of the present invention, and not a limitation thereof. Those skilled in the art can make various equivalent technical solutions without departing from the scope of the present invention; therefore, all equivalent technical solutions should be included within the protection scope of the present invention.

Claims

1. A method for sparse arraying of ultrasonic phased arrays, characterized in that: Includes the following steps Step 1: Construct a rectangular planar ultrasound array and determine the basic parameters of the array; Step 2: Using minimizing the maximum sidelobe level as the optimization criterion, set the fitness function and establish a mathematical model for the optimization function; Step 3: In the initialization phase of the NOA algorithm, the tent chaotic mapping-optimal point set hybrid method is introduced to obtain the classical solution population; Step 4: In the encoding stage, a qubit encoding strategy is introduced to represent individuals in the population as qubits; the standard NOA strategy is applied to the classical solution population to update the population, and the update is then synchronized to the qubits. Finally, a new generation of classical solution population is generated through quantum rotation and collapse operations, and its fitness is evaluated. Step 5: In the iteration phase, an adaptive mechanism for the covariance matrix is ​​introduced to calculate the fitness of the new classical solution population, select the individual with the smallest fitness, and dynamically adjust the shape, direction, and step size of the search distribution. Step 6: Finally, update the global optimum to obtain a low sidelobe, high gain radiation pattern and array element position pattern.

2. The method for sparse arraying of an ultrasonic phased array according to claim 1, characterized in that, The specific method of the tent chaotic mapping-optimal point set hybrid method in step three is as follows: 3.1 First, a chaotic sequence with a population size of N is generated using the Tent chaotic map, where each component is between [0,1]. The expression is as follows: Where, x i It is the value of the i-th iteration, a represents the shape of the control mapping, ξ ~ U(0,10) -4 ) represents a small perturbation; Then, a sequence with a population size of N is generated using the optimal point set, where each component is between [0,1]. In d-dimensional space, the coordinates of the k-th point in the optimal point set are: Where, p j Let j be the j-th prime number, and {·} denote taking the fractional part; 3.2 By mixing the Tent chaotic map with the sequence of optimal point sets and mapping it to the search space, we obtain the classical solution population, expressed as follows: Where β is the mixture weight, taking a value between 0 and 1, U j ,L j This represents the boundary of the search space.

3. The method for sparse arraying of an ultrasonic phased array according to claim 1, characterized in that: The specific steps of step four include: 4.1 Introduce a qubit encoding strategy during the encoding stage to represent individuals in the population as qubits: The classical solution space is linearly mapped to the qubit angle space, such that each classical solution corresponds to a quantum state. Let the classical population be P = {X1, X2, ..., X}. N }, where X i ={x i1 ,x i2 ,…,x id }and x ij ∈[L j U j ]; Each individual Q in the quantum bit population Q i Represented by a set of qubit angles: 4.2 Update the four strategies (foraging strategy, storage strategy, cache search strategy, and recovery strategy) of the standard NOA for the current classical solution population P to obtain a new classical solution population P. new ,Right now P new =S_NOA(P,t) Where t is the current iteration number; Calculate the update amount for each individual in the classical solution space: ΔX i =P new,i -X i Among them, X i It's the classic solution before the update, P new,i It is the updated classic solution; The updates of NOA in the classical solution space are synchronized to the qubit population, causing the quantum states to move in the search direction of NOA; the update amounts are mapped proportionally to the qubit angle space. Updated from a quantum bit perspective: Where η is the learning rate, used to control the update magnitude; 4.3 The quantum rotation gate operation rotates the qubits towards the global optimum by adjusting their angles. First, the rotation angle is calculated: Where, θ best,j γ is the qubit angle corresponding to the global optimal solution, γ is the perturbation coefficient, and N(0,1) is a random number from the standard normal distribution. Update the qubit angle and crop it to the range [0, π / 2]. The collapse process of the quantum state transforms the probability amplitude represented by the qubit into a deterministic classical solution in order to evaluate fitness (minimize the maximum sidelobe); observing the qubit population yields a new classical solution population:

4. The method for sparse arraying of an ultrasonic phased array according to claim 1, characterized in that: Step five introduces a covariance matrix adaptive mechanism in the standard NOA recovery strategy phase: 5.1 Calculate the fitness f(X) for the current classical solution population P. i By selecting the μ individuals with the smallest fitness, elite selection ensures that subsequent operations are based on high-quality solutions, thus improving search efficiency. P elite ={X (1) ,X (2) ,…,X (μ) }, where f(X) (1) )≤f(X (2) )≤…≤f(X (μ) ) 5.2 Calculate the mean vector, which represents the distribution center of the elite population and serves as a reference point for generating new solutions: 5.3 Calculate the covariance matrix. The covariance matrix describes the variance and covariance of the elite population across various dimensions, reflects the spatial distribution shape of the solutions, and guides the direction of new individual generation. 5.4 Generate λ new individuals based on the distribution information of the elite population, and conduct a directed search around the elite solutions to balance exploration and exploitation: X new,k =m+σ·N(0,C),k=1,...,λ Where N(0,C) represents a multidimensional normal distribution with a mean of 0 and a covariance matrix of C, and σ is the step size.

5. The method for sparse arraying of an ultrasonic phased array according to claim 1, characterized in that: Step six updates the global optimum and compares it with the current optimal solution X. best And the current population's optimal solution, record the best solution found during the search process as the output result:

6. The method for sparse arraying of an ultrasonic phased array according to claim 1, characterized in that: In step one, the planar rectangular array has M·N elements, a wavelength of λ, an element spacing of λ / 2, and the elements are of equal amplitude and orientation. Its radiation pattern function is expressed as: Where, d m d represents the distance between the (m,n)th array element and the (0,0)th reference array element in the direction position. n The elevation distance between the (m,n)th array element and the (0,0)th reference array element. (φ0,θ0) represents the direction of the maximum value of the array's main beam, α mn Let Δφ represent the phase of the (m,n)th element. mn This represents the phase difference between the (m,n)th array element and the (0,0)th reference array element.

7. The method for sparse arraying of an ultrasonic phased array according to claim 1, characterized in that: The fitness function in step two is expressed as follows: Where max represents the function for finding the maximum value, S1 represents the side lobe interval of the azimuth pattern when θ = θ0, and S2 represents the side lobe interval of the pitch pattern when φ = φ0.

8. The method for sparse arraying of an ultrasonic phased array according to claim 1, characterized in that: The optimization function for minimizing the maximum sidelobe level in step two is: Here, min represents the minimum value function. By optimizing the value of f, the position of the array elements is optimized so that the sum of the maximum sidelobe level of the azimuth pattern and the maximum sidelobe level of the pitch pattern of the planar rectangular array is minimized.

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