A delay accuracy control method for ultrasonic phased array system based on iterative optimization

Abstract

The present invention discloses a delay accuracy control method for an ultrasonic phased array system based on iterative optimization, and the specific steps are as follows: S1: using interval folding to pre-process the transmission or reception deflection angle θ collected by the ultrasonic phased array system, and converting the deflection angle θ into an equivalent angle θ' between 0≤θ≤π / 4; S2: inputting the pre-processed equivalent angle into a calculation unit and performing conventional iterative calculation using the CORDIC calculation method; S3: using the CORDIC calculation method to continue to perform jump iterative calculation of the cosine value of the equivalent angle, and each iteration matches the nearest residual angle z i The preselected angle θ i,n Calculate until z i ≤Minimum fixed angle θ min The iteration is ended and the cosine value of the deflection angle θ is output. The present invention can optimize the number of iterative calculations of the deflection angle and the calculation accuracy of the high delay amount, thereby ensuring that the problem of reducing the internal resource consumption of the FPGA is reduced while obtaining the high-precision delay amount.

Description

Technical Field

[0001] The present invention belongs to the field of phase control of ultrasonic phased array systems, and in particular relates to a delay accuracy control method of an ultrasonic phased array system based on iterative optimization. Background Art

[0002] Ultrasonic phased array systems utilize a number of piezoelectric elements to form an array transducer. By controlling the phase delay between each element's emission and reception of ultrasonic waves, various phased effects, such as focusing and deflecting the ultrasonic coherent beam, are achieved. Therefore, relative delay resolution plays a decisive role in the focusing effect of the phased array. The key technology of ultrasonic phased arrays lies in precisely controlling the phase of the transmitted and received signals to achieve focusing and deflection.

[0003] Traditional ultrasonic phased array systems often use hardware delay technologies, such as LC networks or dedicated delay chips, to achieve phase delay. However, LC networks typically require large LC delay lines and complex switching circuits, resulting in poor interference immunity. Dedicated delay chips also have low integration and portability, and their control is difficult to modify. Therefore, digital delay technology, due to its high resolution, ease of control, and excellent stability, has gradually replaced hardware delay technology as the primary delay control technology for ultrasonic phased array systems.

[0004] Currently, the dynamic focusing algorithm processed by the FPGA module of an ultrasonic phased array system involves the real-time solution of numerous sine and cosine functions. The main methods for solving these functions are the lookup table method, the Taylor series expansion method, and the coordinate rotation digital computation (CORDIC) method. As the precision requirements of applications increase, the series method and the lookup table method struggle to meet the required accuracy and speed. The CORDIC algorithm, however, fully leverages the computing characteristics of hardware and can simplify the nonlinear operations of some complex functions into iterative calculations of addition, subtraction, and shift operations. This optimized solution combines hardware and algorithms, offering advantages such as low resource usage and controllable precision.

[0005] The traditional CORDIC algorithm's computational accuracy gradually decreases with increasing iterations. Due to bit width limitations, further accuracy improvement becomes difficult after reaching a certain number of iterations. Furthermore, increasing iterations, while improving accuracy, also results in a significant increase in area and computational time. Therefore, how to optimally configure the number of CORDIC iterations to meet accuracy requirements while minimizing FPGA internal resource consumption has become a key concern for those skilled in the art. Summary of the Invention

[0006] In response to the above technical problems, the present invention discloses a delay accuracy control method for an ultrasonic phased array system based on iterative optimization, which can optimize the number of iterative calculations of the deflection angle and the calculation accuracy of the high delay amount, thereby ensuring that while obtaining a high-precision delay amount, the internal resource consumption of the FPGA is reduced.

[0007] The specific technical solutions of the present invention are as follows:

[0008] A delay accuracy control method for an ultrasonic phased array system based on iterative optimization, the specific steps are as follows:

[0009] S1: pre-processing the transmission or reception deflection angle θ collected by the ultrasonic phased array system by using interval folding, and converting the deflection angle θ into an equivalent angle θ' within the range of 0≤θ≤π / 4;

[0010] S2: Input the pre-processed equivalent angle into the calculation unit, use the CORDIC calculation method to perform conventional iterative calculation of the cosine value and output the modulus factor K C , after each iteration, the modulus factor K C The error Ω is compared with the preset accuracy ε. If Ω≤ε, the condition is met and the iteration ends and step S3 is performed. Otherwise, the iterative calculation continues.

[0011] S3: Use the CORDIC calculation method to continue to jump and iterate the cosine value of the equivalent angle, and each iteration matches the closest residual angle z i The preselected angle θ i,n Calculate until z i ≤Minimum fixed angle θ min End the iteration and output the cosine value of the deflection angle θ.

[0012] Preferably, the iteration method in S2 is as follows:

[0013] S2-1: Based on the known preselected angle set {θ i , i=0,1,2,…,m}, where the preselected angles are arranged in descending order. After the preselected angles are converted into fixed-point numbers, the highest bit of the binary number of each preselected angle is shifted right one bit as i increases. The number of iterations is initialized to C=1, i=0, and the preselected angle θ is selected using the CORDIC calculation method. i Calculate the trigonometric function value of the input equivalent angle and output the corresponding modulus factor K C ;

[0014] S2-2: Calculate the modulus factor error Ω, as shown in formula (1):

[0015] Ω=|K C -K| (1);

[0016] Where K is a fixed constant value;

[0017] S2-3: Compare the modulus factor error Ω with the preset accuracy ε. If Ω≤ε, output C and enter step S3 for jump iteration. Otherwise, set C=C+1, i=i+1 and return to step S2-1 for iterative operation.

[0018] Preferably, the jump iteration method in S3 is as follows:

[0019] S3-1: Initialize the jump iteration number n=1, i=C, based on the output result of step S2, from the preselected angle set {θ C ,θ C+1 ,…,θ m}Select the preselected angle θ i,n Calculate the residual angle z according to formula (2) i :

[0020] z i =θ'-θ i,n (2);

[0021] Among them, θ' is the equivalent angle, θ i,n Indicates that at the nth iteration, in the preselected angle set {θ C ,θ C+1 ,…,θ m} the i-th preselected angle in;

[0022] S3-2: Let θ i,n The number of the most significant bits of the corresponding binary number except the sign bit is j. When the residual angle z i >0, the preselected angle θ i,n The binary code uses the original code to determine whether jn is equal to 0. If not, set n = n + 1, i = i + 1 and return to step S3-1 to recalculate the residual angle z i If so, select the current θ i,n As the closest residual angle z i The preselected angle goes to step S3-3, when the residual angle z i <0, the preselected angle θ i,n The binary code uses the complement code to determine whether jn is equal to 0. If not, set n = n + 1, i = i + 1 and return to step S3-1 to recalculate the residual angle z i If so, select the current θ i,n As the closest residual angle z i The preselected angle goes to step S3-3;

[0023] S3-2: According to the preselected angle θ i,n The trigonometric function values ​​of the equivalent angle θ' are calculated using the CORDIC calculation method;

[0024] S3-3: Determine the residual angle z i Is ≤θ m If not, set i=i+1 and return to step S3-1 to recalculate the residual angle z i , select the angle closest to the residual angle z i Otherwise, the iteration ends and the trigonometric function value of the equivalent angle θ' is output, which is the trigonometric function value of the deflection angle θ.

[0025] Preferably, the interval folding process in S1 is as follows:

[0026] When the input deflection angle is 0≤θ≤π / 4, the equivalent angle θ'=θ;

[0027] When the input deflection angle is π / 4≤θ≤π / 2, the equivalent angle θ'=π / 2-θ;

[0028] When the input deflection angle is π / 2≤θ≤3π / 4, the equivalent angle θ'=θ-π / 2;

[0029] When the input deflection angle is 3π / 4≤θ≤π, the equivalent angle θ'=π-θ;

[0030] When the input deflection angle is π≤θ≤5π / 4, the equivalent angle θ'=θ-π;

[0031] When the input deflection angle is 5π / 4≤θ≤3π / 2, the equivalent angle θ'=3π / 2-θ;

[0032] When the input deflection angle is 3π / 2≤θ≤7π / 4, the equivalent angle θ'=θ-3π / 2;

[0033] When the input deflection angle is 7π / 4≤θ≤2π, the equivalent angle θ'=2π-θ.

[0034] Beneficial effects: The present invention discloses a delay accuracy control method for an ultrasonic phased array system based on iterative optimization, which has the following advantages:

[0035] (1) The present invention combines interval folding to improve the preset angle selection mechanism, so that the angle selected in each iteration is sufficiently close to the residual angle. Each iteration approaches the target value with the best approximation angle, which can effectively reduce the number of iterations, thereby reducing the system's consumption of FPGA internal storage resources, further reducing the development cost of the ultrasonic phased array system, and improving the data processing capability of the phased array system.

[0036] (2) The present invention corrects the modulus factor error caused by the irregularity of the angle selected by the jump structure, ensuring that the calculation accuracy level of the delay amount meets the requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a jump iterative flow chart of the present invention;

[0038] Figure 2 It is an interval division diagram of interval folding of the present invention;

[0039] Figure 3 is an interval conversion diagram of interval folding of the present invention;

[0040] Figure 4 It is the preselected angle fixed point number conversion table of the present invention;

[0041] Figure 5 is a comparison chart of the number of iterations for calculating cos26° in Example 1;

[0042] Figure 6 This is a comparison chart of the number of iterations for calculating cos321° in Example 1;

[0043] Figure 7 Schematic diagram of the calculation accuracy of the traditional iteration in Example 2;

[0044] Figure 8 This is a schematic diagram of the calculation accuracy of the jump iteration in Example 2. DETAILED DESCRIPTION

[0045] Several improvements and modifications are made to the present invention below in conjunction with the accompanying drawings, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0046] A delay accuracy control method for an ultrasonic phased array system based on iterative optimization, the specific steps are as follows:

[0047] S1: Interval folding is used to pre-process the transmitted or received deflection angle θ collected by the ultrasonic phased array system. The FPGA in the system determines the quadrant where the rotation angle θ is located through the quadrant conversion module, and maps [0, 2π] to [0, π / 4]. The FPGA converts the deflection angle θ into an equivalent angle θ' between 0≤θ≤π / 4, thereby realizing iterative calculation of any input angle; wherein, Figure 2 and 3 The following are the interval division diagram and interval conversion diagram of the interval folding of the present invention. The interval folding process of the present invention is specifically as follows:

[0048] When the input deflection angle is 0≤θ≤π / 4, the equivalent angle θ'=θ;

[0049] When the input deflection angle is π / 4≤θ≤π / 2, the equivalent angle θ'=π / 2-θ;

[0050] When the input deflection angle is π / 2≤θ≤3π / 4, the equivalent angle θ'=θ-π / 2;

[0051] When the input deflection angle is 3π / 4≤θ≤π, the equivalent angle θ'=π-θ;

[0052] When the input deflection angle is π≤θ≤5π / 4, the equivalent angle θ'=θ-π;

[0053] When the input deflection angle is 5π / 4≤θ≤3π / 2, the equivalent angle θ'=3π / 2-θ;

[0054] When the input deflection angle is 3π / 2≤θ≤7π / 4, the equivalent angle θ'=θ-3π / 2;

[0055] When the input deflection angle is 7π / 4≤θ≤2π, the equivalent angle θ'=2π-θ.

[0056] S2: Input the pre-processed equivalent angle into the calculation unit, use the CORDIC calculation method to perform conventional iterative calculation of the cosine value and output the modulus factor K C , after each iteration, the modulus factor K C The error Ω is compared with the preset accuracy ε. If Ω≤ε, the condition is met and the iteration ends and step S3 is performed. Otherwise, the iterative calculation continues. The specific iterative steps are as follows:

[0057] S2-1: Based on the known preselected angle set {θ i , i=0,1,2,…,m}, where the preselected angles are arranged in descending order. After the preselected angles are converted into fixed-point numbers, the highest bit of the binary number of each preselected angle is shifted right one bit as i increases. The number of iterations is initialized to C=1, i=0, and the preselected angle θ is selected using the CORDIC calculation method. i Calculate the trigonometric function value of the input equivalent angle and output the corresponding modulus factor K C ;

[0058] S2-2: Calculate the modulus factor error Ω, as shown in formula (1):

[0059] Ω=|K C -K| (1);

[0060] Wherein, K is a fixed constant value. In this embodiment, the value of K is 0.607253;

[0061] S2-3: Compare the modulus factor error Ω with the preset accuracy ε. If Ω≤ε, output C and enter step S3 for jump iteration. Otherwise, set C=C+1, i=i+1 and return to step S2-1 for iterative operation.

[0062] The conventional iteration mentioned in the present invention is to select a set of preselected angles one by one according to the set of preselected angles for iterative calculation.

[0063] S3: The CORDIC calculation method is used to continue to perform jump iteration to calculate the cosine value of the equivalent angle. In the present invention, the jump iteration method is used to change the selection method of the preselected angle before each iteration. When cosθ i When the adjustment of the coordinates no longer affects the accuracy of the terminal coordinates, the calculation is switched to the jump iteration method to speed up the convergence speed and make it quickly approach the accurate value. During the jump iteration process, each iteration selects the angle closest to the residual angle z i The preselected angle θ i,n Calculate until z i ≤Minimum fixed angle θ min End the iteration and output the cosine value of the deflection angle θ.

[0064] The specific jump iteration method in the present invention is as follows:

[0065] S3-1: Initialize the jump iteration number n=1, i=C, based on the output result of step S2, from the preselected angle set {θ C ,θ C+1 ,…,θ m}Select the preselected angle θ i,n Calculate the residual angle z according to formula (2) i :

[0066] z i =θ'-θ i,n (2);

[0067] Among them, =θ' is the equivalent angle, θ i,n Indicates that at the nth iteration, in the preselected angle set {θ C ,θ C+1 ,…,θ m} the i-th preselected angle in;

[0068] S3-2: Let θ i,n The number of the most significant bits of the corresponding binary number except the sign bit is j. When the residual angle z i >0, the preselected angle θ i,n The binary code uses the original code to determine whether jn is equal to 0. If not, set n = n + 1, i = i + 1 and return to step S3-1 to recalculate the residual angle z i , if so, select the current θ i,n As the closest residual angle z i The preselected angle goes to step S3-3, when the residual angle z i <0, the preselected angle θ i,n The binary code uses the complement code to determine whether jn is equal to 0. If not, set n = n + 1, i = i + 1 and return to step S3-1 to recalculate the residual angle z iIf so, select the current θ i,n As the closest residual angle z i The preselected angle goes to step S3-3;

[0069] S3-2: According to the preselected angle θ i,n The trigonometric function values ​​of the equivalent angle θ' are calculated using the CORDIC calculation method;

[0070] S3-3: Determine the residual angle z i Is ≤θ m If not, set i=i+1 and return to step S3-1 to recalculate the residual angle z i , select the angle closest to the residual angle z i Otherwise, the iteration ends and the trigonometric function value of the equivalent angle θ' is output, which is the trigonometric function value of the deflection angle θ.

[0071] Example 1

[0072] Under the same error accuracy conditions, the ultrasonic phased array system uses the traditional iterative CORDIC calculation method and the jump iterative CORDIC algorithm to calculate the cosine values ​​of the collected transmit deflection angle and receive deflection angle. Figure 5 The figure shows the comparison of the number of iterations required to calculate the cosine value of a launch deflection angle of 26°. In the traditional iterative calculation method, the number of iterations is 32, while the jump iterative calculation method only requires 15. Figure 6 Figure 2 shows a comparison of the number of iterations required to calculate the cosine value of a receive deflection angle of 321°. While the traditional iterative calculation method requires 32 iterations, the skip-iteration method of the present invention only requires 17. This demonstrates that the skip-iteration algorithm of the present invention significantly reduces the number of iterations, helping to reduce the system's consumption of FPGA internal memory resources and improve the data processing capability of the phased array instrument.

[0073] Example 2

[0074] Analysis of the accuracy and efficiency of the jump-iteration CORDIC calculation method

[0075] The cosine values ​​of angles from 0 to 45° are calculated in MATLAB using the traditional iterative CORDIC calculation method with a step size of 0.05, as shown in the following example: Figure 7 As shown, the absolute error of each angle calculation is within 8×10 -7 Within.

[0076] Jump Iteration CORDIC Calculation Method If the maximum error of the trigonometric function calculation is ε and the error of K is Ω, then C takes the minimum value that satisfies Ω<ε. So the maximum error ε is set to 8×10 -7, at this time, the minimum number of iterations C that satisfies Ω<ε is 16 times, and then the jump iteration CORDIC calculation method is used to calculate the cosine values ​​of various angles from 0 to 45° in MATLAB with a step size of 0.05, as shown in Figure 8 As shown, the absolute error of each angle calculated is within 4×10 -10 Therefore, compared with the traditional method, the error value is significantly reduced and the error accuracy is significantly improved.

[0077] The above description is only an illustration of the present invention and is a preferred embodiment of the present invention. It should be noted that those skilled in the art may make several improvements and modifications without departing from the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A delay accuracy control method for an ultrasonic phased array system based on iterative optimization, characterized in that: The specific steps are as follows: S1: pre-processing the transmission or reception deflection angle θ collected by the ultrasonic phased array system by using interval folding, and converting the deflection angle θ into an equivalent angle θ' within the range of 0≤θ≤π / 4; S2: Input the pre-processed equivalent angle into the calculation unit, use the CORDIC calculation method to perform conventional iterative calculation of the cosine value and output the modulus factor K C , after each iteration, the modulus factor K C The error Ω is compared with the preset accuracy ε. If Ω≤ε, the condition is met and the iteration ends and step S3 is performed. Otherwise, the iterative calculation continues. S3: Use the CORDIC calculation method to continue to iterate and jump the cosine value of the equivalent angle, and each iteration matches the closest residual angle z i The preselected angle θ i,n Calculate until z i ≤Minimum fixed angle θ min End the iteration and output the cosine value of the deflection angle θ; The jump iteration method is as follows: S3-1: Initialize the jump iteration number n=1, i=C, based on the output result of step S2, from the preselected angle set {θ C ,θ C+1 ,…,θ m }Select the preselected angle θ i,n Calculate the residual angle z according to formula (2) i : z i =θ'-θ i,n (2); Among them, θ' is the equivalent angle, θ i,n Indicates that at the nth iteration, in the preselected angle set {θ C ,θ C+1 ,…,θ m } the i-th preselected angle in; S3-2: Let θ i,n The number of the most significant bits of the corresponding binary number except the sign bit is j. When the residual angle z i >0, the preselected angle θ i,n The binary code uses the original code to determine whether jn is equal to 0. If not, set n = n + 1, i = i + 1 and return to step S3-1 to recalculate the residual angle z i If so, select the current θ i,n As the closest residual angle z i The preselected angle goes to step S3-3, when the residual angle z i <0, the preselected angle θ i,n The binary code uses the complement code to determine whether jn is equal to 0. If not, set n = n + 1, i = i + 1 and return to step S3-1 to recalculate the residual angle z i If so, select the current θ i,n As the closest residual angle z i The preselected angle goes to step S3-3; S3-3: According to the preselected angle θ i,n The trigonometric function values ​​of the equivalent angle θ' are calculated using the CORDIC calculation method; S3-4: Determine the residual angle z i Is ≤θ m If not, set i=i+1 and return to step S3-1 to recalculate the residual angle z i , select the angle closest to the residual angle z i Otherwise, the iteration ends and the trigonometric function value of the equivalent angle θ' is output, which is the trigonometric function value of the deflection angle θ.

2. The delay accuracy control method of an ultrasonic phased array system based on iterative optimization according to claim 1, characterized in that: The iteration method in S2 is as follows: S2-1: Based on the known preselected angle set {θ i , i=0,1,2,…,m}, where the preselected angles are arranged in descending order. After the preselected angles are converted into fixed-point numbers, the highest bit of the binary number of each preselected angle is shifted right one bit as i increases. The number of iterations is initialized to C=1, i=0, and the preselected angle θ is selected using the CORDIC calculation method. i Calculate the trigonometric function value of the input equivalent angle and output the corresponding modulus factor K C ; S2-2: Calculate the modulus factor error Ω, as shown in formula (1): Ω=|K C -K| (1); Where K is a fixed constant value; S2-3: Compare the modulus factor error Ω with the preset accuracy ε. When Ω≤ε, output C and enter step S3 for jump iteration. Otherwise, set C=C+1, i=i+1 and return to step S2-1 for iterative operation.

3. The delay accuracy control method of an ultrasonic phased array system based on iterative optimization according to claim 1, characterized in that: The interval folding process in S1 is as follows: When the input deflection angle is 0≤θ≤π / 4, the equivalent angle θ'=θ; When the input deflection angle is π / 4≤θ≤π / 2, the equivalent angle θ'=π / 2-θ; When the input deflection angle is π / 2≤θ≤3π / 4, the equivalent angle θ'=θ-π / 2; When the input deflection angle is 3π / 4≤θ≤π, the equivalent angle θ'=π-θ; When the input deflection angle is π≤θ≤5π / 4, the equivalent angle θ'=θ-π; When the input deflection angle is 5π / 4≤θ≤3π / 2, the equivalent angle θ'=3π / 2-θ; When the input deflection angle is 3π / 2≤θ≤7π / 4, the equivalent angle θ'=θ-3π / 2; When the input deflection angle is 7π / 4≤θ≤2π, the equivalent angle θ'=2π-θ.

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