Omnidirectional pressure measurement system and method

Abstract

The invention relates to the technical field of pressure testing, and discloses an omni-directional pressure measuring system and method.The omni-directional pressure measuring system comprises a spherical piezoelectric sensor array module, a signal conditioning module, a signal storage and transmission module and an upper computer; the data are processed by the signal conditioning module and transmitted to the upper computer through the storage and transmission module, the pressure field intensity and the pressure source position of each point are calculated on the upper computer, and the pressure field is reconstructed by using the data. According to the invention, the design of the spherical array with the regular dodecahedron vertex topology is adopted, so that the system realizes multi-angle information acquisition and depth perception, and a detection blind area is eliminated; according to the method, the weighting function is constructed in the spherical coordinate system, the pressure intensity of each point in the space is calculated through weighted average, then the initial position of the pressure source is estimated according to the square of the measured value, and accurate positioning is performed in combination with the iterative algorithm. According to the invention, the measurement precision and efficiency are improved, and the dynamic pressure field can be reconstructed.

Description

Technical Field

[0001] The present invention relates to the field of pressure testing technology, and in particular to an omnidirectional pressure measurement system and method. Background Art

[0002] Dynamic pressure field measurement is a crucial tool in scientific research and engineering applications, widely used in aerospace, automotive, explosion mechanics, acoustic analysis, and gas leak detection. Furthermore, information about the distribution, rate of change, and fluctuation characteristics of the dynamic pressure field can be applied to areas such as aircraft design optimization, explosion power assessment, noise control, and gas equipment testing.

[0003] Traditional pressure field measurement instruments typically use single-point sensors or arrays of a limited number of sensors. While these instruments can measure pressure at specific locations or localized areas, existing measurement systems not only suffer from a limited measurement range and an inability to fully reflect the spatial distribution of the pressure field, but also from insufficient measurement accuracy and poor real-time performance. Especially in complex and dynamically changing scenarios like acoustic field propagation and explosion shock wave propagation, existing technologies often struggle to capture all key information, leading to biased or missed measurement results. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide an omnidirectional pressure measurement system and method, which is based on a spherical array structure with regular dodecahedron vertex topology. By constructing a weight function in a spherical coordinate system and using weighted average combined with an iterative algorithm for calculation and optimization, it can effectively solve the problems of limited measurement range, detection blind spots, insufficient accuracy, poor real-time performance, etc. of traditional pressure field measuring instruments, and realize high-precision, omnidirectional, depth perception and reconstruction of spatial dynamic pressure fields.

[0005] In order to achieve the above-mentioned purpose of the invention, the technical solutions adopted are as follows:

[0006] An omnidirectional pressure measurement system includes a spherical piezoelectric sensor array module, a signal conditioning module, a signal storage and transmission module, and a host computer;

[0007] The spherical piezoelectric sensor array module includes 19 piezoelectric sensors, each of which includes a piezoelectric sensor probe composed of a hemispherical piezoelectric element, whose surface faces the object to be measured. When an external force acts on the probe, the piezoelectric element will deform, causing an electric charge to be generated on its surface. Each piezoelectric sensor enters the signal conditioning module through an independent signal conditioning channel. The 19 piezoelectric sensors are embedded in a spherical shell according to the topological symmetry of the vertices of a regular dodecahedron to form a spherical array. By being evenly distributed around a central point, the normal of the hemispherical piezoelectric sensor probe is strictly pointed in the direction of the vertex extension, forming a seamless detection domain on the spherical surface. By adjusting the mathematical model parameters according to actual needs, omnidirectional and accurate detection of dynamic pressure waves can be achieved;

[0008] The signal conditioning module includes a filtering circuit, an integrated amplifier circuit, an isolation circuit, an analog-to-digital conversion module and a protection circuit, and is used to filter, amplify, isolate and perform analog-to-digital conversion on the weak charge signal output by the piezoelectric sensor;

[0009] The signal storage and transmission module includes a storage module and a transmission module. The storage module stores the digital signal processed by the signal conditioning module, and the transmission module transmits the stored data to the host computer.

[0010] The host computer includes a calculation module and a display module for receiving digital signals and performing further algorithm optimization on the digital signals. The display module displays the measured pressure field intensity, pressure source position, and reconstructed spatial pressure field in real time.

[0011] As a further improvement of the present invention, the piezoelectric sensor probe adopts a four-wire connection method and uses a ratio method to eliminate lead errors and improve measurement accuracy. The four wires are two positive and negative leads and two signal lines. The positive and negative leads connect the piezoelectric element to the power supply, and the signal line is connected to the signal conditioning module.

[0012] As a further improvement of the present invention, in view of the multi-frequency noise that the sensor signal may carry in a complex measurement environment, the filtering circuit is used to accurately filter out interference in a specific frequency band and improve the signal quality; the integrated amplifier circuit amplifies the weak electrical signal generated by the sensor under the action of the pressure wave and converts it into a voltage signal; laying a solid foundation for subsequent optimization, since the sensors are widely distributed and numerous, the isolation circuit is used to prevent loop interference and signal crosstalk. To ensure the purity of signal transmission, the analog-to-digital conversion module is used to convert the processed voltage signal into a digital signal; the protection circuit is used to prevent circuit damage caused by sensor failure or external interference.

[0013] As a further improvement of the present invention, the spherical array is a regular dodecahedron vertex topology structure, with densely arranged sensors on the top and no sensors on the bottom for device fixation. The omnidirectional pressure measurement system is placed on the test platform, which can measure the pressure intensity of the dynamic field in space at the same time and different positions, and display the measured pressure field intensity and pressure source position in real time, and at the same time, display the reconstructed spatial pressure field.

[0014] As a further improvement of the present invention, the piezoelectric sensor probe is strictly aligned with the outer vertex of the regular dodecahedron in the normal direction, and an accurate parameter mapping relationship between the array topological coordinate system and the spherical coordinate system is established, so that the orientation parameters of each piezoelectric sensor can accurately correspond to the direction of the face-center symmetry axis of the pentagon of the regular dodecahedron, and the geometric characteristics of the regular dodecahedron are integrated into the construction of the weight function, optimizing the algorithm process and reducing computational redundancy, so that the system can achieve high-precision measurement while greatly improving measurement efficiency and real-time performance.

[0015] A method for measuring omnidirectional pressure, comprising the following steps:

[0016] S1: The omnidirectional pressure measurement system is fixedly installed on the test platform, and a pressure source is arranged in the experimental site. When the pressure source is activated, it generates a pressure wave. The spherical piezoelectric sensor array module contacts the pressure wave. Based on the piezoelectric effect, the piezoelectric element inside the sensor deforms and generates a charge signal.

[0017] S2: Due to the relatively low intensity of the pressure field, the charge signal measured by the spherical piezoelectric sensor array module is relatively weak and noisy. To meet subsequent processing requirements, the charge signal is filtered and amplified in the signal conditioning module, converted into a voltage signal, and then converted into a digital signal through the analog-to-digital conversion module.

[0018] The spherical piezoelectric sensor array module measures the pressure field in space based on the piezoelectric effect principle to obtain the output voltage. Under ideal conditions, the pressure intensity of the piezoelectric sensor is:

[0019]

[0020] Where U i is the voltage value output by the piezoelectric sensor i, d is the voltage coefficient of the piezoelectric sensor, S is the effective area of ​​the diaphragm, A0 is the amplification factor, C a is the capacitance of the amplifier circuit, C f is the feedback capacitor;

[0021] S3: Signal storage and transmission module, which stores the digital signal processed by the signal conditioning module and transmits the stored data to the host computer through the transmission module;

[0022] S4: The host computer calculates the pressure intensity and the position of the pressure source at each point in the space through the received pressure field data, and uses the data to reconstruct the pressure field. The measured pressure field intensity and the position of the pressure source are then displayed through the display module, and the reconstructed spatial pressure field is also displayed.

[0023] As a further improvement of the present invention, in step S4, the pressure intensity of each point in space and the position of the pressure source are calculated as follows:

[0024] The radius of the spherical piezoelectric sensor array module is R. In the spherical coordinate system with the center of the sphere as the origin, the position coordinate of the piezoelectric sensor i is r i is (R,θ i ,φ i ), the coordinates of the target point r are (p, θ, φ), where p is the distance from the target point to the center of the sphere, θ is the angle between the target point and the positive z-axis, and φ is the angle between the target point and the positive x-axis. The pressure intensity P of any target point in space is:

[0025]

[0026] Among them, ω i is the weight function, β is the medium attenuation coefficient, α i is the angle between the normal direction of the piezoelectric sensor i and the direction of the target point, φ i is the azimuth angle difference between the piezoelectric sensor and the target point;

[0027] The data measured by the piezoelectric sensor are compared to estimate the initial position of the pressure source. Then, the iterative algorithm is used to continuously update the position and intensity of the pressure source. When the position change is less than the radius R of the sphere and the pressure change rate is less than 5%, the position of the pressure source can be accurately determined. The position of the pressure source r1 and the pressure intensity P1 of the pressure source are:

[0028]

[0029] Among them, ‖r s -r i ‖ is the Euclidean distance between the pressure source and the piezoelectric sensor i, r s (k+1) The estimated position coordinates of the pressure source after the k+1th iteration.

[0030] The beneficial effects of the present invention are as follows: the present invention provides an omnidirectional pressure measurement system and method, which combines a spherical piezoelectric sensor array with a hardware circuit for signal conditioning, signal storage and transmission, and can measure spatial dynamic pressure. The present invention integrates 19 piezoelectric sensors in an array form with a regular dodecahedron vertex topological distribution on a spherical shell, and the sensor probe is strictly aligned with the outer vertex of the regular dodecahedron in the normal direction, so that the system can realize multi-angle information collection and depth perception, eliminate detection blind spots, and adjust the sensor layout according to needs to optimize data. The present invention establishes a precise parameter mapping relationship between the array topological coordinate system and the spherical coordinate system, constructs a weight function by integrating the geometric features of the regular dodecahedron into the spherical coordinate system, uses weighted averaging to calculate the pressure intensity of any point in space, uses the square of the sensor measurement value as the weight to estimate the initial position of the pressure source, and combines the iterative algorithm to continuously update the position and pressure intensity of the pressure source to achieve precise positioning of the pressure source. This method reduces computational redundancy, so that the system can achieve high-precision measurement while greatly improving measurement efficiency and real-time performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0032] Figure 1 It is a structural schematic diagram of an omnidirectional pressure measurement system of the present invention;

[0033] Figure 2 It is a flow chart of an omnidirectional pressure measurement system;

[0034] Figure 3 is a distribution diagram of the piezoelectric sensor of the present invention;

[0035] Figure 4 It is a system connection diagram of the present invention. DETAILED DESCRIPTION

[0036] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0037] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0038] An omnidirectional pressure measurement system, such as Figure 1 As shown, it includes a spherical piezoelectric sensor array module, a signal conditioning module, a signal storage and transmission module and a host computer;

[0039] The spherical piezoelectric sensor array module includes 19 piezoelectric sensors, each of which includes a piezoelectric sensor probe composed of a hemispherical piezoelectric element, whose surface faces the object to be measured. When an external force acts on the probe, the piezoelectric element will deform, causing an electric charge to be generated on its surface. Each piezoelectric sensor enters the signal conditioning module through an independent signal conditioning channel. The 19 piezoelectric sensors are embedded in a spherical shell according to the topological symmetry of the vertices of a regular dodecahedron to form a spherical array. By being evenly distributed around a central point, the normal of the hemispherical piezoelectric sensor probe is strictly pointed in the direction of the vertex extension, forming a seamless detection domain on the spherical surface. By adjusting the mathematical model parameters according to actual needs, omnidirectional and accurate detection of dynamic pressure waves can be achieved;

[0040] The signal conditioning module includes a filtering circuit, an integrated amplifier circuit, an isolation circuit, an analog-to-digital conversion module and a protection circuit, and is used to filter, amplify, isolate and perform analog-to-digital conversion on the weak charge signal output by the piezoelectric sensor;

[0041] The signal storage and transmission module includes a storage module and a transmission module. The storage module stores the digital signal processed by the signal conditioning module, and the transmission module transmits the stored data to the host computer.

[0042] The host computer includes a calculation module and a display module for receiving digital signals and performing further algorithm optimization on the digital signals. The display module displays the measured pressure field intensity, pressure source position, and reconstructed spatial pressure field in real time.

[0043] The piezoelectric sensor probe adopts a four-wire connection method and uses a ratio method to eliminate lead errors and improve measurement accuracy. The four wires are two positive and negative leads and two signal lines. The positive and negative leads connect the piezoelectric element to the power supply, and the signal line is connected to the signal conditioning module.

[0044] In view of the multi-frequency noise that the sensor signal may carry in a complex measurement environment, the filtering circuit is used to accurately filter out interference in a specific frequency band and improve signal quality; the integrated amplifier circuit amplifies the weak electrical signal generated by the sensor under the action of the pressure wave and converts it into a voltage signal; laying a solid foundation for subsequent optimization. Since the sensors are widely distributed and numerous, the isolation circuit is used to prevent loop interference and signal crosstalk. To ensure the purity of signal transmission, the analog-to-digital conversion module is used to convert the processed voltage signal into a digital signal; the protection circuit is used to prevent circuit damage caused by sensor failure or external interference.

[0045] like Figure 3 As shown, the piezoelectric sensor probes are symmetrically distributed on the spherical shell in a regular dodecahedron vertex topology, and the system is a spherical shell structure, as shown in FIG. Figure 4 As shown, the omnidirectional pressure measurement system is placed in the test platform, which can measure the pressure intensity of the dynamic field in space at the same time and different positions, and display the measured pressure field intensity and pressure source position in real time, and at the same time, display the reconstructed spatial pressure field.

[0046] The piezoelectric sensor probe is strictly aligned with the outer vertex of the regular dodecahedron in the normal direction, and an accurate parameter mapping relationship between the array topological coordinate system and the spherical coordinate system is established, so that the orientation parameters of each piezoelectric sensor can accurately correspond to the direction of the face-centered symmetry axis of the pentagon of the regular dodecahedron. The geometric characteristics of the regular dodecahedron are integrated into the construction of the weight function, the algorithm process is optimized, and computational redundancy is reduced, so that the system can achieve high-precision measurement while greatly improving measurement efficiency and real-time performance.

[0047] An omnidirectional pressure measurement method, such as Figure 2 As shown, the following steps are included:

[0048] S1: The omnidirectional pressure measurement system is fixedly installed on the test platform, and a pressure source is arranged in the experimental site. When the pressure source is activated, it generates a pressure wave. The spherical piezoelectric sensor array module contacts the pressure wave. Based on the piezoelectric effect, the piezoelectric element inside the sensor deforms and generates a charge signal.

[0049] S2: Due to the relatively low intensity of the pressure field, the charge signal measured by the spherical piezoelectric sensor array module is relatively weak and noisy. To meet subsequent processing requirements, the charge signal is filtered and amplified in the signal conditioning module, converted into a voltage signal, and then converted into a digital signal through the analog-to-digital conversion module.

[0050] The spherical piezoelectric sensor array module measures the pressure field in space based on the piezoelectric effect principle to obtain the output voltage. Under ideal conditions, the pressure intensity of the piezoelectric sensor is:

[0051]

[0052] Where U i is the voltage value output by the piezoelectric sensor i, d is the voltage coefficient of the piezoelectric sensor, S is the effective area of ​​the diaphragm, A0 is the amplification factor, C a is the capacitance of the amplifier circuit, C f is the feedback capacitor;

[0053] S3: Signal storage and transmission module, which stores the digital signal processed by the signal conditioning module and transmits the stored data to the host computer through the transmission module;

[0054] S4: The host computer calculates the pressure intensity and the position of the pressure source at each point in the space through the received pressure field data, and uses the data to reconstruct the pressure field. The measured pressure field intensity and the position of the pressure source are then displayed through the display module, and the reconstructed spatial pressure field is also displayed.

[0055] In step S4, the pressure intensity at each point in space and the position of the pressure source are calculated as follows:

[0056] The radius of the spherical piezoelectric sensor array module is R. In the spherical coordinate system with the center of the sphere as the origin, the position coordinate of the piezoelectric sensor i is r i is (R,θ i ,φ i ), the coordinates of the target point r are (p, θ, φ), where p is the distance from the target point to the center of the sphere, θ is the angle between the target point and the positive z-axis, and φ is the angle between the target point and the positive x-axis. The pressure intensity P of any target point in space is:

[0057]

[0058] Among them, ω i is the weight function, β is the medium attenuation coefficient, α i is the angle between the normal direction of the piezoelectric sensor i and the direction of the target point, φ i is the azimuth angle difference between the piezoelectric sensor and the target point;

[0059] The data measured by the piezoelectric sensor are compared to estimate the initial position of the pressure source. Then, the iterative algorithm is used to continuously update the position and intensity of the pressure source. When the position change is less than the radius R of the sphere and the pressure change rate is less than 5%, the position of the pressure source can be accurately determined. The position of the pressure source r1 and the pressure intensity P1 of the pressure source are:

[0060]

[0061] Among them, ‖r s -r i ‖ is the Euclidean distance between the pressure source and the piezoelectric sensor i, r s (k+1) The estimated position coordinates of the pressure source after the k+1th iteration.

[0062] The present invention, based on a spherical array structure with a regular dodecahedron vertex topology, achieves multi-angle information acquisition and depth perception, and can optimize sensor layout on demand. By constructing a weight function in a spherical coordinate system, the pressure intensity at any point in space is calculated using a weighted average, and the square of the sensor measurement value is used as the weight to estimate the initial position of the pressure source. An iterative algorithm is used to continuously update the pressure source position and pressure intensity. When the position change is less than the sphere radius R and the pressure change rate is less than 5%, the pressure source can be accurately located. Software is then used to reconstruct the pressure field, effectively addressing the limited measurement range of traditional single-point pressure sensors, the detection blind spots of planar array sensors, and the difficulty in obtaining high-precision pressure field distribution.

[0063] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, improvements, component splits, or combinations, etc., that fall within the spirit and principles of the present invention, shall be included within the scope of protection of the present invention.

Claims

1. An omnidirectional pressure measurement system, characterized in that: It includes a spherical piezoelectric sensor array module, a signal conditioning module, a signal storage and transmission module and a host computer; The spherical piezoelectric sensor array module includes 19 piezoelectric sensors, each of which includes a piezoelectric sensor probe composed of a hemispherical piezoelectric element, whose surface faces the object to be measured. When an external force acts on the probe, the piezoelectric element will deform, causing an electric charge to be generated on its surface. Each piezoelectric sensor enters the signal conditioning module through an independent signal conditioning channel. The 19 piezoelectric sensors are embedded in a spherical shell according to the topological symmetry of the vertices of a regular dodecahedron to form a spherical array. By being evenly distributed around a center point, the normal of the hemispherical piezoelectric sensor probe is strictly pointed in the direction of the vertex extension, forming a seamless detection domain on the spherical surface. The signal conditioning module includes a filtering circuit, an integrated amplifier circuit, an isolation circuit, an analog-to-digital conversion module and a protection circuit, and is used to filter, amplify, isolate and perform analog-to-digital conversion on the weak charge signal output by the piezoelectric sensor; The signal storage and transmission module includes a storage module and a transmission module. The storage module stores the digital signal processed by the signal conditioning module, and the transmission module transmits the stored data to the host computer. The host computer includes a computing module and a display module for receiving digital signals and performing algorithm optimization on the digital signals. The display module displays the measured pressure field intensity, pressure source position, and reconstructed spatial pressure field in real time.

2. The omnidirectional pressure measurement system according to claim 1, characterized in that: The piezoelectric sensor probe adopts a four-wire connection method and uses a ratio method to eliminate lead errors and improve measurement accuracy. The four wires are two positive and negative leads and two signal lines. The positive and negative leads connect the piezoelectric element to the power supply, and the signal line is connected to the signal conditioning module.

3. The omnidirectional pressure measurement system according to claim 1, characterized in that: The filtering circuit is used to accurately filter out interference in a specific frequency band and improve signal quality; the integrated amplifier circuit amplifies the weak electrical signal generated by the sensor under the action of the pressure wave and converts it into a voltage signal; the isolation circuit is used to prevent loop interference and signal crosstalk, and the analog-to-digital conversion module is used to convert the processed voltage signal into a digital signal; the protection circuit is used to prevent circuit damage caused by sensor failure or external interference.

4. The omnidirectional pressure measurement system according to claim 1, characterized in that: The omnidirectional pressure measurement system is placed on the test platform and can measure the pressure intensity of the dynamic field in space at the same time and different positions, and display the measured pressure field intensity and pressure source position in real time, and at the same time, display the reconstructed spatial pressure field.

5. The omnidirectional pressure measurement system according to claim 1, characterized in that: The piezoelectric sensor probe is strictly aligned with the outer vertex of the regular dodecahedron in the normal direction, and an accurate parameter mapping relationship between the array topological coordinate system and the spherical coordinate system is established, so that the orientation parameters of each piezoelectric sensor can accurately correspond to the direction of the face-centered symmetry axis of the pentagon of the regular dodecahedron, and the geometric characteristics of the regular dodecahedron are integrated into the construction of the weight function.

6. A method for measuring omnidirectional pressure, characterized in that: The following steps are involved: S1: The omnidirectional pressure measurement system is fixedly installed on the test platform, and a pressure source is arranged in the experimental site. When the pressure source is activated, it generates a pressure wave. The spherical piezoelectric sensor array module contacts the pressure wave. Based on the piezoelectric effect, the piezoelectric element inside the sensor deforms and generates a charge signal. S2: Due to the relatively low intensity of the pressure field, the charge signal measured by the spherical piezoelectric sensor array module is relatively weak and noisy. To meet subsequent processing requirements, the charge signal is filtered and amplified in the signal conditioning module, converted into a voltage signal, and then converted into a digital signal through the analog-to-digital conversion module. The spherical piezoelectric sensor array module measures the pressure field in space based on the piezoelectric effect principle to obtain the output voltage. Under ideal conditions, the pressure intensity of the piezoelectric sensor is: Where U i is the voltage value output by the piezoelectric sensor i, d is the voltage coefficient of the piezoelectric sensor, S is the effective area of ​​the diaphragm, A0 is the amplification factor, C a is the capacitance of the amplifier circuit, C f is the feedback capacitor; S3: Signal storage and transmission module, which stores the digital signal processed by the signal conditioning module and transmits the stored data to the host computer through the transmission module; S4: The host computer calculates the pressure intensity and the position of the pressure source at each point in the space through the received pressure field data, and uses the data to reconstruct the pressure field. The measured pressure field intensity and the position of the pressure source are then displayed through the display module, and the reconstructed spatial pressure field is also displayed.

7. The omnidirectional pressure measurement method according to claim 6, characterized in that: In step S4, the pressure intensity at each point in space and the position of the pressure source are calculated as follows: The radius of the spherical piezoelectric sensor array module is R. In the spherical coordinate system with the center of the sphere as the origin, the position coordinate of the piezoelectric sensor i is r i is (R,θ i ,φ i ), the coordinates of the target point r are (p, θ, φ), where p is the distance from the target point to the center of the sphere, θ is the angle between the target point and the positive z-axis, and φ is the angle between the target point and the positive x-axis. The pressure intensity P of any target point in space is: Among them, ω i is the weight function, β is the medium attenuation coefficient, α i is the angle between the normal direction of the piezoelectric sensor i and the direction of the target point, φ i is the azimuth angle difference between the piezoelectric sensor and the target point; The data measured by the piezoelectric sensor are compared to estimate the initial position of the pressure source. Then, the iterative algorithm is used to continuously update the position and intensity of the pressure source. When the position change is less than the radius R of the sphere and the pressure change rate is less than 5%, the position of the pressure source can be accurately determined. The position of the pressure source r1 and the pressure intensity P1 of the pressure source are: Among them, ‖r s -r i ‖ is the Euclidean distance between the pressure source and the piezoelectric sensor i, r s (k+1) The estimated position coordinates of the pressure source after the k+1th iteration.

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