Micro-seismic monitoring piezoelectric acceleration sensor optimization method based on NSGA-II algorithm

Abstract

The invention discloses a micro-seismic monitoring piezoelectric acceleration sensor optimization method based on an NSGA-II algorithm, provides a piezoelectric sensor based on a triangular shear structure, and relates to the technical field of piezoelectric acceleration sensors. According to the micro-seismic monitoring piezoelectric acceleration sensor optimization method based on the NSGA-II algorithm, the NSGA-II genetic algorithm is adopted to optimize the structural size of the designed sensor, and an optimal structural parameter combination is obtained, that is, when the height of a mass block is 10.6 mm, the thickness of a piezoelectric patch is 3.29 mm, the height of the piezoelectric patch is 8.1 mm and the height of a central column is 19 mm, the sensor design is optimal, and the optimal structural parameter combination is obtained. The working frequency of the optimized sensor is improved by 2.68%, and the voltage sensitivity is improved by 8.96%. And finally, respectively carrying out a calibration experiment and a micro-seismic signal test on the designed sensor by building an experiment platform. Experimental results show that the working frequency range of the designed sensor is 0.1-2123 Hz, and the voltage sensitivity is 173.49 mv / g.

Description

Technical Field

[0001] This invention relates to the field of piezoelectric acceleration sensor technology, specifically to an optimization method for a micro-vibration monitoring piezoelectric acceleration sensor based on the NSGA-II algorithm. Background Technology

[0002] Mining inevitably creates goaf areas, and the dynamic instability of the overlying rock in these goaf areas alters the geological structure and stress properties, easily leading to hidden disasters both on the surface and underground. This results in complex dynamic disasters such as rock bursts and water inrushes. Therefore, obtaining information on soil and rock deformation and understanding its patterns is essential. Soil and rock deformation monitoring, by detecting and analyzing the minute vibration signals generated during the deformation process of soil and rock in goaf areas, can accurately predict and forecast the deformation and stability of the overlying rock in goaf areas. It is widely used in projects such as deep-buried tunnels, large hydropower stations, and deep mining. The acquisition of soil and rock deformation signals is accomplished through sensors; therefore, improving the sensitivity of sensors within their operating frequency range is crucial for comprehensively and accurately acquiring minute vibration signals, significantly enhancing the accuracy of predictions and forecasts.

[0003] Currently, there are few sensors used for monitoring the deformation of rock and soil in goaf areas. To address the problem of low sensitivity of existing sensors for monitoring the deformation of rock and soil in goaf areas, this invention proposes an optimization method for a piezoelectric acceleration sensor for microseismic monitoring based on the NSGA-II algorithm. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] To address the shortcomings of existing technologies, this invention provides an optimization method for a piezoelectric accelerometer for microseismic monitoring based on the NSGA-II algorithm. By addressing the problem of low sensitivity of existing sensors for monitoring the deformation of rock and soil in mining goaf areas, a piezoelectric sensor based on a triangular shear structure is proposed.

[0006] (II) Technical Solution

[0007] To achieve the above objectives, the present invention provides the following technical solution: an optimization method for a piezoelectric accelerometer for microseismic monitoring based on the NSGA-II algorithm, specifically comprising the following steps:

[0008] S1. Based on the working principle of piezoelectric sensors, a mechanical model is established, the theoretical expressions for the resonant frequency and sensitivity of piezoelectric sensors are derived, the structure of a rock and soil deformation monitoring sensor for mining goaf areas is designed, and the material selection of each component is determined.

[0009] S2. Then, establish the finite element model of the designed sensor and perform modal analysis, harmonic vibration response, piezoelectric analysis and experimental analysis respectively.

[0010] S3. Then, using the height of the mass block, the height of the piezoelectric element, the thickness of the piezoelectric element, and the height of the central column as design variables, the NSGA-II genetic algorithm is used to optimize the structural dimensions of the designed sensor to obtain the optimal combination of structural parameters, namely, the height of the mass block is 10.6 mm and the thickness of the piezoelectric element is 3.29 mm.

[0011] S4. The designed sensor was calibrated and tested for micro-vibration signals by building an experimental platform.

[0012] Preferably, the working principle of the piezoelectric sensor is based on the piezoelectric effect to convert the measured mechanical vibration into electrical energy. The working mode of the simplified dynamic model of the piezoelectric sensor is represented by a single-degree-of-freedom model, including a mass block m, a damper c, and a spring k.

[0013] Preferably, the piezoelectric sensor is fixedly connected to the surface of the vibration generator by bottom bolts, and fasteners connect the mass block, piezoelectric element and central support, and a certain prestress is applied to ensure the rigid connection of the sensor as a whole;

[0014] When the piezoelectric sensor detects a change in acceleration, due to the inertia of the mass block and the rigid compression of the fasteners, the central support and the mass block exert tangential stress on the piezoelectric element in the same direction as the vibration. This causes the piezoelectric element to deform, resulting in a change in charge, thus converting the acceleration load into electrical energy. The equilibrium equation of the mass block can be derived from the equivalent system, as follows:

[0015]

[0016] In the formula: m is the mass block; k is the spring constant; c is the viscous damping coefficient; x1 is the actual displacement of the vibration table; x0 is the displacement of the mass block relative to the vibration table.

[0017] Preferably, the formula of the equilibrium equation of the mass block is transformed into the differential equation of the equivalent system as follows:

[0018]

[0019] In the formula: a is the acceleration load;

[0020] Performing a Fourier transform again yields:

[0021]

[0022] In the formula: ω n ζ is the sensor's natural frequency; ζ is the sensor's damping ratio; ω is the operating frequency.

[0023] The calculation is as follows:

[0024]

[0025] As can be seen from the above formula, the natural frequency is one of the most important performance indicators in piezoelectric accelerometers, and it is determined by the equivalent stiffness and the mass of the mass block.

[0026] Preferably, the resonant frequency of the piezoelectric sensor can be given by the following formula:

[0027]

[0028] The sensor displacement frequency response function for each fundamental acceleration can be expressed as:

[0029]

[0030] Assuming the piezoelectric sensor is subjected to an inertial load, the tangential stress acting on the mass block is as follows:

[0031] F = ma;

[0032] The piezoelectric element generates electrical energy Q that is proportional to the tangential stress F:

[0033] Q = d ij F = d ij ma=d ij kx0(t);

[0034] In the formula: d ij It is the piezoelectric constant;

[0035] The charge sensitivity of the piezoelectric sensor is further obtained as follows:

[0036]

[0037] In the formula: Q is the amount of charge generated; S Q This refers to the sensor's charge sensitivity.

[0038] Preferably, the equivalent capacitance of a single element is expressed as:

[0039]

[0040] Where: ε r ε is the relative permittivity. o Where is the vacuum dielectric constant, S is the area of ​​the piezoelectric element, and d is the thickness of the piezoelectric element;

[0041] The voltage sensitivity of the piezoelectric sensor is further obtained as follows:

[0042]

[0043] Preferably, the piezoelectric sensor has low phase distortion within its operating frequency range, which is beneficial to improving the quality of the recorded signal. When the sensor's operating frequency is greater than one-third of the resonant frequency, the sensor's sensitivity will be distorted, and the degree of distortion reaches its maximum when it approaches the resonant frequency.

[0044] Preferably, the NSGA-II genetic algorithm in step S3 specifically includes the following steps:

[0045] The optimal solution set of T1 and Pareto has a total of 'a' solutions. Using the two objective functions as evaluation metrics, we obtain the metric matrix S:

[0046] S=(s mn ) a×2 (m = 1, 2, ..., a; n = 1, 2);

[0047] T2, elements of the range standardization index matrix:

[0048]

[0049] In the formula: x ij It is the value in the i-th row and j-th column of the data, max(x) j ) and min(x j ) are the maximum and minimum values ​​in the j-th column of data, respectively, and r ij It is standardized data;

[0050] T3. Evaluate and rank the solutions using the minimum difference method:

[0051]

[0052] In the formula: x1 is the difference between the calculated targets, and f1(x1) and f2(x2) are two target values ​​of x1.

[0053] Preferably, the NSGA-II genetic algorithm is programmed using MATLAB-R2020b software, with the population size set to 200, the number of iterations to 500, the crossover probability to 0.9, and the mutation probability to 0.2. The Pareto optimal solution set is then obtained using MATLAB-R2020b programming software.

[0054] (III) Beneficial Effects

[0055] This invention provides an optimization method for a piezoelectric accelerometer sensor for microseismic monitoring based on the NSGA-II algorithm. Compared with existing technologies, it has the following advantages: This optimization method for a piezoelectric accelerometer sensor for microseismic monitoring, based on the NSGA-II algorithm, establishes a mechanical model of the piezoelectric sensor based on its working principle, and derives the theoretical expressions for the resonant frequency and sensitivity of the piezoelectric sensor. The structure of a sensor for monitoring the deformation of rock and soil in a mining goaf is designed, and the material selection for each component is determined. Then, a finite element model of the designed sensor is established, and modal analysis, harmonic vibration response, piezoelectric analysis, and experimental analysis are performed. Using the height of the mass block, the height and thickness of the piezoelectric element, and the height of the central column as design variables, the NSGA-II genetic algorithm is used to optimize the structural dimensions of the designed sensor, obtaining the optimal combination of structural parameters. Specifically, when the mass block height is 10.6 mm, the piezoelectric element thickness is 3.29 mm, the piezoelectric element height is 8.1 mm, and the central column height is 19 mm, the sensor design reaches its optimal state. The optimized sensor frequency is increased by 2.68%, and the voltage is increased by 8.96%. Finally, calibration experiments and microseismic signal tests were conducted on the designed sensor using an experimental platform. Experimental results show that the designed sensor operates in the frequency range of 0.1-2123 Hz and has a voltage sensitivity of 173.49 mV / g. This sensor can meet the requirements for monitoring deformation of rock and soil in mining goaf areas. Attached Figure Description

[0056] Figure 1 This is a flowchart of the optimization method for micro-vibration monitoring piezoelectric accelerometers based on the NSGA-II algorithm of this invention;

[0057] Figure 2 This is a schematic diagram of the geometric structure of the piezoelectric sensor of the present invention;

[0058] Figure 3 This is a diagram showing the Pareto optimal solution set results of this invention;

[0059] Figure 4 This is a frequency response curve of the sensor of the present invention;

[0060] Figure 5 The waveform of the vibration signal detected by the sensor designed for this invention.

[0061] In the diagram: 1. Housing, 2. Piezoelectric plate, 3. Base, 4. Socket core, 5. Mass block, 6. Conductive plate, 7. Insulating plate, 8. Fastener. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] Please see Figure 1-5 This invention provides a technical solution: an optimization method for a piezoelectric accelerometer sensor for microseismic monitoring based on the NSGA-II algorithm, specifically including the following steps:

[0064] S1. Based on the working principle of piezoelectric sensors, a mechanical model is established, the theoretical expressions for the resonant frequency and sensitivity of piezoelectric sensors are derived, the structure of a rock and soil deformation monitoring sensor for mining goaf areas is designed, and the material selection of each component is determined.

[0065] S2. Then, establish the finite element model of the designed sensor and perform modal analysis, harmonic vibration response, piezoelectric analysis and experimental analysis respectively.

[0066] S3. Using the height of the mass block, the height of the piezoelectric element, the thickness of the piezoelectric element, and the height of the central column as design variables, the NSGA-II genetic algorithm is used to optimize the structural dimensions of the designed sensor to obtain the optimal combination of structural parameters. That is, when the height of the mass block is 10.6 mm, the thickness of the piezoelectric element is 3.29 mm, the height of the piezoelectric element is 8.1 mm, and the height of the central column is 19 mm, the sensor design reaches the optimal level. The optimized sensor frequency is increased by 2.68%, and the voltage is increased by 8.96%.

[0067] S4. The designed sensor was calibrated and tested using a micro-vibration signal by building an experimental platform.

[0068] In this embodiment of the invention, the phenomenon that the polarization state of a crystal changes and generates charge when an object is subjected to an external force is called the piezoelectric effect. The working principle of the piezoelectric sensor is based on the piezoelectric effect, which converts the measured mechanical vibration into electrical energy. The simplified dynamic model of the piezoelectric sensor is represented by a single-degree-of-freedom model, including a mass m, a damper c, and a spring k.

[0069] In this embodiment of the invention, the piezoelectric sensor is fixedly connected to the surface of the vibration generator by bottom bolts, and fasteners connect the mass block, piezoelectric element and central support, and apply a certain prestress to ensure the rigid connection of the sensor as a whole.

[0070] When the piezoelectric sensor detects a change in acceleration, due to the inertia of the mass block and the rigid compression of the fasteners, the central support and the mass block exert tangential stress on the piezoelectric element in the same direction as the vibration. This causes the piezoelectric element to deform, resulting in a change in charge, thus converting the acceleration load into electrical energy. The equilibrium equation of the mass block can be derived from the equivalent system, as follows:

[0071]

[0072] In the formula: m is the mass block; k is the spring constant; c is the viscous damping coefficient; x1 is the actual displacement of the vibration table; x0 is the displacement of the mass block relative to the vibration table.

[0073] The equilibrium equations of the mass block can be transformed into the differential equations of the equivalent system as follows:

[0074]

[0075] In the formula: a is the acceleration load;

[0076] Performing a Fourier transform again yields:

[0077]

[0078] In the formula: ω n ζ is the sensor's natural frequency; ζ is the sensor's damping ratio; ω is the operating frequency.

[0079] The calculation is as follows:

[0080]

[0081]

[0082] As can be seen from the above formula, the natural frequency is one of the most important performance indicators in piezoelectric accelerometers, and it is determined by the equivalent stiffness and the mass of the mass block.

[0083] The resonant frequency of a piezoelectric sensor can be given by the following formula:

[0084]

[0085] The sensor displacement frequency response function for each fundamental acceleration can be expressed as:

[0086]

[0087] Assuming the piezoelectric sensor is subjected to an inertial load, the tangential stress acting on the mass block is as follows:

[0088] F = ma;

[0089] The piezoelectric element generates electrical energy Q that is proportional to the tangential stress F:

[0090] Q = d ij F = d ij ma=d ij kx0(t);

[0091] In the formula: d ij It is the piezoelectric constant;

[0092] The charge sensitivity of the piezoelectric sensor is further obtained as follows:

[0093]

[0094] In the formula: Q is the amount of charge generated; S Q This refers to the sensor's charge sensitivity.

[0095] The equivalent capacitance of a single component is expressed as:

[0096]

[0097] Where: ε r ε is the relative permittivity. o Where is the vacuum dielectric constant, S is the area of ​​the piezoelectric element, and d is the thickness of the piezoelectric element;

[0098] The voltage sensitivity of the piezoelectric sensor is further obtained as follows:

[0099]

[0100] In this embodiment of the invention, the piezoelectric sensor has low phase distortion within its operating frequency range, which is beneficial for improving the quality of the recorded signal. When the sensor's operating frequency is greater than one-third of the resonant frequency, the sensor's sensitivity will be distorted, and the degree of distortion reaches its maximum when it approaches the resonant frequency.

[0101] In this embodiment of the invention, step S3 of the NSGA-II genetic algorithm specifically includes the following steps:

[0102] The optimal solution set of T1 and Pareto has a total of 'a' solutions. Using the two objective functions as evaluation metrics, we obtain the metric matrix S:

[0103] S=(s mn ) a×2 (m = 1, 2, ..., a; n = 1, 2);

[0104] T2, elements of the range standardization index matrix:

[0105]

[0106] In the formula: x ij It is the value in the i-th row and j-th column of the data, max(x)j ) and min(x j ) are the maximum and minimum values ​​in the j-th column of data, respectively, and r ij It is standardized data;

[0107] T3. Evaluate and rank the solutions using the minimum difference method:

[0108]

[0109] In the formula: x1 is the difference between the calculated targets, and f1(x1) and f2(x2) are two target values ​​of x1.

[0110] In this embodiment of the invention, the NSGA-II genetic algorithm is programmed using MATLAB-R2020b software. The population size of the NSGA-II genetic algorithm is set to 200, the number of iterations is 500, the crossover probability is 0.9, and the mutation probability is 0.2. The Pareto optimal solution set is obtained using MATLAB-R2020b programming software.

[0111] Optimization results:

[0112] In this invention, MATLAB-R2020b software was used to program the NSGA-II genetic algorithm. The population size of the NSGA-II genetic algorithm was set to 200, the number of iterations to 500, the crossover probability to 0.9, and the mutation probability to 0.2. The Pareto optimal solution set was obtained using MATLAB-R2020b software as follows: Figure 3 As shown.

[0113] Decision outcome:

[0114] The top 10 solutions in the Pareto optimal solution set obtained by minimizing the difference method are shown in Table 1:

[0115] Table 1 shows the top 10 solutions in the Pareto optimal solution set obtained from the decision.

[0116]

[0117] The solution of order 1 is taken as the optimal scheme of this optimization design. The results of the optimal scheme are compared with the initial scheme. The comparison results are shown in Table 2:

[0118] Table 2 Comparison of the optimal solution and the initial solution

[0119]

[0120]

[0121] As shown in Table 2, the optimal scheme increases the frequency by 2.68% and the voltage by 8.96% compared to the initial scheme. According to formula (12), the voltage sensitivity can be calculated to be 173.49 mV / g, which proves the effectiveness of the method in this paper for sensor optimization design.

[0122] In summary, this invention establishes a mechanical model of the piezoelectric sensor based on its working principle, and derives the theoretical expressions for the resonant frequency and sensitivity of the piezoelectric sensor. A structure for a rock and soil deformation monitoring sensor in a mining goaf area was designed, and the material selection for each component was determined. Then, a finite element model of the designed sensor was established, and modal analysis, harmonic vibration response, piezoelectric analysis, and experimental analysis were performed. Using the height of the mass block, the height and thickness of the piezoelectric element, and the height of the central column as design variables, the NSGA-II genetic algorithm was used to optimize the structural dimensions of the designed sensor, obtaining the optimal combination of structural parameters: a mass block height of 10.6 mm, a piezoelectric element thickness of 3.29 mm, a piezoelectric element height of 8.1 mm, and a central column height of 19 mm. The optimized sensor achieved an optimal design, with a 2.68% increase in frequency and an 8.96% increase in voltage. Finally, calibration experiments and micro-vibration signal tests were conducted on the designed sensor using an experimental platform. Experimental results show that the designed sensor operates in the frequency range of 0.1-2123Hz and has a voltage sensitivity of 173.49 mV / g. This sensor can meet the requirements for monitoring deformation of soil and rock masses in mining goaf areas.

[0123] Sensor calibration experiment:

[0124] Calibration testing is a prerequisite for ensuring the normal operation of piezoelectric sensors. Through calibration, technical specifications such as sensitivity and operating frequency of the piezoelectric sensor can be obtained. The calibration test setup for a piezoelectric sensor consists of a computer, a vibration table controller and signal acquisition instrument, a power amplifier, a vibrator, a standard sensor, a sensor to be calibrated, and a charge amplifier. The standard piezoelectric accelerometer used is model CK-8305, with a charge sensitivity of 1.25 pC / g and an operating frequency of 1-10000 Hz. The vibration table controller and signal acquisition instrument is model WS-5932 / U160216-DA2, the power amplifier is model GF-500W, the vibrator is model JZ-50, and the charge amplifier is model WS-2411Z.

[0125] In the calibration experiment, the signal was continuously sampled. The standard sensor and the sensor to be calibrated were mounted back-to-back on the vibrator, and low-noise shielded cables were selected to reduce the impact of noise signals on the calibration experiment. The signal conditioner controlled the magnitude of the external load through the Vib'SOK vibration table control software on the computer. The vibration table control and signal acquisition instrument generated a sinusoidal impact signal, which, after processing by the power amplifier, generated the required vibration signal from the vibrator. At this time, the sensor generated a charge signal, which was amplified by the charge amplifier and transmitted again to the vibration table control and signal acquisition instrument. The analog signal was converted into a digital signal by an A / D converter and then transmitted to the computer for data processing using software.

[0126] Calibration experiment results:

[0127] Due to limitations of the experimental equipment, the operating frequency of the exciter was 0–3000 Hz. Test vibration frequencies of 160 Hz, 500 Hz, 1000 Hz, and 2000 Hz were selected. The gain of the charge amplifier connected to the standard sensor was adjusted to 0.1, and the gain of the charge amplifier connected to the sensor to be calibrated was adjusted to 1. Under a 1g acceleration load, the exciter's excitation signal scan range was 1–3000 Hz, and the operating frequency of the designed sensor was acquired in real time. Figure 4 This represents the amplitude of the frequency response curve.

[0128] The frequency response curve of the designed sensor is approximately a straight line within the range of 1-3000Hz, with an amplitude variation of less than 3dB. This indicates that the designed sensor can operate stably within the range of 0.1-2123Hz. This is similar to the simulation results, but there is a certain deviation. The main reasons are as follows: (1) There are processing errors in the manufacturing process of the sensor parts. (2) Assembly errors and appropriate bolt preload were not taken into account.

[0129] Microseismic signal test:

[0130] To verify the feasibility of the designed sensor in detecting vibration signals, a vibration experiment was conducted on the platform. A micro-vibration signal was selected for experimental verification. By sending a micro-vibration signal to the exciter, the vibration table received the command and generated a small vibration. Figure 5 The experimental results show that the designed piezoelectric sensor is feasible for detecting vibration signals, and it has high sensitivity within the operating frequency range.

[0131] Furthermore, any content not described in detail in this specification is existing technology known to those skilled in the art.

[0132] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0133] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An optimization method for a piezoelectric accelerometer sensor for microseismic monitoring based on the NSGA-II algorithm, characterized in that: Specifically, the following steps are included: S1. Based on the working principle of piezoelectric sensors, a mechanical model is established, the theoretical expressions for the resonant frequency and sensitivity of piezoelectric sensors are derived, the structure of a rock and soil deformation monitoring sensor for mining goaf areas is designed, and the material selection of each component is determined. S2. Then, establish the finite element model of the designed sensor and perform modal analysis, harmonic vibration response, piezoelectric analysis and experimental analysis respectively. S3. Then, using the height of the mass block, the height of the piezoelectric element, the thickness of the piezoelectric element, and the height of the central column as design variables, the NSGA-II genetic algorithm is used to optimize the structural dimensions of the designed sensor to obtain the optimal combination of structural parameters, namely, the height of the mass block is 10.6 mm and the thickness of the piezoelectric element is 3.29 mm. S4. The designed sensor was calibrated and tested for micro-vibration signals by building an experimental platform.

2. The optimization method for a piezoelectric accelerometer based on the NSGA-II algorithm for microseismic monitoring according to claim 1, characterized in that: The NSGA-II genetic algorithm in step S3 specifically includes the following steps: The optimal solution set of T1 and Pareto has a total of 'a' solutions. Using the two objective functions as evaluation metrics, we obtain the metric matrix S: S=(s mn ) a×2 (m=1,2,...,a;n=1,2); T2, elements of the range standardization index matrix: In the formula: x ij It is the value in the i-th row and j-th column of the data, max(x) j ) and min(x j ) are the maximum and minimum values ​​in the j-th column of data, respectively, and r ij It is standardized data; T3. Evaluate and rank the solutions using the minimum difference method: In the formula: x1 is the difference between the calculated targets, and f1(x1) and f2(x2) are two target values ​​of x1.

3. The optimization method for a piezoelectric accelerometer based on the NSGA-II algorithm for microseismic monitoring according to claim 2, characterized in that: The NSGA-II genetic algorithm was programmed using MATLAB-R2020b software. The population size of the NSGA-II genetic algorithm was set to 200, the number of iterations to 500, the crossover probability to 0.9, and the mutation probability to 0.

2. The Pareto optimal solution set was obtained using MATLAB-R2020b programming software.

Images