Piezoelectric admittance calculation method and device, storage medium and computer equipment

Abstract

The present application relates to the technical field of civil engineering structure monitoring and simulation, in particular to a piezoelectric admittance calculation method. The present application divides the model by different sizes of grids, respectively calculates the elastic modulus discrete coefficients of different unit size models, determines the characteristic unit size according to the change curve of the elastic modulus discrete coefficients with the unit size, and further determines the characteristic model, and then disperses the characteristic model into a finite number of units by using the three-dimensional time domain spectral element method. The characteristic unit size is the maximum unit size that can be divided under the premise that the non-homogeneity of concrete is basically unchanged, which is larger than the unit size divided by the finite element method, and the number of dispersed units is less, thereby reducing the calculation cost, improving the efficiency, and solving the technical problem of low efficiency of calculating the piezoelectric admittance of the concrete three-dimensional mesoscopic model in the prior art.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structure monitoring and simulation technology, and in particular to a piezoelectric admittance calculation method, device, storage medium and computer equipment. Background Technology

[0002] Piezoelectric admittance technology operates at high frequencies (1kHz-1MHz), making it sensitive to initial structural damage. It possesses both sensing and actuation effects, is lightweight, and has minimal impact on the structural integrity. It can be adhered to the surface of existing structures or embedded within new structures for monitoring, making it a proactive health monitoring method. Research indicates that piezoelectric ceramic actuation / sensing units can identify micro-damage in concrete, accurately locating and qualitatively describing its size. In current piezoelectric admittance-based concrete health monitoring research, concrete is often simplified as a homogeneous material. However, concrete is actually a multiphase composite material, which develops microcracks and microvoids of varying sizes (micro-damage) during construction and operation. During use, micro-damage at different levels and scales initiation, propagation, and connection occur within the concrete material, which are difficult to reflect in a homogeneous model. Therefore, it is necessary to establish a heterogeneous concrete model incorporating piezoelectric ceramic actuation / sensing units to explore the changes in piezoelectric admittance caused by the development of micro-cracks within the concrete, thereby improving the monitoring accuracy of the piezoelectric admittance method. The concrete microstructure model simplifies concrete into a three-phase composite material consisting of aggregate particles, mortar matrix, and the interfacial transition zone (ITZ) between the two, thus considering the heterogeneous properties of concrete. However, the three-dimensional concrete microstructure model based on the finite element method requires dividing the material into small elements to obtain a stable numerical solution, resulting in low computational efficiency. This significantly limits the application of numerical models considering the piezoelectric admittance of concrete heterogeneity, necessitating the search for a simulation method that balances computational accuracy and efficiency. Summary of the Invention

[0003] This invention provides a method for calculating piezoelectric admittance, which solves the technical problem of low efficiency in calculating piezoelectric admittance using a three-dimensional microscopic model of concrete in the prior art.

[0004] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows:

[0005] In some embodiments, the present invention provides a method for calculating piezoelectric admittance, comprising the following steps:

[0006] Based on the concrete aggregate fraction, a three-dimensional meso-geometric model of concrete containing piezoelectric ceramic driving / sensing units is established using an aggregate random generation and placement algorithm.

[0007] The model is divided into several grids of different specifications to obtain several models with different size elements. According to the mesoscopic element equivalence method, the mean and standard deviation of the element elastic modulus of the model are calculated, and the elastic modulus dispersion coefficient is further obtained.

[0008] Based on the curve of the variation coefficient of elastic modulus with the element size, the maximum element size that can be divided under the premise that the non-homogeneity of concrete remains basically unchanged is determined as the characteristic element size, and the model corresponding to the characteristic element size is taken as the characteristic model.

[0009] The feature model is discretized into a finite number of units using a three-dimensional time-domain spectral unit;

[0010] Based on the piezoelectric coupling equation, the mass matrix, stiffness matrix, and damping matrix of the discretized three-dimensional time-domain spectral unit of concrete, and the piezoelectric stiffness matrix and dielectric stiffness matrix of the three-dimensional time-domain spectral unit of the piezoelectric ceramic driving / sensing unit are established, and the governing equations are obtained.

[0011] The displacement of the piezoelectric ceramic driving / sensing unit under unit voltage at different excitation frequencies is obtained according to the control equation; the surface charge of the piezoelectric ceramic driving / sensing unit at each excitation frequency is obtained according to the node potential and displacement at each excitation frequency, and then the piezoelectric admittance value of the piezoelectric ceramic driving / sensing unit at each excitation frequency is obtained.

[0012] In some implementations, the model building process includes:

[0013] Fine aggregates with a particle size smaller than the threshold are simplified into cement mortar, and coarse aggregates with a particle size larger than the threshold are simplified into spheres;

[0014] Based on the concrete aggregate fraction, a model containing piezoelectric ceramic driving / sensing units is established using a random aggregate generation and placement algorithm. When establishing the model, the coordinates of the center of the spheres are determined using the Monte Carlo method. The spheres conform to a random distribution, do not intersect with the boundary of the model, do not overlap or intersect with each other, and the content of the spheres reaches the concrete aggregate fraction.

[0015] In some implementations, the process of obtaining the element elastic modulus discrepancy coefficients of the model includes:

[0016] The model is divided into several grids of different specifications to obtain several models with units of different sizes. The unit size of the region below the piezoelectric ceramic driving / sensing unit matches the piezoelectric ceramic driving / sensing unit.

[0017] For a single model, based on the volume fraction of each phase material in each unit, the mechanical properties of each unit are processed using the composite material equivalence method, and are equivalent to an isotropic homogeneous medium; the elastic modulus of each unit in the single model is calculated respectively.

[0018] Based on the elastic modulus of each unit, the average value and standard deviation of the elastic modulus of a single model are calculated, and the coefficient of variation of the elastic modulus is further obtained.

[0019] Calculate the coefficient of variation of the elastic modulus for all the aforementioned models according to the steps described above.

[0020] In some implementations, the process of determining the size of the feature unit includes:

[0021] Plot the curve of the variation coefficient of elastic modulus with element size;

[0022] The cell size corresponding to the inflection point of the curve is taken as the feature cell size, and the cell corresponding to the feature cell size is the feature cell.

[0023] In some implementations, the process of discretizing the feature model into a finite number of units includes:

[0024] Based on the size of the feature unit, the model is discretized using a three-dimensional time-domain spectral unit, and each time-domain spectral unit and node is numbered sequentially.

[0025] Configure interpolation nodes within the spectral unit according to the GLL integration points;

[0026] Lagrange interpolation is performed on the interpolation nodes to obtain the shape function of the time-domain spectral unit in the ξγη direction, and the displacement function of the time-domain spectral unit is further obtained.

[0027] In some implementations, the process of obtaining the governing equations includes:

[0028] Establish the element mass matrix M of the three-dimensional time-domain spectral element of concrete. e Element stiffness matrix K e and damping matrix C e ;

[0029] Establish the piezoelectric stiffness matrix of the three-dimensional time-domain spectral unit of the piezoelectric ceramic driving / sensing unit. and dielectric stiffness matrix

[0030] By assembling the stiffness matrix, mass matrix, damping matrix, piezoelectric stiffness matrix, and dielectric stiffness matrix of each unit, the governing equations of the piezoelectric coupling system are obtained, expressed as:

[0031]

[0032] In the formula, M, C, K u , φ, F, K uφ K φ Q and Q represent the overall mass matrix, overall damping matrix, overall stiffness matrix, equivalent potential vector, equivalent nodal force vector, overall piezoelectric stiffness matrix, overall dielectric stiffness matrix, and charge vector of the characteristic model structure, respectively.

[0033] In some embodiments, the process of obtaining the piezoelectric admittance value includes:

[0034] The piezoelectric ceramic driving / sensing unit is regarded as a driver, with its lower surface grounded and an electric potential applied to its upper surface. The equivalent nodal force caused by the electric potential and the displacement caused by the piezoelectric ceramic driving / sensing unit as a driver at different excitation frequencies are calculated.

[0035] The piezoelectric ceramic driving / sensing unit is regarded as a sensor, and the surface charge of the piezoelectric ceramic driving / sensing unit at each excitation frequency is obtained based on the nodal potential and displacement at each excitation frequency.

[0036] Calculate the piezoelectric admittance value.

[0037] In a second aspect embodiment, the present invention provides a piezoelectric admittance calculation device, comprising:

[0038] The modeling module is used to build a three-dimensional micro-geometric model of concrete containing piezoelectric ceramic driving / sensing units based on the concrete aggregate fraction and using an aggregate random generation and placement algorithm.

[0039] The element division module is used to divide the model into several grids of different specifications to obtain several elements of the model with different specifications and sizes. According to the meso-equalization method, the mean and standard deviation of the element elastic modulus of the model are calculated, and the elastic modulus dispersion coefficient is further obtained.

[0040] The feature element size determination module is used to determine the maximum element size that can be divided under the premise that the non-homogeneity of concrete remains basically unchanged, based on the curve of the variation coefficient of elastic modulus with element size, and to use the model corresponding to the feature element size as the feature model.

[0041] A discrete module is used to discretize the feature model into a finite number of units using a three-dimensional time-domain spectral unit;

[0042] The first data processing module is used to establish the mass matrix, stiffness matrix and damping matrix of the discretized three-dimensional time-domain spectral unit of concrete, and the piezoelectric stiffness matrix and dielectric stiffness matrix of the three-dimensional time-domain spectral unit of the piezoelectric ceramic driving / sensing unit, based on the piezoelectric coupling equation, and to obtain the governing equation.

[0043] The second data processing module is used to obtain the displacement of the piezoelectric ceramic driving / sensing unit under unit voltage at different excitation frequencies according to the control equation; and to obtain the surface charge of the piezoelectric ceramic driving / sensing unit at each excitation frequency according to the nodal potential and displacement at each excitation frequency, thereby obtaining the piezoelectric admittance value of the piezoelectric ceramic driving / sensing unit at each excitation frequency.

[0044] In a third aspect embodiment, the present invention provides a storage medium comprising: at least one instruction that, when executed, implements the method as described in any of the preceding embodiments.

[0045] In a fourth aspect embodiment, the present invention provides a computer device including a processor, a memory, and a computer program stored in the memory, the computer program being executable on the processor, the computer program performing the method as described in any of the preceding claims.

[0046] Beneficial effects

[0047] This invention divides the model into grids of different sizes, calculates the elastic modulus dispersion coefficients for models with different element sizes, determines the characteristic element size based on the variation curve of the elastic modulus dispersion coefficients with element size, and thus determines the characteristic model. The characteristic model is then discretized into a finite number of elements using the three-dimensional time-domain spectral element method. The governing equations are obtained based on the piezoelectric coupling equations, and the displacements caused by the piezoelectric ceramic driven sensing elements under unit voltages at different excitation frequencies are calculated based on the governing equations. The surface charge is then calculated based on the nodal potentials and displacements at each excitation frequency, thereby obtaining the piezoelectric admittance value. The characteristic element size is the maximum element size that can be divided under the premise that the heterogeneity of concrete remains essentially unchanged. Compared with the element size divided by the finite element method, it is larger, and the number of discretized elements is less, reducing computational cost and improving efficiency. This solves the technical problem of low efficiency in calculating piezoelectric admittance of three-dimensional microstructure models of concrete in existing technologies.

[0048] Additional aspects and advantages of embodiments of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of embodiments of the invention. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] The methods, systems, and / or procedures shown in the accompanying drawings will be further described with reference to exemplary embodiments. These exemplary embodiments will be described in detail with reference to the drawings. These exemplary embodiments are non-limiting exemplary embodiments, wherein example figures represent similar mechanisms in the various views of the drawings.

[0051] Figure 1 This is a flowchart of the piezoelectric admittance calculation method in the first aspect embodiment;

[0052] Figure 2 This is a flowchart of the model creation process in one embodiment;

[0053] Figure 3 This is a schematic diagram of a three-dimensional micro-geometric model of concrete in one embodiment;

[0054] Figure 4 This is a flowchart of the discrete coefficients of the element elastic modulus of the model obtained in one embodiment;

[0055] Figure 5 This is a schematic diagram of the unit dimensions in one embodiment;

[0056] Figure 6 This is a flowchart illustrating the process of determining the size of a feature unit in one embodiment;

[0057] Figure 7 This is a curve showing the variation of the elastic modulus dispersion coefficient with the element size and a schematic diagram of the characteristic element size in one embodiment;

[0058] Figure 8 This is a flowchart of discretizing the feature model into a finite number of units in one embodiment;

[0059] Figure 9 This is a schematic diagram of the feature model after it has been discretized into a finite number of units in one embodiment;

[0060] Figure 10 This is a flowchart of the process for obtaining the control equations in one embodiment;

[0061] Figure 11 This is a flowchart of the piezoelectric admittance calculation in one embodiment;

[0062] Figure 12 This is a comparison chart of admittance curves for heterogeneous and homogeneous concrete models with different aggregate fractions (10%, 20%, 30%, 40%) provided in one embodiment.

[0063] Figure 13 This is a structural block diagram of the piezoelectric admittance calculation device provided in the second aspect embodiment;

[0064] Figure 14 This is a structural block diagram of the computer device provided in the fourth aspect embodiment. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0066] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0067] Please see Figure 1 In a first aspect embodiment, this application provides a method for calculating piezoelectric admittance, characterized in that it includes:

[0068] S1. Based on the concrete aggregate fraction, a three-dimensional micro-geometric model of concrete containing piezoelectric ceramic driving / sensing units is established using an aggregate random generation and placement algorithm.

[0069] Preferably, the piezoelectric ceramic driving / sensing unit can be PZT (lead zirconate titanate piezoelectric ceramic sensor), and PZT will be used as an example of the piezoelectric ceramic driving / sensing unit in the following text.

[0070] Specifically, the PZT in the model can be attached to the model surface or embedded in the model. In this embodiment, the PZT is attached to the middle position of the model surface.

[0071] Please see Figure 2 and Figure 3 In some implementations, the model building process specifically includes:

[0072] S11. Fine aggregates with a particle size smaller than the threshold are simplified to cement mortar, and coarse aggregates with a particle size larger than the aforementioned threshold are simplified to spheres.

[0073] Specifically, in this embodiment, the threshold is set to 5mm.

[0074] S12. Based on the concrete aggregate fraction, a model containing PZT is established using a random aggregate generation and placement algorithm. When establishing the model, the Monte Carlo method is used to determine the coordinates of the center of each coarse aggregate sphere. The spheres are randomly distributed, do not intersect with the model boundary, do not overlap or intersect with each other, and the sphere content reaches the aforementioned concrete aggregate fraction.

[0075] S2. Divide the model into several grids of different specifications to obtain several models with different element sizes. Based on the mesoscopic element equivalence method, calculate the mean and standard deviation of the element elastic modulus of the model, and further obtain the elastic modulus dispersion coefficient.

[0076] Please see Figure 4 In some implementations, the process of obtaining the discrete coefficients of the element elastic modulus of the model specifically includes:

[0077] S21. Divide the model into several grids of different specifications to obtain several models with different unit sizes. The size of the region below PZT matches that of PZT.

[0078] Specifically, matching the size of the region below the PZT with the PZT means that the element size of the region below the PZT matches the excitation frequency of the PZT, ensuring that the PZT element is coupled with the bonding layer and concrete nodes below it.

[0079] Please see Figure 5 Specifically, during mesh generation, to ensure coupling between the externally attached PZT and the concrete nodes, the element sizes resulting from the meshing of a single model are not consistent. The element sizes can be categorized into three regions. Region I consists of elements directly beneath the PZT, whose element sizes match the PZT excitation frequency; Region II elements are only related to the model's own mesh generation; Region III elements are transitional elements connecting Region I and Region II elements, and their size is jointly determined by the Region I and Region II elements.

[0080] S22. For a single model, based on the volume fraction of each phase material in each unit, the mechanical properties of each unit are processed by the composite material equivalence method, and equivalent to an isotropic homogeneous medium; forming a model with the same properties and isotropic within the unit, but different properties between units; calculate the elastic modulus of each unit in the single model respectively.

[0081] Specifically, the elastic modulus, shear modulus, and Poisson's ratio of the equivalent element are calculated using the following formula:

[0082]

[0083]

[0084]

[0085] In the formula, n represents the quantity of coarse aggregate, ITZ, and fine aggregate, and their volume fractions are C1, C2, ..., C6, respectively. n The elastic moduli are E1, E2, ..., E n The shear moduli are G1, G2, ..., G n Poisson's ratios are v1, v2, ..., v n E m G m and v m These are the elastic modulus, shear modulus, and Poisson's ratio of the equivalent element, respectively.

[0086] S23. Based on the elastic modulus of each element, calculate the average value and standard deviation of the elastic modulus of a single model, and further obtain the coefficient of variation of the elastic modulus.

[0087] Specifically, the coefficient of variation of the elastic modulus is calculated using the following formula:

[0088] C=E(x) / S(x) (4)

[0089] In the formula, E(x) is the average elastic modulus of the model, S(x) is the standard deviation, and C is the coefficient of variation of the elastic modulus.

[0090] S24. Calculate the coefficient of variation of the elastic modulus for all models according to steps S22 to S23.

[0091] S3. Based on the curve of the variation of the elastic modulus dispersion coefficient with the element size, the maximum element size that can be divided under the premise that the non-homogeneity of concrete remains basically unchanged is determined as the characteristic element size, and the model corresponding to the characteristic element size is taken as the characteristic model.

[0092] Please see Figure 6 In some implementations, the process of determining the feature unit size specifically includes:

[0093] S31. Plot the curve of the variation of the elastic modulus dispersion coefficient with the unit size.

[0094] S32. The unit size corresponding to the inflection point of the curve is taken as the feature unit size, and the unit corresponding to the feature unit size is the feature unit.

[0095] Please see Figure 7According to the curve of the coefficient of variation of elastic modulus with element size, the coefficient of variation of the modulus of the model before the inflection point is small, indicating that the non-homogeneity of the concrete is small. After the inflection point, the coefficient of variation of the modulus of the model decreases, indicating that the non-homogeneity of the concrete decreases. That is, the element size after the inflection point has a greater impact on the non-homogeneity of the concrete. Therefore, the element size corresponding to the inflection point is the maximum element size that can be divided under the premise that the non-homogeneity of the concrete remains basically unchanged.

[0096] S4. The feature model is discretized into a finite number of units using three-dimensional time-domain spectral units;

[0097] Please see Figure 8 and Figure 9 In some implementations, the process of discretizing the feature model into a finite number of units specifically includes:

[0098] S41. Based on the size of the feature element, the model is discretized using a three-dimensional time-domain spectral element to obtain a concrete three-dimensional time-domain spectral element and a PZT three-dimensional time-domain spectral element. Each time-domain spectral element and node is numbered sequentially.

[0099] S42. Configure the interpolation nodes within the spectral unit according to the GLL integration points, with the node coordinates being the root of the following formula:

[0100]

[0101] in, and Let N1, N2, and N3 be the first derivatives of the Legendre polynomials in the directions ξ, γ, and η, respectively.

[0102] S43. Perform Lagrange interpolation on the above interpolation nodes to obtain the shape functions of the time-domain spectral element in the directions of ξ, γ, and η, and further obtain the displacement function of the time-domain spectral element.

[0103] S5. Based on the piezoelectric coupling equation, establish the mass matrix, stiffness matrix, and damping matrix of the discretized three-dimensional time-domain spectral element of concrete, and the piezoelectric stiffness matrix and dielectric stiffness matrix of the three-dimensional time-domain spectral element of PZT, and obtain the governing equations.

[0104] Please see Figure 10 In some implementations, the process of obtaining the governing equations specifically includes:

[0105] S51. Establish the element mass matrix M of the three-dimensional time-domain spectral element of concrete. e Element stiffness matrix K e and damping matrix C e , can be represented as:

[0106]

[0107]

[0108] C e =ηM e (8)

[0109] In the formula, ρ is the mass density, and ω i ,ω j ,ω k The integral weights for ξ, γ, and η are respectively, N is the unit shape function matrix, and J is the integral weights for ξ, γ, and η. e Let C be the Jacobin matrix mapping from the xyz natural space to the ξγη parameter space, and B be the material elasticity matrix. e Let η be the structural strain matrix, and η be the mass damping proportionality coefficient.

[0110] S52. Establish the piezoelectric stiffness matrix of the PZT three-dimensional time-domain spectral unit. and dielectric stiffness matrix It can be represented as:

[0111]

[0112]

[0113] In the formula, Q e Let be the charge at the nodes on the element surface. This is the unit potential matrix.

[0114] S53. Assemble the stiffness matrix, mass matrix, damping matrix, piezoelectric stiffness matrix, and dielectric stiffness matrix of each unit to obtain the governing equations of the piezoelectric coupling system, which can be expressed as:

[0115]

[0116] In the formula, M, C, K u , φ, F, K uφ K φ Q and Q represent the overall mass matrix, overall damping matrix, overall stiffness matrix, equivalent potential vector, equivalent nodal force vector, overall piezoelectric stiffness matrix, overall dielectric stiffness matrix, and charge vector of the characteristic model structure, respectively.

[0117] S6. Calculate the displacement of PZT under unit voltage at different excitation frequencies according to the control equation; calculate the surface charge of PZT at each excitation frequency according to the nodal potential and displacement at each excitation frequency, and then obtain the piezoelectric admittance value of PZT at each excitation frequency.

[0118] Please see Figure 11 In some implementations, the process of obtaining the piezoelectric admittance value specifically includes:

[0119] S61. Consider the PZT as a actuator, with its lower surface grounded and a potential V applied to its upper surface. Calculate the equivalent nodal force caused by the upper surface potential V and the displacement U caused by the PZT as an actuator at different excitation frequencies ω. e .

[0120] S62. Treating the PZT as a sensor, based on the nodal potential φ at each excitation frequency ω. e and displacement U e The surface charge Q of PZT at various excitation frequencies ω was obtained. e .

[0121] S63. Calculate the piezoelectric admittance value using the following formula:

[0122]

[0123] In the formula, i is the imaginary unit.

[0124] To make the features and advantages of this patent more apparent and understandable, a preferred embodiment is provided below, and the invention is described in detail as follows:

[0125] The main content of this embodiment is to simulate the piezoelectric admittance of a primary concrete specimen, considering... Figure 3 The concrete test block shown has a side length of 100mm, a coarse aggregate volume fraction of 30%, and an aggregate particle size between 5-20mm.

[0126] In mesh generation, to ensure coupling between the external PZT and the concrete nodes, the element sizes are not entirely uniform. For example... Figure 5 As shown, concrete element sizes can be divided into three categories in the PZT-concrete microstructure model. The concrete mesh generation depends on the element sizes of region I and region II. For example... Figure 7 As shown, in this embodiment, the I region unit and the II region unit are respectively taken as six groups: 0.5*0.5*2, 2*2*2; 2.5*2.5*2, 4*4*2; 2.5*2.5*2, 6*6*2; 2.5*2.5*2, 6*6*4; 2.5*2.5*2, 12*12*2; 2.5*2.5*2, 46*46*2. The dispersion coefficient of the elastic modulus of the six groups of models is calculated, and the trend graph of the dispersion coefficient of the elastic modulus with the unit size is plotted. The size corresponding to the inflection point is taken as the characteristic unit size, that is, the size of the I region unit is 2.5*2.5*2, and the size of the II region unit is 6*6*2.

[0127] Based on the determined characteristic element size, the mechanical properties of each element are processed using the mesoscopic element equivalence method, equivalent to an isotropic homogeneous medium, thus forming a model where the properties within each element are the same and isotropic, but the properties between elements are different. Different elements have different colors, representing different mechanical properties. Then, based on the Legendre orthogonal polynomial three-dimensional time-domain spectral element method, concrete and PZT are discretized, and the model is discretized into 20032 three-dimensional time-domain spectral elements. The number of displacement interpolation nodes in the x, y, and z axes (ξ, γ, η directions) of each element are 3, 3, and 2 respectively (e.g., ...). Figure 9 As shown in the figure, w, u, and v represent the displacements in the directions ξ, γ, and η, respectively. Compared with the finite element method, the size of the finite element element should not exceed 2 mm. A cubic concrete specimen with a side length of 100 mm needs to be discretized into 217,800 elements, which is computationally expensive and difficult to apply in practical engineering.

[0128] The motion equations of 20032 discretized three-dimensional time-domain spectral elements were established using the elastic dynamics control equations. The element mass matrix, element stiffness matrix, element damping matrix, element piezoelectric stiffness matrix, and element dielectric stiffness matrix were calculated. The element mass matrix and element damping matrix, which were formed in strict diagonal form, were stored in vector form and used in subsequent calculations. The control equations of the system were obtained by assembling the element mass matrix, element stiffness matrix, element damping matrix, element piezoelectric stiffness matrix, and element dielectric stiffness matrix of the 20032 three-dimensional time-domain spectral elements. The piezoelectric admittance of the PZT-concrete structure under the excitation of element voltages with frequencies of 40Hz-400kHz was calculated, and the piezoelectric admittance curve was plotted.

[0129] Please see Figure 12 Based on the above solution process, admittance curves for the heterogeneous concrete model with different aggregate fractions (10%, 20%, 30%, 40%) were calculated and compared with the results of the homogeneous model. For the homogeneous model ( Figure 12 (a) indicates that the coarse aggregate content has the least impact on the EMA signal. As the aggregate content increases, the peak amplitude remains essentially constant, while the frequency increases slightly. This is because the coarse aggregate content only changes the model's elastic modulus and density. However, in heterogeneous models ( Figure 12 (b) The conductivity characteristics in the 150-250 kHz range, which contain the main modal information of the interaction between PZT and the structure, generally show a downward shift at the resonance peak, accompanied by a slight frequency increase. This is because the increase in aggregate content enhances the heterogeneity of concrete, thereby amplifying the dispersion and attenuation of stress waves.

[0130] The simulation results show that the use of the mesoscopic element equivalence method and the Legendre orthogonal polynomial three-dimensional time-domain spectral element method can take into account the heterogeneous characteristics of concrete, making the simulation results closer to the actual situation and significantly reducing the computational cost of the piezoelectric admittance curve. This is of great significance for improving the accuracy of piezoelectric admittance method in identifying concrete damage and promoting the engineering application of piezoelectric admittance method.

[0131] Please see Figure 13 In a second aspect embodiment, this application provides a piezoelectric admittance calculation device, including a modeling module, a unit partitioning module, a feature unit size determination module, a discretization module, a first data processing module, and a second data processing module.

[0132] The modeling module is used to establish a three-dimensional mesoscopic geometric model of concrete containing piezoelectric ceramic driving / sensing units based on the concrete aggregate fraction and using a random aggregate generation and placement algorithm. The element division module is used to divide the model into several meshes of different specifications, resulting in several models with elements of different sizes. Based on the mesoscopic element equivalence method, the mean and standard deviation of the element elastic modulus of the model are calculated, and the elastic modulus dispersion coefficient is further obtained. The feature element size determination module is used to determine the maximum element size that can be divided under the premise that the non-homogeneity of concrete remains basically unchanged, based on the curve of the elastic modulus dispersion coefficient with element size. The model corresponding to the feature element size is used as the feature model. The discretization module is used to discretize the feature model into a finite number of elements using a three-dimensional time-domain spectral unit. The first data processing module is used to establish the mass matrix, stiffness matrix, and damping matrix of the discretized concrete three-dimensional time-domain spectral unit, as well as the piezoelectric stiffness matrix and dielectric stiffness matrix of the three-dimensional time-domain spectral unit of the piezoelectric ceramic driving / sensing unit, based on the piezoelectric coupling equation, to obtain the governing equation. The second data processing module is used to obtain the displacement caused by the piezoelectric ceramic driving / sensing unit under unit voltage at different excitation frequencies based on the governing equation. Based on the nodal potential and displacement at each excitation frequency, the surface charge of the piezoelectric ceramic driving / sensing unit at each excitation frequency is obtained, and then the piezoelectric admittance value of the piezoelectric ceramic driving / sensing unit at each excitation frequency is obtained.

[0133] Each module can be integrated on a single processor, or each module can exist independently in a different processor. Alternatively, two or more modules can be integrated into a single processor. In addition to being implemented in hardware such as processors, these modules can also be implemented as software functional modules.

[0134] In a third aspect of the embodiment, this application provides a computer-readable storage medium including at least one instruction that, when executed, implements any of the above-described piezoelectric admittance calculation methods.

[0135] Please see Figure 14 In a fourth aspect embodiment, this application provides a computer device including a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program implements any of the above-described piezoelectric admittance calculation methods when it is executed.

[0136] The processor and memory are connected via a bus, which can include any number of interconnect buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits such as peripherals, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein.

[0137] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention, which is defined by the claims and their equivalents.

Claims

1. A method for calculating piezoelectric admittance, characterized in that, Includes the following steps: Based on the concrete aggregate fraction, a three-dimensional meso-geometric model of concrete containing piezoelectric ceramic driven sensing units is established using an aggregate random generation and placement algorithm. The concrete three-dimensional micro-geometric model is divided into several grids of different specifications to obtain several concrete three-dimensional micro-geometric models with different size elements. According to the micro-element equivalence method, the mean and standard deviation of the element elastic modulus of the concrete three-dimensional micro-geometric model are calculated, and the elastic modulus dispersion coefficient is further obtained. Based on the curve of the variation coefficient of elastic modulus with the element size, the maximum element size that can be divided under the premise that the heterogeneity of concrete remains unchanged is determined as the characteristic element size, and the model corresponding to the characteristic element size is taken as the characteristic model. The feature model is discretized into a finite number of units using a three-dimensional time-domain spectral unit; Based on the piezoelectric coupling equation, the mass matrix, stiffness matrix, and damping matrix of the discretized three-dimensional time-domain spectral unit of concrete, and the piezoelectric stiffness matrix and dielectric stiffness matrix of the three-dimensional time-domain spectral unit of the piezoelectric ceramic driven sensing unit are established, and the governing equations are obtained. The displacement of the piezoelectric ceramic driven sensing unit under different excitation frequencies and unit voltages is obtained according to the control equation. Based on the nodal potential and displacement at each excitation frequency, the surface charge of the piezoelectric ceramic driven sensing unit at each excitation frequency is obtained, and then the piezoelectric admittance value of the piezoelectric ceramic driven sensing unit at each excitation frequency is obtained.

2. The piezoelectric admittance calculation method as described in claim 1, characterized in that, The process of establishing the three-dimensional micro-geometric model of concrete includes: Fine aggregates with a particle size smaller than the threshold are simplified into cement mortar, and coarse aggregates with a particle size larger than the threshold are simplified into spheres; Based on the concrete aggregate fraction, a three-dimensional micro-geometric model of the concrete containing a piezoelectric ceramic driven sensing unit is established using an aggregate random generation and placement algorithm; when establishing the three-dimensional micro-geometric model of the concrete, the coordinates of the center of the spheres are determined using the Monte Carlo method; the spheres conform to a random distribution and do not intersect with the boundary of the three-dimensional micro-geometric model of the concrete, the spheres do not cross or overlap, and the content of the spheres reaches the concrete aggregate fraction.

3. The piezoelectric admittance calculation method as described in claim 1, characterized in that, The process of obtaining the element elastic modulus discrepancy coefficients of the three-dimensional micro-geometric model of concrete includes: The concrete three-dimensional micro-geometric model is divided into several grids of different specifications to obtain several concrete three-dimensional micro-geometric models with different unit sizes. The unit size of the region below the piezoelectric ceramic driven sensing unit is matched with the piezoelectric ceramic driven sensing unit. For a single three-dimensional mesoscopic geometric model of concrete, based on the volume fraction of each phase material in each element, the mechanical properties of each element are processed by the composite material equivalence method, and it is equivalent to an isotropic homogeneous medium; the elastic modulus of each element in the single three-dimensional mesoscopic geometric model of concrete is calculated respectively. Based on the elastic modulus of each unit, the average value and standard deviation of the elastic modulus of a single concrete three-dimensional micro-geometric model are calculated, and the coefficient of variation of the elastic modulus is further obtained. Based on the aforementioned steps, calculate the coefficient of variation of the elastic modulus for all three-dimensional micro-geometric models of concrete.

4. The piezoelectric admittance calculation method as described in claim 1, characterized in that, The process of determining the size of the feature unit includes: Plot the curve of the variation coefficient of elastic modulus with element size; The cell size corresponding to the inflection point of the curve is taken as the feature cell size, and the cell corresponding to the feature cell size is the feature cell.

5. The piezoelectric admittance calculation method as described in claim 1, characterized in that, The process of discretizing the feature model into a finite number of units includes: Based on the size of the feature unit, the feature model is discretized using a three-dimensional time-domain spectral unit, and each time-domain spectral unit and node is numbered sequentially. Configure interpolation nodes within the spectral unit according to the GLL integration points; The time-domain spectral unit is obtained by performing Lagrange interpolation on the interpolation nodes. , , The shape function of the direction is obtained, and the displacement function of the time-domain spectral unit is further obtained.

6. The piezoelectric admittance calculation method as described in claim 1, characterized in that, The process of obtaining the governing equations includes: Establish the element mass matrix of the three-dimensional time-domain spectral element of concrete. Element stiffness matrix and damping matrix ; Establish the piezoelectric stiffness matrix of the three-dimensional time-domain spectral unit of the piezoelectric ceramic driven sensing unit. and dielectric stiffness matrix ; By assembling the stiffness matrix, mass matrix, damping matrix, piezoelectric stiffness matrix, and dielectric stiffness matrix of each unit, the governing equations of the piezoelectric coupling system are obtained, expressed as: ； In the formula, , , , , , , and These are the overall mass matrix, overall damping matrix, overall stiffness matrix, equivalent potential vector, equivalent nodal force vector, overall piezoelectric stiffness matrix, overall dielectric stiffness matrix, and charge vector of the characteristic model structure, respectively.

7. The piezoelectric admittance calculation method as described in claim 1, characterized in that, The process of obtaining the piezoelectric admittance value includes: The piezoelectric ceramic driving sensing unit is regarded as a driver, with its lower surface grounded and an electric potential applied to its upper surface. The equivalent nodal force caused by the electric potential and the displacement caused by the piezoelectric ceramic driving sensing unit as a driver at different excitation frequencies are calculated. The piezoelectric ceramic driving sensing unit is regarded as a sensor, and the surface charge of the piezoelectric ceramic driving sensing unit at each excitation frequency is obtained according to the nodal potential and displacement at each excitation frequency. Calculate the piezoelectric admittance value.

8. A piezoelectric admittance calculation device, characterized in that, include: The modeling module is used to establish a three-dimensional micro-geometric model of concrete containing piezoelectric ceramic driven sensing units based on the concrete aggregate fraction and using an aggregate random generation and placement algorithm. The unit division module is used to divide the concrete three-dimensional micro-geometric model into several grids of different specifications to obtain several concrete three-dimensional micro-geometric models with different unit sizes. According to the micro-unit equivalence method, the mean and standard deviation of the unit elastic modulus of the concrete three-dimensional micro-geometric model are calculated, and the elastic modulus dispersion coefficient is further obtained. The feature element size determination module is used to determine the maximum element size that can be divided under the premise that the heterogeneity of concrete remains unchanged, based on the curve of the variation coefficient of elastic modulus with element size, and to use the model corresponding to the feature element size as the feature model. A discrete module is used to discretize the feature model into a finite number of units using a three-dimensional time-domain spectral unit; The first data processing module is used to establish the mass matrix, stiffness matrix and damping matrix of the discretized three-dimensional time-domain spectrum unit of concrete, and the piezoelectric stiffness matrix and dielectric stiffness matrix of the three-dimensional time-domain spectrum unit of the piezoelectric ceramic driven sensing unit according to the piezoelectric coupling equation, and obtain the control equation. The second data processing module is used to obtain the displacement of the piezoelectric ceramic driving sensing unit under unit voltage at different excitation frequencies according to the control equation; and to obtain the surface charge of the piezoelectric ceramic driving sensing unit at each excitation frequency according to the nodal potential and displacement at each excitation frequency, thereby obtaining the piezoelectric admittance value of the piezoelectric ceramic driving sensing unit at each excitation frequency.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes at least one instruction that, when executed, implements the method as claimed in any one of claims 1 to 7.

10. A computer device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory, the computer program being run on the processor, and the computer program implementing the method as claimed in any one of claims 1 to 7 when it is executed.

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