Multi-dimensional strain rosette sensor and stress-strain field model construction method
By using a multidimensional strain flower sensor and a stress-strain field model construction method, and utilizing a piezoelectric-resistance composite sensor array and a data processing terminal, a priori maps of structural discontinuities are generated. Regularized inverse problem solving and strain coordination reconstruction are then performed, solving the problems of insufficient strain field accuracy and stress calculation error in traditional methods, and achieving high-precision stress-strain field analysis.
Patent Information
- Application Number
- CN202511593863.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-03
- Publication Date
- 2026-01-02
AI Technical Summary
Traditional strain measurement methods cannot capture the complex gradient distribution in stress concentration regions. The ill-conditioned nature of resistance tomography inversion leads to insufficient accuracy and fidelity of the strain field. The inversion results are highly sensitive to measurement noise. The strain field is physically inconsistent, and the stress calculation relies on fixed material constants, which introduces errors.
A multidimensional strain flower sensor, including a piezoelectric-resistance composite sensing array and a data processing terminal, is used. A priori map of structural discontinuities is generated through a priori extraction module. A regularized inverse problem is solved by combining a conductivity inversion module. The strain compatibility equation is introduced for reconstruction. The real-time elastic modulus field is obtained by a modulus inversion module, thereby realizing automatic compensation of the stress field.
It improves the inversion accuracy and spatial resolution of conductivity variation field and original strain field, ensures the physical consistency of strain field and the accuracy of stress field, solves the ill-conditioning and error problems in traditional methods, and enhances the reliability and accuracy of stress analysis.
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Figure CN121252633A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of sensor technology and structural health monitoring, in particular to a multi-dimensional strain rosette sensor and a stress-strain field model construction method. BACKGROUND
[0002] In the fields of aerospace, civil engineering and advanced manufacturing, it is of great importance to obtain the stress-strain full-field distribution of key structural components in real time and accurately, in order to assess their service safety and predict their residual life. Traditional strain measurement mainly relies on the pasting of metal foil strain gauges, but it can only provide discrete point strain information and cannot capture the complex gradient distribution in the stress concentration area. Moreover, the wiring is complicated and susceptible to electromagnetic interference.
[0003] In recent years, electrical resistivity tomography (ERT) based on conductive thin film has attracted attention as a potential full-field strain sensing method. This technology applies excitation to the boundary of the conductive thin film and measures the response, inverts the internal electrical conductivity change, and then converts it to a strain field based on the piezoresistive effect. However, ERT technology itself faces a serious challenge, which is that the inversion solution is a ill-posed inverse problem. This ill-posedness leads to a high sensitivity of the inversion result to measurement noise and a low resolution of the solution, with blurred image edges. Especially when dealing with areas with sharp changes in strain such as crack tips, the inversion accuracy and fidelity are difficult to meet engineering requirements.
[0004] In addition, the original strain field obtained directly from the above inversion process often contains inversion artifacts and measurement noise, leading to a physically incoherent strain field that does not satisfy the strain compatibility equation in continuum mechanics. This physical incoherence can seriously affect the reliability of subsequent stress analysis.
[0005] Furthermore, when calculating the stress field from the strain field, traditional methods usually rely on the generalized Hooke's law and assume that the elastic modulus of the material is a pre-calibrated constant that does not change with space and time. However, in actual working conditions, the elastic modulus of the structure is significantly affected by the service environment and the damage state of the structure itself. Continuing to use a fixed, idealized elastic modulus constant to calculate the stress will introduce significant and non-negligible errors, leading to misjudgment of the structural safety state. SUMMARY
[0006] To overcome the deficiencies of the prior art, the present application provides a multi-dimensional strain rosette sensor and a stress-strain field model construction method, which solves the problems of insufficient accuracy and fidelity of the strain field due to the ill-posedness of the resistivity tomography inversion, the physical incoherence of the original strain field obtained by inversion, and the introduction of significant calculation errors in stress calculation due to the reliance on fixed material constants.
[0007] To achieve the above object, the application is implemented by the following technical solutions: a multi-dimensional strain gauge sensor, comprising: a piezoresistive composite sensing array, comprising a continuous resistive layer and an arrayed piezoelectric layer; a data processing terminal, comprising: a priori extraction module for driving the piezoelectric layer to emit sound waves and receive responses, and generating a structural discontinuity a priori map according to the responses; a boundary data acquisition module for exciting the resistive layer to obtain resistive tomographic boundary data; a modulus inversion module for processing the responses of the piezoelectric layer to obtain an elastic modulus field; a conductivity inversion module for solving a regularized inverse problem of the resistive tomographic boundary data in combination with the structural discontinuity a priori map to obtain a conductivity variation field; a strain conversion module for converting the conductivity variation field into an original strain field based on the piezoresistive effect; a strain reconstruction module for introducing a strain compatibility equation as a physical constraint to reconstruct the original strain field to obtain a physically compatible strain field; a stress calculation module for calculating a stress field in combination with the elastic modulus field and the physically compatible strain field.
[0008] Preferably, the a priori extraction module is specifically used for: analyzing sound wave energy attenuation or scattering characteristics in the responses, and inverting the characteristics by an acoustic tomographic algorithm to obtain the structural discontinuity a priori map.
[0009] Preferably, the conductivity inversion module is specifically used for: constructing a spatially weighted regularization term, which applies a strong smoothing constraint in an intact area indicated by the structural discontinuity a priori map and weakens the smoothing constraint in a discontinuous area.
[0010] Preferably, the strain reconstruction module is specifically used for: constructing a functional containing a data fidelity term and a physical compatibility constraint term, and obtaining the physically compatible strain field by solving the minimum value of the functional.
[0011] Preferably, the modulus inversion module is specifically used for: analyzing wave velocity distribution in the responses to invert the elastic modulus field reflecting real-time physical properties of the material; and the stress calculation module uses the elastic modulus field for calculation, achieving automatic compensation for changes in material properties.
[0012] A stress-strain field model construction method of a multi-dimensional strain gauge sensor, comprising the following steps: S1: driving the piezoelectric layer in the piezoresistive composite sensing array to emit acoustic waves, and receiving the response of the acoustic waves after propagating in the structure by the piezoelectric layer, and generating a structure discontinuity priori map according to the response; S2: exciting the boundary electrodes of the resistive layer in the piezoresistive composite sensing array, and measuring the voltage on the boundary electrodes to obtain resistive tomographic boundary data; S3: processing the response of the piezoelectric layer to obtain an elastic modulus field by inversion; S4: combining the structure discontinuity priori map to solve the resistive tomographic boundary data to obtain a conductivity change field; S5: converting the conductivity change field into an original strain field based on the piezoresistive effect; S6: introducing a strain compatibility equation as a physical constraint to reconstruct the original strain field to obtain a physically compatible strain field; S7: combining the elastic modulus field and the physically compatible strain field to calculate a stress field.
[0013] Preferably, the step of generating the structure discontinuity priori map in S1 specifically comprises: analyzing the acoustic energy attenuation or scattering characteristics in the response, and inverting the characteristics by an acoustic tomographic algorithm to obtain the structure discontinuity priori map.
[0014] Preferably, the step of combining the structure discontinuity priori map to solve the resistive tomographic boundary data in S4 specifically comprises: constructing a spatially weighted regularization term, which applies strong smoothing constraints in the intact area indicated by the structure discontinuity priori map and weakens the smoothing constraints in the discontinuous area.
[0015] Preferably, the step of introducing the strain compatibility equation for reconstruction in S6 specifically comprises: constructing a functional containing a data fidelity term and a physical compatibility constraint term, and obtaining the physically compatible strain field by solving the minimum value of the functional.
[0016] Preferably, the step of inverting the elastic modulus field in S3 specifically comprises: analyzing the wave velocity distribution in the response to invert the elastic modulus field reflecting the real-time physical properties of the material; And, combining the elastic modulus field for calculation in S7 realizes automatic compensation for changes in material properties.
[0017] The application provides a multi-dimensional strain rosette sensor and a stress-strain field model construction method. 1、The application obtains a structural discontinuity priori graph through the priori extraction module, and utilizes the priori graph to constrain the resistive tomography inverse problem solving in the conductivity inversion module. This cross-modal data fusion solves the ill-conditioned and image blur problems of the traditional resistive tomography in inverting the high gradient area such as cracks, and significantly improves the inversion accuracy and spatial resolution of the conductivity change field and the subsequent original strain field.
[0018] 2、The application introduces a strain compatibility equation as a physical constraint through the strain reconstruction module to reconstruct the original strain field. This step utilizes the physical constitutive relationship of continuous medium mechanics, can effectively suppress the non-physical fluctuations caused by measurement noise or inversion error, ensures that the final obtained physical compatible strain field is continuous and meets the compatibility equation constraint in the whole sensing area, and improves the reliability and physical authenticity of the strain field result.
[0019] 3、The application utilizes the piezoelectric layer response to obtain the elastic modulus field through the modulus inversion module in real time, and utilizes the spatial and time-varying elastic modulus field and the physical compatible strain field to calculate the stress field in the stress calculation module. This design realizes the automatic compensation of the physical property changes of the material caused by temperature changes or local damage, and greatly improves the accuracy of the finally calculated stress field. BRIEF DESCRIPTION OF DRAWINGS
[0020] Figure 1 It is a structural diagram of the multi-dimensional strain rosette sensor system of the application. Figure 2 It is a method flowchart of the application. DETAILED DESCRIPTION
[0021] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the specification of the application. Obviously, the described embodiments are only a part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the application.
[0022] Please refer to the drawings in the specification of the application Figure 1 - the drawings in the specification of the application Figure 2 The embodiments of the application provide a multi-dimensional strain rosette sensor and a stress-strain field model construction method.
[0023] The application provides a multi-dimensional strain rosette sensor system, which comprises: A piezoresistive composite sensing array, which comprises a continuous resistive layer and an arrayed piezoelectric layer. A data processing terminal, the data processing terminal comprising: An a priori extraction module for driving the piezoelectric layer to emit acoustic waves and receive responses, and generating a structural discontinuity a priori map according to the responses; A boundary data acquisition module for exciting the resistive layer to obtain resistive tomography boundary data; A modulus inversion module for processing the responses of the piezoelectric layer to obtain an elastic modulus field by inversion; A conductivity inversion module for solving a regularized inverse problem of the resistive tomography boundary data in combination with the structural discontinuity a priori map to obtain a conductivity variation field; A strain conversion module for converting the conductivity variation field into an original strain field based on the piezoresistive effect; A strain reconstruction module for introducing a strain compatibility equation as a physical constraint to reconstruct the original strain field to obtain a physically compatible strain field; A stress calculation module for calculating a stress field in combination with the elastic modulus field and the physically compatible strain field.
[0024] The piezoelectric-resistive composite sensing array is a sensing component for obtaining multi-modal physical signals on the surface of a structure. In a specific embodiment, the piezoelectric-resistive composite sensing array comprises a continuous resistive layer and an arrayed piezoelectric layer.
[0025] The continuous resistive layer can be a continuous deposition of a piezoresistive material film, such as a graphene composite material, a carbon nanotube composite material, or a doped semiconductor film, whose electrical conductivity is sensitive to applied strain. A plurality of boundary electrodes are arranged on the four peripheral edges of the resistive layer for applying excitation current and measuring boundary voltage.
[0026] The arrayed piezoelectric layer can be composed of a plurality of discrete piezoelectric units, such as an M×N grid layout. The material of the piezoelectric units can be PVDF (polyvinylidene fluoride) or PZT (lead zirconate titanate). Each piezoelectric unit can be independently driven to emit acoustic waves, or used as a sensor to receive acoustic wave responses.
[0027] The data processing terminal can be an embedded system, a computer, or a cloud platform, which is connected to the piezoelectric-resistive composite sensing array for executing the stress-strain-field model construction method.
[0028] In a specific embodiment, the data processing terminal comprises an a priori extraction module, a boundary data acquisition module, a modulus inversion module, a conductivity inversion module, a strain conversion module, a strain reconstruction module, and a stress calculation module.
[0029] Both the priori extraction module and the modulus inversion module are used to process the response signal of the piezoelectric layer. Specifically, the priori extraction module is used to drive the piezoelectric layer to emit sound waves and receive responses. For example, one piezoelectric unit is selected as an excitation source to emit a broadband ultrasonic pulse, and all other units in the array are used as sensors to synchronously receive the response waveform.
[0030] The priori extraction module generates a structural discontinuity priori map by analyzing the acoustic energy attenuation or scattering characteristics in the response. Specifically, when there is a discontinuity such as a crack on the acoustic wave path, it will cause significant energy attenuation. By inverting the energy attenuation data of the entire network through an acoustic tomography algorithm (such as algebraic reconstruction technique), the acoustic attenuation coefficient field within the sensing area can be reconstructed The structural discontinuity priori map can be obtained by normalizing the attenuation coefficient field, for example:
[0031] wherein and are the preset attenuation coefficient reference values of the healthy area and the high damage area, respectively. The value of close to 1 indicates a high probability of the presence of discontinuity at the position, and close to 0 indicates that the structure is intact.
[0032] The priori extraction module is specifically used to analyze the acoustic energy attenuation or scattering characteristics in the response, and to obtain a structural discontinuity priori map by inverting the characteristics through an acoustic tomography algorithm.
[0033] The step of generating the structural discontinuity priori map in S1 specifically includes analyzing the acoustic energy attenuation or scattering characteristics in the response, and obtaining a structural discontinuity priori map by inverting the characteristics through an acoustic tomography algorithm.
[0034] The modulus inversion module is used to process the response of the piezoelectric layer, and to obtain an elastic modulus field by inversion. Specifically, the modulus inversion module analyzes the wave velocity distribution in the response, for example, by calculating the acoustic time of flight (ToF) between different pairs of transmitting and receiving units, to invert the wave velocity distribution field c(x, y) within the sensing area.
[0035] There is a certain physical relationship between the elastic modulus E of the material and the wave velocity c, for example, for a specific mode of Lamb wave, the relationship can be expressed as:
[0036] wherein is a known acoustic-elastic coupling function, is the Poisson's ratio of the material (which can be pre-calibrated or assumed to be a constant), and d is the thickness of the structure. Through this step, the real-time physical property of the material under the current temperature and damage state, i.e., the elastic modulus field E(x, y), can be obtained.
[0037] The boundary data acquisition module is configured to stimulate the resistive layer to obtain electrical resistivity tomography boundary data. Specifically, the module applies stimulation current to the boundary electrodes of the resistive layer according to a preset stimulation mode (for example, an adjacent stimulation-adjacent pickup mode) , and synchronously measures the voltage on all the boundary electrodes , to form an electrical resistivity tomography boundary data set.
[0038] The conductivity inversion module is configured to combine the structural discontinuity prior map to solve a regularized inverse problem of the electrical resistivity tomography boundary data, to obtain a conductivity variation field . The electrical resistivity tomography inverse problem is to invert the internal conductivity distribution from the boundary voltage measurement , which is a pathological problem.
[0039] The conductivity inversion module solves the inverse problem by constructing an optimization objective functional containing a data fidelity term and a piezoelectric prior regularization term :
[0040] wherein is the actual measured voltage vector obtained by the boundary data acquisition module.- is a forward problem model of the electrical resistivity tomography, that is, a mapping from the conductivity field to the boundary predicted voltage.- is a regularization parameter.- is the structural discontinuity prior map generated by the prior extraction module.- is the gradient amplitude of the conductivity field.
[0041] The regularization is a spatially weighted regularization term. Its physical meaning is that in the area close to 0 (the intact area confirmed by the piezoelectric layer), close to 1, at which time the regularization term applies a strong smoothing constraint; and in the area close to 1 (the discontinuous area confirmed by the piezoelectric layer), close to 0, at which time the regularization constraint is weakened, allowing the algorithm to reconstruct a high-gradient conductivity mutation (for example, a crack) at the place. By solving the minimum value of the functional, a high-fidelity conductivity variation is obtained. The conductivity inversion module is specifically configured to construct a spatially weighted regularization term, which applies a strong smoothing constraint in the intact area indicated by the structural discontinuity prior map and weakens the smoothing constraint in the discontinuous area.
[0042] The conductivity inversion module is specifically configured to construct a spatially weighted regularization term, which applies a strong smoothing constraint in the intact area indicated by the structural discontinuity prior map and weakens the smoothing constraint in the discontinuous area.
[0043] The step of solving the inverse problem by combining the structural discontinuity prior map for regularization in S4 specifically comprises: constructing a spatially weighted regularization term, which applies strong smoothing constraint in the intact region indicated by the structural discontinuity prior map and weakens the smoothing constraint in the discontinuous region.
[0044] The strain conversion module is used to convert the conductivity variation field into an original strain field based on the piezoresistive effect. The relationship between the relative change of conductivity and the strain tensor is described by the piezoresistive effect tensor :
[0045] where is the initial conductivity, is the fourth-order piezoresistive tensor of the material (which needs to be calibrated in advance). Through the relationship, the conductivity variation field can be converted into the original strain tensor field .
[0046] The strain reconstruction module is used to introduce the strain compatibility equation as a physical constraint to reconstruct the original strain field to obtain a physically compatible strain field . Due to measurement noise or inversion error, the original strain field may not satisfy the physical constraints of continuum mechanics. The strain compatibility equation is a strong constraint to ensure the continuity and physical compatibility of the strain field. In two-dimensional plane problems, the equation is:
[0047] The strain reconstruction module specifically constructs a functional containing a data fidelity term and a physical compatibility constraint term, and obtains a physically compatible strain field by solving the minimum value of the functional. The functional can be expressed as:
[0048] where is the strain field to be optimized, is the norm, is the compatibility constraint weight factor. By solving numerically (such as finite element method), a physically compatible strain field is obtained which approximates the measured data and satisfies the physical constitutive constraints.
[0049] The strain reconstruction module specifically constructs a functional containing a data fidelity term and a physical compatibility constraint term, and obtains a physically compatible strain field by solving the minimum value of the functional.
[0050] The step of introducing the strain compatibility equation for reconstruction in S6 specifically comprises: constructing a functional containing a data fidelity term and a physical compatibility constraint term, and obtaining a physical compatibility strain field by solving the minimum value of the functional.
[0051] The stress solving module is used to combine the elastic modulus field with the physical compatibility strain field , and calculate a stress field . The calculation is realized through the generalized Hooke's law:
[0052] wherein is a stress vector, is a spatially varying elastic matrix. The elastic matrix here is constructed using the real-time elastic modulus field (and Poisson's ratio ) obtained by the modulus inversion module, instead of using a fixed material constant. For example, under the plane stress assumption:
[0053] In this way, the stress solving module uses the elastic modulus field for calculation, realizes automatic compensation for the change of material properties caused by temperature change or structural damage, and thus obtains a high-precision stress field .
[0054] The modulus inversion module is specifically used to: analyze the wave velocity distribution in the response, and invert an elastic modulus field reflecting real-time physical properties of the material; and the stress solving module uses the elastic modulus field for calculation, realizing automatic compensation for the change of material properties.
[0055] The step of inverting the elastic modulus field in S3 specifically comprises: analyzing the wave velocity distribution in the response, and inverting an elastic modulus field reflecting real-time physical properties of the material; and the calculation in S7 combines the elastic modulus field, realizing automatic compensation for the change of material properties.
[0056] The application also provides a stress-strain field model construction method, which can be executed by the multi-dimensional strain rosette sensor system described above. The specific steps S1 to S7 of the method have been described in detail in the description of the functions of the modules of the system, which correspond to the complete work flow of the priori extraction module, the boundary data acquisition module, the modulus inversion module, the conductivity inversion module, the strain conversion module, the strain reconstruction module and the stress solving module.
[0057] A stress-strain field model construction method comprises the following steps: S1: drive the piezoelectric layer in a piezoresistive composite sensor array to emit acoustic waves, and use the piezoelectric layer to receive the response of the acoustic waves after propagating in the structure, and generate a structure discontinuity priori map according to the response; S2: excite the boundary electrodes of the resistive layer in the piezoresistive composite sensor array, and measure the voltage on the boundary electrodes to obtain resistivity tomography boundary data; S3: process the response of the piezoelectric layer to obtain an elastic modulus field by inversion; S4: combine the structure discontinuity priori map to solve the resistivity tomography boundary data to obtain a conductivity change field; S5: convert the conductivity change field into an original strain field based on the piezoresistive effect; S6: introduce strain compatibility equations as physical constraints to reconstruct the original strain field to obtain a physically compatible strain field; S7: combine the elastic modulus field and the physically compatible strain field to calculate a stress field.
[0058] For example, S1 corresponds to the structure discontinuity priori map generated by the priori extraction module; S2 corresponds to the boundary data acquisition module to obtain the resistivity tomography boundary data; S3 corresponds to the modulus inversion module to invert the elastic modulus field; S4 corresponds to the conductivity inversion module to perform the inverse problem solving of the piezoelectric priori regularization; S5 corresponds to the strain conversion module based on the piezoresistive effect; S6 corresponds to the strain reconstruction module to perform the reconstruction based on the strain compatibility equation; S7 corresponds to the stress calculation module to combine the results of S3 and S6 to calculate the final stress field. The implementation details of these steps and the formulas involved are consistent with the foregoing, and will not be repeated here.
[0059] Although embodiments of the present application have been shown and described, it is to be understood that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the present application, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A multidimensional strain gauge sensor, characterized in that, include: A piezoelectric-resistance composite sensing array, comprising a continuous resistive layer and an arrayed piezoelectric layer; A data processing terminal, the data processing terminal comprising: A priori extraction module is used to drive the piezoelectric layer to emit sound waves and receive responses, and generate a priori maps of structural discontinuities based on the responses; A boundary data acquisition module is used to excite the resistive layer to acquire resistive layer boundary data; The modulus inversion module is used to process the response of the piezoelectric layer and invert the elastic modulus field. The conductivity inversion module is used to solve the regularized inverse problem of the resistance tomography boundary data by combining the prior diagram of the structural discontinuity, and to obtain the conductivity variation field. The strain conversion module is used to convert the conductivity change field into the original strain field based on the piezoresistive effect. The strain reconstruction module is used to introduce strain compatibility equations as physical constraints to reconstruct the original strain field and obtain a physically compatible strain field. The stress calculation module is used to calculate the stress field by combining the elastic modulus field and the physically compatible strain field.
2. A multidimensional strain gauge sensor according to claim 1, characterized in that, The prior extraction module is specifically used for: The acoustic energy attenuation or scattering characteristics in the response are analyzed, and the characteristics are inverted using an acoustic tomography algorithm to obtain the prior map of the structural discontinuity.
3. A multidimensional strain rose sensor according to claim 1, characterized in that, The conductivity inversion module is specifically used for: A spatial weighted regularization term is constructed, which applies strong smoothing constraints to the intact regions indicated by the structural discontinuity prior graph and weakens the smoothing constraints in the indicated discontinuous regions.
4. A multidimensional strain gauge sensor according to claim 1, characterized in that, The strain reconstruction module is specifically used for: A functional containing data fidelity terms and physical compatibility constraints is constructed, and the physical compatibility strain field is obtained by solving for the minimum value of the functional.
5. A multidimensional strain rose sensor according to claim 1, characterized in that, The modulus inversion module is specifically used for: Analyze the wave velocity distribution in the response to retrieve the elastic modulus field that reflects the real-time physical properties of the material. Furthermore, the stress calculation module utilizes the elastic modulus field for calculation, thereby achieving automatic compensation for changes in material properties.
6. A method for constructing a stress-strain field model for a multidimensional strain rose sensor, characterized in that, Includes the following steps: S1: Drive the piezoelectric layer in the piezoelectric-resistance composite sensing array to emit sound waves, and use the piezoelectric layer to receive the response of the sound waves after they propagate in the structure, and generate a priori map of structural discontinuities based on the response; S2: Excite the boundary electrode of the resistive layer in the piezoelectric-resistive composite sensing array, and measure the voltage on the boundary electrode to obtain resistive tomography boundary data; S3: Process the response of the piezoelectric layer to obtain the elastic modulus field; S4: Combine the prior diagram of the structural discontinuity to solve the regularized inverse problem of the resistance tomography boundary data to obtain the conductivity variation field; S5: Based on the piezoresistive effect, the conductivity change field is converted into the original strain field; S6: Introduce strain compatibility equations as physical constraints to reconstruct the original strain field and obtain a physically compatible strain field; S7: The stress field is calculated by combining the elastic modulus field and the physical compatibility strain field.
7. The method for constructing a stress-strain field model for a multidimensional strain rose sensor according to claim 6, characterized in that, The steps in S1 for generating the prior map of the structural discontinuity specifically include: The acoustic energy attenuation or scattering characteristics in the response are analyzed, and the characteristics are inverted using an acoustic tomography algorithm to obtain the prior map of the structural discontinuity.
8. The method for constructing a stress-strain field model for a multidimensional strain rose sensor according to claim 6, characterized in that, The steps in S4 for solving the regularized inverse problem using the prior graph of the structural discontinuity specifically include: A spatial weighted regularization term is constructed, which applies strong smoothing constraints to the intact regions indicated by the structural discontinuity prior graph and weakens the smoothing constraints in the indicated discontinuous regions.
9. The method for constructing a stress-strain field model for a multidimensional strain rose sensor according to claim 6, characterized in that, The specific steps of reconstructing the strain compatibility equation in S6 include: A functional containing data fidelity terms and physical compatibility constraints is constructed, and the physical compatibility strain field is obtained by solving for the minimum value of the functional.
10. The method for constructing a stress-strain field model for a multidimensional strain flower sensor according to claim 6, characterized in that, The specific steps in S3 to obtain the elastic modulus field by inversion include: Analyze the wave velocity distribution in the response to retrieve the elastic modulus field that reflects the real-time physical properties of the material. Furthermore, the calculation in step S7, combined with the elastic modulus field, enables automatic compensation for changes in material properties.