A Sensitivity Analysis Method for Flexural Electrical Cantilever Beam Structures Based on Sobol Sequence Sampling

Abstract

This invention discloses a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling, comprising the following steps: S1: establishing a flexural electric cantilever beam structure model; S2: performing uncertainty analysis on the parameters of the flexural electric cantilever beam structure model based on Sobol sequence sampling; S3: substituting the extracted samples into the corresponding model to calculate the mean and standard measure of the output characterization, and analyzing and studying the output performance. This invention employs the aforementioned sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling, which not only points the way to optimizing the performance of flexural electric cantilever beam structures considering parameter randomness, but also provides necessary theoretical and experimental basis for the application of flexural electric cantilever beams as the main structural unit for flexural electrical signal output in next-generation micro / nano electromechanical systems.

Description

Technical Field

[0001] This invention relates to the field of flexural electrical effect technology, and in particular to a sensitivity analysis method for flexural electrical cantilever beam structures based on Sobol sequence sampling. Background Technology

[0002] Multiphysics coupling effects are widespread in nature. The mechanical behavior of materials is not only affected by external loads, but also, due to their unique internal structure, their deformation is often coupled with various physical quantities such as heat, electricity, and magnetism. The emergence of multiphysics problems has led to a great deal of interdisciplinary integration, promoting the rapid development of materials science. Mechanoelectric coupling, as a classic multiphysics coupling effect, includes piezoelectricity, electrostriction, and electrorheological effects. It reflects the conversion relationship between mechanical energy and electrical energy in materials and is widely found in ceramic materials, polymer films, and even biological tissues. Research on mechanoelectric coupling effects has promoted the design and development of various intelligent devices such as novel sensors, actuators, and energy harvesters. Flexoelectricity is a more universal mechanoelectric coupling effect than piezoelectricity. Flexoelectric beams, as the main structural unit for flexoelectric signal output, have broad application prospects in next-generation micro / nanoelectromechanical systems.

[0003] The flexoelectric effect has two significant characteristics: firstly, it is not limited by crystal symmetry and exists in all dielectric materials; secondly, it exhibits a significant size effect. However, the application of the flexoelectric effect in practical engineering is far less mature than that of the piezoelectric effect. Improving the flexoelectric signal output of materials and designing high-performance flexoelectric materials are urgent problems to be solved. Furthermore, during the design process of flexoelectric materials or the operation of flexoelectric structures, the uncertainty of relevant parameters can lead to excessively low flexoelectric output voltage or potential. These random uncertainties in parameters can also cause variations in the output performance of flexoelectric structures, posing a significant challenge to the widespread application of flexoelectric materials. Therefore, the parameter uncertainties existing in the design and operation of flexoelectric beam structures should be fully considered. Thus, uncertainty analysis for flexoelectric beam structures is essential. By implementing reasonable design during the industrial manufacturing stage and allocating resources appropriately under actual working conditions, the reliability and stability of the system can be effectively improved, which has significant research significance and application value.

[0004] Currently, commonly used uncertainty analysis methods include probabilistic analysis and fuzzy set theory analysis. The former is a quantitative analysis method, while the latter is a qualitative analysis method. Probabilistic analysis quantifies the uncertainty of variables through probability distributions, and can accurately describe the random uncertainty of variables in industrial design or physical experiments. Fuzzy set theory analysis studies variables with fuzzy concepts, but due to its current immaturity, it is less commonly used in practice. The most commonly used method in probabilistic analysis is the Monte Carlo method, which calculates the statistical properties of the parameters by generating pseudo-random numbers through sampling experiments on the probabilistic model. Monte Carlo sampling is simple and easy to implement, but it relies heavily on the random number generation mechanism, resulting in low sampling efficiency, slow convergence speed, and often requiring a large sample size. Compared to Monte Carlo, quasi-Monte Carlo methods no longer use uniformly distributed pseudo-random numbers for sampling, but instead use deterministic low-biased sequences for sampling. This better ensures the uniformity and determinism of the sample, improves the convergence speed, and significantly improves sampling efficiency. Commonly used low-biased sequences include Halton sequences, Niederreiter sequences, and Sobol sequences.

[0005] The flexural electricity effect is a more universal electromechanical coupling effect, unrestricted by crystal symmetry and present in all dielectric materials. When a centrosymmetric material undergoes uniform deformation, the positive and negative ion centers within the material do not shift, and the material macroscopically does not exhibit electrical properties. However, when subjected to non-uniform deformation, such as bending, the strain gradient causes the material to exhibit electrical properties.

[0006] The shift in the centers of positive and negative ions causes the material to become polarized by this electric dipole moment, exhibiting electrical properties at the macroscopic level. Therefore, the flexural effect is more universal than the piezoelectric effect, existing in all dielectric materials. However, the application of the flexural effect in practical engineering is far less mature than that of the piezoelectric effect. Many intelligent devices in daily life are designed based on the piezoelectric effect, such as microphones, filters, and shock absorbers, where the piezoelectric effect plays a role in sensing and actuation. The main reason limiting the practical application of the flexural coefficient is that the output of the flexural signal at the macroscopic scale is much smaller than that of the piezoelectric signal. Previous studies, based on cantilever beam structures, quantitatively analyzed the difference in signal output considering the piezoelectric and flexural effects at a given size, showing that the macroscopic output of the flexural effect is much smaller than that of the piezoelectric effect. Therefore, improving the flexural signal output of materials and designing high-performance flexural materials are urgent problems to be solved.

[0007] In practical engineering, even small fluctuations in some key design parameters can lead to significant changes in output performance. Therefore, conducting an importance measurement analysis of the parameters of the flexible electric beam structure and studying the impact of the uncertainty of the flexible electric beam parameters on the output performance is of great significance for the subsequent optimization and development of flexible electric beams, and is beneficial to the application and development of flexible electric beam structures. Summary of the Invention

[0008] The purpose of this invention is to provide a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. This method not only points the way to optimizing the performance of flexural electric cantilever beam structures considering parameter randomness, but also provides the necessary theoretical and experimental basis for the application of flexural electric cantilever beams as the main structural unit for flexural electric signal output in next-generation micro / nano electromechanical systems.

[0009] To achieve the above objectives, this invention provides a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling, comprising the following steps:

[0010] S1: Establish a structural model of the flexural electric cantilever beam;

[0011] S2: Uncertainty analysis of the parameters of the flexural electric cantilever beam structural model based on Sobol sequence sampling;

[0012] S3: Substitute the extracted samples into the corresponding model to calculate the mean and standard measure of the output representation, and analyze and study the output performance.

[0013] Preferably, in step S1, a flexural electric cantilever beam structural model is established to obtain the open-circuit voltage output and short-circuit charge output of the flexural electric cantilever beam under quasi-static conditions, as well as the expressions for the output electrical signals, thereby determining the design parameters. μ 31 , a 33 , L , h .

[0014] Preferably, the open-circuit voltage output expression for the quasi-static deflection cantilever beam is:

[0015]

[0016] In the formula, β is defined as the length-to-thickness ratio, i.e. L / h , S e The electrode area, i.e. L B, L It is the length of the beam. h It is the thickness of the beam. B Let be the width of the beam. μ 31 It is the flexural coefficient. a 33 is the dielectric constant.

[0017] Preferably, the short-circuit charge output expression for the quasi-static flexural cantilever beam is:

[0018]

[0019] The preferred method is to quantitatively characterize flexural materials at the micro-nano scale by measuring the effective bending stiffness under open-circuit conditions. For electrical short-circuit conditions, an effective piezoelectric coefficient is introduced, and the output electrical signal is redefined as follows:

[0020]

[0021] Where E is Young's modulus.

[0022] Therefore, the above-mentioned sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling not only points the way to optimizing the performance of flexural electric cantilever beam structures considering parameter randomness, but also provides the necessary theoretical and experimental basis for the application of flexural electric cantilever beams as the main structural unit for flexural electric signal output in next-generation micro-nano electromechanical systems.

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the deformation and output signal of a flexural electric cantilever beam structure based on Sobol sequence sampling, according to the present invention.

[0025] Figure 2 This invention relates to a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. μ 31 When changing alone φ quasi Schematic diagram of mean and standard deviation;

[0026] Figure 3 This invention relates to a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling, where h varies independently. φ quasi A diagram showing the mean and standard deviation;

[0027] Figure 4 This invention relates to a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. a 33 When changing alone φ quasi A diagram showing the mean and standard deviation;

[0028] Figure 5 This invention relates to a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. μ 31 When changing alone Qquasi A diagram showing the mean and standard deviation;

[0029] Figure 6 This invention relates to a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. L When changing alone Q quasi A diagram showing the mean and standard deviation;

[0030] Figure 7 This invention relates to a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. μ 31 When changing alone A diagram showing the mean and standard deviation;

[0031] Figure 8 This invention relates to a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. h When changing alone A diagram showing the mean and standard deviation;

[0032] Figure 9 This invention relates to a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. L When changing alone A diagram showing the mean and standard deviation. Detailed Implementation

[0033] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0034] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0035] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0036] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity, and those skilled in the art should...

[0037] Taking this specification as a whole, the technical solutions in the various embodiments can also be appropriately combined to form other embodiments that can be understood by those skilled in the art. These other embodiments are also covered within the scope of protection of this invention.

[0038] It should also be understood that the specific embodiments described above are only used to explain the present invention, and the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0039] Techniques, methods, and apparatus known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the specification.

[0040] All prior art documents cited in this specification are incorporated herein by reference in their entirety and are therefore part of the disclosure of this invention.

[0041] Example 1: As Figures 1-9 As shown, this invention provides a sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling. First, a flexural electric cantilever beam structure model is established, and the expressions for the open-circuit voltage output and short-circuit charge output of the flexural electric cantilever beam structure under quasi-static conditions, as well as the output electrical signal, are obtained (1)(2)(3). The design parameters are then determined. μ 31 , a 33 , L , h Based on accumulated engineering experience and data, the distribution of given parameters is shown in Table 1.

[0042] The flexural electric cantilever beam structural model is a model of the deformation and output signal of the flexural electric cantilever beam generated by improving the flexural electric response of the material through structural design. The output electrical signal is the forced vibration response and dynamic electrical signal output response under given size and frequency, and the dynamic analysis of the flexural electric cantilever beam structure is carried out.

[0043] (1) The open-circuit voltage output expression of the quasi-static deflected cantilever beam is:

[0044]

[0045] In the formula, β is defined as the length-to-thickness ratio, i.e., L / h. The electrode area, i.e., L B and L are the length of the beam, h is the thickness of the beam, and B is the width of the beam. It is the flexural coefficient and dielectric coefficient. Take 0.79e-8Vm / C;

[0046] (2) The short-circuit charge output expression for the quasi-static deflected cantilever beam is:

[0047]

[0048] Given a length-to-thickness ratio β, the charge output value is directly proportional to the beam width; increasing the beam width can increase the output charge. Furthermore, when the beam size is reduced to the micro-nano scale, the charge output becomes too small to measure in practical engineering applications. To better measure flexural electrical signals, excessively small beam sizes should be avoided.

[0049] Quantitative characterization of flexural electrical materials at the micro-nano scale is achieved by measuring the effective bending stiffness under open-circuit conditions. For electrical short-circuit conditions, an effective piezoelectric coefficient is introduced, and the output electrical signal is redefined as follows:

[0050]

[0051] Table 1. Distribution of structural parameters of the flexural electrocantilever beam.

[0052]

[0053] Table 1 shows the flexural coefficients. Dielectric coefficient The mean range, typical mean value, and standard deviation of the four parameters (beam length L, beam thickness h) are analyzed. Then, using Sobol sequence sampling to analyze the uncertainty of the flexural cantilever beam structural parameters, the corresponding output voltage is obtained when these parameters change. φ quasi and charge The changes in the mean and standard deviation.

[0054] Uncertainty analysis of parameters in a flexural electric cantilever beam structural model based on Sobol sequence sampling is an uncertainty analysis of the system. Compared with other sampling methods, Sobol sequence sampling can better simulate the random uncertainty of parameters, ensure the uniformity and determinism of the sample, improve the convergence speed, and significantly improve sampling efficiency.

[0055] Sobol sequence sampling was used to analyze the uncertainty of the structural parameters of a flexural electric cantilever beam. The flexural electric cantilever beam structure is affected by its own structural features during operation. Furthermore, the structural parameters are also uncertain due to the influence of mechanical manufacturing processes during the production of the flexural electric cantilever beam material. These factors all affect the output of the flexural electric cantilever beam structure. Among the parameters of the flexural electric cantilever beam structure, the flexural coefficient is... Dielectric coefficient The beam length L and beam thickness h are structural parameters, and these parameters have a certain degree of randomness, which will affect the output.

[0056] Secondly, uncertainty analysis based on Sobol sequence sampling is performed on the design parameters of the flexural electric cantilever beam structure model. By randomly sampling the system design parameters, a random combination of the flexural electric cantilever beam structure parameters is obtained. Then, these parameters are substituted into the model to calculate the corresponding system output power and conversion efficiency data, and the distribution parameters of the data are estimated. The specific steps are as follows:

[0057] (1) Based on the normal distribution of the design parameters, the design parameters of the flexural electric cantilever beam structure are sampled and a 6-D Sobol point set is generated. The first value is skipped, and then every 3 points are retained. The Sobol sequence is used to generate random numbers in the quasi-Monte Carlo simulation.

[0058] (2) Divide the distribution interval of the mean values ​​of each design parameter of the flexural electric cantilever beam structure into M non-overlapping sub-intervals with equal probability.

[0059] (3) Extract a sample point from each sub-interval and store the sample point in M. In matrix N

[0060]

[0061] (4) Rearrange the elements of each row of the matrix to simulate the random combination of parameters of the flexural cantilever beam structure;

[0062] =

[0063] The elements in the matrix S subscript X 11 , X 12 , X 13 ... X 1M It is a random permutation of the row vector components of the matrix. l This is the sample matrix for the Sobol sequence, where the column vectors are the N-dimensional samples extracted.

[0064] (5) Then, the random numbers generated by sampling each parameter are substituted into the flexural electric cantilever beam structure system model and the corresponding charge output and electrical signal are calculated according to formulas (1), (2), and (3).

[0065] (6) Estimate the parameter distribution of the system and obtain the corresponding output voltage. , charge and effective piezoelectric

[0066] coefficient The changes in the mean and standard deviation.

[0067] Finally, using the Sobel sequence sampling method, the extracted samples are substituted into the corresponding model to calculate the estimates of the mean and standard deviation of the output representation. Based on the changes in the mean and standard deviation of the output parameters, the output performance is analyzed and studied.

[0068] Figure 2 Flexural coefficient When the mean changes, the corresponding output voltage of the flexural cantilever beam structure φ quasi The graph shows the changes in the mean and standard deviation of the output voltage. φ quasi The mean and standard deviation both vary with the flexural coefficient. It increases with increasing flexural conductivity, exhibiting a linear relationship. The larger the output voltage, the higher the output voltage. φ quasi The larger the mean, the larger the output voltage, but the standard deviation also increases, meaning the data fluctuates more and the accuracy decreases. This indicates that the flexural coefficient... Increasing the voltage can improve the output voltage of the flexural cantilever beam structure, but it will reduce the stability of the output results.

[0069] Figure 3 The figure shows the changes in the mean and standard deviation of the output voltage puts i of the flexural electric cantilever beam structure as the mean thickness h of the flexural electric cantilever beam changes. As can be seen from the figure, the output voltage... φ quasi Both the mean and standard deviation of the flexural cantilever beam increase with increasing thickness h, and this relationship is non-linear. The larger the thickness h of the flexural cantilever beam, the higher the output voltage. φ quasi The larger the mean, the larger the output voltage, but the standard deviation also increases, meaning the data fluctuations become larger and the accuracy decreases. This indicates that the larger the thickness h of the flexural cantilever beam, the higher the output voltage of the flexural cantilever beam structure, but the lower the stability of the output results.

[0070] Figure 4 Dielectric coefficient of the flexural cantilever beam structure When the mean changes, the corresponding output voltage of the flexural cantilever beam structure φ quasi The graph shows the changes in the mean and standard deviation of the output voltage. φ quasi The mean and standard deviation both vary with the dielectric constant of the flexural cantilever beam. The dielectric constant of the flexural cantilever beam increases and decreases, and the relationship is non-linear. The larger the output voltage, the higher the output voltage. φ quasi The smaller the mean, the smaller the output voltage, and the smaller the standard deviation, meaning the data fluctuation is smaller and the accuracy is higher. This indicates that the dielectric constant of the flexural cantilever beam is... Increasing the voltage will decrease the output voltage of the flexural cantilever beam structure, but will increase the stability of the output results.

[0071] Figure 5 Flexural coefficient When the mean changes, the corresponding output charge of the flexural cantilever beam structure The graph shows the changes in the mean and standard deviation of the output charge. The mean and standard deviation both vary with the flexural coefficient. It increases with increasing flexural conductivity, exhibiting a linear relationship. The larger the output charge The larger the mean, the larger the output charge, but the standard deviation also increases, meaning the data fluctuates more and the accuracy decreases. This indicates that the flexural coefficient... Increasing the charge can improve the output charge of the flexural cantilever beam structure, but it will reduce the stability of the output results.

[0072] Figure 6 The output charge of the flexural electric cantilever beam structure when the mean length L of the flexural electric cantilever beam changes. The graph shows the changes in the mean and standard deviation of the output charge. The mean and standard deviation both decrease with increasing length L of the flexural electric cantilever beam, and this relationship is non-linear. The larger the length L of the flexural electric cantilever beam, the greater the output charge. The smaller the mean, the smaller the output voltage, and the smaller the standard deviation, meaning the data fluctuation is smaller and the accuracy is higher. This indicates that increasing the length L of the flexural cantilever beam will reduce the output charge of the flexural cantilever beam structure, but will increase the stability of the output results.

[0073] Figure 7 Flexural coefficient When the mean changes, the effective piezoelectric coefficient of the corresponding flexural cantilever beam structure The graph shows the variation of the mean and standard deviation of the effective piezoelectric coefficient. The mean and standard deviation both vary with the flexural coefficient. It increases with increasing flexural conductivity, exhibiting a linear relationship. The larger the value, the higher the effective piezoelectric coefficient. The larger the mean value, the greater the effective piezoelectric coefficient, but the standard deviation also increases, meaning the data fluctuates more and the accuracy decreases. This indicates that the flexural coefficient... Increasing the piezoelectric coefficient can improve the effective piezoelectric coefficient of the flexural cantilever beam structure, but it will reduce the stability of the output results.

[0074] Figure 8 The effective piezoelectric coefficient of the flexural electric cantilever beam structure when the mean thickness h varies.

[0075] The graph shows the changes in the mean and standard deviation. The effective piezoelectric coefficient can be seen from the graph. The mean and standard deviation of the effective piezoelectric coefficient decrease with increasing thickness h of the flexural electric cantilever beam, and this relationship is non-linear. The larger the thickness h of the flexural electric cantilever beam, the higher the effective piezoelectric coefficient.

[0076] The smaller the mean, the smaller the effective piezoelectric coefficient, but the standard deviation also decreases, meaning the data fluctuations are smaller and the accuracy is higher. This indicates that increasing the thickness h of the flexural cantilever beam will reduce the effective piezoelectric coefficient of the flexural cantilever beam structure, but will increase the stability of the output results.

[0077] Figure 9 The effective piezoelectric coefficient of the flexural electric cantilever beam structure when the mean length L of the flexural electric cantilever beam varies. The graph shows the variation of the mean and standard deviation of the effective piezoelectric coefficient. The mean and standard deviation both decrease with increasing length L of the flexural electric cantilever beam, and this relationship is non-linear. The larger the length L of the flexural electric cantilever beam, the higher the effective piezoelectric coefficient. The smaller the mean, the smaller the effective piezoelectric coefficient, and the smaller the standard deviation, meaning the data fluctuation is smaller and the accuracy is higher. This indicates that increasing the length L of the flexural cantilever beam will reduce the effective piezoelectric coefficient of the flexural cantilever beam structure, but will increase the stability of the output results.

[0078] Therefore, the above-mentioned sensitivity analysis method for flexural electric cantilever beam structures based on Sobol sequence sampling not only points the way to optimizing the performance of flexural electric cantilever beam structures considering parameter randomness, but also provides the necessary theoretical and experimental basis for the application of flexural electric cantilever beams as the main structural unit for flexural electric signal output in next-generation micro-nano electromechanical systems.

[0079] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for sensitivity analysis of flexoelectric cantilever beam structure based on Sobol sequence sampling, characterized in that: Comprising the following steps: S1: Establish a flexoelectric cantilever structure model; S2: Sobol sequence sampling-based flexoelectric cantilever structure model parameter uncertainty analysis; The design parameters of the flexoelectric cantilever structure model are subjected to Sobol sequence sampling-based uncertainty analysis, the random combination of the flexoelectric cantilever structure parameters is obtained by random sampling of the system design parameters, then the corresponding system output power and conversion efficiency data are calculated by substituting the model, and the distribution parameter estimation is performed on the data, the specific steps are as follows: (1) According to the normal distribution of the design parameters, the flexoelectric cantilever structure design parameters are sampled and a 6-D Sobol point set is generated, the first value is skipped, then every 3 points are reserved; Sobol sequence is used to generate random numbers in quasi-Monte Carlo simulation; (2) The distribution interval of the mean value of each design parameter of the flexoelectric cantilever structure is divided into M non-overlapping and equal probability subintervals; (3) Extract a sample point on each sub-interval, and store the sample point into the M N matrix. (4) Rearrange the elements of each row of the matrix to simulate the random combination of each parameter of the flexoelectric cantilever structure; = where the subscript S X 11 , X 12 , X 13 ... X 1M is a random permutation of the matrix row vector components, l is a Sobol sequence sampling matrix, with column vectors being the drawn N-dimensional samples;​ (5) Then the random numbers generated by sampling each parameter are substituted into the flexoelectric cantilever structure system model to calculate the corresponding charge output and electrical signal according to formulas (1), (2) and (3); (6) Estimate the parameter distribution of the system, and obtain the corresponding output voltage φ quasi , the mean and standard deviation of the charge Q quasi and the effective piezoelectric coefficient ​ S3: Substitute the extracted samples into the corresponding model to obtain the mean value and standard measurement of the output representation, and analyze and study the output performance.

2. The method of claim 1, wherein the method is based on Sobol sequence sampling. In step S1, a model of a flexoelectric cantilever structure is established, to obtain an expression of an open-circuit voltage output of the flexoelectric cantilever structure under quasi-static state and a short-circuit charge output of the flexoelectric cantilever under quasi-static state, and to determine a design parameter μ 31 、 ɑ 33 、 L 、 h .

3. The method of claim 2, wherein the method is based on Sobol sequence sampling. The open-circuit voltage output expression of the flexoelectric cantilever under quasi-static state is: where β is defined as the aspect ratio, i.e. L / h , S e is the electrode area, i.e. L B, L is the length of the beam, h is the thickness of the beam, B is the width of the beam, μ 31 is the flexoelectric coefficient, ɑ 33 is the dielectric coefficient.

4. The method of claim 3, wherein the Sobol sequence sampling based sensitivity analysis method for a flexoelectric cantilever beam structure is characterized by: The short-circuit charge output expression of the flexoelectric cantilever under quasi-static state is:

5. The method of claim 4, wherein the Sobol sequence sampling based sensitivity analysis of a flexoelectric cantilever beam structure is characterized by: By measuring the effective bending stiffness under open circuit, the quantitative characterization of flexoelectric material in micro-nanometer scale is realized, for the case of electrical short circuit, the effective piezoelectric coefficient is introduced, and the output electrical signal is redefined as: Wherein, E is the Young's modulus.

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