An adaptive strain detection method, system, and medium

Abstract

The present application relates to the field of strain detection, and particularly to a self-adaptive strain detection method, system and medium. The method comprises: inputting grid point coordinates, noisy displacement data and a maximum smoothing half window; calculating an overall noise level sigma through local linear regression analysis; extracting a local strain curvature characteristic quantity through cubic polynomial regression; establishing a noise and curvature balance relationship based on sigma and the curvature characteristic quantity, and calculating an adaptive smoothing half window; obtaining strain estimation values of each grid point through linear polynomial regression, and finally obtaining overall strain distribution. The method can automatically adjust the optimal smoothing window without manual intervention, balances between noise suppression and detail preservation, solves the problem of insufficient accuracy of traditional fixed window methods in non-uniform deformation areas, realizes high-precision full-field strain detection of noisy displacement fields, and is suitable for derivative calculation of digital image correlation systems and various noisy continuous signals.

Description

Technical Field

[0001] This invention relates to the field of strain detection, and specifically to an adaptive strain detection method, system, and medium. Background Technology

[0002] In high-end equipment manufacturing, advanced materials research and development, and service monitoring and safety assessment of major engineering structures, stress and strain, as core physical quantities characterizing the mechanical state of components, directly determine the accuracy of structural design safety margin assessment, material fatigue life prediction, and equipment service reliability analysis. As high-end equipment develops towards lightweighting, complexity, and extreme operating conditions, the requirements for spatial resolution, accuracy, and stability in strain measurement are becoming increasingly stringent, and traditional measurement methods are no longer sufficient to meet practical needs. Traditional strain measurement mainly relies on point sensors such as resistance strain gauges. While these sensors are based on mature principles and have sensitive responses, they can only acquire local single-point strain data and cannot reflect the full-field strain distribution characteristics of complex structures under load. Especially under multiaxial loading conditions, they are difficult to cover key areas such as stress concentration, resulting in significant limitations in the assessment of the overall mechanical state.

[0003] In recent years, digital image correlation (DIC) technology, with its advantages of non-contact and full-field measurement, has become the mainstream strain measurement method in civil engineering, mechanical manufacturing, aerospace and other fields, and its accuracy and reliability in uniform strain measurement have been widely recognized. However, when applied to non-uniform deformation regions such as stress concentration areas, crack tips or material microscale, the accuracy and stability of DIC strain measurement are easily affected by noise, resulting in problems such as large errors and fluctuating results. Strain extraction in DIC technology usually relies on smoothing methods such as local least squares or Savitzky-Golay filtering, and the selection of the local smoothing window is a key factor affecting the accuracy of strain calculation: if the window size is too small, the smoothing result is easily affected by random displacement noise and fluctuates drastically; if the window size is too large, it will mask the true local curvature changes, leading to over-smoothing of the strain result and producing systematic bias. Especially in regions where the strain field changes drastically, the optimal smoothing scale varies significantly at different locations. Traditional fixed window methods rely on manual experience or prediction of strain distribution to set the window size. When the strain distribution in the area to be measured is unknown, it is difficult to determine a suitable smoothing range. Even if the local area is set reasonably, the fixed window cannot take into account the strain characteristics of different areas, ultimately leading to insufficient accuracy and distorted results in global strain measurement.

[0004] Existing technologies, such as CN107255454B "A Multi-scale, Multifunctional Strain Measurement System and Method Based on Ultraviolet Imaging DIC," achieve high-precision strain measurement under ultra-high temperature conditions. However, this technology focuses on image acquisition and multi-scale measurement under ultra-high temperature conditions, without addressing the adaptive adjustment of the smooth window. It still relies on a fixed window or manually set window size, failing to solve the problem of balancing random errors and systematic biases under noisy and non-uniform deformation conditions. Therefore, how to achieve adaptive determination of the smooth window under noisy and non-uniform deformation conditions, thereby achieving the optimal balance between random errors and systematic biases, has become a key problem urgently needing to be solved in the fields of DIC and generalized strain measurement. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive strain detection method, system, and medium to solve the problems of traditional fixed window methods being unable to adaptively adjust the smooth scale and having difficulty balancing random errors and system deviations.

[0006] To achieve the above objectives, the following technical solution is adopted.

[0007] An adaptive strain detection method includes the following steps:

[0008] Input grid step size is d Grid point coordinates x i and the corresponding noisy displacement data u i Simultaneously input the maximum smooth half-window used to limit the window search range. n max ,in i =1,2,..., m , m This represents the total number of data points.

[0009] For each internal grid point x i Linear regression analysis is performed within its local neighborhood interval. Based on the regression results, the local random noise estimate of the internal grid point is calculated. The local random noise estimates of all internal grid points are then statistically averaged to obtain the overall noise level, which reflects the overall noise level of the displacement data. σ ;

[0010] For each internal grid point x i In the maximum smooth half window n max Perform cubic polynomial regression analysis within the defined neighborhood interval, and extract the coefficients of the cubic term from the regression results as a local strain curvature characteristic quantity characterizing the intensity of the strain field at that point. a3,i ;

[0011] Based on the overall noise level σ and the local strain curvature characteristic quantity a 3,i By establishing a balance between noise variance and curvature square, the adaptive smoothing half-window corresponding to each internal grid point is calculated. n i * ;

[0012] For each internal grid point x i In adaptive smooth half-window n i * Perform a first-order polynomial regression analysis within the defined neighborhood interval, and extract the coefficients of the first-order term as the local strain estimate for that internal grid point. ε i After processing all internal grid points in sequence, the adaptive strain distribution of the entire field is obtained.

[0013] Optionally, calculate the local random noise estimate and the overall noise level. σ The specific steps include:

[0014] For each internal grid point x i In the neighborhood interval [ x i – 2 d , x i +2 d Five displacement data points, including the center point, were selected. Linear least squares regression analysis was performed on these five data points to establish a local linear approximation function. This function was then used to calculate the fitted values ​​for each data point within the neighborhood interval. The actual displacement data of each data point was then... u i+j The difference between the fitted value and the actual value is used as the residual sequence. r i+j ,in j =-2,-1,0,1,2;

[0015] For the residual sequence r i+j Perform second-order difference processing to obtain the second-order difference sequence Δ 2 r i+k ,in k=-1,0,1. Based on the variance characteristics of the second-order difference sequence, the local random noise estimate of the internal grid point is calculated. After calculating the local random noise estimate of all internal grid points, the arithmetic mean of all local random noise estimates is taken to obtain the overall noise level. σ .

[0016] Optionally, the estimated local random noise value is calculated using the following formula:

[0017]

[0018] Where Var(·) represents variance operation, Δ 2 r For the second-order difference sequence, The overall noise level is a local noise estimate. σ It is calculated using the following formula:

[0019]

[0020] This formula averages the local random noise estimates of all internal grid points to obtain the overall noise level, which represents the noise level of the entire displacement field. σ .

[0021] Optionally, extract local strain curvature features. a 3,i The specific steps include:

[0022] For each internal grid point x i In the case of the maximum smooth half window n max Determined neighborhood interval [ x i – n max d , x i + n max d [Select 2 points including the center point] n max +1 displacement data points, for the 2 n max A cubic polynomial regression analysis was performed on +1 displacement data points to establish a cubic polynomial regression function containing constant, linear, quadratic, and cubic terms. The coefficient of the cubic term in this function was taken as the local strain curvature characteristic of the internal grid point. a 3,i The local strain curvature characteristic quantity a3,i Used to quantify the severity of non-uniformity in the strain field at that location.

[0023] Optionally, the adaptive smoothing half-window n i * The following piecewise function is used to calculate the overall noise level, which represents the noise level of the entire displacement field. This formula averages the local random noise estimates of all internal grid points. σ .

[0024] Optionally, extract local strain curvature features. a 3,i The specific steps include:

[0025] For each internal grid point x i In the case of the maximum smooth half window n max Determined neighborhood interval [ x i – n max d , x i + n max d [Select 2 points including the center point] n max +1 displacement data points, for the 2 n max A cubic polynomial regression analysis was performed on +1 displacement data points to establish a cubic polynomial regression function containing constant, linear, quadratic, and cubic terms. The coefficient of the cubic term in this function was taken as the local strain curvature characteristic of the internal grid point. a 3,i The local strain curvature characteristic quantity a 3,i Used to quantify the severity of non-uniformity in the strain field at that location.

[0026] Optionally, the adaptive smoothing half-window n i * It is obtained through the following piecewise function:

[0027]

[0028] The piecewise function establishes the overall noise level. σ With local strain curvature characteristic quantity a 3,iThe balance relationship is as follows: when the calculated value is less than 1, the minimum half-window size of 1 is used; when the calculated value is within the valid range, the calculated value itself is used; when the calculated value exceeds the maximum smoothing half-window size... n max Time to take n max .

[0029] Optionally, the correction coefficient in the piecewise function c The correction coefficient is used to adjust the sensitivity of the noise-curvature balance relationship. c The value range is 1.05 to 1.2, and this correction coefficient is used. c The adjustment enables adaptive smooth half-window n i * It can achieve an optimal balance between random noise suppression and system deviation control, ensuring that the window size is appropriately increased in areas with high noise levels to smooth out noise, and that the window size is appropriately reduced in areas with drastic curvature changes to preserve local strain characteristics.

[0030] Optionally, the maximum smooth half-window n max Based on grid step size d and the characteristic length corresponding to the presence of a significant strain gradient change. L The predictions determine that the two satisfy an approximate relationship.

[0031] ,

[0032] This relationship determines the upper limit of the window search range based on the spatial scale characteristics of strain gradient changes, and is used to constrain the adaptive smoothing half-window. n i * The range of values ​​ensures that a larger window size can be used in regions with gentle strain changes to improve the signal-to-noise ratio, while limiting the window size in regions with drastic strain changes to avoid over-smoothing.

[0033] Optionally, the steps of a first-order polynomial regression analysis specifically include:

[0034] For each internal grid point x i In adaptive smooth half-window n i * Determined neighborhood interval [ x i – n i * d , x i + ni * d [Select 2 points including the center point] n i * +1 displacement data point, for this 2 n i * A first-order polynomial regression analysis was performed on +1 displacement data points to establish a first-order polynomial regression function containing a constant term and a first-order term. The coefficient of the first-order term in this function was taken as the local strain estimate for that internal grid point. ε i The estimated local strain value ε i This is the final strain detection result for that internal grid point.

[0035] An adaptive strain detection system, comprising,

[0036] The data input module is used to receive data with a grid step size of [value missing]. d Grid point coordinates x i and the corresponding noisy displacement data u i and receive the maximum smooth half window n max The set value, of which i =1,2,..., m , m This represents the total number of data points.

[0037] The noise level calculation module, connected to the data input module, is used to calculate the noise level for each internal grid point. x i Linear regression analysis is performed within the neighborhood interval. Based on the regression residuals, the local random noise estimate is calculated, and the overall noise level is statistically obtained. σ ;

[0038] The curvature feature extraction module, connected to the data input module, is used to extract features from each internal grid point. x i In the maximum smooth half window n max A cubic polynomial regression analysis was performed within the neighborhood of the range, and the coefficients of the cubic term were extracted as local strain curvature characteristics. a 3,i ;

[0039] The window calculation module, connected to the noise level calculation module and the curvature feature extraction module, is used to calculate based on the overall noise level. σ and the local strain curvature characteristic quantity a3,i The adaptive smoothing half-window corresponding to each internal grid point is calculated by balancing the noise and curvature. n i * ;

[0040] The strain estimation module, connected to the window calculation module, is used to perform calculations on each internal grid point. x i In the adaptive smooth half window n i * Perform a first-order polynomial regression analysis within the neighborhood of the range, and extract the coefficients of the first-order term as the local strain estimate. ε i Each module executes sequentially to complete the adaptive strain distribution calculation for the entire field.

[0041] A computer-readable storage medium storing at least one instruction that, when executed by a processor, implements the adaptive strain detection method described above.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The adaptive strain detection method of this application, by inputting grid point coordinates, noisy displacement data, and the maximum smoothing half-window, calculates the overall noise level through local linear regression analysis, extracts local strain curvature characteristics through cubic polynomial regression, establishes a balance between noise and curvature to determine the adaptive smoothing half-window, and finally obtains the local strain estimate through first-order polynomial regression. This effectively solves the problems of traditional fixed-window methods, such as the inability to adaptively adjust the smoothing scale and the difficulty in balancing random errors and systematic biases, achieving high-precision full-field strain detection under noisy and non-uniform deformation conditions. This method does not rely on manual experience or multiple trial calculations. It can automatically adjust the optimal smoothing window size according to the displacement field noise level and local strain curvature characteristics. In areas with high noise levels, the window size is increased to smooth the noise; in areas with drastic curvature changes, the window size is decreased to preserve local strain characteristics. Simultaneously, in uniform strain regions, the maximum allowable window is automatically adopted, naturally degenerating the method into the traditional fixed-window form, thus balancing measurement stability and reliability under different deformation characteristics.

[0044] By employing 5-point linear least squares regression, residual second-order difference, and variance calculation to estimate local random noise and overall noise level, the accuracy of noise level assessment is further improved, providing reliable data support for the precise calculation of the adaptive window. Cubic polynomial regression is used to extract cubic term coefficients as local strain curvature characteristics, enabling precise quantification of the severity of strain field non-uniformity and providing a scientific basis for adaptive window adjustment. Piecewise functions, correction coefficient adjustment, and maximum smooth half-window prediction methods optimize the balance between noise and curvature, ensuring flexible adjustment of the adaptive window within its effective range and further improving the accuracy of strain measurement. Extracting strain estimates through first-order polynomial regression within the adaptive window simplifies the calculation process while ensuring the reliability of the strain results. The adaptive strain detection system, through modular design, automates data input, noise calculation, curvature extraction, window adjustment, and strain estimation, enhancing the engineering practicality of the technology. Computer-readable storage media provides a convenient carrier for the application of this method, allowing it to be flexibly embedded in various strain measurement devices or systems, expanding the applicable scenarios of the technology. Attached Figure Description

[0045] Figure 1 This is a schematic flowchart of an embodiment of the adaptive strain detection method of the present invention;

[0046] Figure 2 This is a schematic diagram of a module of an embodiment of the adaptive strain detection system of the present invention;

[0047] Figure 3 yes T =300, σ Comparison of the true sinusoidal displacement field and the noisy displacement data under the condition of 0.02;

[0048] Figure 4 yes T =300, σ Comparison of strain detection results of various methods under the condition of 0.02;

[0049] Figure 5 yes T =300, σ Comparison of strain detection errors of various methods under the condition of 0.02;

[0050] Figure 6 Different periods T Comparison of root mean square error (RMSE) of strain under the given conditions;

[0051] Figure 7 Different noise standard deviations σ Comparison of root mean square error (RMSE) of strain under the given conditions. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0053] The following detailed description is exemplary and intended to provide further detailed explanation of the invention. Unless otherwise specified, all technical terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terminology used in this invention is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention.

[0054] Example 1

[0055] like Figure 1 As shown, this embodiment details the specific implementation process of an adaptive strain detection method. This method is suitable for extracting high-precision strain fields from noisy displacement data, and is particularly applicable to displacement field data obtained in digital image correlation techniques. It can also be extended to the calculation of derivatives of other types of noisy continuous signals.

[0056] This embodiment details a window-adaptive strain detection method based on the principle of noise and curvature balance. This method analyzes the dynamic relationship between noise characteristics and strain field curvature characteristics in displacement data to automatically optimize and adjust the size of the smooth window, thereby improving strain calculation accuracy while maintaining spatial resolution.

[0057] The method begins by receiving the necessary input parameters. These parameters include the location information of grid points distributed at fixed intervals and their corresponding displacement data including measurement noise. It also requires a parameter to limit the maximum window range. This maximum window parameter is determined based on the density of the measurement grid and the characteristic scale of strain field changes, ensuring that subsequent calculations are performed within a reasonable window range.

[0058] Next, we proceed to the noise level assessment phase. In this phase, local noise characteristic analysis is performed on each valid internal data point. Specifically, within a small neighborhood of each data point, several neighboring data points, including the data point itself, are selected, and the displacement values ​​of these points are fitted with a straight line. By comparing the difference between the actual displacement values ​​and the predicted values ​​of the fitted line, a set of residual data is obtained. Then, specific mathematical processing is performed on this set of residual data to separate the random fluctuation component, thereby estimating the noise intensity of that local area. After completing the local noise estimation for all data points, these local estimates are averaged to obtain a global noise assessment value representing the noise level of the entire displacement field.

[0059] After noise assessment, the next stage is strain field curvature characteristic analysis. This stage aims to quantify the severity of strain changes at each location. For each valid internal data point, multiple neighboring data points, including that point, are selected within a larger neighborhood defined by the maximum window parameter. The displacement distribution of these points is then subjected to cubic curve fitting. A parameter representing the curvature of the curve is extracted from the fitting results; this parameter effectively reflects the local variation characteristics of the strain field at that location. A larger value of this curvature characteristic parameter indicates a more rapid strain change at that location; a smaller value indicates a more gradual strain change.

[0060] Based on the global noise assessment and local curvature feature parameters obtained from the preceding steps, the core adaptive window calculation stage begins. This stage determines the most suitable smoothing window size for each data point using specific calculation rules. The design of these rules ensures that larger windows are automatically selected in noisy regions to effectively suppress random errors, while smaller windows are automatically selected in regions with drastic strain changes to preserve local detail features. Furthermore, the calculation rules ensure that the window size remains within a preset reasonable range, avoiding extreme cases of excessively small or large windows. This balancing mechanism also includes an adjustable parameter for fine-tuning the weighting relationship between noise and curvature, enabling the method to adapt to different application scenarios.

[0061] Finally, the strain value calculation stage begins. Based on the determined optimization window size for each data point, an appropriate number of neighboring data points are selected within their corresponding neighborhood, and the displacement distribution of these points is linearly fitted. The slope parameter is extracted from the fitting result as the strain estimate for that point. This operation is performed on all valid data points sequentially to obtain the complete strain field distribution result.

[0062] This method demonstrates significant advantages in practical applications. It can automatically adjust calculation parameters based on the actual characteristics of the strain field, using a larger smoothing window to improve the signal-to-noise ratio in regions with gentle strain changes, and a smaller window to maintain spatial resolution in regions with drastic strain changes. This adaptability allows the method to maintain high computational accuracy under different noise levels and strain distribution characteristics, making it particularly suitable for precise measurements of complex strain fields such as those with stress concentrations and crack tips.

[0063] The entire process forms a complete technical closed loop, with each step from data input to result output designed to achieve optimal strain calculation accuracy. This method is not only applicable to one-dimensional strain analysis but can also be extended to two-dimensional and three-dimensional cases, providing reliable technical support for engineering applications such as material performance testing and structural health monitoring.

[0064] Example 2

[0065] The method of the present invention includes the following main steps:

[0066] 1) Input grid step size is d Grid point coordinates x i and the corresponding noisy displacement data u i ,in i =1,2,..., m , m This represents the total number of data points. Additionally, input the maximum smoothing half-window size used for strain detection. n max This parameter can be adjusted based on the grid step size. d and the characteristic length corresponding to the presence of a significant strain gradient change. L For estimation, a general guideline is to take... n max ≈ L / (2 d An integer. It should be noted that here... n max It serves only as an empirical upper limit to limit the search range of the window; its value is an estimate and does not need to be too precise.

[0067] 2) For each internal data point x i (Excluding 4 invalid data points at both ends), calculate its local random noise estimate. The overall noise level is obtained using the following formula:

[0068] ,

[0069] in, The local noise estimate is calculated as follows:

[0070] For each valid data point x i In its neighborhood interval [ x i – 2 d , x i +2 d Five displacement data points were selected within this local data set. Linear least squares regression was performed on this local data to establish a local approximation function:

[0071] ,

[0072] in a 0, a 1 represents the regression coefficient. Calculate the residual sequence for each data point within the neighborhood interval:

[0073] .

[0074] Furthermore, by performing a second-order difference on the residual sequence, we obtain:

[0075] ,

[0076] Based on the second-order difference sequence obtained from the above formula, the noise standard deviation estimate for this local region is calculated using the following formula:

[0077] ,

[0078] 3) For each internal grid point x i (excluding both ends, a total of 2) n max (invalid data), in its neighborhood interval [ x i – n max d , x i + n max d ] Select 2 in total n max Given +1 displacement data, perform a cubic polynomial regression on this local data. The regression function is:

[0079] ,

[0080] in a 0, a 1, a 2, a 3 represents the regression coefficients. The coefficient of the cubic term is taken. a 3 as grid point x i Local strain curvature characteristic quantity a 3,i ,Right now:

[0081] .

[0082] 4) For each internal grid point x i The noise level is obtained based on the above two steps. σ and strain curvature characteristic quantity a 3,i The smooth half-window size is determined using the following formula. n i * :

[0083] ,

[0084] Where, constant c The correction factor is typically set to 1.05 to 1.2, with 1.18 being preferred.

[0085] 5) For each valid grid point x i According to its corresponding n i * Adaptive selection of smooth window intervals [ x i – n i * d , x i + n i * d ], for the smooth window within 2 n i * Perform a polynomial regression once with +1 data point to establish the regression function:

[0086] ,

[0087] in, b 0, b 1 represents the regression coefficient. The coefficient of the first-order term is taken. b 1 is used as the estimated local strain value at this location:

[0088] .

[0089] By sequentially performing the above operation on all data points after removing invalid boundary data points, the adaptive strain distribution of the entire field can be obtained. ε i .

[0090] As a specific example of the above example, it includes:

[0091] A one-dimensional sinusoidal displacement field is selected for testing, and its displacement function is defined as follows:

[0092] ,

[0093] in, η (x) ~ N (0, σ ²) is a property that follows a zero mean and a variance of . σ ² random error. By adjusting the period parameter TThe magnitude of strain curvature (i.e., the degree of strain nonuniformity) can be changed by adjusting the noise standard deviation. σ To simulate random noise levels of varying intensities.

[0094] In this embodiment, the grid step size is taken as... d =2, number of grid points m =400, grid point coordinates xᵢ = 2, 4, 6,…, 800. The grid point displacements are:

[0095] ,

[0096] The noise standard deviation is taken respectively σ = 0.005, 0.02, 0.04, with periods of respectively. T = 150, 300, 450, Feature length L Pick T / 2, maximum smooth half-window n max = round( T / 8). Further, the adaptive windowing method based on noise-curvature balance proposed in this invention is used to adaptively smooth and extract strain from the above-mentioned noisy displacement data. The specific steps are as follows:

[0097] 1) For each internal data point xᵢ For the variable ∈[6, 796], calculate its local random noise estimate. The overall noise level is obtained using the following formula:

[0098] ,

[0099] Among them, local noise estimation The calculation method is as follows:

[0100] For each valid data point x i In its neighborhood interval [ x i – 2 d , x i +2 d Perform linear regression; the regression function is:

[0101] ,

[0102] in a 0, a 1 represents the regression coefficient. Calculate the residual sequence for each sampling point within the neighborhood interval:

[0103] .

[0104] Furthermore, for the residual sequence r i+j Perform second-order difference:

[0105] ,

[0106] Based on the second-order difference sequence obtained from the above formula, the noise standard deviation estimate for this local region is calculated using the following formula:

[0107] ,

[0108] Var(·) represents variance operation.

[0109] 2) For each internal grid point x i (excluding both ends, a total of 2) n max (invalid data), in its neighborhood interval [ x i – n max d , x i + n max d A cubic polynomial regression was performed within the range, and the regression function was:

[0110] ,

[0111] in a 0, a 1, a 2, a 3 represents the regression coefficients. The coefficient of the cubic term is taken. a 3 as grid point x i Local strain curvature characteristic quantity a 3,i ,Right now:

[0112] .

[0113] 3) For each internal grid point x i The smooth half-window size is determined using the following formula. n i *

[0114] ,

[0115] Among them, the correction coefficient in the piecewise function c Sensitivity used to adjust the relationship between noise and curvature balance, correction coefficient c The value range is 1.05 to 1.2, and the correction factor is... c Take 1.18, and use this correction factor. c The adjustment enables adaptive smooth half-window n i * It can achieve an optimal balance between random noise suppression and system deviation control, ensuring that the window size is appropriately increased in areas with high noise levels to smooth out noise, and that the window size is appropriately reduced in areas with drastic curvature changes to preserve local strain characteristics.

[0116] 4) For each valid grid point x i According to the calculation in step 3) n i * Adaptive selection of smooth window intervals [ x i – n i * d , x i + n i * d ], for the smooth window within 2 n i * Perform a polynomial regression once with +1 data point to establish the regression function:

[0117] ,

[0118] in, b 0, b 1 represents the regression coefficient. The coefficient of the first-order term is taken. b 1 is used as the estimated local strain value at this location:

[0119] .

[0120] By sequentially performing the above operation on all data points after removing invalid boundary data points, the adaptive strain distribution of the entire field can be obtained. ε i .

[0121] See Figures 3-7Compared to traditional fixed-window methods, this invention can automatically adjust the smoothing scale according to the non-uniformity of the strain field, achieving higher accuracy strain results under different noise levels and strain curvature conditions. This method exhibits good noise robustness and curvature adaptability, achieving an optimal balance between random errors and systematic biases, thereby significantly improving the global accuracy and stability of strain calculations.

[0122] Example 3

[0123] like Figure 2 As shown, this embodiment details the specific implementation architecture of an adaptive strain detection system. The system adopts a modular design, with each functional module working collaboratively to achieve a complete detection process. It can be implemented based on hardware circuits or software programs.

[0124] The data input module is responsible for receiving external data and configuring system parameters, and includes a displacement data receiving unit and a parameter configuration unit. The displacement data receiving unit connects to a digital image correlation system or external measurement equipment via a data interface, including but not limited to USB, Ethernet, CameraLink, and wireless transmission modules. The displacement data receiving unit has a built-in data buffer and protocol parser, capable of handling displacement data in different formats, including text, binary, and standard image correlation software output formats. The data buffer uses a circular queue structure, and its capacity is dynamically adjusted according to the data volume to ensure the continuity and integrity of data transmission. The parameter configuration unit provides a human-machine interface, which can be a graphical user interface or a command-line interface, allowing users to input the grid step size. d Maximum smooth half window n max Correction coefficient c Key parameters, etc. The parameter configuration unit has a built-in parameter validation function to check the reasonableness of input parameters and ensure... d Greater than zero n max positive integers c Within the range of 1.05 to 1.2. The parameter configuration unit supports the import and export of parameter files, facilitating batch processing and repeated experiments.

[0125] The noise level calculation module is connected to the data input module and includes a linear regression processor and a noise estimation processor. The linear regression processor has a built-in linear least squares algorithm unit, using matrix operations to achieve fast regression calculations. For each internal grid point, the linear regression processor obtains the neighborhood interval from the data input module. x i – 2 d to x i +2 dFive displacement data points within the range are used to construct a design matrix and observation vector. Regression coefficients are obtained by solving the normal equation. a 0 and a 1. The linear regression processor supports both single-precision and double-precision floating-point operations, selectable according to accuracy requirements. The noise estimation processor has a built-in second-order difference operation unit and variance statistics unit. It receives the regression coefficients and original displacement data output by the linear regression processor and first calculates the residual sequence. r i+j Then, perform a second-order difference operation to obtain Δ. 2 r i+k Finally, the variance is calculated and the square root is taken to obtain the local random noise estimate. The noise estimation processor uses a sliding window technique to avoid redundant calculations and improve processing efficiency. The noise estimation processor has a built-in accumulator that accumulates the local random noise estimates for all internal grid points, and finally obtains the overall noise level through division. σ .

[0126] The curvature feature extraction module is connected to the data input module and includes a cubic polynomial regression processor. The cubic polynomial regression processor incorporates a cubic polynomial least squares algorithm unit and uses the generalized inverse matrix method to solve for the regression coefficients. For each internal grid point... x i The cubic polynomial regression processor obtains the neighborhood interval from the data input module. x i – n max d , x i + n max d ] within the range of 2 n max With +1 displacement data points, a design matrix is ​​constructed containing constant, linear, quadratic, and cubic terms. The regression coefficients are then obtained by solving the least squares method. a 0, a 1, a 2, a 3. Extracting the coefficients of the cubic term using a cubic polynomial regression processor. a 3 as a characteristic quantity of local strain curvature a 3,i Output. The cubic polynomial regression processor supports polynomial regressions of different orders. Users can select the regression order through the parameter configuration unit; the default is cubic. The cubic polynomial regression processor has a built-in condition number check function, which automatically uses regularization methods to improve numerical stability when the design matrix is ​​ill-conditioned.

[0127] The window calculation module is connected to the noise level calculation module and the curvature feature extraction module, and includes a balance relationship operator and a comparison and judgment unit. The balance relationship operator has built-in exponential operation unit and multiplication operation unit, and receives the overall noise level σ and local strain curvature feature quantities. a 3,i As input, execute the following formula

[0128] .

[0129] The exponentiation unit employs either a fast exponentiation algorithm or a lookup table method to ensure both calculation accuracy and speed. The comparison unit has a built-in threshold storage register that stores a preset threshold of 1 and... n max It receives intermediate calculated values ​​from the balance relation arithmetic unit and performs numerical comparison judgments. The comparison judgment unit adopts a pipelined structure, sequentially judging whether the intermediate calculated value is less than 1, whether it is between 1 and... n max Between, whether greater than n max Based on the judgment result, the corresponding output value is selected as the adaptive smooth half-window. n i * The comparison and judgment unit supports vectorized comparison, which can handle the judgment task of multiple grid points simultaneously.

[0130] The strain estimation module is connected to the window calculation module and includes a first-order polynomial regression processor. The first-order polynomial regression processor incorporates a first-order polynomial least squares algorithm unit, employing a matrix operation method similar to that of the linear regression processor. For each internal grid point... x i The first-order polynomial regression processor obtains an adaptive smoothed half-window from the data input module. n i * Determine the neighborhood interval [ x i – n i * d , x i + n i * d ] within the range of 2 n i * With one displacement data point, construct the design matrix and observation vector, and solve the regression coefficients using the least squares method. b 0 and b 1. Extracting coefficients of the first-order term using a first-order polynomial regression processor. b 1 as a local strain estimate ε i Output. The first-order polynomial regression processor has a built-in error estimation unit that can calculate the standard deviation of strain estimates, providing users with a confidence assessment of the results.

[0131] The system's internal data bus adopts a high-speed serial or parallel bus architecture to connect various functional modules, ensuring that the data transmission rate meets real-time processing requirements. The data bus width is selected according to the data precision, supporting 32-bit or 64-bit data transmission. The data bus has a built-in arbitration mechanism; when multiple modules request data simultaneously, they are scheduled according to priority, ensuring that the data needs of the noise level calculation module and the curvature feature extraction module are prioritized. For software implementation, the data bus can be replaced with a shared memory mechanism, where modules exchange data by accessing shared memory, using mutexes and semaphores for synchronization.

[0132] The system clock management unit provides a unified clock signal for all modules, supporting both synchronous and asynchronous operating modes. In synchronous mode, all modules execute according to a fixed timing cycle, suitable for scenarios with high real-time requirements. In asynchronous mode, each module is triggered to execute when data is ready, suitable for non-real-time or event-driven scenarios. The clock frequency is selected according to processing speed requirements, ranging from tens of megahertz to several gigahertz.

[0133] The system power management unit (PMU) features a low-power design and supports dynamic voltage and frequency adjustment. When the system load is low, it automatically reduces the operating voltage and clock frequency to save power. Each functional module supports independent power control, and unused modules can be individually shut down. The PMU has a built-in temperature sensor that automatically reduces the frequency for protection when the chip temperature exceeds a threshold.

[0134] The system can be implemented using application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or digital signal processors (DSPs). ASIC solutions offer high integration, low power consumption, and fast processing speed, making them suitable for mass production. FPGA solutions offer high flexibility, short development cycles, and reconfigurability, making them suitable for algorithm iteration and customization needs. DSP solutions are easy to program, have a mature ecosystem, and strong floating-point arithmetic capabilities, making them suitable for complex algorithm implementation and scientific research applications.

[0135] For software implementation, the system can be deployed on personal computers, servers, or embedded platforms. Programming languages ​​include C / C++, Python, and MATLAB. C / C++ offers high execution efficiency, making it suitable for real-time processing. Python provides high development efficiency, making it suitable for rapid prototyping. MATLAB facilitates mathematical operations, making it suitable for algorithm research and simulation. The software architecture employs a modular design, with each functional module encapsulated as an independent function or class, and data exchange achieved through parameter passing and return values.

[0136] The system supports distributed deployment. For ultra-large-scale data, the data domain can be divided into multiple sub-regions and distributed to different computing nodes for parallel processing. Each node independently performs noise level calculation, curvature feature extraction, window calculation, and strain estimation, with the master node finally summarizing the results. Nodes are interconnected via a high-speed network, communicating using MPI or TCP / IP protocols.

[0137] The system has built-in self-testing and diagnostic functions. Upon startup, it performs functional tests on each module, including memory testing, arithmetic unit testing, and interface testing. During operation, it monitors the status of each module in real time, logging errors and triggering alarms when errors are detected. The error log includes information such as error type, occurrence time, and relevant parameters, facilitating troubleshooting.

[0138] In terms of user interface, the system provides a graphical user interface (GUI) and an application programming interface (API). The GUI displays input data, intermediate results, and the final strain field, supporting various visualization methods such as 2D curves, 3D surfaces, and color contour plots. Users can adjust parameters, start calculations, and save results through the interface. The API provides standard function call interfaces, supporting integration with other software systems. Interface functions include initialization, parameter setting, data input, calculation execution, and result acquisition.

[0139] In terms of performance optimization, the system employs a multi-level caching mechanism to store frequently accessed data in a high-speed cache, reducing memory access latency. Linear regression and multinomial regression operations are accelerated using the SIMD instruction set, with a single instruction processing multiple data points. For large-scale matrix operations, GPU parallel computing can be used, leveraging CUDA or OpenCL programming models to divide the computational task into a large number of threads for parallel execution.

[0140] In terms of accuracy assurance, the system supports double-precision floating-point operations, and high-precision algorithms are used for key calculation steps. Linear regression and polynomial regression are solved using singular value decomposition to avoid numerical errors introduced by matrix inversion. Noise estimation and variance calculation employ compensated summation algorithms to reduce accumulated floating-point operation errors. The system provides result verification functions, evaluating the reliability of strain results through residual analysis, consistency checks, and other methods.

[0141] In practical engineering applications, the system can seamlessly integrate with digital image processing (DIP) software. After the DIP software completes the displacement field calculation, it outputs the displacement data in a standard format. This system reads this data through the data input module and automatically executes the subsequent strain detection process. The detection results can be imported into finite element analysis software for verification or compared with theoretical solutions to evaluate accuracy. The system supports batch processing and can automatically process data from multiple samples or various working conditions to generate statistical reports.

[0142] For two-dimensional digital image correlation systems, the system is expanded into a dual-channel architecture to process images separately.x direction and y Directional displacement. The data input module receives two-dimensional mesh coordinates and displacement data. The noise level calculation module and curvature feature extraction module process the two directions in parallel. The window calculation module can share noise and curvature information or calculate them separately. The strain estimation module outputs... x Directional strain, y Normal strain and shear strain. The system supports color image display, overlaying the strain field as a contour map onto the image of the object under test, intuitively displaying the strain distribution.

[0143] For the 3D digital image correlation system, the system is expanded to a three-channel architecture for processing. x , y , z The system supports three-directional displacement. The data input module receives 3D mesh coordinates and displacement data, while the noise level calculation module and curvature feature extraction module process the data in parallel across the three directions. The strain estimation module outputs three normal strains and three shear strains, forming a complete strain tensor. The system supports 3D visualization, displaying the strain field as a 3D contour plot or slices.

[0144] In materials mechanical property testing applications, the system is used for strain measurement in experiments such as tension, compression, and bending. A speckle pattern is created on the sample surface, and the displacement field is acquired through a digital image correlation system. This system calculates the strain field, thereby obtaining material parameters such as stress-strain curves, elastic modulus, and Poisson's ratio. The system supports real-time processing, displaying strain distribution and monitoring sample deformation during the experiment.

[0145] In structural health monitoring applications, the system is used for strain monitoring of structures such as bridges, buildings, and machinery. By periodically capturing images of the structural surface, it calculates changes in the strain field and identifies the location and development trend of damage. The system supports long-term data storage and trend analysis, and allows users to set strain thresholds; when the strain exceeds the threshold, an alarm is triggered.

[0146] In micromechanical research applications, the system is used for strain measurement in micro-regions of materials. It acquires images of the material surface using a high-resolution microscope, calculates the micro-strain field, and studies local deformation behaviors such as crack propagation, interface slip, and phase transformation. The system supports fine-grained analysis of micro-regions and can extract strain singularity information at crack tips.

[0147] In impact dynamics applications, the system is used for strain measurement during high-speed deformation processes. By capturing the impact process with a high-speed camera to obtain the transient displacement field, the system quickly calculates the strain field and analyzes dynamic phenomena such as stress wave propagation and localized deformation. The system optimizes algorithm efficiency and supports high frame rate data processing.

[0148] In fatigue testing applications, the system is used for strain measurement under cyclic loading. By continuously recording the fatigue process, the strain field for each cycle is calculated to study fatigue behaviors such as cyclic hardening, softening, and crack initiation. The system supports phase-locked averaging, improving the signal-to-noise ratio of cyclic strain measurements.

[0149] In creep testing applications, the system is used for strain measurement under long-term loading. By periodically recording the creep process, the creep strain field is calculated to study the creep deformation mechanism and damage evolution. The system supports time series analysis, which can extract the variation of creep strain rate over time.

[0150] In thermomechanical fatigue applications, the system considers the effects of temperature changes. By simultaneously recording the temperature and displacement fields, thermal strain and mechanical strain are separated, and the strain caused by actual stress is calculated. The system supports multiphysics coupling analysis, which can study the influence of temperature on strain distribution.

[0151] In the characterization of the mechanical properties of composite materials, the system is used for multiaxial strain measurement of anisotropic materials. By measuring strain components in different directions, the anisotropic parameters of the material are calculated, and the constitutive model is verified. The system supports simultaneous measurement of strain in multiple directions, enabling comprehensive characterization of the deformation behavior of composite materials.

[0152] In welded joint performance evaluation, the system is used for strain measurement of the weld and heat-affected zone. It captures the distribution of residual strain in the weld through high-resolution measurements to assess weld quality and joint strength. The system supports fine measurements in high-gradient areas, accurately capturing strain concentrations near the weld.

[0153] Example 4

[0154] A computer-readable storage medium storing at least one instruction that, when executed by a processor, implements an adaptive strain detection method.

[0155] If the modules / units integrated in the electronic device 100 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, and read-only memory (ROM). Those skilled in the art should understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0156] As is known from common technical knowledge, this invention can be implemented through other embodiments that do not depart from its spirit or essential characteristics. Therefore, the disclosed embodiments described above are merely illustrative in all respects and are not the only ones. All modifications within the scope of this invention or its equivalents are included in this invention.

Claims

1. An adaptive strain detection method, characterized in that, Includes the following steps: Input grid step size is d Grid point coordinates x i and the corresponding noisy displacement data u i Simultaneously input the maximum smooth half-window used to limit the window search range. n max ,in i =1,2,..., m , m This represents the total number of data points. For each internal grid point x i Linear regression analysis is performed within its local neighborhood interval. Based on the regression results, the local random noise estimate of the internal grid point is calculated. The local random noise estimates of all internal grid points are then statistically averaged to obtain the overall noise level, which reflects the overall noise level of the displacement data. σ ; For each internal grid point x i In the maximum smooth half window n max Perform a cubic polynomial regression analysis within the determined neighborhood interval, and extract the coefficients of the cubic term from the regression results as a characterization of the internal grid points. x i Local strain curvature characteristic of the intensity of the strain field a 3,i ; Based on the overall noise level σ and the local strain curvature characteristic quantity a 3,i By establishing a balance between noise variance and curvature square, the adaptive smoothing half-window corresponding to each internal grid point is calculated. n i * ; For each internal grid point x i In adaptive smooth half-window n i * Perform a first-order polynomial regression analysis within the defined neighborhood interval, and extract the coefficients of the first-order term as the local strain estimate for that internal grid point. ε i After processing all internal grid points in sequence, the adaptive strain distribution of the entire field is obtained.

2. The adaptive strain detection method according to claim 1, characterized in that, Calculate the local random noise estimate and the overall noise level. σ The specific steps include: For each internal grid point x i In the neighborhood interval [ x i – 2 d , x i +2 d Five displacement data points, including the center point, were selected. Linear least squares regression analysis was performed on these five data points to establish a local linear approximation function. This function was then used to calculate the fitted values ​​for each data point within the neighborhood interval. The actual displacement data of each data point was then... u i+j The difference between the fitted value and the actual value is used as the residual sequence. r i+j ,in j =-2,-1,0,1,2; For the residual sequence r i+j Perform second-order difference processing to obtain the second-order difference sequence Δ 2 r i+k ,in k =-1,0,1. Based on the variance characteristics of the second-order difference sequence, the local random noise estimate of the internal grid point is calculated. After calculating the local random noise estimate of all internal grid points, the arithmetic mean of all local random noise estimates is taken to obtain the overall noise level. σ .

3. The adaptive strain detection method according to claim 2, characterized in that, The estimated value of the local random noise is calculated using the following formula: ； Where Var(·) represents variance operation, Δ 2 r For the second-order difference sequence, The overall noise level is a local noise estimate. σ It is calculated using the following formula: ； This formula averages the local random noise estimates of all internal grid points to obtain the overall noise level, which represents the noise level of the entire displacement field. σ .

4. The adaptive strain detection method according to claim 1, characterized in that, Extracting local strain curvature characteristics a 3,i The specific steps include: For each internal grid point x i In the case of the maximum smooth half window n max Determined neighborhood interval [ x i – n max d , x i + n max d [Select 2 points including the center point] n max +1 displacement data points, for the 2 n max A cubic polynomial regression analysis was performed on +1 displacement data points to establish a cubic polynomial regression function containing constant, linear, quadratic, and cubic terms. The coefficient of the cubic term in this function was taken as the local strain curvature characteristic of the internal grid point. a 3,i The local strain curvature characteristic quantity a 3,i Used to quantize the internal grid points x i The degree of nonuniformity and intensity of the strain field.

5. The adaptive strain detection method according to claim 1, characterized in that, The adaptive smooth half-window n i * It is obtained through the following piecewise function: ； The correction coefficient c in the piecewise function is used to adjust the sensitivity of the noise-curvature balance relationship; this piecewise function establishes the overall noise level. σ With local strain curvature characteristic quantity a 3,i The balance relationship is as follows: when the calculated value is less than 1, the minimum half-window size of 1 is used; when the calculated value is within the valid range, the calculated value itself is used; when the calculated value exceeds the maximum smoothing half-window size... n max Time to take n max .

6. The adaptive strain detection method according to claim 5, characterized in that, The correction coefficient c The value range is 1.05 to 1.2, and this correction coefficient is used. c The adjustment enables adaptive smooth half-window n i * It can achieve an optimal balance between random noise suppression and system deviation control, ensuring that the window size is appropriately increased in areas with high noise levels to smooth out noise, and that the window size is appropriately reduced in areas with drastic curvature changes to preserve local strain characteristics.

7. The adaptive strain detection method according to claim 1, characterized in that, The maximum smooth half window n max Based on grid step size d and the characteristic length corresponding to the presence of a significant strain gradient change. L The predictions determine that the two satisfy an approximate relationship. ； This relationship determines the upper limit of the window search range based on the spatial scale characteristics of strain gradient changes, and is used to constrain the adaptive smoothing half-window. n i * The range of values ​​ensures that a larger window size can be used in regions with gentle strain changes to improve the signal-to-noise ratio, while limiting the window size in regions with drastic strain changes to avoid over-smoothing.

8. The adaptive strain detection method according to claim 1, characterized in that, The specific steps of a first-order polynomial regression analysis include: For each internal grid point x i In adaptive smooth half-window n i * Determined neighborhood interval [ x i – n i * d , x i + n i * d [Select 2 points including the center point] n i * +1 displacement data point, for this 2 n i * A first-order polynomial regression analysis was performed on +1 displacement data points to establish a first-order polynomial regression function containing a constant term and a first-order term. The coefficient of the first-order term in this function was taken as the local strain estimate for that internal grid point. ε i The estimated local strain value ε i This is the final strain detection result for that internal grid point.

9. An adaptive strain detection system, based on the adaptive strain detection method according to any one of claims 1-8, characterized in that, include, The data input module is used to receive data with a grid step size of [value missing]. d Grid point coordinates x i and the corresponding noisy displacement data u i and receive the maximum smooth half window n max The set value, of which i =1,2,..., m , m This represents the total number of data points. The noise level calculation module, connected to the data input module, is used to calculate the noise level for each internal grid point. x i Linear regression analysis is performed within the neighborhood interval. Based on the regression residuals, the local random noise estimate is calculated, and the overall noise level is statistically obtained. σ ; The curvature feature extraction module, connected to the data input module, is used to extract features from each internal grid point. x i In the maximum smooth half window n max A cubic polynomial regression analysis was performed within the neighborhood of the range, and the coefficients of the cubic term were extracted as local strain curvature characteristics. a 3,i ; The window calculation module, connected to the noise level calculation module and the curvature feature extraction module, is used to calculate based on the overall noise level. σ and the local strain curvature characteristic quantity a 3,i The adaptive smoothing half-window corresponding to each internal grid point is calculated by balancing the noise and curvature. n i * ; The strain estimation module, connected to the window calculation module, is used to perform calculations on each internal grid point. x i In the adaptive smooth half window n i * Perform a first-order polynomial regression analysis within the neighborhood of the range, and extract the coefficients of the first-order term as the local strain estimate. ε i Each module executes sequentially to complete the adaptive strain distribution calculation for the entire field.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one instruction, which, when executed by a processor, implements an adaptive strain detection method as described in any one of claims 1 to 8.

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