A method for automatically locating the elastic range of material tensile deformation

Abstract

The present invention discloses an automatic positioning method for elastic intervals of material tensile deformation, comprising the following steps: S100, data set segmentation; S200, initial straight line segment fitting; S300, error calculation; S400, re-estimation of straight line segments according to an inner point set; if the number of inner points is greater than half of the data volume of the segmented interval, all the inner points in the segmented interval are used to re-estimate the straight line, and the residual value of the fitted straight line segment is calculated, and the fitted straight line segment is recorded this time; otherwise, the current fitting fails and the current fitting result is discarded; S500, iterative calculation; S600, segmented interval diffusion fitting straight line segment; S700, determining the two end points of the elastic interval. The present invention utilizes the RANSAC principle and adopts segmented fitting diffusion straight line segments to automatically locate the left and right end points of the elastic interval, thereby realizing the automatic positioning of the elastic interval of the material tensile deformation, and then realizing the automatic calculation of the elastic modulus of the material.

Description

Technical Field

[0001] The invention relates to the technical field of three-dimensional measurement, and in particular to an automatic positioning method for an elastic range of a material under tensile deformation. Background Art

[0002] The key to calculating material mechanical parameters (such as elastic modulus and Poisson's ratio) is to determine the elastic range of the material, that is, to accurately find the straight line segment on the tensile stress-strain curve of the material. However, it is difficult to accurately determine this straight line segment through automated methods in actual material performance testing. On the one hand, in the actual tensile test process, due to the insufficient clamping stability of the test machine on the specimen during the initial stretching, the real stress-strain curve often has a non-elastic interval with abnormal data jumps before the elastic stage begins. The stress-strain curve in this interval changes irregularly, which may be a straight line segment with a large slope deviation from the elastic interval straight line segment, or it may be a messy point with a large jump amplitude. On the other hand, the real tensile stress-strain data will have many noise points, that is, the elastic straight line segment on the real stress-strain curve is not a standard straight line, but an approximate straight line segment composed of a group of stress-strain point pairs that jump up and down, which makes it more difficult to automatically locate the two endpoints of the elastic interval.

[0003] The existing material elastic modulus calculation method requires manual determination of the material's tensile elastic range and is unable to automatically locate the two endpoints of the elastic range.

[0004] It should be noted that the information disclosed in the above background technology section is only used for understanding the background of the present application, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the invention

[0005] The main purpose of the present invention is to overcome the defects of the above-mentioned background technology and provide a method for automatically locating the elastic range of material tensile deformation to solve the problem that the material elastic modulus calculation method cannot automatically locate the two endpoints of the elastic range.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention discloses an automatic positioning method for elastic interval of material stretching deformation, comprising the following steps:

[0008] S100, data set segmentation: the total amount of data D is segmented in the interval [0, i*D / t], 1≤i≤t;

[0009] S200, initial straight line segment fitting: randomly select two points in the first segment interval [0,1*D / t] to perform seed straight line segment fitting;

[0010] S300, error calculation: calculating the distances from all points in each segment interval to the straight line to determine the inner point set of each segment interval;

[0011] S400, re-estimating the straight line segment according to the interior point set: judging whether the number of interior points of the current fitted straight line segment is greater than half of the data volume of the segmented interval; if the number of interior points is greater than half of the data volume of the segmented interval, re-estimating the straight line using all the interior points in the segmented interval, calculating the residual value of the fitted straight line segment, and recording the current fitted straight line segment; otherwise, the current fitting fails and the current fitting result is discarded;

[0012] S500, iterative calculation: continue to randomly select points in the segmented interval to fit the segmented straight line segment. If the current fitting result is better than the previous fitting result, update the output and record the current fitting result as the best model until the number of iterations is reached and stop the fitting calculation.

[0013] S600, diffuse fitting of straight line segments in segmented intervals: according to steps S200-S500, randomly select points in each segmented interval [0, i*D / t], 1≤i≤t to iteratively fit the segmented straight line segments;

[0014] S700, determining the two end points of the elastic range: calculating the increase rate of the number of inner points of the two segmented fitting straight line segments, and the mutation points of the number of inner points are the two end points of the elastic range.

[0015] In some embodiments, in step S100, t is the number of equal segments, which is a constant, and t can be selected according to the size of the total data volume D; when the total data volume D is large, t takes a larger value, and when the total data volume D is small, t takes a smaller value.

[0016] In some embodiments, in step S200, the initial straight line segment fitting includes: determining parameters A0, B0, C0 of the initial fitting straight line segment;

[0017] A0=Δy

[0018] B0=-Δx

[0019] C0=-x2Δy+y2Δx

[0020] Among them, Δx and Δy represent the strain change and stress change of the point respectively; x2 and y2 represent the stress-strain value of any point different from the points corresponding to Δx and Δy respectively.

[0021] In some embodiments, in step S300, the error calculation includes: calculating the distance d from all points in each segment interval to the straight line to determine the inner point set S of each segment interval. in ;

[0022]

[0023] Among them, x and y represent the stress and strain values of any point within the segmented interval;

[0024] Among them, the distance threshold d0 from a point to a straight line is set; when the distance d from the point to the straight line is < d0, the point is considered an inlier and is assigned to the inlier set S in ; when the distance d from the point to the straight line is > d0, the point is considered an outlier and is removed.

[0025] In some embodiments, in step S400, the re - estimating the straight - line segment according to the inlier set includes determining whether the number of inliers of the currently fitted straight - line segment is greater than half of the data volume of this segmented interval;

[0026] If the number of inliers is greater than half of the data volume of this segmented interval, then perform the following steps:

[0027] S4001. Calculate the sum of the quadratic terms of the stress - strain values;

[0028]

[0029]

[0030]

[0031] Among them, respectively represent the average values of the stress and strain of the inliers of the currently fitted straight - line segment; S in is the inlier set applicable to the segmented model;

[0032] S4002. Discuss and find the least - squares estimate of y = kx + b in the following three cases;

[0033] The first case: when the segmented model is perpendicular to the x - coordinate axis;

[0034] At this time: A0 = 1, B0 = 0,

[0035] The second case: when the segmented model is parallel to the x - coordinate axis;

[0036] At this time: A0 = 0, B0 = 1,

[0037] The third case: when it is the general case of the straight line;

[0038] At this time:

[0039] Among them, k and b are the slope and intercept of the fitted straight - line segment respectively;

[0040] S4003. Regularize the segmented model so that A02 +B0 2 =1, the general form of the segmented model is obtained;

[0041] Regularization factor A0=NF*k, B0=-NF, C0=NF*b.

[0042] S4004, calculate the residual value of the segmented model;

[0043] Residual value

[0044] In some embodiments, in step S500, the iterative calculation includes the following steps:

[0045] S5001, judging whether the segmentation model is fitted successfully;

[0046] The condition for successful fitting is that the number of internal points applicable to the model is greater than the number of data N required to determine whether the model is applicable to the segmented data set; among them, the minimum data amount threshold N applicable to the segmented model is set t , the setting value is half of the segmented data volume. If the amount of data applicable to the segmented model is greater than N t , then the fitting is considered successful and the model is included in the better model set M; otherwise, the fitting fails and the model is discarded;

[0047] S5002, if the fitting is successful, then according to steps S4001-S4004, the straight line is re-estimated using all the internal point sets applicable to the model, and the process is repeated to obtain the residual values ​​of all the segmented models within the segmented interval;

[0048] S5003, compare the residual values ​​of all successfully fitted segmented models within the segmented interval to obtain the best model M within the segmented interval b , and get the number of internal points N of the best model fitted in each segment in and the slope value S bs ;

[0049] S5004: If the fitting fails, randomly select points in the segmented interval to fit the segmented straight line segments again according to steps S200-S400 until the iteration number threshold K is reached, and then stop fitting.

[0050] In some embodiments, in step S600, the segmented interval diffusion fitting straight line segment includes randomly selecting points in each segmented interval [0, i*D / t], 1≤i≤t to iteratively fit the segmented straight line segment according to steps S200-S500;

[0051] The number of data sets in the i-th segment interval is always D / t more than the number of data sets in the i-1-th segment interval; the value of t is a constant and can be selected according to the size of the total data set D.

[0052] In some embodiments, in step S700, determining the two end points of the elastic range includes the following two situations:

[0053] Case 1: There are fewer noise points at the beginning of the tensile test; perform the following steps:

[0054] S7001, locate the left end point of the elastic range;

[0055] If the internal point increase rate I in >0.5, then the straight line segment interval where the number of internal points suddenly increases for the first time is the left endpoint of the elastic interval;

[0056] S7002, locate the right end point of the elastic range;

[0057] If the internal point increase rate I in <ΔI in0 , and determine that the increase rate of the number of inner points of the fitted straight line segment at the left endpoint of the elastic interval and the decrease rate of the number of inner points of the fitted straight line segment at the right endpoint are both low. At this time, the straight line segment where the number of inner points suddenly decreases for the second time is the right endpoint of the elastic interval;

[0058] In other cases, the straight line segment interval where the number of internal points suddenly decreases for the first time is taken as the right endpoint of the elastic interval;

[0059] The second case: There are many noise points at the beginning of the tensile test; at this time, perform the following steps:

[0060] S7003, locate the left end point of the elastic range;

[0061] If the internal point increase rate I in <ΔI in0 , then the straight line segment interval where the number of internal points suddenly decreases for the first time is the left endpoint of the elastic interval;

[0062] S7004, locate the right end point of the elastic range;

[0063] If the internal point increase rate I in <0.5, then the straight line segment interval where the number of internal points suddenly decreases for the second time is the right endpoint of the elastic interval;

[0064] Among them, ΔI in0 is the threshold of the increase rate of the number of internal points.

[0065] Furthermore, the inner point number increase rate I in >0.5, indicating that the fitting effect of the latter section is better than that of the former section, and the increase rate of the number of internal points I in <0.5, indicating that the fitting effect of the latter segment is not as good as the previous segment, and it is believed that this fitting has a tendency to deviate from the current fitting straight line segment; when ΔI in0=0.5, the increase rate of the number of inner points of the two fitted segmented straight line segments is the same; when ΔI in0 =0, the number of inner points of the segmented straight line segments fitted by the two segments before and after is the same, that is, the number of inner points has not increased. At this time, it means that the points added in this segment interval relative to the previous segment interval have no contribution to the current fitting model, and this point is considered to be an inflection point; the closer the rate of increase in the number of inner points is to 1, the higher the degree of linear fit between the segmented straight line segment fitted by the latter segment and the segmented straight line segment fitted by the former segment; when ΔI in0 When =1, it means that the latter fitting straight line segment is the same as the former fitting straight line segment.

[0066] The present invention has the following beneficial effects:

[0067] The method for automatically locating the elastic interval of a material under tensile deformation provided by the present invention utilizes the RANSAC (Random Sample Consensus) principle to continuously expand the local points that approximately pass through the straight line and eliminate the local points that deviate from the straight line, and adopts segmented fitting diffusion straight line segments to quickly and automatically locate the left and right end points of the elastic interval. There is no need to manually locate the straight line segments of the elastic interval, and the problem of being unable to accurately locate the straight line segments due to large data fluctuations can be well solved, thereby realizing the automatic positioning of the elastic interval of the material under tensile deformation, and further realizing the automatic calculation of the elastic modulus of the material. The method for automatically locating the elastic interval of the present invention has high accuracy, good robustness, high efficiency, and high degree of automation. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 The figure is a flow chart of a method for automatically locating an elastic interval according to an embodiment of the present invention.

[0069] Figure 2 Schematic diagram of the piecewise fitting method according to an embodiment of the present invention.

[0070] Figure 3 Schematic diagram of RANSAC in an embodiment of the present invention.

[0071] Figure 4 Schematic diagram of the straight line segment fitting principle of an embodiment of the present invention.

[0072] Figure 5 This is a graph showing the test results of tensile stress-strain data of an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0074] An embodiment of the present invention provides an automatic positioning method for the elastic interval of a material under tensile deformation. The automatic positioning method for the elastic interval is based on RANSAC (Random Sample Consensus) piecewise fitting. The elastic modulus of the material is obtained by automatically positioning the left and right endpoints of the elastic interval, and the deformation mechanism of the material is studied. The method can be widely used in scientific fields such as materials, machinery, and civil engineering.

[0075] like Figure 1 As shown, the elastic range automatic positioning method of the material tensile deformation according to the embodiment of the present invention comprises the following steps:

[0076] S100, data set segmentation: the total amount of data D is segmented in the interval [0, i*D / t], 1≤i≤t (t is the number of equal segments);

[0077] S200, initial straight line segment fitting: randomly select two points in the first segment interval [0,1*D / t] to perform seed straight line segment fitting;

[0078] S300, error calculation: calculating the distances from all points in each segment interval to the straight line to determine the inner point set of the segment interval;

[0079] S400, re-estimate the straight line segment based on the set of interior points: determine whether the number of interior points of the current fitted straight line segment is greater than half of the data volume of the segmented interval. If the number of interior points is greater than half of the data volume of the segmented interval, re-estimate the straight line using all the interior points in the segmented interval, calculate the residual value of the fitted straight line segment, and record the current fitted straight line segment. Figure 4 The straight line segment fitted by the solid line in is the straight line segment that is successfully fitted. Otherwise, the fitting fails and the fitting result is discarded. Figure 4 The straight line segment fitted by the middle dotted line is the straight line segment where the fitting fails;

[0080] S500, iterative calculation: continue to randomly select points in the segmented interval to fit the segmented straight line segment. If the current fitting result is better than the previous fitting result, update the output and record the current fitting result as the best model until the number of iterations is reached and stop the fitting calculation.

[0081] S600, diffuse fitting of straight line segments in segmented intervals: according to steps S200-S500, randomly select points in each segmented interval [0, i*D / t], 1≤i≤t to iteratively fit the segmented straight line segments;

[0082] S700, determining the two end points of the elastic range: calculating the increase rate of the number of inner points of the two segmented fitting straight line segments, and the mutation points of the number of inner points are the two end points of the elastic range.

[0083] In this embodiment, the RANSAC principle belongs to the prior art, and the fitting of the segmented straight line segments in each segmented interval in this embodiment adopts the basic idea of ​​RANSAC.

[0084] In some embodiments, the principle diagram of the piecewise fitting method is as follows Figure 2 As shown, the schematic diagram omits some point cloud data and only draws a rough point cloud distribution diagram.

[0085] In some embodiments, Figure 2 The four points A, B, C, and D are four equal points, and there are D / t data points in each equal interval. When using the RANSAC principle for piecewise fitting, AB is the first piecewise fitting interval, corresponding to the interval [0,1*D / t]; AC is the second piecewise fitting interval, corresponding to the interval [0,2*D / t]; AD is the third piecewise fitting interval, corresponding to the interval [0,3*D / t]; and so on, the i-th piecewise fitting interval corresponds to the interval [0,i*D / t]. When fitting the i-th piecewise straight line segment, the random points are selected in the interval [0,i*D / t].

[0086] In some embodiments, Figure 3 As shown in the figure, it is a schematic diagram of RANSAC searching for straight line segments. The data set contains many external points. The straight line fitting method based on the RANSAC idea can accurately fit the straight line segments that only contain the internal point set. The RANSAC idea does not consider all the external points, that is, these external points will not affect the fitting of the straight line segment. When fitting the straight line segment, these external points are treated as interference and removed. This ensures the robustness and accuracy of the results.

[0087] In some embodiments, Figure 4 As shown in FIG. 1 , the schematic diagram only draws the segmented straight line segment fitting within a segmented interval. Among them, the dotted line is the straight line segment where the fitting fails, and the solid line is the straight line segment where the fitting succeeds.

[0088] This embodiment overcomes the defects and shortcomings of the existing elastic modulus calculation method, and realizes automatic calculation of the elastic modulus of the material by segmentally fitting straight line segments based on the idea of ​​RANSAC and automatically locating the elastic range of the material. Figure 5 As shown, it can be seen from the actual tensile stress-strain data test result diagram that the method of this embodiment can accurately locate the two end points of the elastic range.

[0089] The number of equal segments t can be selected according to the size of the total data volume D, and t directly affects the size of the data volume of each segment interval. If the value of t is large, the data volume of the segment interval is small, and vice versa. In general, the value of t should be appropriate. When the value of t is too small, it is easy to cause the positioning of the left and right end points of the elastic interval to be too rough, and the left end point of the elastic interval will be positioned backward and the right end point will be positioned forward. To avoid this error, the value of t should not be too small.

[0090] The fitting of the segmented straight line segment is to randomly select two points in the corresponding segment interval each time to fit the straight line segment. The straight line segment fitted by two points must first be subjected to error judgment in the segment interval to find the inner and outer point sets of the straight line segment in the segment interval. If the inner point set is larger than the outer point set, the straight line segment is successfully fitted. Figure 4 Otherwise, the straight line segment fails to fit and is not considered, such as Figure 4 The straight line segment fitted by the dotted line in .

[0091] The internal point set has at least two elements and at most the number of segmented interval data elements.

[0092] The successfully fitted straight line segment must be refitted using all the inner point sets that meet the straight line segment, and the straight line segment refitted with the inner point set is the possible segmented interval optimal model.

[0093] The number of point pairs used for the successfully fitted straight line segment is at least half of the amount of segmented interval data, and at most the amount of segmented interval data.

[0094] There are t optimal models, and an optimal segmented model is fitted in each segmented interval. The model with the smallest segmented straight line segment residual value in each segmented interval is the optimal model in the segmented interval.

[0095] In this embodiment, multiple threshold parameters need to be set during the implementation of the elastic interval automatic positioning method: (1) the distance threshold d0 from the point to the line; (2) the minimum data volume threshold N applicable to the segmentation model t ; (3) Iteration threshold K; (4) Inlier number increase rate threshold ΔI in0 ; (5) The best model M for segmented datasets b .

[0096] In some embodiments, the number of equal segments t in step S100 can be selected according to the total amount of stretched data. When the total amount of data D is large, t takes a larger value, but the value of t should not be too large, as an excessively large t value will lead to a large error in the result; when the total amount of data D is small, t takes a smaller value.

[0097] In some embodiments, in step S200:

[0098] The parameter A0 of the initial fitted straight line segment is Δy;

[0099] The parameter B0 of the initial fitted straight line segment is -Δx;

[0100] The parameter C0 of the initial fitted straight line segment is -x2Δy + y2Δx.

[0101] Where Δx and Δy respectively represent the strain change amount and stress change amount of the point; x2 and y2 respectively represent the stress-strain values of any point different from the point corresponding to Δx and Δy.

[0102] In this embodiment, the parameters A0, B0, and C0 determine the initial estimation model A0x + B0y + C0 = 0

[0103] In some embodiments, in step S300:

[0104] The distance from all points in each segmented interval to the straight line

[0105] Where x and y represent the stress-strain values of any point in the segmented interval;

[0106] Where a distance threshold d0 from the point to the straight line is set; when the distance d from the point to the straight line is d < d0, the point is considered an inlier and is assigned to the inlier set S in ; when the distance d from the point to the straight line is d > d0, the point is considered an outlier and is excluded.

[0107] In some embodiments, step S400 includes the following steps:

[0108] S4001. Calculate the sum of the quadratic terms of the stress-strain values;

[0109]

[0110]

[0111]

[0112] Where respectively represent the average values of the stress and strain of the inliers of the currently fitted straight line segment; S in is the set of inliers applicable to the segmented model.

[0113] S4002. Discuss and find the least squares estimation of y = kx + b in the following three cases;

[0114] The first case: when the segmented model is perpendicular to the x coordinate axis;

[0115] At this time: A0 = 1, B0 = 0,

[0116] The second case: when the segmented model is parallel to the x-axis;

[0117] At this time: A0=0, B0=1,

[0118] The third case: when it is the general case of a straight line;

[0119] At this time there are:

[0120] Among them, k and b are the slope and intercept of the fitted straight line segment respectively.

[0121] S4003, regularization term This segmented model makes A0 2 +B0 2 =1, the general form of the segmented model is obtained;

[0122] Regularization factor A0=NF*k, B0=-NF, C0=NF*b.

[0123] S4004, calculate the residual value of the segmented model;

[0124] Residual value

[0125] In this embodiment, before each re-estimation of the model, it is necessary to determine whether the fitting model meets the conditions for successful fitting, that is, whether the number of inliers applicable to the fitting model is greater than half of the data volume of the segmented interval. If the number of inliers is greater than half of the data volume of the segmented interval, the above steps S4001-S4004 are executed.

[0126] In some embodiments, step S500 includes the following steps:

[0127] S5001, judging whether the segmentation model is fitted successfully;

[0128] S5002, if the fitting is successful, then according to steps S4001-S4004, the straight line is re-estimated using all the internal point sets applicable to the model, and the process is repeated to obtain the residual values ​​of all the segmented models within the segmented interval;

[0129] S5003, compare the residual values ​​of all successfully fitted segmented models within the segmented interval to obtain the best model M within the segmented interval b , and get the number of internal points N of the best model fitted in each segment in and the slope value S bs ;

[0130] S5004: If the fitting fails, randomly select points in the segmented interval to fit the segmented straight line segments again according to steps S200-S400 until the iteration number threshold K is reached, and then stop fitting.

[0131] In some embodiments, the step S600 is performed according to the steps S200 - S500 , and randomly selects points in each segment interval [0, i*D / t], 1≤i≤t to iteratively fit the piecewise straight line segment.

[0132] In this embodiment, the number of data sets in the i-th segment interval is always D / t more than the number of data sets in the i-1-th segment interval; the value of t is a constant and can be selected according to the size of the total data set D.

[0133] In some embodiments, step S700 includes two cases, and the specific steps are as follows:

[0134] Case 1: There are fewer noise points at the beginning of the tensile test. At this time, perform the following steps:

[0135] S7001, locate the left end point of the elastic range;

[0136] If the internal point increase rate I in >0.5, then the straight line segment interval where the number of internal points suddenly increases for the first time is the left endpoint of the elastic interval.

[0137] S7002, locate the right end point of the elastic range;

[0138] If the internal point increase rate I in <ΔI in0 , and determine that the increase rate of the number of inner points of the fitted straight line segment at the left endpoint of the elastic interval and the decrease rate of the number of inner points of the fitted straight line segment at the right endpoint are both low. At this time, the straight line segment where the number of inner points suddenly decreases for the second time is the right endpoint of the elastic interval.

[0139] In other cases, the straight line segment interval where the number of internal points suddenly decreases for the first time is taken as the right endpoint of the elastic interval.

[0140] The second situation: There are many noise points at the beginning of the tensile test. At this time, perform the following steps:

[0141] S7003, locate the left end point of the elastic range;

[0142] If the internal point increase rate I in <ΔI in0 , then the straight line segment interval where the number of internal points suddenly decreases for the first time is the left endpoint of the elastic interval.

[0143] S7004, locate the right end point of the elastic range;

[0144] If the internal point increase rate I in<0.5, then the straight line segment interval where the number of internal points suddenly decreases for the second time is the right endpoint of the elastic interval.

[0145] In this embodiment, the two end points of the positioning elastic range include the first case and the second case.

[0146] In this embodiment, the amount of noise data at the beginning of the stretching experiment is determined by the slope of the first fitting straight line segment. bs If the slope of the first segment of the fitted straight line is less than the set slope threshold, that is, the slope of the fitted straight line is close to 0, it means that the number of noise points is large, that is, the first segment of the fitted straight line is in the noise data area.

[0147] In this embodiment, the ΔI in0 It is the threshold of the increase rate of the number of internal points, which is used to locate the two endpoints of the elastic range.

[0148] In one embodiment, the present invention proposes an elastic interval automatic positioning method based on RANSAC segmented fitting. The basic process is as follows: Figure 1 As shown in Figure 2. Taking the tensile test curve of aluminum alloy specimen as an example, the total data volume D = 2812, and the total data volume is divided into t = 20 parts. The size of the first segment data volume N s =[1*D / 20]=140, the size of the second segment data N s =[2*D / 20]=281, and so on, the data size of the 20th segment is N s =[20*D / 20]=2812. Figure 5 The test results show that the left endpoint of the elastic interval is in the first segmented interval, with the left endpoint index = 140, and the right endpoint of the elastic interval is in the fourth segmented interval, with the right endpoint index = 562. The results show that the method proposed by the present invention can accurately and automatically locate the left and right endpoints of the elastic interval.

[0149] The steps for automatic positioning of elastic intervals are as follows:

[0150] The first step is to segment the data set. Divide the entire data set D into t equal parts, such as Figure 2 As shown in AB, BC, and CD in . Fit straight line segments in each segment interval [0, i*D / t], such as Figure 2 As shown in AB, AC, AD in the figure, 1≤i≤t. Set the distance threshold d0 and the minimum amount of data N suitable for the segmentation model. t set to half of the segmented data set), iteration threshold K, internal point increase rate threshold ΔI in0 , the best model M for segmented datasets b .

[0151] Step 2, initial straight-line segment fitting. In the first sub-interval [0, 1*D / t], that is, Figure 2 randomly select two points in the AB segment of

[0152] for initial straight-line segment fitting. Calculate the values of the initial fitting model parameters A0, B0, and C0. Points that satisfy the error condition d < d0 are classified into the inlier set, and points that do not satisfy the error condition are classified into the outlier set and excluded.

[0153] Step 4, re-estimate the straight-line segment based on the inlier set. Determine whether the number of inliers of the currently fitted straight-line segment is greater than half of the data volume of the AB segment in this sub-interval. If the number of inliers is greater than half of the data volume of the AB segment, perform the following steps:

[0154] (1) Calculate the sum of the quadratic terms of the stress-strain values:

[0155]

[0156]

[0157]

[0158] Among them,

[0159] (2) Discuss in different cases to find the least squares estimate of y = kx + b:

[0160] Case 1: This sub-model is perpendicular to the x-axis;

[0161] At this time: A0 = 1, B0 = 0,

[0162] Case 2: This sub-model is parallel to the x-axis;

[0163] At this time: A0 = 0, B0 = 1,

[0164] Case 3: The general case of the straight line;

[0165] At this time:

[0166] (3) Regularize this sub-model so that A0 2 + B0 2 = 1, and obtain the general form of this sub-model:

[0167] Regularization factor A0=NF*k, B0=-NF, C0=NF*b.

[0168] (4) Calculate the residual value of the segmented model:

[0169] Residual value

[0170] Step 5: Iterative calculation. First, determine whether the segmented model is successfully fitted; if it is successfully fitted, execute the above step 4, use all the internal point sets applicable to the model to re-estimate the straight line, iterate, and obtain the residual values ​​of all segmented models in the segmented interval AB. Then, compare the residual values ​​of all successfully fitted segmented models in the segmented interval AB to obtain the best model M in the segmented interval AB. b , and obtain the best segmentation model M fitted in the segmentation interval AB b The number of interior points N in and the slope value S bs If the fitting fails, execute the second to fourth steps above, and re-select points randomly in the segmented interval AB to fit the segmented straight line segments until the iteration number threshold K is reached, and then stop fitting.

[0171] Step 6: Diffusion fitting of straight line segments in segmented intervals. In the segmented interval [0,2*D / t], i.e., segment AC, perform the above steps 2 to 5 to fit the second straight line segment. In the same way, fit the i-th straight line segment in segmented intervals such as segment AD.

[0172] The seventh step is to locate the two end points of the elastic range. There are two cases to discuss:

[0173] Case 1: There are fewer noise points at the beginning of the tensile test. At this time, perform the following steps:

[0174] (1) Locate the left endpoint of the elastic range:

[0175] If the internal point increase rate I in >0.5, then the straight line segment interval where the number of internal points suddenly increases for the first time is the left endpoint of the elastic interval.

[0176] (2) Locate the right endpoint of the elastic range:

[0177] If the internal point increase rate I in <ΔI in0 , and determine that the increase rate of the number of inner points of the fitted straight line segment at the left endpoint of the elastic interval and the decrease rate of the number of inner points of the fitted straight line segment at the right endpoint are both low. At this time, the straight line segment where the number of inner points suddenly decreases for the second time is the right endpoint of the elastic interval.

[0178] In other cases, the straight line segment interval where the number of internal points suddenly decreases for the first time is taken as the right endpoint of the elastic interval.

[0179] The second situation: There are many noise points at the beginning of the tensile test. At this time, perform the following steps:

[0180] (3) S7003, locate the left endpoint of the elastic range;

[0181] If the internal point increase rate I in <ΔI in0 , then the straight line segment interval where the number of internal points suddenly decreases for the first time is the left endpoint of the elastic interval.

[0182] (4) Locate the right endpoint of the elastic range;

[0183] If the internal point increase rate I in <0.5, then the straight line segment interval where the number of internal points suddenly decreases for the second time is the right endpoint of the elastic interval.

[0184] The above content is a further detailed description of the present invention in combination with specific / preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, without departing from the concept of the present invention, it can also make several substitutions or modifications to these described embodiments, and these substitutions or modifications should be regarded as belonging to the protection scope of the present invention. In the description of this specification, the description of the reference terms "an embodiment", "some embodiments", "preferred embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in combination with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily target the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In the absence of mutual contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples. Although the embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions and modifications can be made herein without departing from the scope of protection of the patent application.

Claims

1. A method for automatically positioning the elastic range of a material under tensile deformation, characterized in that: The steps include: S100, data set segmentation: the total amount of data D is segmented in the interval [0, i*D / t], 1≤i≤t; S200, initial straight line segment fitting: randomly select two points in the first segment interval [0,1*D / t] for seed straight line segment fitting; S300, error calculation: calculating the distances from all points in each segment interval to the straight line to determine the inner point set of each segment interval; S400, re-estimating the straight line segment according to the interior point set: judging whether the number of interior points of the current fitted straight line segment is greater than half of the data volume of the segmented interval; if the number of interior points is greater than half of the data volume of the segmented interval, re-estimating the straight line using all the interior points in the segmented interval, calculating the residual value of the fitted straight line segment, and recording the current fitted straight line segment; otherwise, the current fitting fails and the current fitting result is discarded; S500, iterative calculation: continue to randomly select points in the segmented interval to fit the segmented straight line segment. If the current fitting result is better than the previous fitting result, update the output and record the current fitting result as the best model until the number of iterations is reached and stop the fitting calculation. S600, diffuse fitting of straight line segments in segmented intervals: according to steps S200-S500, randomly select points in each segmented interval [0, i*D / t], 1≤i≤t to iteratively fit the segmented straight line segments; S700, determining the two end points of the elastic interval: calculating the increase rate of the number of inner points of the two segmented fitting straight line segments, and the mutation points of the number of inner points are the two end points of the elastic interval; In step S100, t is the number of equal segments, which is a constant and can be selected according to the size of the total data volume D; In step S200, the initial straight line segment fitting includes: determining the parameters of the initial fitting straight line segment , , ; ； in, and They represent the strain change and stress change of a point respectively; and Respectively different from and The stress-strain value of any corresponding point; In step S300, the error calculation includes: calculating the distance d from all points in each segment interval to the straight line to determine the inner point set of each segment interval ; ； in, , Represents the stress and strain value of any point in the segmented interval; Among them, the distance threshold from the set point to the straight line ; When the distance d from the point to the line < When , the point is considered to be an interior point and is assigned to the interior point set. ; When the distance from the point to the line d> When , the point is considered to be an external point and is removed; In step S400, the re-estimation of the straight line segment according to the interior point set includes determining whether the number of interior points of the current fitted straight line segment is greater than half of the data volume of the segmented interval; If the number of internal points is greater than half of the data volume of the segment interval, perform the following steps: S4001. Find the sum of the quadratic terms of stress and strain values; ； in, , , respectively represent the average values ​​of stress and strain of the inner points of this fitting straight line segment; is the set of interior points applicable to the piecewise model; S4002. Discuss the least squares estimate of y=kx+b in the following three cases; The first case: when the segmented model is perpendicular to the x-axis; At this time there are: =1, =0, = ; The second case: when the segmented model is parallel to the x-axis; At this time there are: =0, =1, = ; The third case: when it is the general case of a straight line; At this time there are: ; Among them, k and b are the slope and intercept of the fitted straight line segment respectively; S4003, regularization term of the segmented model, so that , find the general form of the segmented model; Regularization factor ; S4004, calculate the residual value of the segmented model; Residual value ; In step S500, the iterative calculation includes the following steps: S5001, judging whether the segmentation model is fitted successfully; The condition for successful fitting is that the number of internal points applicable to the model is greater than the number of data N used to determine whether the model is applicable to the segmented data set; among them, the minimum data amount threshold applicable to the segmented model is set , The set value is half of the segmented data volume. If the data volume applicable to the segmented model is greater than , then the fitting is considered successful and the model is included in the better model set M; otherwise, the fitting fails and the model is discarded; S5002, if the fitting is successful, then according to steps S4001-S4004, the straight line is re-estimated using all the internal point sets applicable to the model, and the process is repeated to obtain the error values ​​of all the segmented models within the segmented interval; S5003. Compare the error values ​​of all successfully fitted segmented models within the segmented interval to obtain the best model within the segmented interval , and get the number of internal points of the best model fitted in each segment and slope value ; S5004, if the fitting fails, randomly select points in the segmented interval to fit the segmented straight line segments again according to steps S200-S400, until the iteration number threshold K is reached, and then stop fitting; In step S600, the segmented interval diffusion fitting straight line segment includes randomly selecting points in each segmented interval [0, i*D / t], 1≤i≤t to iteratively fit the segmented straight line segment according to steps S200-S500; The number of data sets in the i-th segment interval is always D / t more than the number of data sets in the i-1-th segment interval; the value of t is a constant and can be selected according to the size of the total data set D; In step S700, the determination of the two end points of the elastic range includes the following two situations: Case 1: There are fewer noise points at the beginning of the tensile test; perform the following steps: S7001, locate the left end point of the elastic range; If the internal point increase rate >0.5, then the straight line segment interval where the number of internal points suddenly increases for the first time is the left endpoint of the elastic interval; S7002, locate the right end point of the elastic range; If the internal point increase rate < , and determine that the increase rate of the number of inner points of the fitted straight line segment at the left endpoint of the elastic interval and the decrease rate of the number of inner points of the fitted straight line segment at the right endpoint are both low. At this time, the straight line segment where the number of inner points suddenly decreases for the second time is the right endpoint of the elastic interval; In other cases, the straight line segment interval where the number of internal points suddenly decreases for the first time is taken as the right endpoint of the elastic interval; The second case: There are many noise points at the beginning of the tensile test; at this time, perform the following steps: S7003, locate the left end point of the elastic range; If the internal point increase rate < , then the straight line segment interval where the number of internal points suddenly decreases for the first time is the left endpoint of the elastic interval; S7004, locate the right end point of the elastic range; If the internal point increase rate <0.5, then the straight line segment interval where the number of internal points suddenly decreases for the second time is the right endpoint of the elastic interval; in, is the threshold of the increase rate of the number of internal points.

2. The method for automatically positioning the elastic range of a material under tensile deformation according to claim 1, characterized in that: The internal point number increase rate >0.5, indicating that the fitting effect of the latter section is better than that of the former section, and the increase rate of the number of internal points <0.5, indicating that the fitting effect of the latter segment is not as good as that of the former segment, and it is believed that this fitting has a tendency to deviate from the current fitting straight line segment; =0.5, the increase rate of the number of inner points of the two fitted segmented straight line segments is the same; when =0, the number of inner points of the segmented straight line segments fitted by the previous and next segments is the same, that is, the number of inner points has not increased. At this time, it means that the points added to the segmented interval relative to the previous segmented interval have no contribution to the current fitting model, and this point is considered to be an inflection point; the closer the rate of increase in the number of inner points is to 1, the higher the degree of linear fit between the segmented straight line segment fitted by the latter segment and the segmented straight line segment fitted by the former segment; when =1, it means that the latter fitting straight line segment is the same as the former fitting straight line segment.

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