An error correction method for Euler beam shape inversion based on the superposition method

Abstract

The present invention provides a method for correcting the form inversion error of an Euler beam based on the superposition method, comprising the following steps: Step 1, perform form inversion without correction; Step 2, collect calibration information for the superposition method; Step 3, correct the form inversion error based on the superposition method. By means of the information fusion concept combining points and lines, the present invention integrates the advantages of point-type measurement and distributed measurement of fiber optic sensors, and can timely reduce the cumulative error caused by the form inversion algorithm, so as to improve the accuracy and reliability of the form inversion of the beam structure.

Description

Technical Field

[0001] The present invention belongs to the field of structural health monitoring based on fiber optic sensors, and particularly relates to a method for correcting the inversion error of the Euler beam shape based on the superposition method. Background Technique

[0002] Carrying out the inversion of the Euler beam structure shape based on distributed fiber optic sensors and the strain-shape algorithm is of great significance for the research in many fields such as the load analysis of wind turbine towers, the monitoring of the bending deformation during the stress process of bridges, and the prevention and early warning of highway slope disasters based on the shape information of inclinometers.

[0003] However, during the strain-shape inversion process, there is a certain deviation between the calculated value and the actual value. In addition to factors such as noise interference and uneven temperature changes, there are also certain errors in the devices themselves such as sensors and demodulators. The relevant algorithms for inverting the deflection from strain all have an error accumulation effect, and the cumulative error of shape inversion caused by strain error may accumulate within the full length of the beam and affect the inversion accuracy. Therefore, conducting research on the method for correcting the shape inversion error is crucial for improving the accuracy of the beam structure shape inversion.

[0004] Error correction technology is an important part of modern metrology and manufacturing. The traditional error compensation method of correcting each error item one by one has a complex process, is time-consuming and laborious, and it is difficult to guarantee the effect. Liu Peng et al. realized the shape inversion and error correction of a fixed-ended crossbeam structure based on fiber optic sensors, and its error correction process is based on real-time error separation technology. Under the premise that the specific error items are unknown, their influence is directly eliminated during the measurement or data processing process.

[0005] The main advantage of the above error correction process is that it can achieve error self-compensation without the need to additionally arrange sensors to obtain other relevant information of the measured structure. However, this method requires a large number of experiments to establish an error library, and if error self-compensation is to be achieved, the correction effect depends on the cognitive process of the error law of the test system and lacks a theoretical basis. Since the establishment of the correction error library is only based on the measured values, even if a large and redundant error library is established, there are still limitations in the lack of generalization ability. Summary of the Invention

[0006] Object of the Invention: The object of the present invention is to superimpose and compensate the deflection to reduce the influence of the cumulative error on the calculation of the deflection curve within the full length of the structure, thereby improving the shape inversion accuracy. The present invention specifically provides a method for correcting the inversion error of the Euler beam shape based on the superposition method, including the following steps:

[0007] Step 1, carry out shape inversion without correction;

[0008] Step 2, collect calibration information for the superposition method;

[0009] Step 3: Perform the morphological inversion error correction based on the superposition method.

[0010] Step 1 includes: If the measured structure is equivalent to an Euler beam, according to the approximate relationships among strain, curvature, and deflection, collect the strain distribution information of the measured structure by a distributed fiber optic sensor to obtain the variation relationship of strain with the distance x from the left end of the beam. Invert the structure morphology to obtain the following inversion rotation angle equation and the inversion deflection curve equation

[0011]

[0012]

[0013] where dx is the differential of x, and C and D are constants, whose values can be determined by the boundary conditions. ho is the distance from a point on the structure surface to the neutral layer.

[0014] Step 2 includes:

[0015] Based on the deflection, obtain the deflection calibration information of the structure based on the displacement constraint or displacement sensor at the known position point P as the corrected deflection at point P, and set the distance between point P and the left end of the beam as x P , and the deflection calibration information is

[0016] Step 2 includes:

[0017] Based on the rotation angle, obtain the rotation angle calibration information of the structure based on the rotation angle constraint or rotation angle sensor at the known position point P as the corrected rotation angle at point P, and set the distance between point P and the left end of the beam as x P , and the rotation angle calibration information is

[0018] Step 3 includes: For the working condition where there is only one calibrated deflection or rotation angle on a beam, perform the morphological inversion error correction based on the superposition method:

[0019] Case 1: Based on the deflection calibration information at a point P:

[0020] Set the structure deflection curve inverted by the strain-curvature-deflection repeated integration method as Superimpose the compensation deflection equation Δw(x) on the inversion deflection curve equation to make the corrected deflection curve conform to the deflection calibration information:

[0021]

[0022] where is the corrected deflection at point P. When the Euler beam equivalent to the measured structure has no bending, assume the distance from the left end of the beam is x aApply a compensating concentrated force load F at a point, with the direction of the load F being positive, and the distance from the left end of the beam being x b The deflection at this point is W F (F, x a , x b ), then the compensating deflection equation Δw(x) is expressed as:

[0023] Δw(x) = W F (F, x P , x)

[0024] Substitute x = x P :

[0025]

[0026] Solve for the compensating load F to obtain the compensating deflection equation Δw(x), and obtain the corrected deflection curve equation:

[0027]

[0028] Case 2, based on the angular calibration information at a point P:

[0029] Set the structural angular equation obtained by inverse integration of strain - curvature - deflection as Superimpose the compensating angular equation Δθ(x) on the inverse angular equation to make the corrected angular equation conform to the angular calibration information:

[0030]

[0031] Where is the corrected angle at point P. When the Euler beam equivalent to the measured structure has no bending, assume that a compensating concentrated moment load M is applied at a distance x from the left end of the beam, with the direction of the load M being positive, and the distance from the left end of the beam being x a The angle at this point is Theta(M, x b , x a , x b ), and the deflection is W M (M, x a , x b ), then the compensating angular equation Δθ(x) is expressed as:

[0032] Δθ(x) = Theta(M, x P , x)

[0033] Substitute x = x P :

[0034]

[0035] Where is the inverse value of the angle at point P before correction;

[0036] Solve for the compensation load M to obtain the compensation deflection equation Δw(x):

[0037] Δw(x) = W M (M, x P , x)

[0038] Obtain the corrected deflection curve equation:

[0039]

[0040] Step 3 includes: For the working condition where there are two or more calibrated deflections or rotations on a beam, based on the morphological inversion error correction of the superposition method, an inversion morphological correction method based on the superposition method - force method normal equation is proposed:

[0041] When the beam is corrected by n deflection and rotation calibration information, n ≥ 2, calculate the corresponding compensation concentrated force load and compensation concentrated moment load, and solve for the compensation loads X1, X2,..., X n :

[0042]

[0043] where X n represents the nth compensation load, and δ ij is the deflection or rotation generated at the ith load application position when the load X j = 1 acts alone. The values of i and j range from 1 to n. Taking the application direction of X j as positive, we get:

[0044]

[0045] where W F (1, x j , x i ) represents the deflection calibration corresponding to the compensation load X i Theta(1, x j , x i ) represents the rotation calibration corresponding to the compensation load X i ; It was previously defined that W F (F, x a , x b ) is "the deflection at a distance x a from the left end of the beam when a compensation concentrated force load F is applied at a distance x b from the left end of the beam, with the direction of the load F as positive". All W F follow the above definition. Here, we substitute "F = 1, x a = x j , x b = x"i ”, Theta(1, x j , x i ) Similarly;

[0046] According to the defined Substitute x = x P , the difference Δ between the deflection or rotation angle of the i-th load application position obtained by inversion and the calibrated deflection or rotation angle i is expressed as:

[0047]

[0048] Wherein, represents the compensation load X i corresponding to the deflection calibration, represents the compensation load X i corresponding to the rotation angle calibration;

[0049] Solve the component Δw of the compensation deflection equation corresponding to each load i (x):

[0050]

[0051] Wherein, W F (X i , x i , x) represents the compensation load X i corresponding to the deflection calibration, W M (X i , x i , x) represents the compensation load X i corresponding to the rotation angle calibration;

[0052] Then the compensation deflection equation Δw(x) is expressed as:

[0053]

[0054] The corrected deflection curve equation is obtained as:

[0055]

[0056] The present invention also provides a storage medium storing a computer program or instruction, and when the computer program or instruction is run, the described Euler beam shape inversion error correction method based on the superposition method is implemented.

[0057] Comparing with the common beam structure shape inversion method based on the strain-curvature-deflection double integral method without correction and the existing beam structure shape inversion error correction methods, the Euler beam strain-shape inversion error correction method based on the superposition method proposed by the present invention, by means of the information fusion concept of combining points and lines, synthesizes the advantages of point measurement and distributed measurement of fiber optic sensors, can timely reduce the cumulative error caused by the shape inversion algorithm, so as to improve the accuracy and reliability of the beam structure shape inversion, and has extremely high practical application value.

[0058] The present invention has the following beneficial effects: By means of the information fusion concept of combining points and lines, the present invention synthesizes the advantages of point measurement and distributed measurement of fiber optic sensors, can timely reduce the cumulative error caused by the shape inversion algorithm, so as to improve the accuracy and reliability of the beam structure shape inversion. Compared with the traditional error correction method, this method overcomes the limitations that the traditional method needs to conduct a large number of experiments to establish an error library, and if error self-compensation is to be achieved, the correction effect depends on the cognitive process of the error law of the test system, lacks theoretical basis, and due to the establishment of the correction error library only based on the measured values, even if a large and redundant error library is established, there is still the limitation of insufficient generalization ability. Combining the two numerical simulation results of the solid finite element model of a hyperstatic pipeline with large length-diameter ratio and both ends fixed, the root mean square errors of the uncorrected pipeline shape inversion are 1.243 mm and 0.733 mm respectively, the root mean square errors of the pipeline shape inversion based on the superposition method and the deflection calibration of the right fixed end are 0.214 mm and 0.496 mm respectively, the root mean square errors of the pipeline shape inversion based on the superposition method and the rotation angle calibration of the right fixed end are 0.553 mm and 0.537 mm respectively, and the root mean square errors of the pipeline shape inversion based on the superposition method - force method normal equation and the deflection and rotation angle calibration of the right fixed end are 0.207 mm and 0.327 mm respectively. The inversion deflections corrected by the above methods are significantly more accurate than the uncorrected inversion deflections. Therefore, the inversion deflection correction method based on the superposition method is of great significance for improving the accuracy of the structure shape inversion. Among them, the shape inversion error correction method based on the superposition method - force method normal equation has the highest accuracy, proving that this method has extremely high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The following further specifically describes the present invention in conjunction with the drawings and specific embodiments, and the above and / or other advantages of the present invention will become clearer.

[0060] Figure 1a It is the relationship between the true strain and the corresponding equivalent load of the simply supported beam structure.

[0061] Figure 1b It is the relationship between the measured strain with error and the corresponding equivalent load of the simply supported beam structure.

[0062] Figure 2a It is a schematic diagram of a micro-segment on the beam.

[0063] Figure 2b It is a schematic diagram of the equivalent approximate load corresponding to the selected micro-segment.

[0064] Figure 3a For the beam under the action of F Pi It is a schematic diagram of the deflection generated.

[0065] Figure 3b For the beam under the action of F qi It is a schematic diagram of the deflection generated.

[0066] Figure 4 It is a schematic diagram of the finite element simulation model of the boundary conditions and the loads on the doubly clamped pipeline.

[0067] Figure 5a It is a schematic diagram of the first simulation result and the correction effect of the inversion shape error.

[0068] Figure 5b It is a schematic diagram of the second simulation result and the correction effect of the inversion shape error.

[0069] Figure 6 It is a flow chart of the Euler beam strain-shape inversion error correction method based on the superposition method. Specific implementation manner

[0070] As Figure 6 shown, the present invention provides an Euler beam shape inversion error correction method based on the superposition method, including the following steps:

[0071] Step 1: Conduct shape inversion without correction;

[0072] If the measured structure is equivalent to an Euler beam, according to the approximate relationship between strain-curvature-deflection, the strain distribution information of the measured structure can be collected by a distributed fiber optic sensor, that is, the relationship between the strain and the distance x from the left end of the beam Invert the structure shape, that is, invert the deflection curve equation:

[0073]

[0074]

[0075] where ho is the distance from a point on the surface of the structure to the neutral layer.

[0076] Step 2: Collect calibration information for the superposition method

[0077] Method 1: Based on deflection, obtain the deflection calibration information of the structure based on the displacement constraints or displacement sensors with known positions, that is, the deflection here. Assume the distance from here to the left end of the beam is x P , and the deflection calibration information is

[0078] Method 2: Based on the corner, obtain the corner calibration information of the structure based on the known corner constraint or corner sensor at a known position, that is, the corner here. Assume the distance from this point to the left end of the beam is x P , and the corner calibration information is

[0079] Step 3: Carry out the morphological inversion error correction based on the superposition method

[0080] Method 1: Based on the superposition method

[0081] If it is assumed that the relationship between the true strain on the measurement path of the distributed optical fiber sensor and the distance x from its position to the left end of the beam is ε(x), and the relationship between the equivalent distributed load and the distance x from its position to the left end of the beam is q(x), then the following relationship exists between the two:

[0082]

[0083] As Figure 1a , Figure 1b shown, the deflection inversed from the true strain ε(x) can be equivalent to the deflection under the action of the corresponding distributed load q(x). According to the deflection inversed from the measured strain with error , it can be equivalent to the deflection under the action of the corresponding distributed load . Then, according to the superposition of loads, it can be known that as long as the difference Δq(x) between and q(x) is reversely superimposed while the beam is subjected to , the true deflection curve can be obtained by correction.

[0084] Take a micro-segment with a length of Δx on the beam, and the load it bears can be equivalently approximated as a constant q x , as Figure 2a , Figure 2b shown. Then, the deflection generated by the force on this micro-segment on the beam can be equivalent to the deflection w q produced by the continuous distribution of several concentrated loads F q .

[0085] For a certain micro-segment on the beam, the concentrated load F q it bears is expressed as:

[0086] F q = q x ·Δx

[0087] For the whole beam, divide the beam evenly along the axial direction into micro-segments with a length of Δx. The deflection generated by the i-th segment is approximately the load F qi . Then, when calculating the deflection, it is assumed that the superimposed loads are respectively When Δx is small enough, the deflection curve obtained theoretically is consistent with the actual one, thus completely eliminating the influence of errors.

[0088] However, in practical applications, the magnitude of F qi cannot be truly known. Therefore, the concentrated force F Pi acting on a certain point P can be used to replace F qi , that is, the use of approximate replacement And the superposition effect of F Pi is equivalent to the effect of F P , where F P is the resultant force. The following explores the feasibility of using F Pi to replace F qi :

[0089] If the strain of a cantilever beam with a length of l is measured by a distributed fiber optic sensor, the deflection at the free end is known, and the distance from an unknown point on it to the fixed end is a, then after the beam is subjected to the force F qi , the beam deflection w2 is expressed as:

[0090]

[0091] The deflection w 2P produced at point P at the free end is:

[0092]

[0093] If a concentrated load F P is applied at the free end, then the resulting deflection w1 is expressed as:

[0094]

[0095] The deflection w 1P produced at point P at the free end is:

[0096]

[0097] As Figure 3a , Figure 3b shown, if there is:

[0098] w 1P = w 2P

[0099] Then there is:

[0100]

[0101]

[0102] According to the above derivation, it can be seen that the relative deviation δ Pi of the deflections generated by F qi and F F at each point of the beam is:

[0103]

[0104] After arrangement, we get:

[0105]

[0106] In the range of 0 ≤ a ≤ l, δ F decreases as a increases. When δ F reaches the maximum value, a approaches 0, then we have:

[0107]

[0108] The partial derivative of the above formula with respect to x is 0 at .

[0109] From the zero point and monotonicity of the partial derivative, it is not difficult to prove that is the only maximum point within 0 ≤ x ≤ l, and when a → 0, x = 0, l, δ F reaches the minimum value, i.e., minδ F = 0.

[0110] Substitute into Equation (5.28), and we get the maximum relative deviation maxδ F = 0.1925.

[0111] From this, we can see that the deflections generated by F Pi and F qi have an approximation of more than 80.75% at each point on the beam. Therefore, F Pi can be used to replace F qi , greatly eliminating the shape inversion error. For different boundary conditions of the beam and different calibration information, the above derivation process is similar.

[0112] Case 1: Based on the deflection calibration information at a point P

[0113] Assume that the structural deflection curve obtained by inverting through the strain - curvature - deflection double integral method is Superimpose the compensation deflection equation Δw(x) on the inverted deflection curve equation to make the corrected deflection curve conform to the deflection calibration information:

[0114]

[0115] When the beam is not bent, assume that a compensation concentrated force load F is applied at a distance x a from the left end of the beam. Taking the direction of the load F as positive, the deflection at a distance x b from the left end of the beam is W F (F, x a , x b),then the compensated deflection equation is expressed as:

[0116] Δw(x) = W F (F, x P , x)

[0117] Substitute x = x P :

[0118]

[0119] The compensated load F can be solved, and then the compensated deflection equation Δw(x) can be obtained. On this basis, the corrected deflection curve equation is obtained:

[0120]

[0121] Case 2: Based on the angular displacement calibration information at a point P

[0122] Suppose the structural angular displacement equation obtained by the inverse integration method of strain - curvature - deflection is Superimpose the compensated angular displacement equation Δθ(x) on the inverse - solved angular displacement equation to make the corrected angular displacement equation conform to the angular displacement calibration information:

[0123]

[0124] When the beam has no bending, assume that a compensated concentrated moment load M is applied at a distance x a from the left end of the beam. Taking the direction of the load M as positive, the angular displacement at a distance x b from the left end of the beam is Theta(M, x a , x b ), and the deflection is W M (M, x a , x b ). Then the compensated angular displacement equation is expressed as:

[0125] Δθ(x) = Theta(M, x P , x)

[0126] Substitute x = x P :

[0127]

[0128] The compensated load M can be solved, and then the compensated deflection equation Δw(x) can be obtained:

[0129] Δw(x) = W M (M, x P , x)

[0130] On this basis, the corrected deflection curve equation is obtained:

[0131]

[0132] Method 2: Based on the superposition method - the normal equation of the force method

[0133] For the statically indeterminate equivalent model, the inversion form correction method described in Method 1 has the problem that the load coordination equations to be superimposed are relatively complex. Therefore, on the basis of Method 1, an inversion form correction method based on the superposition method - the normal equation of the force method is proposed to solve the form characteristics of the statically indeterminate equivalent model.

[0134] When the beam is corrected by several deflection and rotation calibration information, the corresponding compensating concentrated force load and compensating concentrated moment load need to be calculated, and the compensating loads X1, X2,..., X are solved based on the superposition method - the normal equation of the force method n :

[0135]

[0136] where δ ij is the deflection or rotation generated at the i-th load application position when the single acting load X j = 1 (positive in the application direction of X j ):

[0137]

[0138] Δ i is the difference between the deflection or rotation at the i-th load application position obtained by inversion and the calibrated deflection or rotation:

[0139]

[0140] On this basis, the component of the compensating deflection equation corresponding to each load is solved:

[0141]

[0142] Then the compensating deflection equation is expressed as:

[0143]

[0144] On this basis, the corrected deflection curve equation is obtained:

[0145]

[0146] Example

[0147] For a large aspect ratio pipeline with an outer diameter of 70 mm, an inner diameter of 60 mm, a length l = 3000 mm, a material elastic modulus of 3 GPa, and a Poisson's ratio of 0.33, the boundary conditions are set as fixed at both ends. A concentrated upward force F1 = 400 N is applied at x = 500 mm, and a clockwise concentrated moment M e = 50 N·m is applied at x = 1200 mm, and a downward concentrated force F2 = 300 N is applied synchronously at x = 2200 mm, as Figure 4 shown.

[0148] This embodiment includes the following steps:

[0149] Step 1: Conduct uncorrected shape inversion;

[0150] By setting the strain in the interval of 900 mm - 1200 mm from the fixed end to 0, the interference error introduced due to local sensor failure is simulated. If the measured structure is equivalent to an Euler beam, according to the approximate relationship between strain, curvature, and deflection, the strain distribution information of the measured structure can be collected by a distributed fiber optic sensor, that is, the variation relationship of strain with the distance x from the left end of the beam Invert the structure shape, that is, invert the deflection curve equation:

[0151]

[0152]

[0153] where ho is the distance from a point on the structure surface to the neutral layer. The result of uncorrected shape inversion is as Figure 5a , and the vertical axis w in the figure is the deflection.

[0154] Step 2: Conduct calibration information acquisition for the superposition method

[0155] Method 1: Based on deflection, obtain the deflection calibration information of the structure based on known displacement constraints or displacement sensors at known positions, that is, the deflection here. Assume the distance from here to the left end of the beam is x P , and the deflection calibration information is

[0156] Method 2: Based on rotation angle, obtain the rotation angle calibration information of the structure based on known rotation angle constraints or rotation angle sensors at known positions, that is, the rotation angle here. Assume the distance from here to the left end of the beam is x P , and the rotation angle calibration information is

[0157] In this embodiment, according to the boundary conditions of the equivalent Euler beam, there are:

[0158]

[0159]

[0160] Step 3: Conduct form inversion error correction based on the superposition method

[0161] Method 1: Based on the superposition method

[0162] Case 1: Based on the deflection calibration information at a point P

[0163] Assume that the structural deflection curve obtained by the strain-curvature-deflection repeated integration method is Superimpose the compensation deflection equation Δw(x) on the inversion deflection curve equation to make the corrected deflection curve Conform to the deflection calibration information:

[0164]

[0165] When the beam has no bending, assume that a compensation concentrated force load F is applied at a distance x from the left end of the beam a Taking the direction of the load F as positive, the deflection at a distance x from the left end of the beam is W b (F, x F , x a , x b )), then the compensation deflection equation is expressed as:

[0166]

[0167] Substitute x = l = 3000:

[0168]

[0169] The compensation load F can be solved to satisfy:

[0170] F = EI·2.594×10 -10 N

[0171] Where E is the elastic modulus of the pipeline and I is the cross-sectional coefficient of the pipeline. Both are related to the pipeline structure and are constants. Then, the compensation deflection equation Δw(x) is obtained. On this basis, the corrected deflection curve equation is obtained:

[0172]

[0173] The inversion deflection correction result based on deflection calibration is as Figure 5a shown.

[0174] Case 2: Based on the rotation angle calibration information at a point P

[0175] Assume that the structural rotation angle equation obtained by the strain-curvature-deflection repeated integration method is Superimpose the compensation rotation angle equation Δθ(x) on the inversion rotation angle equation to make the corrected rotation angle equation Conform to the rotation angle calibration information:

[0176]

[0177] When the beam has no bending, let a compensating concentrated moment load M be applied at a distance x from the left end of the beam. Taking the direction of the load M as positive, the rotation angle at a distance x from the left end of the beam is Theta(M, x a b a , x b , x M ), and the deflection is W M (M, x a , x b ). Then the compensating rotation angle equation can be expressed as:

[0178] Δθ(x) = Theta(M, 3000, x)

[0179] Substitute x = l = 3000:

[0180]

[0181] The compensating load M can be solved to satisfy:

[0182] M = EI·3.514×10 -7 N·mm

[0183] Furthermore, the compensating deflection equation Δw(x) is obtained:

[0184] Δw(x) = W M (M, 3000, x)

[0185] On this basis, the corrected deflection curve equation is obtained:

[0186]

[0187] The inversion deflection correction result based on the rotation angle calibration is as Figure 5a shown.

[0188] Method 2: Based on the superposition method - the normal equation of the force method

[0189] For the statically indeterminate equivalent model, the inversion form correction method described in Method 1 has the problem that the load coordination equation to be superimposed is relatively complex. Therefore, on the basis of Method 1, an inversion form correction method based on the superposition method - the normal equation of the force method is proposed to solve the form characteristics of the statically indeterminate equivalent model.

[0190] When the beam is corrected by several deflection and rotation angle calibration information, the corresponding compensating concentrated force load and compensating concentrated moment load need to be calculated, and the compensating loads X1, X2,..., X n are solved based on the superposition method - the normal equation of the force method:

[0191]

[0192] wherein, δ ij is the deflection or rotation angle generated at the i-th load application position when the separate acting load X j = 1 (with the application direction of X j being positive):

[0193]

[0194] Δ i is the difference between the deflection or rotation angle at the i-th load application position obtained by inversion and the calibrated deflection or rotation angle:

[0195]

[0196] On this basis, solve the component of the compensation deflection equation corresponding to each load:

[0197]

[0198] In this embodiment, the displacement and rotation angle constraints at the right fixed end of the pipeline under test are regarded as the deflection calibration information and rotation angle calibration information. The equivalent statically determinate structure of the pipeline is a cantilever beam. At the same time, there is a concentrated force X1 and a concentrated moment X2 at the right end of the pipeline. Therefore, it can be obtained that:

[0199]

[0200]

[0201] By solving the force method normal equation, the expressions for the loads X1 and X2 can be obtained:

[0202]

[0203] Then the compensation deflection equation is expressed as:

[0204]

[0205] On this basis, the corrected deflection curve equation is obtained:

[0206]

[0207] The inversion deflection correction result based on the superposition method - force method normal equation is as Figure 5a shown. By setting the strain in the interval of 1500 mm - 1800 mm from the fixed end to 0 and repeating the above process for the second inversion deflection correction, the effects of each correction method are as Figure 5bAs shown. It can be seen from this embodiment that the superposition method based on the force method regular equation can effectively reduce errors, has a better correction effect than the correction method based on a single boundary condition (such as deflection constraint or rotation angle constraint), and has good adaptability in the bending shape error correction of statically indeterminate pipeline structures.

[0208] In specific implementation, the present application provides a computer storage medium and a corresponding data processing unit. Among them, the computer storage medium can store a computer program, and when the computer program is executed by the data processing unit, it can run the inventive content of a method for correcting the inversion error of the Euler beam shape based on the superposition method and some or all of the steps in each embodiment. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0209] Those skilled in the art can clearly understand that the technical solutions in the embodiments of the present invention can be implemented by means of a computer program and its corresponding general hardware platform. Based on such an understanding, the technical solutions in the embodiments of the present invention, in essence, or the part that contributes to the prior art can be embodied in the form of a computer program, that is, a software product. The computer program software product can be stored in the storage medium, including several instructions to enable a device (which can be a personal computer, a server, a single-chip microcomputer, a MUU, or a network device, etc.) containing a data processing unit to execute the methods described in each embodiment or some parts of the embodiments of the present invention.

[0210] The present invention provides a method for correcting the inversion error of the Euler beam shape based on the superposition method. There are many methods and ways to specifically implement this technical solution. The above is only the preferred implementation manner of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by the prior art.

Claims

1. A method for correcting the inversion error of the Euler beam shape based on the superposition method, characterized in that, It includes the following steps: Step 1, perform uncorrected shape inversion; Step 2, collect calibration information for the superposition method; Step 3, perform shape inversion error correction based on the superposition method; Step 1 includes: If the structure under test is equivalent to an Euler beam, based on the approximate relationships among strain, curvature, and deflection, the strain distribution information of the structure under test is collected by a distributed optical fiber sensor, and the variation relationship of the strain with the distance x from the left end of the beam is obtained. Invert the structural form to obtain the following inversion rotation angle equation and the inversion deflection curve equation where dx is the differential of x, C and D are constants, and ho is the distance from a point on the structure surface to the neutral layer; Step 2 includes: Based on the deflection, the deflection calibration information of the structure is obtained from the displacement constraint or displacement sensor at the known point P of the position, and used as the corrected deflection at point P. The distance between point P and the left end of the beam is set as x P , and the deflection calibration information is Step 2 includes: Based on the rotation angle, obtain the rotation angle calibration information of the structure based on the rotation angle constraint or rotation angle sensor at the position-known point P as the corrected rotation angle at point P, and set the distance between point P and the left end of the beam as x P , the rotation angle calibration information is Step 3 includes: For the condition where there is only one calibrated deflection or rotation angle on a beam, perform shape inversion error correction based on the superposition method: Based on the deflection calibration information at a point P: Assume that the structural deflection curve obtained by the inverse integration method of strain-curvature-deflection is Superimpose the compensation deflection equation Δw(x) on the inverse deflection curve equation so that the corrected deflection curve Conforms to the deflection calibration information: Among them is the deflection of point P after correction. When the equivalent Euler beam of the measured structure has no bending, assume that a compensating concentrated force load F is applied at a distance x from the left end of the beam. Taking the direction of the load F as positive, the deflection at a distance x from the left end of the beam is W a At this point, the deflection at a distance x from the left end of the beam is W b At this point, the deflection is W F (F, x a , x b ), then the compensating deflection equation Δw(x) is expressed as: Δw(x) = W F (F, x P , x) Substitute \(x = x\) P : Solve for the compensation load F, obtain the compensation deflection equation Δw(x), and obtain the corrected deflection curve equation:

2. A method for correcting the inversion error of the Euler beam shape based on the superposition method, characterized in that It includes the following steps: Step 1, perform uncorrected shape inversion; Step 2, collect calibration information for the superposition method; Step 3, perform shape inversion error correction based on the superposition method; Step 1 includes: If the structure under test is equivalent to an Euler beam, based on the approximate relationships among strain, curvature, and deflection, collect the strain distribution information of the structure under test by a distributed optical fiber sensor, and obtain the variation relationship of strain with the distance x from the left end of the beam. Invert the structure shape to obtain the following inversion rotation angle equation and the inversion deflection curve equation where dx is the differential of x, C and D are constants, and ho is the distance from a point on the structure surface to the neutral layer; Step 2 includes: Based on the deflection, the deflection calibration information of the structure is obtained based on the displacement constraint or displacement sensor at the known point P of the position, and used as the corrected deflection at point P. Set the distance between point P and the left end of the beam as x P , the deflection calibration information is Step 2 includes: Based on the rotation angle, obtain the rotation angle calibration information of the structure based on the rotation angle constraint or rotation angle sensor at the position-known point P as the corrected rotation angle of point P, and set the distance between point P and the left end of the beam as x P , the rotation angle calibration information is Step 3 includes: For the condition where there is only one calibrated deflection or rotation angle on a beam, perform shape inversion error correction based on the superposition method: Based on the rotation angle calibration information at a point P: Assume that the structural rotation angle equation obtained by the inverse integration method of strain-curvature-deflection is Superimpose the compensation rotation angle equation Δθ(x) on the inverse rotation angle equation to make the corrected rotation angle equation Conform to the rotation angle calibration information: Among them is the corrected rotation angle at point P. When the Euler beam equivalent to the measured structure has no bending, assume that a compensating concentrated moment load M is applied at a distance x from the left end of the beam. The direction of the load M is positive, and the rotation angle at a distance x from the left end of the beam a is Theta(M, x b , x a , x b ), and the deflection is W M (M, x a , x b ). Then the compensation rotation angle equation Δθ(x) is expressed as: Δθ(x) = Theta(M, x P , x) Substitute \(x = x\) P : Among them is the inversion value of the rotation angle of point P before correction; Solve for the compensation load M, obtain the compensation deflection equation Δw(x): Δw(x) = W M (M, x P , x) Obtain the corrected deflection curve equation:

3. The method according to claim 1 or 2, characterized in that, Step 3 includes: For the condition where there are two or more calibrated deflections or rotation angles on a beam, on the basis of the shape inversion error correction of the superposition method, propose an inversion shape correction method based on the superposition method - force method normal equation: When the beam is corrected by n deflection and rotation calibration information, n≥2, calculate the corresponding compensating concentrated force load and compensating concentrated moment load, and solve the compensating loads X1, X2, …, X based on the superposition method - the normal equation of the force method n : Among them, X n represents the nth compensation load, and δ ij is the deflection or rotation angle generated at the ith load application position when the single acting load X j = 1. The values of i and j range from 1 to n. Taking the application direction of X j as positive, we get: Among them, W F (1, x j , x ij ) represents the compensation load X i corresponding to the deflection calibration, Theta(1, x j , x i ) represents the compensation load X i corresponding to the rotation angle calibration; According to the defined Substitute x = x P , the difference Δ between the deflection or rotation angle of the i-th load application position obtained by inversion and the calibrated deflection or rotation angle i is expressed as: Among them, represents the compensation load X i corresponding to deflection calibration, represents the compensation load X i corresponding to rotation calibration; Solve the component Δw of the compensation deflection equation corresponding to each load i (x): Among them, W F (X i , x i , x) represents the compensation load X i corresponding to the deflection calibration, W M (X i , x i , x) represents the compensation load X i corresponding to the rotation angle calibration; Then the compensation deflection equation Δw(x) is expressed as: The obtained corrected deflection curve equation is:

4. A storage medium, characterized in that, There is a computer program or instruction stored, and when the computer program or instruction is run, the method described in any one of claims 1 to 3 is implemented.

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