A method for real-time measurement of beam deformation under pre-deformation condition

Abstract

The application discloses a method for measuring deformation of a beam in real time under a pre-deformation condition, and comprises the following steps: obtaining an initial shape of the measured beam; arranging a sensor measuring point along an axial direction of the beam to obtain a strain value in the axial direction of the beam; and calculating a deformation deflection of the beam according to the obtained strain value, and superimposing the calculation result with an initial state to obtain a real deformation value of the beam. The method can measure the deformation of the beam in real time under the pre-deformation condition.

Description

Technical Field

[0001] This invention relates to the field of beam measurement technology, and specifically to a method for real-time measurement of beam deformation under pre-deformation conditions. Background Technology

[0002] When measuring or monitoring the deformation of flexible structures such as beams, the structure has already deformed. Attaching strain gauges to measure this deformation after deformation means the measured deformation does not reflect the total, or true, deformation of the structure, which significantly impacts the assessment of the structure's health condition. Currently, most structural deformation measurements are offline, such as photogrammetry, GPS measurement, and 3D laser scanning. These methods can only measure deformation offline, not in real-time online mode. Furthermore, these methods suffer from drawbacks such as high requirements for the shooting environment, susceptibility to signal interference, low measurement accuracy, and high installation costs. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for real-time measurement of beam deformation under pre-deformation conditions, which addresses the above-mentioned deficiencies in the existing technology and enables real-time measurement of beam deformation under pre-deformation conditions.

[0004] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0005] A method for real-time measurement of beam deformation under pre-deformation conditions includes the following steps:

[0006] Step 1: Obtain the initial shape of the beam under test;

[0007] Step 2: Evenly set sensor measurement points along the beam axis to obtain strain values ​​along the beam axis.

[0008] Step 3: Calculate the beam's deformation deflection based on the obtained strain value. Then, superimpose the calculated result with the initial state from Step 1 to obtain the beam's true deformation value.

[0009] According to the above technical solution, the cross-section of the beam being tested is square or circular.

[0010] According to the above technical solution, in step 2, the sensor is attached to the surface of the beam structure along the beam axis.

[0011] According to the above technical solution, the beam has already undergone slight deformation in its initial position under the action of its own weight or external force;

[0012] In step 2, based on the slight deformation of the beam, (n+1) strain sensors are installed at equal intervals on the outer side of the beam where the deformation occurs.

[0013] Let the total length of the beam be L, then the spacing between any two adjacent sensors is...

[0014] Furthermore, the beam, based on its slight deformation, undergoes further deformation under external force, resulting in a strain of ε' to ε. The deformation of cantilever beams, simply supported beams, and overhanging beams under further force after slight deformation is shown in Figure 1.

[0015] According to the above technical solution, when the beam under test is a cantilever beam, the specific calculation process for the beam's deformation deflection in step 3 is as follows:

[0016] According to the principles of mechanics of materials

[0017]

[0018] In the formula, x is the coordinate of the beam length direction, y is the vertical displacement at the measuring point, the fixed end point O of the cantilever beam is taken as the origin, i.e., the deflection, M(x) is the bending moment of the beam, E is the elastic modulus of the material, and I(x) is the moment of inertia of the beam section at position x.

[0019] Assuming the radius of curvature of the neutral layer at position x is ρ(x), from the static equations we can obtain...

[0020]

[0021] Assuming the strain at position x is ε(x), the radius of curvature is ρ(x), and the distance from the beam surface to the neutral layer is c(x), by the plane assumption, the relationship between ε(x) and ρ(x) and c(x) is as follows:

[0022]

[0023] By integrating formulas (1) and (3), we can obtain

[0024]

[0025] When the beam is a uniform beam, c(x) is a constant value, let it be c, then we can obtain

[0026]

[0027] Let ε(x) be the strain of the beam at any point x between any two strain sensors. i-1 ≤x≤x i x i-1 x represents the position coordinates of the (i-1)th sensor. i This represents the position coordinates of the i-th sensor, and the strain between the two strain sensors is related to (xx). i-1 If the relationship is linear, then we have

[0028]

[0029] Let the slope between any two strain gauges be tanθ(x), x i-1 ≤x≤x i If the slope at the starting position on the left is tanθ0, then we can obtain...

[0030]

[0031] In the formula, tanθi represents the value at x i The slope of the beam at position (i.e., the position of the i-th sensor), tanθi-1 represents the slope at x. i-1 The slope of the beam at the location (i.e., the location of the (i-1)th sensor);

[0032] And tanθ i ≡tanθ(x i Then, by rearranging, we can obtain...

[0033]

[0034] In the formula, i = 1, 2, 3, ..., n; j = 1, 2, 3, ..., n; ε0 represents the strain of the beam at the origin coordinate position, ε i Let ε represent the strain of the beam at the location of the i-th sensor. j Let θ represent the strain of the beam at the j-th sensor position, and tanθ0 represent the slope of the beam at the origin coordinate position.

[0035] Let y(x) be the deflection of the beam at point x between any two strain gauges. i-1 ≤x≤x i If the deflection at the starting position on the left (i.e., the starting position of the origin coordinate system) is y0, then we can obtain...

[0036]

[0037] In the formula, tan(θ) represents the slope of the beam at position x, and y i-1 θi-1 represents the deflection of the beam at the (i-1)th sensor position, and θi-1 represents the tilt angle of the beam at the (i-1)th sensor position.

[0038] Organizing can yield

[0039]

[0040] Where yi represents the beam deflection at the i-th sensor location, ε i Let ε represent the strain of the beam at the location of the i-th sensor. j This represents the strain of the beam at the location of the j-th sensor;

[0041] As can be seen from formula (10), after obtaining the strain at each point of the beam and the slope and deflection at the initial position of the end, the total slope and deflection of the beam can be obtained.

[0042] According to the above technical solution, if the slope and deflection at the initial position are both 0, then formula (10) can be used to obtain

[0043]

[0044] In the formula ε i Let ε represent the strain of the beam at the location of the i-th sensor. j This represents the strain of the beam at the j-th sensor location.

[0045] According to the above technical solution, when the beam under test is a simply supported beam, the specific calculation process for the beam's deformation deflection in step 3 is as follows:

[0046] When the left end of the beam is a simple support and the right end is a simple or fixed support, the slope at the initial position is not 0 and the deflection at the initial position is 0. Then, from formula (11), we can obtain...

[0047]

[0048] The deflection equation for a simply supported beam is:

[0049]

[0050] Among them, i=1,2,3,…,n,y i Let y represent the deflection of the beam at the location of the i-th sensor. n This represents the beam deflection at the location of the last sensor (the total number of sensors is n).

[0051] According to the above technical solution, when the beam under test is an overhanging beam, the specific calculation process for the beam's deformation deflection in step 3 is as follows:

[0052] As shown in Figure 1(c), the cantilever beam can also be viewed as follows: the middle part is a simple supported beam, and the two cantilevered parts are cantilever beams. The strain values ​​measured by the sensors set at the two support points O1 and O2 are respectively set as ε. 01 and ε 02 ;

[0053] The portion between points O1 and O2 is treated as a simply supported beam, with strains ranging from ε0 to ε1 from left to right. n The deflections from left to right are y0 to y1. n The portion of the beam between point O1 on the left and point A at the leftmost end is treated as a cantilever beam. From point O1 to point A, the strain is ε. 01 ~ε n1 The deflections are in the following order: y 01 ~y n1The section between point O2 on the right and point B at the rightmost end of the beam is considered a cantilever beam. From point O2 to point B, the strain is ε. 02 ~ε n2 The deflections are in the following order: y 02 ~y n2 ;

[0054] At points O1 and O2, ε0 = ε 01 , ε n =ε 02 The beam's deflection is 0, but its slope is not 0;

[0055] (4) In segment O1O2 of the beam, according to formula (13), we can obtain

[0056]

[0057] Among them, there is the boundary condition y0=y n =0

[0058] (5) In segment O1A of the beam, according to formula (10), we can obtain

[0059]

[0060] Where, ε j1 ε represents the strain of the beam at the j-th sensor location on segment O1A. i1 tanθ represents the strain of the beam at the i-th sensor location on segment O1A. 01 ε represents the slope of the beam at support point O1. 01 y represents the strain of the beam at support point O1. 01 y represents the deflection of the beam at support point O1. i1 Let y represent the beam deflection at the i-th sensor location on segment O1A, with boundary condition y. 01 =y0=0,tanθ 01 =tanθ0. y0 represents the deflection of the beam at support point O1 when the portion between points O1 and O2 is a simply supported beam, and tanθ0 represents the slope of the beam at support point O1 when the portion between points O1 and O2 is a simply supported beam;

[0061] (6) In segment O2B of the beam, according to formula (10), we can obtain

[0062]

[0063] Where, ε j2 ε represents the strain of the beam at the j-th sensor location on segment O2B. i2 tanθ represents the strain of the beam at the i-th sensor location on segment O2B. 02 ε represents the slope of the beam at support point O2. 02y represents the strain of the beam at support point O2. 02 This represents the deflection of the beam at support point O2, with boundary condition y. 02 =y n =0, tanθ 02 =tanθ n y n tanθ represents the deflection of the beam at support point O2 when the portion between points O1 and O2 is a simply supported beam. n This represents the slope of the beam at support point O2 when the section between points O1 and O2 is a simply supported beam.

[0064] The deformations of segments O1A, O1O2, and O2B together constitute the deformation of the entire overhanging beam.

[0065] The beam deformation value obtained above is superimposed with the initial state of the beam in step 1 to obtain the beam's true real-time online deformation value.

[0066] According to the above technical solution, the sensor is a fiber optic grating sensor.

[0067] The present invention has the following beneficial effects:

[0068] 1. This method can quickly and accurately measure the actual deformation value of a beam even after it has already deformed, enabling real-time measurement of beam deformation under pre-deformation conditions.

[0069] 2. For measuring the morphology of square or circular interface beam structures under bending deformation conditions, fiber optic grating sensors are used to measure the strain along the beam's axial direction. Simultaneously, the initial morphology of the beam is measured using other measurement methods as a benchmark. Based on this benchmark, Ko displacement theory is used to measure the actual deformation value of the beam under pre-deformation conditions. Other measurement methods include scanning and measurement using a three-dimensional laser scanner, as well as measurement using some conventional measuring tools such as rulers. Attached Figure Description

[0070] Figure 1(a) is a schematic diagram of the cantilever beam before and after deformation in an embodiment of the present invention;

[0071] Figure 1(b) is a schematic diagram of the simply supported beam before and after deformation in an embodiment of the present invention;

[0072] Figure 1(c) is a schematic diagram of the cantilever beam before and after deformation in an embodiment of the present invention;

[0073] Figure 2 This is a schematic diagram of the stress simulation of the cantilever beam in Embodiment 2 of the present invention;

[0074] Figure 3 This is a schematic diagram comparing the deformation result curve of the beam reconstructed by Ko displacement theory under pre-deformation conditions with the deformation result curve obtained directly from simulation in Embodiment 2 of the present invention. Detailed Implementation

[0075] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0076] In the description of this invention, it should be understood that if terms such as "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise" are used to indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, they are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0077] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection. They can refer to a mechanical connection or an electrical connection. They can refer to a direct connection or an indirect connection through an intermediate medium, and they can refer to the internal communication of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances.

[0078] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0079] Reference Figures 1(a) to 1(c) As shown, an embodiment 1 of the present invention provides a method for real-time measurement of beam deformation under pre-deformation conditions, comprising the following steps:

[0080] Step 1: Obtain the initial shape of the square or circular interface beam to be measured;

[0081] Step 2: Evenly set sensor measurement points along the central axis of the beam to obtain the strain value in the beam axis direction;

[0082] Step 3: Based on the obtained strain value, calculate the beam's deformation deflection using Ko displacement theory. Then, superimpose the calculated result with the initial state from Step 1 to obtain the beam's true deformation value.

[0083] Furthermore, the cross-section of the beam being measured is square or circular.

[0084] Furthermore, in step 2, the sensor is attached to the surface of the beam structure along the beam axis.

[0085] Furthermore, the beam, in its initial position, has already undergone slight deformation under the influence of its own weight or external forces;

[0086] In step 2, based on the slight deformation of the beam, (n+1) strain sensors are installed at equal intervals on the outer side of the beam where the deformation occurs.

[0087] Let the total length of the beam be L, then the spacing between any two adjacent sensors is...

[0088] Furthermore, the beam, based on its slight deformation, undergoes further deformation under external force, resulting in a strain of ε' to ε. The deformation of cantilever beams, simply supported beams, and overhanging beams under further force after slight deformation is shown in Figure 1.

[0089] Furthermore, when the beam under test is a cantilever beam, as shown in Figure 1(a), the specific calculation process for the beam's deformation deflection in step 3 is as follows:

[0090] According to the principles of mechanics of materials

[0091]

[0092] In the formula, x is the coordinate of the structural beam along its length, y is the vertical displacement at the measuring point, the fixed end of the cantilever beam is taken as the origin, i.e., the deflection, M(x) is the bending moment of the structural beam, E is the elastic modulus of the material, and I(x) is the moment of inertia of the beam section at position x.

[0093] Assuming the radius of curvature of the neutral layer at position x is ρ(x), from the static equations we can obtain...

[0094]

[0095] Assuming the strain at position x is ε(x), the radius of curvature is ρ(x), and the distance from the beam surface to the neutral layer is c(x), by the plane assumption, the relationship between ε(x) and ρ(x) and c(x) is as follows:

[0096]

[0097] By integrating formulas (1) and (3), we can obtain

[0098]

[0099] When the beam is a uniform beam, c(x) is a constant value, let it be c, then we can obtain

[0100]

[0101] Let ε(x) be the strain of the beam at any point x between any two strain sensors. i-1 ≤x≤x i x i-1 x represents the position coordinates of the (i-1)th sensor. i This represents the position coordinates of the i-th sensor, and the strain between the two strain sensors is related to (xx). i-1 If the relationship is linear, then we have

[0102]

[0103] Let the slope between any two strain gauges be tanθ(x), x i-1 ≤x≤x i If the slope at the starting position on the left is tanθ0, then we can obtain...

[0104]

[0105] In the formula, tanθi represents the value at x i The slope of the beam at position (i.e., the position of the i-th sensor), tanθi-1 represents the slope at x. i-1 The slope of the beam at the location (i.e., the location of the (i-1)th sensor);

[0106] And tanθ i ≡tanθ(x i Then, by rearranging, we can obtain...

[0107]

[0108] In the formula, i = 1, 2, 3, ..., n; j = 1, 2, 3, ..., n; ε0 represents the strain of the beam at the origin coordinate position, ε i Let ε represent the strain of the beam at the location of the i-th sensor. j Let θ represent the strain of the beam at the j-th sensor position, and tanθ0 represent the slope of the beam at the origin coordinate position.

[0109] Let y(x) be the deflection of the beam at point x between any two strain gauges. i-1 ≤x≤x i If the deflection at the starting position on the left (i.e., the starting position of the origin coordinate system) is y0, then we can obtain...

[0110]

[0111] In the formula, tan(θ) represents the slope of the beam at position x, and y i-1 θi-1 represents the deflection of the beam at the (i-1)th sensor position, and θi-1 represents the tilt angle of the beam at the (i-1)th sensor position.

[0112] Organizing can yield

[0113]

[0114] Where yi represents the beam deflection at the i-th sensor location; i = 1, 2, 3, ..., n; ε i Let ε represent the strain of the beam at the location of the i-th sensor. j This represents the strain of the beam at the location of the j-th sensor;

[0115] As can be seen from formula (10), after obtaining the strain at each point of the beam and the slope and deflection at the initial position of the end, the total slope and deflection of the beam can be obtained.

[0116] Furthermore, if the slope and deflection at the initial position are both 0, then from formula (10) we can obtain

[0117]

[0118] In the formula ε i Let ε represent the strain of the beam at the location of the i-th sensor. j This represents the strain of the beam at the j-th sensor location.

[0119] Furthermore, when the beam under test is a simply supported beam, as shown in Figure 1(b), the specific calculation process for the beam's deformation deflection in step 3 is as follows:

[0120] When the left end of the beam is a simple support, taking one fixed end support point of the beam as the origin of the coordinate system, and the right end is a simple or fixed support, the slope at the initial position is not 0, and the deflection at the initial position is 0. Then, from formula (11), we can obtain...

[0121]

[0122] The deflection equation for a simply supported beam is:

[0123]

[0124] Among them, i=1,2,3,…,n,y i Let y represent the deflection of the beam at the location of the i-th sensor. n This represents the beam deflection at the location of the last sensor (the total number of sensors is n).

[0125] Furthermore, when the beam being measured is an overhanging beam, the specific calculation process for the beam's deformation deflection in step 3 is as follows:

[0126] As shown in Figure 1(c), the cantilever beam can also be viewed as follows: the middle part is a simple supported beam, and the two cantilevered parts are cantilever beams. The strain values ​​measured by the sensors set at the two support points O1 and O2 are respectively set as ε. 01 and ε 02 ;

[0127] The portion between points O1 and O2 is treated as a simply supported beam, with strains ranging from ε0 to ε1 from left to right. n The deflections from left to right are y0 to y1. n The portion of the beam between point O1 on the left and point A at the leftmost end is treated as a cantilever beam. From point O1 to point A, the strain is ε. 01 ~ε n1 The deflections are in the following order: y 01 ~y n1 The section between point O2 on the right and point B at the rightmost end of the beam is treated as a cantilever beam. From point O2 to point B, the strain is ε. 02 ~ε n2 The deflections are in the following order: y 02 ~y n2 ;

[0128] At points O1 and O2, ε0 = ε 01 , ε n =ε 02 The beam's deflection is 0, but its slope is not 0;

[0129] (7) In segment O1O2 of the beam, according to formula (13), we can obtain

[0130]

[0131] Among them, there is the boundary condition y0=y n =0

[0132] (8) In segment O1A of the beam, according to formula (10), we can obtain

[0133]

[0134] Where, ε j1 ε represents the strain of the beam at the j-th sensor location on segment O1A. i1 tanθ represents the strain of the beam at the i-th sensor location on segment O1A. 01 ε represents the slope of the beam at support point O1. 01 y represents the strain of the beam at support point O1. 01 y represents the deflection of the beam at support point O1. i1Let y represent the beam deflection at the i-th sensor location on segment O1A, with boundary condition y. 01 =y0=0,tanθ 01 =tanθ0. y0 represents the deflection of the beam at support point O1 when the portion between points O1 and O2 is a simply supported beam, and tanθ0 represents the slope of the beam at support point O1 when the portion between points O1 and O2 is a simply supported beam;

[0135] (9) In segment O2B of the beam, according to formula (10), we can obtain

[0136]

[0137] Where, ε j2 ε represents the strain of the beam at the j-th sensor location on segment O2B. i2 tanθ represents the strain of the beam at the i-th sensor location on segment O2B. 02 ε represents the slope of the beam at support point O2. 02 y represents the strain of the beam at support point O2. 02 This represents the deflection of the beam at support point O2, with boundary condition y. 02 =y n =0, tanθ 02 =tanθ n y n tanθ represents the deflection of the beam at support point O2 when the portion between points O1 and O2 is a simply supported beam. n This represents the slope of the beam at support point O2 when the section between points O1 and O2 is a simply supported beam.

[0138] The deformations of segments O1A, O1O2, and O2B together constitute the deformation of the entire overhanging beam.

[0139] The beam deformation value obtained above is superimposed with the initial state of the beam in step 1 to obtain the beam's true real-time online deformation value.

[0140] Furthermore, the sensor is a fiber Bragg grating sensor.

[0141] Example 2

[0142] A cantilever beam structure with a total length of 1650mm, a width of 100mm, and a thickness of 10mm is selected, such as... Figure 2As shown, one end is fixed, and a downward force perpendicular to the upper surface of the beam is applied at the middle position of the other end. The magnitude of the force is 4.9 N, and the deformation and strain values ​​of the beam are recorded at this time. Subsequently, the force is applied sequentially to 9.8 N, 14.7 N, and 19.6 N, and the deformation and strain values ​​of the beam are recorded respectively. The deformation generated when a force of 4.9 N is applied is taken as the pre-deformation state of the beam and used as a reference. Based on the 4.9 N force applied to the beam, the deformation values ​​when the applied forces are 9.8 N, 14.7 N, and 19.6 N are derived according to the Ko theory formula mentioned above. The deformation result curves reconstructed by Ko displacement theory under the pre-deformation conditions are compared with the deformation result curves directly obtained from the simulation, as shown. Figure 3 As shown, it can be clearly seen that the deformation curve obtained by Ko displacement theory under pre-deformation conditions is basically consistent with the deformation curve obtained by simulation. The maximum absolute error of the method of this invention is 0.047 mm, and the maximum relative error is 0.6%.

[0143] The above fully demonstrates that under pre-deformation conditions, this method has very high accuracy, verifying its effectiveness.

[0144] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0145] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for real-time measurement of beam deformation under pre-deformation conditions, characterized in that, Includes the following steps: Step 1: Obtain the initial shape of the beam under test; Step 2: Evenly set sensor measurement points along the beam axis to obtain strain values ​​along the beam axis. Step 3: Calculate the beam's deformation deflection based on the obtained strain value. Then, superimpose the calculated result with the initial state from Step 1 to obtain the beam's true deformation value. The cross-section of the beam being measured is square or circular; In step 2, the sensor is attached to the surface of the beam structure along the beam axis. When the beam is in its initial position, it has already undergone slight deformation under the action of its own weight or external forces; In step 2, based on the slight deformation of the beam, n+1 strain sensors are installed at equal intervals on the outer side of the beam where the deformation occurs. Let the total length of the beam be L, then the spacing between any two adjacent sensors is... ; When the beam under test is a cantilever beam, the specific calculation process for the beam's deformation deflection in step 3 is as follows: In the formula, x is the coordinate of the beam length direction, y is the vertical displacement at the measuring point, with the fixed end of the beam as the origin, i.e., the deflection, M(x) is the bending moment of the beam, E is the elastic modulus of the material, and I(x) is the moment of inertia of the beam section at position x. Assuming the radius of curvature of the neutral layer at position x is ρ(x), from the static equations we can obtain... Assuming the strain at position x is ε(x), the radius of curvature is ρ(x), and the distance from the beam surface to the neutral layer is c(x), by the plane assumption, the relationship between ε(x) and ρ(x) and c(x) is as follows: By integrating formulas (1) and (3), we can obtain When the beam is a uniform beam, c(x) is a constant value, let it be c, then we can obtain Let ε(x) be the strain of the beam at any point x between any two strain sensors. i-1 ≤x≤x i x i-1 The x-th sensor represents the position coordinates of the (i-1)th sensor. i This represents the position coordinates of the i-th sensor, and the strain between the two strain sensors is related to xx. i-1 If the relationship is linear, then we have Let the slope between any two strain gauges be tanθ(x), x i-1 ≤x≤x i If the slope at the starting position on the left is tanθ0, then we can obtain... In the formula tanθ i tanθ represents the slope of the beam at the i-th sensor position. i-1 This represents the slope of the beam at the (i-1)th sensor position; again Then, by rearranging, we can obtain In the formula, i = 1, 2, 3, …, n ; j = 1, 2, 3, …, n-1; i is greater than j; ɛ0 represents the strain of the beam at the origin coordinate position, ɛ i Let ɛ represent the strain of the beam at the location of the i-th sensor. j Let θ represent the strain of the beam at the j-th sensor position, and tanθ0 represent the slope of the beam at the origin coordinate position. Let y(x) be the deflection of the beam at point x between any two strain gauges. i-1 ≤x≤x i If the deflection at the origin's initial position is y0, then we can obtain... In the formula, tan(θ) represents the slope of the beam at position x, and y i-1 Let θ represent the deflection of the beam at the (i-1)th sensor location. i-1 This represents the tilt angle of the beam at the (i-1)th sensor position; Organizing can yield Among them, y i Let ɛ represent the deflection of the beam at the location of the i-th sensor. i Let ɛ represent the strain of the beam at the location of the i-th sensor. j This represents the strain of the beam at the location of the j-th sensor; As can be seen from formula (10), after obtaining the strain at each point of the beam and the slope and deflection at the initial position of the end, the total slope and deflection of the beam can be obtained. The sensor is a fiber Bragg grating sensor.

2. The method for real-time measurement of beam deformation under pre-deformation conditions according to claim 1, characterized in that, If the slope and deflection at the initial position are both 0, then we can obtain from formula (10) In the formula ɛ i Let ɛ represent the strain of the beam at the location of the i-th sensor. j This represents the strain of the beam at the j-th sensor location.

3. The method for real-time measurement of beam deformation under pre-deformation conditions according to claim 2, characterized in that, When the beam being measured is a simply supported beam, the specific calculation process for the beam's deformation deflection in step 3 is as follows: When the left end of the beam is a simple support and the right end is a simple or fixed support, the slope at the initial position is not 0 and the deflection at the initial position is 0. Then, from formula (11), we can obtain... The deflection of the simply supported beam is in, i = 1, 2, 3, …, n y i Let y represent the deflection of the beam at the location of the i-th sensor. n This indicates the beam deflection at the location of the last sensor.

4. The method for real-time measurement of beam deformation under pre-deformation conditions according to claim 3, characterized in that, When the beam under test is an overhanging beam, the specific calculation process for the beam's deformation deflection in step 3 is as follows: The cantilever beam is considered as follows: the middle part is a simple supported beam, and the two cantilever ends are cantilever beams. The strain values ​​measured by sensors placed at the two support points O1 and O2 are respectively set as ε. 01 and ε 02 ; The portion between points O1 and O2 is treated as a simply supported beam, with strains ranging from ε0 to ε1 from left to right. n The deflections from left to right are y0~y n The portion of the beam between point O1 on the left and point A at the leftmost end is treated as a cantilever beam. From point O1 to point A, the strain is ε. 01 ~ε n1 The deflections are in the following order: y 01 ~y n1 The section between point O2 on the right and point B at the rightmost end of the beam is considered a cantilever beam. From point O2 to point B, the strain is ε. 02 ~ε n2 The deflections are in the following order: y 02 ~y n2 ; At points O1 and O2, ε0 = ε 01 , ε n =ε 02 The beam's deflection is 0, but its slope is not 0; (1) In segment O1O2 of the beam, according to formula (13), we can obtain Among them, there is the boundary condition y0 = y n = 0 (2) In segment O1A of the beam, according to formula (10), we can obtain Among them, ɛ j1 ɛ represents the strain of the beam at the j-th sensor location on segment O1A. i1 tanθ represents the strain of the beam at the i-th sensor location on segment O1A. 01 The slope of the beam at support point O1 is represented by ɛ. 01 y represents the strain of the beam at support point O1. 01 y represents the deflection of the beam at support point O1. i1 Let y represent the beam deflection at the i-th sensor location on segment O1A, with boundary condition y. 01 =y0= 0, tanθ 01 = tanθ0; y0 represents the deflection of the beam at support point O1 when the part between points O1 and O2 is a simply supported beam, and tanθ0 represents the slope of the beam at support point O1 when the part between points O1 and O2 is a simply supported beam. (3) In segment O2B of the beam, according to formula (10), we can obtain Among them, ɛ j2 This represents the strain of the beam at the j-th sensor location on segment O2B, ɛ i2 tanθ represents the strain of the beam at the i-th sensor location on segment O2B. 02 The slope of the beam at support point O2 is represented by ɛ. 02 y represents the strain of the beam at support point O2. 02 This represents the deflection of the beam at support point O2, with boundary condition y. 02 = y n = 0, tanθ 02 = tanθ n ;y n tanθ represents the deflection of the beam at support point O2 when the portion between points O1 and O2 is a simply supported beam. n This represents the slope of the beam at support point O2 when the section between points O1 and O2 is a simply supported beam. The deformations of segments O1A, O1O2, and O2B together constitute the deformation of the entire overhanging beam. The beam deformation value obtained above is superimposed with the initial state of the beam in step 1 to obtain the beam's true real-time online deformation value.

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