A method for inverting deformation of a tank structure and a method for inverting loads of a tank

Abstract

The present invention discloses a method for inverting the deformation of a nacelle structure and a method for inverting the load of a nacelle. The method calculates the synthetic curvature of the measuring point position based on the strain at the measuring point position obtained by the sensor; obtains the generalized shear strain at the measuring point position after inverse transformation; obtains the actual strain of the monitoring area of ​​the nacelle to be measured based on the Kirchhoff theory; obtains the displacement response and strain response of the nacelle to be measured by combining the inverse finite element theory; establishes the relationship between the load of the nacelle to be measured and the displacement response and strain response, obtains the external load based on the strain response and the displacement response respectively, constructs the error function between the two, and obtains the external excitation load of the nacelle structure. A non-invasive deformation / load monitoring system for the nacelle structure is constructed based on the inverse transformation, which solves the problem that conventional deformation and load reconstruction methods cannot effectively invert areas that cannot be monitored by sensors. A method combining inverse transformation with inverse finite element is proposed to solve the problem of low deformation inversion accuracy based on conventional deflection shape functions.

Description

Technical Field

[0001] The present invention relates to structural health monitoring, and in particular to a method for inverting a nacelle structure deformation and a method for inverting a nacelle load. Background Art

[0002] As a typical underwater submersible structure, the nacelle is subject to factors such as ocean wave impact and underwater pressure during its service. The health status of the nacelle structure directly affects the safe service of the submersible, and structural damage or fatigue may lead to serious accidents. Therefore, by using the discrete measurement point strain data to invert the deformation state and load information of the nacelle structure, it can provide technical support for the real-time evaluation of the safety status of the nacelle in service.

[0003] At present, the research on structural deformation reconstruction methods mainly includes: digital image method (DIC), Ko displacement theory, and curvature recursion method. Among them, the basic principle of DIC is to compare the surface images of the object before and after loading, and calculate the displacement of each point on the surface of the object. However, this method is limited by the harsh service environment of the barrel structure, and the monitoring area has certain limitations, which cannot meet the needs of large-area deformation monitoring of the structure. The latter two methods have the problems of large calculation amount and the inability to invert the blind area of ​​sensor monitoring.

[0004] At present, the main methods for structural load reconstruction are direct method and indirect measurement method. The direct measurement method is to directly measure the load on the structure through force sensors, etc., which can only obtain the load conditions of a single point of the structure and cannot realize the regional load inversion of the structure. The indirect measurement method is to invert the structural load through structural strain, displacement, acceleration, etc. Compared with the direct method, the indirect method is more economical and has a wider range of applications. However, there are also some problems. For example, the strain method is limited by the location and number of strain gauges. For areas where sensors cannot be arranged, the load inversion accuracy may be insufficient. For example, the machine learning method requires a large number of training samples, and insufficient or inaccurate data directly affects the inversion results. Summary of the invention

[0005] Purpose of the invention: In view of the above shortcomings, the present invention provides a method for inverting the deformation of a nacelle structure and a method for inverting the load of a nacelle with improved inversion accuracy.

[0006] Technical solution: To solve the above problems, the present invention adopts a method for inversion of nacelle structure deformation, which includes the following steps:

[0007] (1) The axial strain and tangential strain at the measuring point are obtained by arranging the strain rosette at the measuring point in the monitoring area of ​​the tank to be measured;

[0008] (2) Based on the relationship between the surface strain and the composite curvature of the tank structure, the composite curvature of the measuring point of the tank to be measured is calculated by using the obtained axial strain and tangential strain; based on the composite curvature of the measuring point, the generalized shear strain at the measuring point is obtained based on the Radon transform;

[0009] (3) According to the generalized shear strain at the measuring point, based on the Kirchhoff theory, the actual strain of the monitoring area of ​​the tank to be measured is obtained;

[0010] (4) The nacelle to be measured is discretized based on the finite element method, and the theoretical strain of any point in the four-node unit calculated based on the displacement shape function is obtained according to the finite element theory. The relationship between the displacement vector of the unit node and the displacement vector of the unit node;

[0011] (5) Construct theoretical strain calculation based on displacement shape function The error function between the actual strain obtained in step (3) and the theoretical strain based on the displacement shape function is The relationship between the unit node displacement vector and the unit node displacement vector is calculated. The unit node displacement vector when the function value of the error function is the smallest is calculated. The reconstructed displacement of any point in the unit is obtained through the unit node displacement vector, thereby reconstructing the displacement response in the monitoring area of ​​the nacelle to be measured and realizing the inversion of the nacelle structure deformation.

[0012] Furthermore, the relationship between the synthetic curvature of the measuring point of the nacelle to be measured and the axial strain and tangential strain of the measuring point is expressed as follows:

[0013] ,

[0014] in, represents the composite curvature, It represents half of the thickness of the tank wall to be measured. Indicates Measurement points Directional strain, Indicates Measurement points Directional strain, The direction is along the axial direction of the tank. The direction is the tangent direction of the measuring point;

[0015] Based on Radon transform, the relationship between the generalized shear strain and the composite curvature at the measuring point is expressed as:

[0016] ,

[0017] ,

[0018] in, It represents the composite curvature change between any two measuring points. For along The generalized shear strain per unit length in the direction, For along The generalized shear strain per unit length in the direction, is the proportionality coefficient.

[0019] Furthermore, the specific steps of step (3) are:

[0020] (3.1) will be along Generalized shear strain per unit length in the direction And along Generalized shear strain per unit length in the direction Along direction, Integrate the direction to obtain the synthetic curvature field of the tank to be tested :

[0021] ,

[0022] ,

[0023] in, is the Laplace operator;

[0024] (3.2) The synthetic curvature field of the tank to be tested is Integrate and combine boundary conditions to obtain the deflection of the tank to be measured w , based on Kirchhoff theory, respectively calculate along , Directional strain and Shear strain of a plane :

[0025] ,

[0026] in, For along Directional strain, For along Directional strain, represents the shear strain in the xy plane, represents partial derivative;

[0027] (3.3) Since the strains on the inner and outer surfaces of the tank structure are symmetrically distributed along the neutral plane, the strain components on the inner and outer surfaces are equal in value. The tensile and compressive strains of the neutral surface strain are and bending strain It is expressed as:

[0028] ,

[0029] ,

[0030] in, The outer surface of the tank to be tested is along Directional strain, The outer surface of the tank to be tested is along Directional strain, It represents the shear strain in the xy plane on the outer surface of the tank to be measured; The inner surface of the tank to be tested is along Directional strain, The inner surface of the tank to be tested is along Directional strain, It represents the shear strain in the xy plane of the inner surface of the tank to be measured;

[0031] (3.4) Based on the Radon transform, the actual strain in the monitoring area is calculated as:

[0032] ,

[0033] in, is the actual strain in the monitoring area.

[0034] Furthermore, the theoretical strain of any point in the four-node element calculated based on the displacement shape function is and the element node displacement vector The relationship function between them is:

[0035] ,

[0036] in, is the tensile and compressive strain partial derivative matrix, is the bending strain partial derivative matrix, and Z is the distance between the outer surface of the nacelle structure and the neutral layer of the structure.

[0037] Furthermore, in step (5), a theoretical strain is constructed based on the displacement shape function calculation. The error function between the actual strain and the

[0038] ,

[0039] When the error function takes the minimum value, we have:

[0040] ,

[0041] Simplifying, we get: ,

[0042] in, is the pseudo-stiffness matrix of the four-node element, is the load matrix for the four-node element.

[0043] The present invention also provides a method for inversion of nacelle structure loads, comprising the following steps:

[0044] (1) The axial strain and tangential strain at the measuring point are obtained by arranging the strain rosette at the measuring point in the monitoring area of ​​the tank to be measured;

[0045] (2) Based on the relationship between the surface strain and the composite curvature of the tank structure, the composite curvature of the measuring point of the tank to be measured is calculated by using the obtained axial strain and tangential strain; based on the composite curvature of the measuring point, the generalized shear strain at the measuring point is obtained based on the Radon transform;

[0046] (3) According to the generalized shear strain at the measuring point, based on the Kirchhoff theory, the actual strain of the monitoring area of ​​the tank to be measured is obtained;

[0047] (4) The nacelle to be measured is discretized based on the finite element method, and the theoretical strain of any point in the four-node unit calculated based on the displacement shape function is obtained according to the finite element theory. The relationship between the displacement vector of the element node and the theoretical strain at any point in the four-node element calculated based on the strain deformation function The relationship between the strain vector of the element node and the strain vector of the element node;

[0048] (5) Construct theoretical strains based on displacement shape function calculations , Theoretical strain calculated based on strain deformation function The error function between the actual strain and the measured strain is used to calculate the displacement vector and strain vector of the unit node when the function value of the error function is the smallest, and the displacement response and strain response in the monitoring area of ​​the tank to be measured are obtained;

[0049] (6) The tank to be tested is discretized, and the relationship between the load on the tank to be tested and the displacement response and strain response is established respectively. The external load based on the strain response and the external load based on the displacement response are obtained. The error function between the external load based on the strain response and the external load based on the displacement response is constructed. When the function value of the error function is the minimum, the external excitation load of the tank structure is obtained.

[0050] Furthermore, the theoretical strain of any point in the four-node unit calculated based on the strain deformation function is and the element node strain vector The relationship function between them is:

[0051] ,

[0052] in, is the tensile and compressive strain function matrix of the unit node, is the bending stress deformation function matrix of the unit node.

[0053] Furthermore, a theoretical strain function based on strain deformation function is constructed. The error function between the actual strain and the

[0054] ,

[0055] By minimizing the error function, the structural strain pseudo-stiffness equation is obtained as follows:

[0056] ,

[0057] in, is the structural strain pseudo-stiffness matrix, is the structural strain pseudo load matrix.

[0058] Furthermore, the relationship between the load on the tank to be measured and the displacement response and strain response is:

[0059] ,

[0060] ,

[0061] in, is the system strain frequency response function, is the system displacement frequency response function, is the strain mode function, is the displacement mode function, is the r-th order stiffness of the system, is the r-th order modal mass of the system; is the intrinsic parameter of the system when it is externally excited, is the external load based on the strain response, is the external load based on the displacement response.

[0062] Furthermore, based on the least squares method, the external load based on the strain response is constructed and external loads based on displacement response The error function between:

[0063] ,

[0064] The error function is converted to the displacement mode function Find the partial derivative and minimize the function value of the error function, and you can get the displacement vibration function equation of the nacelle structure: According to the relationship between the measured tank load and the displacement response and strain response, the external excitation load of the tank structure is obtained, and the inversion of the external load of the tank is realized.

[0065] Beneficial effects: Compared with the prior art, the significant advantage of the present invention is that it constructs a non-invasive deformation / load monitoring system for nacelle structures based on the idea of ​​Radon inverse transform, solving the problem that conventional deformation and load reconstruction methods cannot effectively invert areas that sensors fail to monitor. A method combining Radon inverse transform with inverse finite element is proposed to construct an error function between actual strain and theoretical strain, solving the problem of low deformation inversion accuracy based on conventional deflection shape function. The relationship between strain, deformation response and load is constructed, and the idea of ​​least squares solution of vibration mode function is proposed, solving the problem that the frequency response function is difficult to determine in dynamic load identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a schematic diagram of the flow of the tank load inversion method of the present invention.

[0067] Figure 2 This is a diagram of the optical fiber strain sensing array of the nacelle structure in the present invention.

[0068] Figure 3 It is a schematic diagram of the inversion effect curve of the deformation field of the nacelle structure in the present invention.

[0069] Figure 4 It is a schematic diagram of the dynamic load inversion effect curve of the nacelle structure in the present invention. DETAILED DESCRIPTION

[0070] like Figure 1 As shown, a method for inverting deformation and load of a nacelle structure in this embodiment includes the following steps:

[0071] Step 1: Use field theory and Kirchhoff equation to define the geometric deformation equation of the nacelle structure;

[0072] Step 1-1, based on the geometric equations in Kirchhoff theory, define the composite curvature of any point on the surface of the nacelle structure K :

[0073] ,

[0074] in, is the deflection at the surface of the structure, represents the partial derivative, , The surface positions of the structures are x Directional curvature and y Directional curvature, is the Laplace operator.

[0075] Step 1-2, calculate the composite curvature K along x and y The partial derivative in the direction is defined as the resultant curvatureK along x and y The generalized shear strain per unit length in the direction:

[0076] , ,

[0077] in, For along x The generalized shear strain per unit length in the direction, For along y The generalized shear strain per unit length in the direction.

[0078] Step 2: Figure 2 As shown, a fiber optic strain sensing array for a nacelle structure based on an orthogonal fiber optic strain rosette is constructed;

[0079] The synthetic curvature sensing array of the nacelle structure based on orthogonal fiber strain rosettes adopts a rectangular layout, with the six units in the middle of the reinforced surface of the nacelle structure as the monitoring area, and the measuring points are evenly arranged around the edge of the monitoring area. Each measuring point is equipped with an axial / tangential mode fiber Bragg grating strain rosette to obtain the axial and tangential strains at the measuring point position.

[0080] Step 3: The generalized shear strain of the nacelle structure is calculated by combining the projection data of different angles generated between the measuring points with the Radon inverse transform;

[0081] Step 3-1, based on the surface strain of the tank structure ε and curvature The relationship between the synthetic curvature K of the measuring point of the nacelle structure and the strain sensed by the measuring point is ε The relationship can be expressed as:

[0082] ;

[0083] Where, t is half the thickness of the tank structure plate, Indicates Measurement points Directional strain, Indicates Measurement points Directional strain, The direction is along the axial direction of the tank. The direction is tangent to the measuring point.

[0084] Step 3-2: define the straight line between any two measuring points a and b on the nacelle structure as a virtual scanning ray , the output signal of measuring point a is the composite curvature K1, and the output signal of measuring point b is the composite curvature K2. Then the two measuring points are along the virtual scanning ray The output signal difference ΔK can be expressed as: ΔK=K2-K1.

[0085] Step 3-3, based on the idea of ​​Radon transform principle, select the generalized shear strain per unit length , is the measured value, and the output signal of the measuring point is the synthetic curvature K. Then the relationship between the measured value and the output signal of the measuring point is as follows:

[0086] ,

[0087] ,

[0088] Since K is calculated from the actual sensor measurement data, and then based on the projection data in different directions, Radon The inverse transformation is x , y Generalized shear strain in the direction , .

[0089] Step 4: Derivation of the actual strain of the nacelle structure based on Kirchhoff theory;

[0090] Step 4-1, obtain the x , y Generalized shear strain in the direction , Along x, y Directional integration to obtain the synthetic curvature field of the nacelle structure for:

[0091] ,

[0092] .

[0093] Step 4-2, on this basis, synthesize the curvature field of the nacelle structure Integrating and combining the boundary conditions, we can get the deflection of the nacelle. w Based on the deflection of the tank w , combined with Kirchhoff theory to calculate the x , y Directional strain and xy Shear strain in plane as follows:

[0094] ,

[0095] In the formula, For along x Directional strain, For along y Directional strain, represents the shear strain in the xy plane.

[0096] Step 4-3: Since the strains on the inner and outer surfaces of the nacelle structure are symmetrically distributed along the neutral plane, the strain components on the inner and outer surfaces are theoretically equal. and bending strain It can be expressed as:

[0097] ,

[0098] ,

[0099] in, The outer surface of the tank to be tested is along Directional strain, The outer surface of the tank to be tested is along Directional strain, It represents the shear strain in the xy plane on the outer surface of the tank to be measured; The inner surface of the tank to be tested is along Directional strain, The inner surface of the tank to be tested is along Directional strain, It represents the shear strain in the xy plane of the inner surface of the tank to be measured;

[0100] The strain vector calculated based on the inverse radon transform in the monitoring area of ​​the nacelle structure is as follows:

[0101] .

[0102] Step 5: According to the actual strain model, solve the theoretical strain of the four-node unit tank structure; select the four-node inverse shell unit to discretize the tank structure.

[0103] According to the finite element theory, the displacement expression of any point in the four-node unit is:

[0104] ,

[0105] ,

[0106] Where u is the displacement in the x-direction of the four-node element, v is the displacement in the y-direction of the four-node element, is the displacement along the z direction in the four-node unit, θx is the rotation angle along the x axis in the four-node unit, θy is the rotation angle along the y axis of any point in the four-node unit, ui is the displacement of the ith unit node of the four-node unit along the x direction, vi is the displacement of the ith unit node of the four-node unit along the y direction, is the rotation angle of the ith unit node of the four-node unit along the x-axis, is the rotation angle of the ith unit node of the four-node unit along the y-axis, is the rotation angle of the ith unit node of the four-node unit along the z axis, N i , L i 、M i is the interpolation function of the i-th element node in a four-node shell element.

[0107] The theoretical strain component of any point in the four-node element calculated based on the displacement shape function is and the unit node displacement vector u e The functional relationship between them is as follows:

[0108] ,

[0109] in, is the tensile and compressive strain partial derivative matrix, is the bending strain partial derivative matrix, and Z is the distance between the outer surface of the nacelle structure and the neutral layer of the structure.

[0110] From the relationship between the unit node displacement and the unit node strain, the relationship between the strain of any point in the four-node shell element and the strain of the four unit nodes in the element is as follows:

[0111] ,

[0112] , ,

[0113] Among them, ε x is the strain along the x direction in the four-node element, ε y is the strain along the y direction in the four-node unit, Kx is the bending strain along the x axis in the four-node unit, Ky is the bending strain along the y axis in the four-node unit, ε xi is the strain in the ith unit node of the four-node unit along the x direction, ε yi is the strain in the ith unit node of the four-node unit along the y direction, Kxi is the bending strain in the ith unit node of the four-node unit along the x axis, Kyi is the bending strain in the ith unit node of the four-node unit along the y axis, γ xy is the shear strain in the xy plane of the four-node element, Kxy is the generalized bending strain in the xy plane of the four-node element, γ xyi is the shear strain in the XY plane of the ith unit node of the four-node unit, and Kxyi is the generalized bending strain in the xy plane of the ith unit node of the four-node unit.

[0114] The theoretical strain component of any point in the four-node element calculated based on the strain-deformation function is and the element node strain vector ε Node The functional relationship between them is as follows:

[0115] ,

[0116] in, is the tensile and compressive strain function matrix of the unit node, is the bending stress deformation function matrix of the unit node.

[0117] Step 6: Construct theoretical strains based on displacement shape function calculations , Theoretical strain calculated based on strain deformation function With the actual strain error function, the displacement response information and strain response information of the nacelle structure are solved;

[0118] Tank structure displacement response information: The strain calculated based on the inverse radon transform is and the theoretical strain components calculated using the four-node element based on the displacement shape function , the error function between the theoretical value and the actual value is obtained as:

[0119] ,

[0120] For each four-node element in the partition, when the error function When the minimum value is taken, it can be considered that the model at this time can best reflect the deformation of the structure. Therefore, when the error function takes the minimum value, there is:

[0121] ,

[0122] The results of simplification and arrangement are:

[0123] ,

[0124] is the pseudo-stiffness matrix of the four-node element, is the load matrix of the four-node unit, which is only related to the real-time strain value of the structure. The node displacement vector of the four-node unit can be obtained by solving , and then Substituting back into step 5, we can get the reconstructed displacement of any point in the unit, and reconstruct the displacement response in the monitoring area of ​​the nacelle structure. , to realize the deformation inversion of the nacelle structure, such as Figure 3 As shown, Figure 3 (a) and (b) are schematic diagrams of the comparison between the inversion and measurement of the deformation field of the nacelle structure under different nacelle structure deformation conditions.

[0125] Tank structure strain response information: The strain calculated based on the inverse radon transform is and the theoretical strain components calculated using the four-node element based on the strain-deformation function , the error function between the theoretical value and the actual value is obtained as:

[0126] ,

[0127] The error function Strain vectors for element nodes By finding the partial derivative and minimizing the function value of the error function, the structural strain pseudo-stiffness equation can be obtained as follows:

[0128] ,

[0129] in, is the structural strain pseudo-stiffness matrix, is the structural strain pseudo load matrix, expressed as follows:

[0130] ,

[0131] By assembling the strain pseudo-stiffness equation of each four-node shell element into the strain pseudo-stiffness total equation of the overall structure, the unit node strain vector of each unit can be solved. According to step 5, the strain information of any point in the nacelle structure can be obtained, and the strain response in the monitoring area of ​​the nacelle structure can be reconstructed. .

[0132] Step 7: Establish the relationship between the load and displacement / strain response of the nacelle structure and solve the load of the nacelle structure.

[0133] Step 7-1, discretize the nacelle structure and establish the relationship between the system excitation and the structural displacement response and strain response as follows:

[0134] ,

[0135] ,

[0136] in, is the system strain frequency response function, is the system displacement frequency response function, is the strain mode function, is the displacement mode function, is the r-th order stiffness of the system, is the r-th order modal mass of the system; The intrinsic parameters of the system when it is externally excited.

[0137] Step 7-2, from the strain mode function and displacement mode function The derivative relationship of , the relationship between the system strain frequency response function and the system displacement frequency response function can be obtained as follows:

[0138] .

[0139] Step 7-3: The strain response obtained based on the inverse finite element inversion , displacement response Substituting into step 7-1, we can obtain the external loads based on the strain response: , External loads based on displacement response .

[0140] Step 7-4, based on the least squares method, construct and The error function is:

[0141] ,

[0142] The error function Strain vectors for element nodes Find the partial derivative and minimize the function value of the error function, and you can get the displacement vibration function equation of the nacelle structure: ,Will Substituting into step 7-1, the external excitation load of the nacelle structure can be obtained, and the inversion of the external load of the nacelle can be realized, such as Figure 4 As shown, Figure 4 (a) and (b) are schematic diagrams of the comparison between the inversion and actual measurement of the dynamic load of the nacelle structure under different nacelle structure deformation conditions.

Claims

1. A method for inversion of nacelle structure deformation, characterized in that: The following steps are involved: (1) The axial strain and tangential strain at the measuring point are obtained by arranging the strain rosette at the measuring point in the monitoring area of ​​the tank to be measured; (2) Based on the relationship between the surface strain and the composite curvature of the tank structure, the composite curvature of the measuring point of the tank to be measured is calculated by using the obtained axial strain and tangential strain; based on the composite curvature of the measuring point, the generalized shear strain at the measuring point is obtained based on the Radon transform; (3) According to the generalized shear strain at the measuring point, based on the Kirchhoff theory, the actual strain of the monitoring area of ​​the tank to be measured is obtained; (4) The nacelle to be measured is discretized based on the finite element method, and the theoretical strain of any point in the four-node unit calculated based on the displacement shape function is obtained according to the finite element theory. The relationship between the displacement vector of the unit node and the displacement vector of the unit node; (5) Construct theoretical strain calculation based on displacement shape function The error function between the actual strain obtained in step (3) and the theoretical strain based on the displacement shape function is The relationship between the displacement vector of the unit node and the displacement vector of the unit node is calculated, and the displacement vector of the unit node when the function value of the error function is the smallest is calculated. The reconstructed displacement of any point in the unit is obtained through the displacement vector of the unit node, so as to reconstruct the displacement response in the monitoring area of ​​the nacelle to be measured and realize the inversion of the deformation of the nacelle structure; The relationship between the synthetic curvature of the measuring point of the nacelle to be measured and the axial strain and tangential strain of the measuring point is expressed as follows: ； in, represents the composite curvature, It represents half of the thickness of the tank wall to be measured. Indicates Measurement points Directional strain, Indicates Measurement points Directional strain, The direction is along the axial direction of the tank. The direction is the tangent direction of the measuring point; Based on Radon transform, the relationship between the generalized shear strain and the composite curvature at the measuring point is expressed as: ， ， in, It represents the composite curvature change between any two measuring points. For along The generalized shear strain per unit length in the direction, For along The generalized shear strain per unit length in the direction, is the proportionality coefficient; The specific steps of step (3) are: (3.1) will be along Generalized shear strain per unit length in the direction And along Generalized shear strain per unit length in the direction Along direction, Integrate the direction to obtain the synthetic curvature field of the tank to be tested : ， ， in, is the Laplace operator; (3.2) The synthetic curvature field of the tank to be tested is Integrate and combine boundary conditions to obtain the deflection of the tank to be measured w , based on Kirchhoff theory, respectively calculate along , Directional strain and Shear strain of a plane : ， in, For along Directional strain, For along Directional strain, represents the shear strain in the xy plane, represents partial derivative; (3.3) Since the strains on the inner and outer surfaces of the tank structure are symmetrically distributed along the neutral plane, the strain components on the inner and outer surfaces are equal in value. The tensile and compressive strains of the neutral surface strain are and bending strain It is expressed as: ， ， in, The outer surface of the tank to be tested is along Directional strain, The outer surface of the tank to be tested is along Directional strain, It represents the shear strain in the xy plane on the outer surface of the tank to be measured; The inner surface of the tank to be tested is along Directional strain, The inner surface of the tank to be tested is along Directional strain, It represents the shear strain in the xy plane of the inner surface of the tank to be measured; (3.4) Based on the Radon transform, the actual strain in the monitoring area is calculated as: ， in, is the actual strain in the monitoring area.

2. The method for inversion of nacelle structure deformation according to claim 1 is characterized in that: The theoretical strain at any point in the four-node element calculated based on the displacement shape function is and the element node displacement vector The relationship function between them is: ， in, is the tensile and compressive strain partial derivative matrix, is the bending strain partial derivative matrix, and Z is the distance between the outer surface of the nacelle structure and the neutral layer of the structure.

3. The method for inversion of nacelle structure deformation according to claim 2 is characterized in that: In step (5), the theoretical strain is constructed based on the displacement shape function calculation. The error function between the actual strain and the ， When the error function takes the minimum value, we have: ， Simplifying, we get: , in, is the pseudo-stiffness matrix of the four-node element, is the load matrix for a four-node element, ε is the surface strain of the nacelle structure.

4. A method for inversion of tank loads, characterized in that: The following steps are involved: (1) The axial strain and tangential strain at the measuring point are obtained by arranging the strain rosette at the measuring point in the monitoring area of ​​the tank to be measured; (2) Based on the relationship between the surface strain and the composite curvature of the tank structure, the composite curvature of the measuring point of the tank to be measured is calculated by using the obtained axial strain and tangential strain; based on the composite curvature of the measuring point, the generalized shear strain at the measuring point is obtained based on the Radon transform; (3) According to the generalized shear strain at the measuring point, based on the Kirchhoff theory, the actual strain of the monitoring area of ​​the tank to be measured is obtained; (4) The nacelle to be measured is discretized based on the finite element method, and the theoretical strain of any point in the four-node unit calculated based on the displacement shape function is obtained according to the finite element theory. The relationship between the displacement vector of the element node and the theoretical strain at any point in the four-node element calculated based on the strain deformation function The relationship between the strain vector of the element node and the strain vector of the element node; (5) Construct theoretical strains based on displacement shape function calculations , Theoretical strain calculated based on strain deformation function The error function between the actual strain and the measured strain is used to calculate the displacement vector and strain vector of the unit node when the function value of the error function is the smallest, and the displacement response and strain response in the monitoring area of ​​the tank to be measured are obtained; (6) Discretize the tank to be tested, establish the relationship between the load of the tank to be tested and the displacement response and strain response, obtain the external load based on the strain response and the external load based on the displacement response, construct the error function between the external load based on the strain response and the external load based on the displacement response, and obtain the external excitation load of the tank structure when the function value of the error function is the minimum; The relationship between the synthetic curvature of the measuring point of the nacelle to be measured and the axial strain and tangential strain of the measuring point is expressed as follows: ； in, represents the composite curvature, It represents half of the thickness of the tank wall to be measured. Indicates Measurement points Directional strain, Indicates Measurement points Directional strain, The direction is along the axial direction of the tank. The direction is the tangent direction of the measuring point; Based on Radon transform, the relationship between the generalized shear strain and the composite curvature at the measuring point is expressed as: ， ， in, It represents the composite curvature change between any two measuring points. For along The generalized shear strain per unit length in the direction, For along The generalized shear strain per unit length in the direction, is the proportionality coefficient; The specific steps of step (3) are: (3.1) will be along Generalized shear strain per unit length in the direction And along Generalized shear strain per unit length in the direction Along direction, Integrate the direction to obtain the synthetic curvature field of the tank to be tested : ， ， in, is the Laplace operator; (3.2) The synthetic curvature field of the tank to be tested is Integrate and combine boundary conditions to obtain the deflection of the tank to be measured w , based on Kirchhoff theory, respectively calculate along , Directional strain and Shear strain of a plane : ， in, For along Directional strain, For along Directional strain, represents the shear strain in the xy plane, represents partial derivative; (3.3) Since the strains on the inner and outer surfaces of the tank structure are symmetrically distributed along the neutral plane, the strain components on the inner and outer surfaces are equal in value. The tensile and compressive strains of the neutral surface strain are and bending strain It is expressed as: ， ， in, The outer surface of the tank to be tested is along Directional strain, The outer surface of the tank to be tested is along Directional strain, It represents the shear strain in the xy plane on the outer surface of the tank to be measured; The inner surface of the tank to be tested is along Directional strain, The inner surface of the tank to be tested is along Directional strain, It represents the shear strain in the xy plane of the inner surface of the tank to be measured; (3.4) Based on the Radon transform, the actual strain in the monitoring area is calculated as: ， in, To monitor the actual strain in the area; The relationship between the load on the nacelle to be measured and the displacement response and strain response is: ， ， in, is the system strain frequency response function, is the system displacement frequency response function, is the strain mode function, is the displacement mode function, is the r-th order stiffness of the system, is the r-th order modal mass of the system; is the intrinsic parameter of the system when it is externally excited, is the external load based on the strain response, is the external load based on the displacement response; Construct external loads based on strain response based on the least squares method and external loads based on displacement response The error function between: ， The error function is converted to the displacement mode function Find the partial derivative and minimize the function value of the error function, and you can get the displacement vibration function equation of the nacelle structure: According to the relationship between the measured tank load and the displacement response and strain response, the external excitation load of the tank structure is obtained, and the inversion of the external load of the tank is realized.

5. The method for inversion of tank loads according to claim 4, characterized in that: The theoretical strain at any point in the four-node element calculated based on the strain deformation function is and the element node strain vector The relationship function between them is: ， in, is the tensile and compressive strain function matrix of the unit node, is the bending strain function matrix of the unit node, and Z is the distance between the outer surface of the nacelle structure and the neutral layer of the structure.

6. The method for inversion of tank loads according to claim 5, characterized in that: Constructing theoretical strain calculation based on strain-deformation function The error function between the actual strain and the ， By minimizing the error function, the structural strain pseudo-stiffness equation is obtained as follows: ， in, is the structural strain pseudo-stiffness matrix, is the structural strain pseudo load matrix.

Images