A method, equipment, medium, and terminal for controlling static deformation measurement errors.

Abstract

This invention belongs to the field of structural static testing technology, and discloses a method, equipment, medium, and terminal for controlling static deformation measurement errors. Under a given load mode, the static deformation of a structure is approximately expressed as a linear combination of a few contributing modes. The influence of structural parameter changes on static deformation is reflected in the changes in the contributing mode combination coefficients. The problem of monitoring structural static deformation is transformed into the problem of measuring the contributing mode combination coefficients. The measurement error of the contributing mode combination coefficients becomes the decisive factor in the static deformation measurement error. Based on the characteristic that the larger the contributing mode combination coefficient, the smaller the upper bound of the estimation error tends to be, the optimal test load corresponding to each contributing mode of the load to be measured is found sequentially. Then, the static test is carried out on the structure using the optimal test load. Finally, the static deformation of the load to be measured is calculated by indirect measurement, thereby realizing the control of the measurement error of the static deformation of the load to be measured.

Description

Technical Field

[0001] This invention belongs to the field of structural static testing technology, and particularly relates to a method, equipment, medium and terminal for controlling static deformation measurement error. Background Technology

[0002] This invention is applicable to all types of engineering structures, but uses cable-stayed tension structures as an example for background technology explanation. Cable-stayed tension structures are lightweight and efficient structural systems, often used in large-span buildings such as stadiums. Unlike traditional rigid structures, cable-stayed tension structures rely on the geometric stiffness provided by prestress to maintain structural stability. Due to various factors such as environmental corrosion, support deviation, manufacturing errors, and stress relaxation, in-service cable-stayed tension structures may experience component damage or prestress deviation leading to stiffness degradation. To detect changes in structural stiffness in a timely manner, dynamic testing methods are generally used for health monitoring of cable-stayed tension structures. However, dynamic testing methods face challenges such as difficulty in excitation and poor accuracy in identifying dense modalities. Since static response can directly reflect structural stiffness and has high testing accuracy, static testing of cable-stayed tension structures has gradually attracted attention. Due to constraints such as location obstruction and engineering cost, the number of measurement points in static testing is generally far less than the number of degrees of freedom of the structure. To increase testing information, it is necessary to extend the measured deformation of a few measurement points to all degrees of freedom. Existing static deformation extension methods include geometric interpolation, Guyan's method, and contribution modal method. Geometric interpolation methods use linear or spline curve interpolation to fit static deformation at non-measuring points, which is not suitable for complex cable-stayed tension structures. The Guyan method calculates the transformation matrix by dividing the ideal structural stiffness sub-matrix, thus achieving the extension of static deformation. Utilizing the property that static deformation can be approximately linearly expressed by a few identical modes (i.e., contributing modes), the contributing mode method cleverly transforms the static deformation extension problem into the measurement problem of contributing mode combination coefficients. Both the Guyan and contributing mode methods are applicable to all structural types, but both suffer from significant extension errors at non-measuring points (i.e., measurement errors). In practice, before subsequent monitoring work such as deflection verification, model correction, damage identification, and prestress identification, it is necessary to distinguish the extension accuracy of each non-measuring point to prevent the introduction of excessively large errors in the extended static deformation. Therefore, it is necessary to analyze the error mechanism of static deformation extension and control the measurement error of static deformation as much as possible to provide more high-quality test data for subsequent monitoring work.

[0003] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: structural health monitoring based on static testing requires a large amount of high-quality test data; the measurement error of the existing static deformation measurement (or extended) method is relatively large and needs to be actively controlled; at present, there are no reported methods for actively controlling static deformation measurement errors at home and abroad. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method, device, medium, and terminal for controlling static deformation measurement errors.

[0005] This invention is implemented as follows: a method for controlling static deformation measurement error, the method comprising:

[0006] Under a given load mode, the static deformation of a structure is expressed as a linear combination of a few contributing modes. The influence of structural parameter changes on static deformation is reflected in the changes in the contributing mode combination coefficients. The problem of monitoring the static deformation of a structure is transformed into the problem of measuring the contributing mode combination coefficients. The measurement error of the contributing mode combination coefficients becomes the decisive factor in the measurement error of static deformation. Based on the characteristic that the larger the contributing mode combination coefficient, the smaller the upper bound of the estimation error, the optimal test load corresponding to each contributing mode of the load to be measured is found in turn. Then, the static test is carried out on the structure using the optimal test load. Finally, the static deformation of the load to be measured is calculated by indirect measurement, thereby controlling the measurement error of the static deformation of the load to be measured.

[0007] Furthermore, the specific implementation steps of the static deformation measurement error control method are as follows:

[0008] Step 1: Set the load to be measured, p D Based on the finite element model of the structural design, the set of contributing modes E is calculated. pD ;

[0009] Step two, targeting E sequentially pD Find the optimal test load p for the contributing mode j. Tj This makes the load to be measured p D and test load p Tj It contains a common contributing mode j, and p Tj The parameter γ under action j maximum;

[0010] Step 3, sequentially place p Tj The corresponding contribution mode combination coefficient α was applied to the structure and measured. pTj ;

[0011] Step four: Calculate p sequentially according to the indirect measurement formula. D Combination coefficients α of each contributing mode of the action pDj Finally, the contribution modes of each order are linearly combined to obtain p. D Static deformation with controlled error under action.

[0012] Furthermore, the specific process of the contribution mode method for static deformation propagation is as follows:

[0013] When the number of degrees of freedom of a cable-stayed tension structure is n and the number of members is b; let the tangential stiffness of the structure be K. T (n×n), the standard eigenvalue decomposition is:

[0014] (K T -η j I)θ j =0 (1)

[0015] In the formula: I(n×n) is a unit diagonal matrix, considered as a virtual mass matrix; η j and θ j (n×1) represent the eigenvalues ​​and standard eigenvectors of the j-th order feature space, respectively; And η1≤η j ≤…≤η n (j = 1, 2, ..., n);

[0016] K is further expressed in the form of spectral decomposition. T ,have

[0017]

[0018] The linear equilibrium equation for the cable tension structure is:

[0019] K T d=p (3)

[0020] In the formula: p(n×1) is the load vector; d(n×1) is the deformation vector; θ j (j=1,2,…,n) form a set of orthogonal basis vectors in the degree-of-freedom space, which can be expressed by the transformation d as:

[0021]

[0022] In the formula: α r For θ r The combination coefficients are used to measure θ. r Contribution to d; Substitute equations (2) and (4) into equation (3), and multiply both sides of equation (3) by the left side. After sorting, we get:

[0023]

[0024] In the formula: η j and α j These represent the generalized load, generalized stiffness, and generalized deformation corresponding to mode j, respectively; a relative coefficient is defined to measure the contribution of mode j to deformation d:

[0025]

[0026] In the formula: α maxThe maximum value of the absolute values ​​of all generalized transformations; || represents taking the absolute value; set the threshold γ. u , will γ j Greater than γ u If the mode is defined as the contributing mode, then the deformation d is approximately expressed as:

[0027]

[0028] In the formula: E p It is a set of contributing modes; Equation (7) is derived from linear analysis based on an ideal structure; in fact, considering the elastic-plastic and geometrical nonlinearity of the material, the static deformation of the actual structure containing arbitrary parameter deviations is expressed as E p A linear combination of contributing modes, i.e.

[0029]

[0030] In the formula: For θ s Equivalent combination coefficient; θ s This is the s-th mode shape obtained based on an ideal structure; The static deformation of the actual structure under the same load p is given. According to equations (7) and (8), the contribution modes of the ideal structure and the actual structure remain unchanged under the same load. The parameter deviations contained in the actual structure are reflected in the changes in the contribution mode combination coefficients. The problem of measuring the static deformation of the actual structure is transformed into the problem of measuring the contribution mode combination coefficients.

[0031] Furthermore, the specific process of achieving unbiased estimation of the contributing mode combination coefficients by optimizing the measurement point locations is as follows:

[0032] Define the Fisher information matrix in The matrix representing the mode shapes corresponding to the contributing modes; maximizing the determinant of the Fisher information matrix to minimize the variance between the estimated and true values ​​of the contributing mode combination coefficients; the contribution of the degree of freedom k to the determinant of the Fisher information matrix is ​​expressed by the following formula:

[0033]

[0034] In the formula: for The k-th row; the superscript -1 indicates the inverse calculation; the degrees of freedom that contribute the most are selected according to the iterative strategy.

[0035] Furthermore, the specific process of selecting the degrees of freedom that contribute the most according to the iterative strategy is as follows:

[0036] The first step is to calculate S based on the retained degrees of freedom. kAnd Λ, retain all degrees of freedom before the iteration begins;

[0037] The second step is to eliminate the degrees of freedom that contribute the least;

[0038] The third step is to stop iterating when the number of retained degrees of freedom reaches the expected value; otherwise, return to the first step to continue iterating. To ensure the accuracy of the unbiased estimation of the contributing mode combination coefficients, the number of retained measurement points should not be less than the number of contributing modes.

[0039] After the above iterative process is completed, the optimal measurement point location will be obtained; according to equation (8), the unbiased estimate of the contribution mode combination coefficient based on the measured deformation of a few measurement points is obtained. for:

[0040]

[0041] In the formula: To retain only the contribution mode matrix of the degree of freedom where the measurement point is located; This refers to the measured deformation of the actual structure at the measuring point location; based on the established... The expanded static deformation is obtained as follows:

[0042]

[0043] The method described above for achieving static deformation propagation is called the contribution mode method.

[0044] Furthermore, the specific process for the indirect measurement of the static deformation is as follows:

[0045] When a specific load p D and test load p T Projected onto the ideal mode θ s The generalized loads are respectively and The corresponding modal sets are E pD and E pT When any modes in two mode sets are far apart, and E pD and E pT It contains a common ideal mode s; the test load p T Applying this to the structure, the combination coefficients of the ideal mode s are calculated according to equation (11). Then, the specific load p is indirectly obtained. D The combination coefficients of the corresponding mode s under the action;

[0046]

[0047] When multiple test loads p that satisfy the above conditions are found Ts (s∈E pDThe test load is applied to the structure sequentially to conduct static tests, indirectly measuring the specific load p. D Complete static deformation under action.

[0048] Furthermore, the specific process for actively controlling the static deformation propagation error is as follows:

[0049] Under a given load, the contributing modal combination coefficient α j The larger the upper bound of the estimation error ε, the greater the error. uj The smaller the value, the better; based on α j and ε uj The corresponding relationship is used to actively control the expansion error of static deformation under specific loads by employing indirect measurement of static deformation; sequentially targeting E pD Find the optimal test load p for the contributing mode j. Tj This makes a specific load p D and test load p Tj It contains a common contributing mode j, and p Tj The parameter γ under action j Maximum; sequentially set p Tj The corresponding contribution mode combination coefficients were applied to the structure and measured. Calculate p sequentially according to equation (12). D Combination coefficients of each contributing mode of the action

[0050] For a certain order contribution mode j (j∈E) pD Finding the optimal test load p Tj The mathematical model is as follows:

[0051]

[0052] In the formula: G is a vector composed of the load location and magnitude; L k and X k These represent the node number and load size of the k-th loading point, respectively; h is the number of loading points; f() is the fitness function; L max X min and X max These are the upper limit of the node number, the lower limit of the load value, and the upper limit of the load value, respectively; an optimization algorithm is used to find the optimal test load.

[0053] Another object of the present invention is to provide a computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the following steps:

[0054] Step 1: Set the load to be measured, p D Based on the finite element model of the structural design, the set of contributing modes E is calculated.pD ;

[0055] Step two, targeting E sequentially pD Find the optimal test load p for the contributing mode j. Tj This makes the load to be measured p D and test load p Tj It contains a common contributing mode j, and p Tj The parameter γ under action j maximum;

[0056] Step 3, sequentially place p Tj The corresponding contribution mode combination coefficient α was applied to the structure and measured. pTj ;

[0057] Step four: Calculate p sequentially according to the indirect measurement formula. D Combination coefficients α of each contributing mode of the action pDj Finally, the contribution modes of each order are linearly combined to obtain p. D Static deformation with controlled error under action.

[0058] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the following steps:

[0059] Step 1: Set the load to be measured, p D Based on the finite element model of the structural design, the set of contributing modes E is calculated. pD ;

[0060] Step two, targeting E sequentially pD Find the optimal test load p for the contributing mode j. Tj This makes the load to be measured p D and test load p Tj It contains a common contributing mode j, and p Tj The parameter γ under action j maximum;

[0061] Step 3, sequentially place p Tj The corresponding contribution mode combination coefficient α was applied to the structure and measured. pTj ;

[0062] Step four: Calculate p sequentially according to the indirect measurement formula. D Combination coefficients α of each contributing mode of the action pDj Finally, the contribution modes of each order are linearly combined to obtain p. D Static deformation with controlled error under action.

[0063] Another objective of this invention is to provide an information data processing terminal for implementing the method for controlling the static deformation measurement error.

[0064] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions protected by this invention are analyzed from the following aspects:

[0065] First, addressing the technical problems existing in the prior art and the difficulty in solving them, this paper closely analyzes, in conjunction with the technical solution to be protected by this invention and the results and data obtained during the research and development process, how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about by solving these problems. The specific description is as follows:

[0066] This invention demonstrates that the measurement error of the contributing modal combination coefficients is a decisive factor in the static deformation measurement error; furthermore, under the same load, the larger the contributing modal combination coefficients, the smaller the upper bound of the estimation error tends to be. Therefore, for each contributing mode of the load to be measured, the optimal test load corresponding to each mode is sequentially found, and then the static test is performed on the structure using the optimal test load. Finally, an indirect measurement method is used to calculate the static deformation of the load to be measured, thereby achieving control of the measurement error of the static deformation of the load to be measured. A case study of a Geiger cable dome verifies the effectiveness and feasibility of the static deformation measurement error control method.

[0067] Second, considering the technical solution as a whole or from a product perspective, the technical effects and advantages of the technical solution to be protected by this invention are specifically described as follows:

[0068] The method of this invention can significantly reduce the upper bound of measurement error for each degree of freedom. In particular, the upper bound of measurement error for the vertical degree of freedom is much smaller than that for the two horizontal directions, and much smaller than the upper bound of measured displacement error. Therefore, the static deformation of the vertical degree of freedom under a specific load measured using the method of this invention has a much smaller measurement error than the contribution modal method and the Guyan method. The control method, equipment, medium, and terminal involved in this invention can directly provide a large amount of high-precision static test data for subsequent monitoring work such as model correction, damage identification, prestress identification, and safety assessment of various engineering structures.

[0069] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0070] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0071] Currently, a large number of engineering structures are in service, creating a significant demand for static testing, but they are plagued by excessive static testing errors. At present, there are no methods, equipment, media, or terminals available for controlling static deformation measurement errors, either domestically or internationally. This invention can be applied to every engineering structure requiring static testing, thus possessing enormous expected benefits and commercial value.

[0072] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0073] It fills the gap in active control technology for static deformation measurement errors both domestically and internationally.

[0074] (3) Whether the technical solution of the present invention solves the technical problem that people have long wanted to solve but have never been able to solve successfully:

[0075] This solves the technical problem of excessive static deformation measurement error faced by current methods (including the contribution modal method and the Guyan method).

[0076] (4) Does the technical solution of the present invention overcome technical bias?

[0077] It overcomes the technical bias that static deformation measurement errors cannot be actively controlled. Attached Figure Description

[0078] Figure 1 This is a flowchart of the method for controlling static deformation measurement error provided in an embodiment of the present invention;

[0079] Figure 2 This is a schematic diagram of the Geiger cable dome provided in an embodiment of the present invention;

[0080] In the figures: Figure a, 3D view; Figure b, sectional view; Figure c, upper chord node numbering diagram; Figure d, lower chord and rigid ring beam node numbering diagram;

[0081] Figure 3 This is a graph showing the static deformation measurement error curves for each degree of freedom in working condition 1 provided in this embodiment of the invention.

[0082] In the figures: Figure a, measurement error of x-axis degree of freedom; Figure b, measurement error of y-axis degree of freedom; Figure c, measurement error of z-axis degree of freedom;

[0083] Figure 4 This is a graph showing the static deformation measurement error curves in each direction for working condition 2 provided in this embodiment of the invention.

[0084] In the figures: Figure a, measurement error of x-axis degree of freedom; Figure b, measurement error of y-axis degree of freedom; Figure c, measurement error of z-axis degree of freedom;

[0085] Figure 5This is a graph showing the static deformation measurement error curves in each direction for working condition 3 provided in this embodiment of the invention.

[0086] In the figures: Figure a, measurement error of x-axis degree of freedom; Figure b, measurement error of y-axis degree of freedom; Figure c, measurement error of z-axis degree of freedom. Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0088] I. Explanation and Description of Embodiments. To enable those skilled in the art to fully understand how the present invention is specifically implemented, this section provides an explanation and description of the embodiments that expand upon the technical solutions of the claims.

[0089] like Figure 1 As shown, the method for controlling static deformation measurement error provided in this embodiment of the invention includes:

[0090] S101: Set the load to be measured p D Based on the finite element model of the structural design, the set of contributing modes E is calculated. pD .

[0091] S102: Sequentially targeting E pD Find the optimal test load p for the contributing mode j. Tj This makes the load to be measured p D and test load p Tj It contains a common contributing mode j, and p Tj The parameter γ under action j maximum.

[0092] S103: sequentially p Tj The corresponding contribution mode combination coefficient α was applied to the structure and measured. pTj .

[0093] S104: Based on the indirect measurement formula, calculate p sequentially. D Combination coefficients α of each contributing mode of the action pDj Finally, the contribution modes of each order are linearly combined to obtain p. D Static deformation with controlled error under action.

[0094] The specific process of the contribution mode method for static deformation propagation provided in this embodiment of the invention is as follows:

[0095] Assume the cable-stayed tension structure has n degrees of freedom and b members. Let the tangential stiffness of the structure be K. T (n×n), its standard eigenvalue decomposition is:

[0096] (K T -η j I)θ j =0 (1)

[0097] In the formula: I(n×n) is a unit diagonal matrix, which can be regarded as a virtual mass matrix; η j and θ j (n×1) represent the eigenvalues ​​and standard eigenvectors (i.e., virtual modes) of the j-th order characteristic space (i.e., virtual modes); And η1≤η j ≤…≤η n (j = 1, 2, ..., n).

[0098] K is further expressed in the form of spectral decomposition. T ,have

[0099]

[0100] The linear equilibrium equation for the cable tension structure is:

[0101] K T d=p (3)

[0102] In the formula: p(n×1) is the load vector; d(n×1) is the deformation vector. It is not difficult to see that θ j (j = 1, 2, ..., n) actually form a set of orthogonal basis vectors in the degree-of-freedom space. Therefore, the transformation d can be expressed as:

[0103]

[0104] In the formula: α r For θ r The combination coefficients of θ can be used to measure θ r Contribution to d. Substitute equations (2) and (4) into equation (3), and multiply both sides of equation (3) by the left side. After sorting, we get:

[0105]

[0106] In the formula: η j and α j These represent the generalized load, generalized stiffness, and generalized deformation corresponding to (virtual) mode j. To measure the contribution of mode j to deformation d, a relative coefficient is defined:

[0107]

[0108] In the formula: α maxThe maximum absolute value of all generalized transformations; | represents taking the absolute value. Set a threshold γ. u (For example, 0.01), γ j Greater than γ u If the mode is defined as the contributing mode, then the deformation d can be approximately expressed as:

[0109]

[0110] In the formula: E p Let E be the set of contributing modes. It is worth noting that Equation (7) is derived from the linear analysis of an ideal structure. In fact, even considering the elastic-plastic and geometrical nonlinearity of materials, the static deformation of a real structure with arbitrary parameter deviations can still be approximately expressed as E. p A linear combination of contributing modes, i.e.

[0111]

[0112] In the formula: For θ s Equivalent combination coefficient; θ s This is the s-th (virtual) mode shape obtained based on an ideal structure. Let p be the static deformation of the actual structure under the same load p. According to equations (7) and (8), the contribution modes of the ideal structure and the actual structure remain unchanged under the same load. Therefore, the parameter deviations contained in the actual structure are mainly reflected in the changes in the contribution mode combination coefficients. Thus, the problem of measuring the static deformation of the actual structure is cleverly transformed into the problem of measuring the contribution mode combination coefficients.

[0113] The specific process of achieving unbiased estimation of the contributing mode combination coefficients by optimizing the measurement point location provided in this embodiment of the invention is as follows:

[0114] Define the Fisher information matrix in The contributing mode matrix is ​​the matrix of the mode shapes corresponding to the contributing modes. Maximizing the determinant of the Fisher information matrix minimizes the variance between the estimated and true values ​​of the contributing mode combination coefficients. The contribution of the degree of freedom k to the determinant of the Fisher information matrix is ​​expressed by the following formula:

[0115]

[0116] In the formula: for The k-th row; the superscript -1 indicates inversion calculation. The following iterative strategy is used to select the degrees of freedom that contribute the most. First, calculate S based on the retained degrees of freedom. kAnd Λ; retain all degrees of freedom before the iteration begins. Second, remove the degree of freedom with the smallest contribution. Third, if the number of retained degrees of freedom reaches the expected value, stop the iteration; otherwise, return to the first step and continue the iteration. In order to ensure the accuracy of the unbiased estimation of the contributing mode combination coefficients, the number of retained measurement points should not be less than the number of contributing modes. After the above iteration process is completed, the optimal measurement point position will be obtained. According to equation (8), the unbiased estimate of the contributing mode combination coefficients based on the measured deformation of a few measurement points is obtained. for:

[0117]

[0118] In the formula: To retain only the contribution mode matrix of the degree of freedom where the measurement point is located; This represents the measured deformation of the actual structure at the measuring point. Based on the established... The expanded static deformation can then be obtained as follows:

[0119]

[0120] The method described above for achieving static deformation propagation is called the contribution mode method.

[0121] The specific process for indirect measurement of static deformation provided in this embodiment of the invention is as follows:

[0122] Assuming a specific load p D and test load p T They project onto the ideal mode θ s The generalized loads are respectively and The corresponding modal sets are E pD and E pT Furthermore, it is assumed that any modes in these two modality sets are far apart, and E pD and E pT It contains a common ideal mode s. The test load p will be... T Applying this to the structure, the combination coefficients of the ideal mode s are calculated according to equation (11). Then, the specific load p is indirectly obtained. D The combination coefficients of the corresponding mode s under the action;

[0123]

[0124] If multiple test loads p that satisfy the above conditions can be found Ts (s∈E pD Therefore, by applying these test loads sequentially to the structure and conducting static tests, the specific load p can be indirectly measured. D Complete static deformation under action.

[0125] The specific process for actively controlling static deformation propagation error provided in this embodiment of the invention is as follows:

[0126] Under a given load, the contributing modal combination coefficient α j The larger the upper bound ε of its estimation error, the greater the upper bound. uj The smaller the value, the better. Based on α j and ε uj This correspondence can be addressed by using indirect static deformation measurement to actively control the expansion error of static deformation under specific loads (i.e., measurement error at non-measuring points). The basic idea is to sequentially target E... pD Find the optimal test load p for the contributing mode j. Tj This makes a specific load p D and test load p Tj It contains a common contributing mode j, and p Tj The parameter γ under action j Maximum; sequentially set p Tj The corresponding contribution mode combination coefficients were applied to the structure and measured. Calculate p sequentially according to equation (12). D Combination coefficients of each contributing mode of the action

[0127] For a certain order contribution mode j (j∈E) pD Finding the optimal test load p Tj The mathematical model is as follows:

[0128]

[0129] In the formula: G is a vector composed of the load location and magnitude; L k and X k These represent the node number and load size of the k-th loading point, respectively; h is the number of loading points; f() is the fitness function; L max X min and X max These represent the upper limit of the node number, the lower limit of the load value, and the upper limit of the load value, respectively. This invention can employ existing mature optimization algorithms (such as the Jaya algorithm, particle swarm optimization, and genetic algorithms) to find the optimal test load.

[0130] II. Application Examples. To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides application examples of the technical solution of the claims on specific products or related technologies.

[0131] The embodiments of the present invention can be applied to all types of engineering structures, including but not limited to cable domes, cable nets, cable truss tension canopies, space frame structures, tensioned beams, cable-stayed domes, reticulated shell structures, transmission towers, multi-story and high-rise buildings, steel structure corridors, bridge structures, etc.

[0132] III. Evidence of the Relevant Effects of the Embodiments. The embodiments of the present invention have achieved some positive effects during research and development or use, and indeed possess significant advantages compared to existing technologies. The following description, in conjunction with data, charts, and other materials from the experimental process, illustrates these advantages.

[0133] A detailed description will be given using a Geiger cable dome with a span of 100m as an example.

[0134] 1. Geiger cable dome model parameters

[0135] A 100m span axis-symmetric Geiger cable dome ( Figure 2 Taking (a) as an example, we will conduct a numerical analysis. The equilibrium configuration of the cable dome, considering both structural self-weight and prestressing, is as follows: Figure 2 As shown in (b) (only the vertical section is shown; the numbers in parentheses are component numbers, and the units for length and elevation are meters). The numbering of the upper and lower chord nodes and support nodes are as follows: Figure 2 (c) Figure 2 As shown in (d), the cable dome has 62 nodes, with 12 of them serving as support points on the perimeter. The material density of both the cables and rods is 7850 kg / m³. 3 The elastic moduli are 1.70×10⁻⁶. 11 N / m 2 and 2.06×10 11 N / m 2 The cross-sectional area and axial force of each component of the cable dome are listed in Table 1.

[0136] Table 1. Cross-sectional area and axial force of components in the Geiger cable dome

[0137]

[0138] 2. Static Deformation Propagation Error Analysis

[0139] Consider three specific load cases: (1) Case 1 (p D1 (2) Working condition 2 (p) D2 ), apply a 100kN plumb load to each of nodes 20, 22, 40, 42, 60, and 62 (a total of 6); (3) Working condition 3 (p D3 A 100kN plumb bob load is applied to each of the 12 nodes: 10, 12, 20, 22, 30, 32, 40, 42, 50, 52, 60, and 62. The threshold value γ is taken as... u The contribution modes for the three working conditions are E = 0.01. pD1 ={19,38,39,45,46,51}、EpD2 ={19,44,49,51} and E pD3 ={19,51}. Let's assume that the optimal number of measurement points for all three working conditions is 7. Then their optimal positions are {1z,4z,35z,44z,48z,57z,58z}, {1z,45z,47z,48z,55z,57z,58z}, and {1z,2z,30z,50z,52z,60z,62z}, where iz represents the z-direction degree of freedom of node i.

[0140] The actual structure includes the equivalent component length error limit e uk The equivalent component length errors are provided in Table 1, based on national standards and engineering experience. It is assumed that the errors are independent variables and follow a normal distribution with a mean of zero. According to the "3σ criterion," the standard deviation of the equivalent component length errors is σ. k =e uk / 3. By introducing a set of randomly generated equivalent component length errors into the ideal structure, a simulated actual structure containing random prestress deviations can be obtained.

[0141] The Monte Carlo method is used to calculate the upper bound ε of the estimation error of the modal combination coefficients of the ideal and actual structures under specific load conditions. u The noise levels χ = 0% and χ = 5% were considered separately. For any specific load condition, 5000 samples were generated for each condition (the actual structure and deformation noise were randomly generated). The estimation error of the contributing modal combination coefficients in each sample was calculated according to Equation (11), and the maximum absolute values ​​of the upper and lower boundaries of these estimation errors (i.e., the upper bound of the estimation error) were extracted and listed in Tables 2 and 3. As can be seen from Tables 2 and 3, for the same load condition, the relative coefficient γ j The larger the value, the greater the upper bound of the estimation error ε. uj The smaller the value (e.g., modes 19 and 46 in operating condition 1, and mode 19 in operating conditions 2 and 3).

[0142] Table 2 Upper bounds of estimation errors for contribution mode combination coefficients under different conditions (Condition 1, unit: %)

[0143]

[0144] Table 3 Upper bounds of estimation errors for contribution mode combination coefficients under different conditions (conditions 2 and 3, unit: %)

[0145]

[0146] 3. Static deformation propagation error control

[0147] There are a total of 8 contribution modes involved in the three specific loads, namely modes j = 19, 38, 39, 44, 45, 46, 49, and 51. The optimal test load p is then sought for each of these modes. Tj The Jaya algorithm is used for optimization, with a population size of 20 and a maximum number of iterations of 50; it is limited to vertical loading, and X... min =-1, X max =1; the optimization results are shown in Table 4. As can be seen from Table 4, p Tj The required number of loading points varies from 1 to 10, but some p Tj (j = 44, 46, and 49) require the application of a negative upward load at 2 or 3 nodes. This upward load can be applied by rotating the pulleys. When p Tj According to the threshold γ u When the number of contributing modes calculated with a value of 0.01 exceeds nine, only the top nine modes with the largest contributions are selected as contributing modes, and the number of measurement points is uniformly set to nine to save on the number of measurement points. The γ value of the contributing modes under investigation... j The values ​​range from 0.281 to 1.000. Each p... Tj All loads are magnified 1000 times to ensure that the maximum absolute value of the load at each loading point is 1 kN. For each p... Tj 5000 sets of actual structural samples were generated, and considering that the deformation at the measuring points was affected by 5% random noise, E was calculated. pTj After estimating the combination coefficients of each contribution mode, statistical analysis was performed, and the results based on p were examined. Tj The upper bound of the estimation error of the contributing mode j. It is not difficult to see that, based on p Tj The upper bound of the estimation error for the contribution mode j ranges from 6.0982 to 20.4132, which is generally lower than that based on p. D The upper bound of the estimation error for each contribution mode is much smaller.

[0148] Table 4 Optimization Results of Test Loads

[0149]

[0150]

[0151] 5000 sets of actual structures were randomly generated, and three specific loads were applied to each structure. Static deformation propagation was then performed using the contribution mode method and the Guyan method. Simultaneously, the optimal test loads p shown in Table 4 were sequentially applied to each structure. Tj (j=19,38,39,44,45,46,49,51) were used to indirectly measure static deformation under three specific loads. 5% random noise contamination was considered for the measured deformations at all measuring points. After statistical analysis, the upper bounds of the expanded errors for each degree of freedom corresponding to different methods under the three specific load conditions were plotted on [the graph]. Figures 3-5 It is not difficult to observe that the curve corresponding to the method of this invention is always below the curves corresponding to the contribution mode method and the Guyan method, indicating that the method of this invention is beneficial for reducing the expansion error of each degree of freedom. For the horizontal direction (x and y directions), the method of this invention has many degrees of freedom with expansion error upper limits within 15% (the upper limit of measurement error corresponding to 5% noise level is also 15%), but also many degrees of freedom have very large expansion error upper limits, even as high as 2678.5% (the 26th x-direction degree of freedom in working condition 1). For the vertical (z-direction) degree of freedom, the expansion error upper limits of the method of this invention are significantly smaller than those of the contribution mode method and the Guyan method. Considering only the vertical degree of freedom, the minimum value (ε) of the expansion error upper limits of the three methods is... u,min ), maximum value (ε) u,max ) and average value (ε) u,mean The results are listed in Table 5. As can be seen from Table 5, the three indicators of the method of this invention are all significantly smaller than those of the other two methods. Furthermore, the upper limit of the extended error for the vertical degree of freedom of the method of this invention under the three working conditions is between 0.3695% and 7.8447%, which is much smaller than the upper limit of the measured deformation error of 15%.

[0152] As can be seen, the method of this invention can significantly reduce the upper bound of the measurement error (i.e., the extended error) for each degree of freedom. In particular, the upper bound of the measurement error for the vertical degree of freedom is much smaller than that for the two horizontal directions, and much smaller than that for the measured displacement error. Therefore, the static deformation of the vertical degree of freedom under a specific load measured using the method of this invention has a much smaller measurement error than the contribution modal method and the Guyan method, which is beneficial for the smooth progress of subsequent monitoring work such as model correction, damage identification, prestress identification, and safety assessment.

[0153] Table 5 shows the upper bound of the expanded error for the three methods when only the vertical degree of freedom is considered (unit: %).

[0154]

[0155] It should be noted that embodiments of the present invention can be implemented using hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented using hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or using software executed by various types of processors, or using a combination of the above-described hardware circuitry and software, such as firmware.

[0156] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method of controlling static deformation measurement error, characterized by, The static deformation measurement error control method comprises the following steps: Under a given load mode, the static deformation of a structure is expressed as a linear combination of a few contribution modes, and the influence of structural parameter changes on the static deformation is reflected in the changes of the combination coefficients of the contribution modes, so that the monitoring problem of the static deformation of the structure is converted into the measurement problem of the combination coefficients of the contribution modes, and the measurement error of the combination coefficients of the contribution modes becomes a decisive factor of the static deformation measurement error; based on the feature that the greater the contribution mode combination coefficient is, the smaller the upper limit of the estimation error tends to be, the optimal test load corresponding to each order contribution mode of the to-be-measured load is sequentially found, the optimal test load is used to implement the static test on the structure, and finally, the indirect measurement is used to calculate the static deformation of the to-be-measured load, so that the static deformation measurement error of the to-be-measured load is controlled. The static deformation measurement error control method specifically comprises the following steps: Step one, set the load p to be measured D , according to the structure design finite element model, calculate the contribution modal set E pD ; Step two, find the optimal test load p pD for each contribution mode j in E Tj such that the test load p D and the load p Tj under which the parameter γ Tj is maximized contain the common contribution mode j j . Step three, p Tj The structure is subjected to the application and the corresponding contribution modal combination coefficients a pTj ; Step four, according to the indirect measurement formula, sequentially calculate considering p D The contribution modal combination coefficient α of each order of action pDj , finally, the linear combination of each order of contribution modal is obtained p D The static deformation of the error controlled under the action For a certain order contribution modal j (Fj) The mathematical model for finding the optimal test load p Tj is: （1） Where: G is the vector composed of the load position and size; and k and h represent the node number and load size of the kth loading point, respectively; h is the number of loading points; is the fitness function; , and are the upper limit of the node number, the lower limit of the load value, and the upper limit of the load value, respectively; an optimization algorithm is used to find the optimal test load.

2. A computer device, comprising: The computer device comprises a memory and a processor, the memory stores a computer program, and the computer program is executed by the processor to enable the processor to execute the steps of the static deformation measurement error control method in claim 1. 3.A computer readable storage medium storing a computer program, the computer program being executed by a processor to enable the processor to execute the steps of the static deformation measurement error control method in claim 1.

4. An information data processing terminal, characterized by The information data processing terminal is used to implement the static deformation measurement error control method in claim 1.

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