Shear frame structure damage detection method based on dynamic photogrammetry and improved substructure method

Abstract

The application discloses a shearing type frame structure damage detection method based on dynamic photogrammetry and improved substructure method, which comprises the following steps: firstly, regarding the shearing type frame structure as an equivalent spring damping mass model and dividing the shearing type frame structure into multiple substructures; secondly, acquiring displacement and load parameters, constructing input-output relationship between the substructures and establishing an expression; thirdly, based on the input-output relationship between the substructures, modeling by using an ARMAX model and solving relevant coefficients in the expression; and finally, selecting the relevant coefficients and constructing a damage index. The application has the following remarkable effects: the dynamic photogrammetry method is used to obtain the relative displacement response of each substructure, thereby avoiding a large amount of sensor installation and wiring work; secondly, the relative displacement test precision based on the dynamic photogrammetry is higher and the adverse influence of camera vibration can be eliminated. The relative displacement is used as a damage diagnosis data source to construct a substructure-based damage diagnosis method, thereby improving the damage positioning capability.

Description

TECHNICAL FIELD

[0001] The present application relates to the safety maintenance of building structure, in particular to the damage identification of building structure. BACKGROUND

[0002] The safety detection of building is of great significance. For shear type frame structure, the conventional detection methods are:

[0003] ①, the damage index is constructed by using the structural inherent characteristics (such as frequency response function, transfer function, modal strain energy, modal parameters, etc.) to detect the damage of civil structure. Among them, the structural inherent characteristics can be calculated by using experimental modal analysis method and operational modal analysis method.

[0004] ②, the damage index is directly established according to the vibration response of the structure, which avoids the identification of the structural inherent characteristics, and has the methods based on time-frequency analysis and time-domain analysis. Among them, the method based on time-frequency analysis extracts the damage index from the time-frequency spectrum of dynamic response; the method based on time-domain analysis extracts the damage index from the residual or model coefficient of time series model. However, due to the complexity of the connecting structure, it is difficult to establish an accurate structural finite element model. In addition, a large number of sensors need to be installed on the structure at the same time, especially for large civil structures, the economic cost is high and the installation operation is difficult.

[0005] ③, the method based on substructure, which divides a civil structure into multiple substructures according to the corresponding standard, and directly calculates and constructs the damage index using the vibration response of each substructure. However, the traditional vibration response measurement method repeatedly measures each substructure, which still needs a large amount of sensor installation and wiring work. Moreover, it is difficult or dangerous to install sensors and wiring in some parts of the structure. SUMMARY

[0006] The present application provides a new substructure algorithm to overcome the shortcomings of the existing substructure detection method, which divides the shear type frame structure into multiple substructures, then studies the substructure separately, and uses the ARMAX model to fit the correlation coefficient to build the damage index, so as to determine whether damage occurs. At the same time, in order to avoid the large amount of sensor installation and wiring work in the traditional vibration response measurement process, the dynamic photogrammetry method is used to obtain the relative displacement response of each substructure. The main technical scheme is as follows:

[0007] A shear type frame structure damage detection method based on dynamic photogrammetry and improved substructure method, the key is to perform the following steps:

[0008] Step one, the shear type frame structure is regarded as an equivalent spring damping mass model, and the model is divided into multiple substructures;

[0009] Step two, obtaining displacement and load parameters, constructing input-output relationship between each substructure, and establishing expression;

[0010] Step three, based on the input-output relationship between each substructure, modeling by using ARMAX model, and solving relevant coefficients in expression;

[0011] Step four, selecting relevant coefficients, and constructing damage index. DETAILED DESCRIPTION

[0012] The application will be further described below in combination with embodiments and drawings.

[0013] A shear type frame structure damage detection method based on dynamic photogrammetry and improved substructure method is performed according to the following steps:

[0014] Step one, regarding the shear type frame structure as an equivalent spring damping mass model, and dividing the model into multiple substructures;

[0015] Specifically, the substructure division method is as follows: regarding the shear type frame structure as an equivalent spring damping mass model, and dividing the model from bottom to top into n mass blocks, and thereby obtaining n substructures;

[0016] Wherein:

[0017] The first substructure is composed of the first and second mass blocks;

[0018] The second substructure is composed of the first, second and third mass blocks;

[0019] The i-th substructure is composed of the i-2-th, i-1-th, i-th and i+1-th mass blocks;

[0020] The n-th substructure is composed of the n-2-th, n-1-th and n-th mass blocks;

[0021] i = 3, 4, 5, …, n-1;

[0022] The dynamic equation is constructed, as shown in formula (1):

[0023]

[0024] Wherein:

[0025] [M] is a mass matrix;

[0026] [C] is a damping matrix

[0027] [K] is a stiffness matrix;

[0028] {x(t)} is an output displacement vector;

[0029] is an output velocity vector;

[0030] is an output acceleration vector;

[0031] {f(t)} is an input vector.

[0032] Step two, obtain displacement and load parameters, construct the input-output relationship between each substructure, and establish the expression;

[0033] Specifically: the foundation of the building is regarded as the 0th substructure, and the dynamic equation is discretized and sampled, the sampling time interval is Δt, the sampling sequence number is p, p = 3, 4, 5, … g; g is the sequence number corresponding to the sampling end point;

[0034] Obtain the relative displacement of the jth substructure relative to the j-1th substructure at each sampling time, j = 1, 2, 3, …, n;

[0035] Construct the input-output relationship between the jth and j-1th substructures, j = 1, 2, 3, …, n, respectively as shown in equations (2), (3), (4), (5):

[0036] The foundation of the building is regarded as the 0th substructure, and the input-output relationship between the 1st substructure and the 0th substructure is constructed, as shown in equation (2):

[0037]

[0038] Wherein:

[0039] δ 1,0,p is the relative displacement of the 1st mass block relative to the 0th mass block at the pth sampling time;

[0040] δ 1,0,p-1 is the relative displacement of the 1st mass block relative to the 0th mass block at the p-1th sampling time;

[0041] δ 1,0,p-2 is the relative displacement of the 1st mass block relative to the 0th mass block at the p-2th sampling time;

[0042] δ 2,1,p-1 is the relative displacement of the 2nd mass block relative to the 1st mass block at the p-1th sampling time;

[0043] δ 2,1,p-2 is the relative displacement of the 2nd mass block relative to the 1st mass block at the p-2th sampling time;

[0044] m 1,1 is the mass of the 1st mass block;

[0045] f 1,p-1 is the load of the first mass at the (p-1)th sampling moment;

[0046] D 11 , D 21 , E 11 , E 21 are the to-be-solved coefficients of each term;

[0047] The input-output relationship of the second substructure and the first substructure is constructed as formula (3):

[0048]

[0049] Wherein:

[0050] δ 2,1,p is the relative displacement of the second mass relative to the first mass at the pth sampling moment;

[0051] δ 2,1,p-1 is the relative displacement of the second mass relative to the first mass at the (p-1)th sampling moment;

[0052] δ 2,1,p-2 is the relative displacement of the second mass relative to the first mass at the (p-2)th sampling moment;

[0053] δ 3,2,p-1 is the relative displacement of the third mass relative to the second mass at the (p-1)th sampling moment;

[0054] δ 3,2,p-2 is the relative displacement of the third mass relative to the second mass at the (p-2)th sampling moment;

[0055] m 2,2 is the mass of the second mass;

[0056] f 2,p-1 is the load of the second mass at the (p-1)th sampling moment;

[0057] D 12 , D 22 , E 12 , E 22 , G 12 , G 22 are the to-be-solved coefficients of the corresponding term;

[0058] The input-output relationship of the ith substructure and the (i-1)th substructure is constructed as formula (4):

[0059]

[0060] Wherein:

[0061] δ i,i-1,p is the relative displacement of the ith mass block with respect to the (i-1)th mass block at the pth sampling time;

[0062] δ i,i-1,p-1 is the relative displacement of the ith mass block with respect to the (i-1)th mass block at the (p-1)th sampling time;

[0063] δ i,i-1,p-2 is the relative displacement of the ith mass block with respect to the (i-1)th mass block at the (p-2)th sampling time;

[0064] δ i-1,i-2,p-1 is the relative displacement of the (i-1)th mass block with respect to the (i-2)th mass block at the (p-1)th sampling time;

[0065] δ i-1,i-2,p-2 is the relative displacement of the (i-1)th mass block with respect to the (i-2)th mass block at the (p-2)th sampling time;

[0066] δ i+1,i,p-1 is the relative displacement of the (i+1)th mass block with respect to the ith mass block at the (p-1)th sampling time;

[0067] δ i+1,i,p-2 is the relative displacement of the (i+1)th mass block with respect to the ith mass block at the (p-2)th sampling time;

[0068] f i,p-1 is the load of the ith mass block at the (p-1)th sampling time;

[0069] f i-1,p-1 is the load of the (i-1)th mass block at the (p-1)th sampling time;

[0070] m i,i , m i-1,i-1 are the masses of the ith and (i-1)th mass blocks, respectively;

[0071] D 1i , D 2i , E 1i , E 2i , G 1i , G 2i are the to-be-solved coefficients of the corresponding items;

[0072] The input-output relationship of the nth substructure and the (n-1)th substructure is constructed as formula (5):

[0073]

[0074] wherein:

[0075] δ n,n-1,pis the relative displacement of the nth mass block with respect to the (n-1)th mass block at the pth sampling time;

[0076] is the relative displacement of the nth mass block with respect to the (n-1)th mass block at the pth sampling time; n,n-1,p-1 is the relative displacement of the nth mass block with respect to the (n-1)th mass block at the pth sampling time;

[0077] is the relative displacement of the nth mass block with respect to the (n-1)th mass block at the pth sampling time; n,n-1,p-2 is the relative displacement of the nth mass block with respect to the (n-1)th mass block at the pth sampling time;

[0078] is the relative displacement of the nth mass block with respect to the (n-1)th mass block at the pth sampling time; n-1,n-2,p-1 is the relative displacement of the (n-1)th mass block with respect to the (n-2)th mass block at the pth sampling time;

[0079] is the relative displacement of the (n-1)th mass block with respect to the (n-2)th mass block at the pth sampling time; n-1,n-2,p-2 is the relative displacement of the (n-1)th mass block with respect to the (n-2)th mass block at the pth sampling time;

[0080] is the mass of the (n-1)th mass block; n-1,n-1 is the mass of the nth mass block; n,n

[0081] is the load of the nth mass block at the pth sampling time; n,p-1 is the load of the nth mass block at the pth sampling time;

[0082] is the load of the (n-1)th mass block at the pth sampling time; n-1,p-1 is the load of the (n-1)th mass block at the pth sampling time;

[0083] is the relative displacement of the (n-1)th mass block with respect to the (n-2)th mass block at the pth sampling time; 1n is the relative displacement of the (n-1)th mass block with respect to the (n-2)th mass block at the pth sampling time; 2n is the relative displacement of the (n-1)th mass block with respect to the (n-2)th mass block at the pth sampling time; 1n is the relative displacement of the (n-1)th mass block with respect to the (n-2)th mass block at the pth sampling time; 2n are to-be-solved coefficients of each term.

[0084] Step three, based on the input-output relationship between each substructure, an ARMAX model is used for modeling, and the related coefficients in the expression are solved,

[0085] Specifically, based on the obtained relative displacement and load, an ARMAX model is used for mathematical modeling of the input-output relationship of each substructure, and the to-be-solved coefficients a1, a2 are fitted and solved;

[0086] a1=D 1j , a2=D 2j ; j=1, 2, 3, …, n.

[0087] The general expression of the ARMAX model is formula (6):

[0088]

[0089] wherein:

[0090] ​ is an output term of the ARMAX model;

[0091] is a coefficient corresponding to each output term;

[0092] is an input term of the ARMAX model;

[0093] is a coefficient corresponding to each input term;

[0094] is an error term of the ARMAX model;

[0095] is a coefficient corresponding to each error term;

[0096] n a , n b , n c are all orders corresponding to the ARMAX model;

[0097] The input-output relationship of each substructure is modeled by applying the above, and the process of fitting and solving the to-be-solved coefficients a1, a2 is as follows:

[0098] For formula (2) and formula (6)

[0099]

[0100] The following equivalent replacement is performed:

[0101]

[0102] For formula (3) and formula (6):

[0103]

[0104]

[0105] The following equivalent replacement is performed:

[0106] For formula (4) and formula (6):

[0107] The following equivalent replacement is performed:

[0108]

[0109] For formula (5) and formula (6):

[0110]

[0111] The following equivalent replacements are made:

[0112]

[0113] Step four, selecting a correlation coefficient to construct a damage index.

[0114] Specifically, the damage index MD(ff) between each substructure is constructed based on the to-be-sought coefficients a1 and a2 obtained through the above steps, as shown in equation (6):

[0115]

[0116] Wherein, ff={a1, a2};

[0117] is the mean matrix of the coefficient vector ff in the healthy state;

[0118] is the covariance matrix of the coefficient vector ff in the healthy state.

[0119] The dynamic photography method in step two is as follows: first, a standard chessboard is placed on each mass block of each substructure, the standard chessboard contains a plurality of internal corner points, the distance between each internal corner point is known, a photography camera is arranged, the photography camera adopts positive measurement, and the relative displacement of the jth substructure with respect to the j-1th substructure is dynamically obtained. According to the pixel point distance and the actual distance between each internal corner point, a scaling coefficient a can be obtained between the pixel point distance and the actual distance, the camera simultaneously tests the photos of all standard chessboards on each substructure, and then the relative displacement of each mass block is extracted;

[0120] Taking the ith substructure as an example, the camera simultaneously measures the standard chessboard photos of the i-2th mass block, the i-1th mass block, the ith mass block and the i+1th mass block. When the relative displacement of the ith mass block and the i-1th mass block needs to be extracted, the following steps are adopted:

[0121] ①, for each frame of photo, taking the 1st internal corner point of the standard chessboard on the i-1th mass block as a reference, the relative pixel distance of the 1st internal corner point of the standard chessboard on the ith mass block is extracted, the true relative distance value is obtained by using the scaling coefficient a, and then the trend item is eliminated to obtain the relative displacement value between the two points;

[0122] ②, taking the 2nd to bth points of the standard chessboard on the i-1th mass block as references in turn, b is the number of internal corner points on the standard chessboard; repeat step ① to extract the relative displacement values of the 2nd to bth internal corner points of the standard chessboard on the ith mass block;

[0123] ③、Take the average of the extracted b relative displacement values to obtain the final relative displacement value.

[0124] Beneficial effects: by adopting the technical scheme of the present application, the dynamic photogrammetry method is used to obtain the relative displacement response of each substructure, which can avoid a large amount of sensor installation and wiring work; secondly, the relative displacement test based on dynamic photogrammetry has higher accuracy and can eliminate the adverse effects of camera vibration. By using relative displacement as the data source for damage diagnosis, a substructure-based damage diagnosis method is constructed, which can improve the damage positioning capability.

[0125] Finally, it should be noted that the above description is only for the preferred embodiments of the present application, and those skilled in the art can make various similar expressions under the inspiration of the present application without deviating from the purpose of the present application and the claims, and such changes fall within the protection scope of the present application.

Claims

1. A method for detecting damage in a shear type frame structure based on dynamic photogrammetry and an improved substructure method, characterized by The steps are as follows: Step one, the shear type frame structure is regarded as an equivalent spring damping mass model, and the model is divided into multiple substructures; Step two, arrange sensors, obtain load parameters; obtain displacement parameters based on dynamic photography method; build input-output relationship between substructures, and establish expression; Step three, based on the input-output relationship between the substructures, the ARMAX model is used for modeling, and the related coefficients in the expression are solved, Step four, select the correlation coefficient and construct the damage index.

2. The shear type frame structure damage detection method based on dynamic photogrammetry and improved substructure method according to claim 1, wherein: in step one, the substructure division method is: the shear type frame structure is regarded as an equivalent spring damping mass model, and the model is divided into n mass blocks from bottom to top, and n substructures are obtained; wherein: the first substructure is composed of the first and second mass blocks; the second substructure is composed of the first, second and third mass blocks; the i-th substructure is composed of the i-2th, i-1th, i-th and i+1th mass blocks; the n-th substructure is composed of the n-2th, n-1th and n-th mass blocks; i=3,4,5,…,n-1; the dynamic equation is constructed, as formula (1): wherein: [M] is the mass matrix; [C] is the damping matrix [K] is the stiffness matrix; {x(t)} is the output displacement vector; is the output velocity vector; to output an acceleration vector; {f(t)} is the input vector.

3. The shear type frame structure damage detection method based on dynamic photogrammetry and improved substructure method according to claim 2, wherein: in step two, the foundation of the building is regarded as the 0th substructure, and the dynamic equation is discretized and sampled, the sampling time interval is Δt, and the sampling sequence number is p, p=3,4,5,…g; g is the sequence number corresponding to the sampling end point; the relative displacement of the jth substructure with respect to the j-1th substructure is obtained at each sampling time, j=1,2,3,…,n; the input-output relationship between the jth and j-1th substructures is constructed, j=1,2,3,…,n, as shown in formulas (2), (3), (4) and (5) respectively: the foundation of the building is regarded as the 0th substructure, and the input-output relationship between the 1st substructure and the 0th substructure is constructed, as formula (2): wherein: delta 1,0,p delta_p is the relative displacement of the first mass with respect to the zeroth mass at the pth sampling instant; delta 1,0,p-1 delta_p-1 is the relative displacement of the first mass with respect to the zeroth mass at the (p-1)th sampling instant; delta 1,0,p-2 delta_p2 is the relative displacement of the first mass with respect to the zeroth mass at the p-2th sampling instant; delta 2,1,p-1 delta_p-1 is the relative displacement of the second mass with respect to the first mass at the (p-1)th sampling instant; delta 2,1,p-2 delta_p2 is the relative displacement of the second mass with respect to the first mass at the (p-2)th sampling instant; m 1,1 m is the mass of the first mass; f 1,p-1 is the load of the first mass at the (p-1)th sampling time; D 11 、D 21 、E 11 、E 21 are the coefficients to be determined for each term; the input-output relationship between the 2nd substructure and the 1st substructure is constructed as formula (3): wherein: delta 2,1,p delta_p is the relative displacement of the second mass with respect to the first mass at the pth sampling instant; delta 2,1,p-1 delta_p-1 is the relative displacement of the second mass with respect to the first mass at the (p-1)th sampling instant; delta 2,1,p-2 delta_p2 is the relative displacement of the second mass with respect to the first mass at the (p-2)th sampling instant; delta 3,2,p-1 delta_p-1 is the relative displacement of the third mass with respect to the second mass at the (p-1)th sampling instant; delta 3,2,p-2 delta_p2 is the relative displacement of the third mass with respect to the second mass at the (p-2)th sampling instant; m 2,2 m is the mass of the 2nd mass; f 2,p-1 is the load of the 2nd mass at the (p-1)th sampling instant; D 12 、D 22 、E 12 、E 22 、G 12 、G 22 are the to-be-solved coefficients of the corresponding items; the input-output relationship between the i-th substructure and the i-1th substructure is constructed as formula (4): wherein: delta i,i-1,p is the relative displacement of the ith mass with respect to the (i-1)th mass at the pth sampling instant; delta i,i-1,p-1 is the relative displacement of the i-th mass with respect to the i-1-th mass at the (p-1)-th sampling instant; delta i,i-1,p-2 is the relative displacement of the i-th mass with respect to the i-1-th mass at the (p-2)-th sampling instant; delta i-1,i-2,p-1 is the relative displacement of the i-1th mass with respect to the i-2th mass at the p-1th sampling instant; delta i-1,i-2,p-2 is the relative displacement of the i-1th mass with respect to the i-2th mass at the p-2th sampling instant; delta i+1,i,p-1 is the relative displacement of the (i+1)th mass with respect to the ith mass at the (p-1)th sampling instant; delta i+1,i,p-2 is the relative displacement of the (i+1)th mass with respect to the ith mass at the (p-2)th sampling instant; f i,p-1 Qi-1is the load of the ith mass at the (p-1)th sampling instant; f i-1,p-1 Qi-1is the load of the i-1th mass at the p-1th sampling time; m o,i , m i-1,i-1 mi, mi-1are the masses of the i-th and i-1-th mass, respectively. D 1i 、D 2i 、E 1i 、E 2i 、G 1i 、G 2i are the to-be-solved coefficients of each corresponding item; the input-output relationship between the n-th substructure and the n-1th substructure is constructed as formula (5): wherein: delta n,n-1,p delta_pn is the relative displacement of the nth mass with respect to the n-1th mass at the pth sampling instant; delta n,n-1,p-1 delta_p-1,n is the relative displacement of the nth mass with respect to the n-1th mass at the (p-1)th sampling instant; delta n,n-1,p-2 delta_p-2,n is the relative displacement of the n-th mass with respect to the n-1-th mass at the (p-2)-th sampling instant; delta n-1,n-2,p-1 is the relative displacement of the n-1th mass with respect to the n-2th mass at the p-1th sampling instant; delta n-1,n-2,p-2 is the relative displacement of the n-1th mass with respect to the n-2th mass at the p-2th sampling instant; m n-1,n-1 , m n,n are the masses of the (n-1)th, nth mass, respectively. f n,p-1 is the load of the nth mass at the (p-1)th sampling instant; f n-1,p-1 is the load of the nth-1 mass at the p-1 sampling time; D 1n , D 2n , E 1n , E 2n are the coefficients to be determined for each term.

4. The shear type frame structure damage detection method based on dynamic photogrammetry and improved substructure method according to claim 3, wherein: in step three, based on the obtained relative displacement and load, the ARMAX model is used for mathematical modeling of the input-output relationship of each substructure, and the to-be-solved coefficients a1 and a2 are fitted and solved. a1= D 1j , a2= D 2j ; j = 1, 2, 3,..., n.

5. The method according to claim 4, wherein the method is a method for detecting damage of a shear type frame structure based on dynamic photogrammetry and improved substructure method. In step four, the damage index MD(ff) between each substructure is constructed based on the coefficients a1 and a2, as shown in equation (6): Wherein, ff = {a1, a2}; is the mean matrix of the coefficient vectors ff in the healthy state; is the covariance matrix of the coefficient vector ff in the healthy state.

6. The method of claim 4 or 5, wherein the method is a method of damage detection of a shear type frame structure based on dynamic photogrammetry and an improved substructure method. In step two, a standard chessboard is placed on each mass of each substructure, and the standard chessboard contains a plurality of inner corner points. A photogrammetry camera is arranged, and the photogrammetry camera is used for positive measurement and dynamically obtains the relative displacement of the jth substructure relative to the (j-1)th substructure.

Images