CN113627047B - Method for quickly identifying post-earthquake structural damage based on flexibility change rate and pattern matching - Google Patents
Method for quickly identifying post-earthquake structural damage based on flexibility change rate and pattern matching Download PDFInfo
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Abstract
The invention discloses a method for quickly identifying post-earthquake structural damage based on flexibility change rate and pattern matching, which comprises the following steps of: establishing a finite element model of the structure, and carrying out modal analysis on various damage working conditions; calculating the flexibility change rate of the injury to form an injury mode library; carrying out modal identification on the structure dynamic response, and calculating a matching vector to form a test set; and (5) carrying out similarity measurement on the matching vectors in the test set and a pattern library in sequence, and judging the damage position and the damage degree according to the matching result. The method has the advantages of small calculation amount and high calculation speed; the influence of excitation can be eliminated, so that the established damage mode library is not influenced by external environmental factors; the damage position and the damage degree can be efficiently and quickly identified, and the defect that the damage degree cannot be quantified by the traditional method for identifying the structural damage based on the flexibility matrix is overcome. Therefore, the method is suitable for damage and safety evaluation of the structure after the earthquake, and has great significance for emergency rescue and emergency decision after the earthquake.
Description
Technical Field
The invention relates to the technical field of building structure safety performance evaluation, in particular to a method for quickly identifying post-earthquake structural damage based on flexibility change rate and mode matching.
Background
The occurrence of earthquake often causes huge casualties and economic losses, and the damage to the society is huge. After decades of development, three working systems with earthquake monitoring and forecasting, earthquake disaster prevention and earthquake emergency rescue as main contents are gradually formed in earthquake work in China. For earthquake emergency rescue, the speed of damage identification after earthquake is the primary consideration, and the purpose is not to pursue absolute accuracy, but to realize damage rapid identification and pre-evaluation within an acceptable range. The research of the rapid identification method of the structural damage after the earthquake provides scientific theoretical basis for emergency rescue and emergency decision after the earthquake, and has great significance for improving the emergency response capability of the government to the earthquake and the efficiency of emergency work after the earthquake and reducing casualties and losses caused by the earthquake disaster to the maximum extent. How to realize rapid damage identification is a main problem studied by emergency and rescue institute after earthquake.
At present, the research of adopting a pattern matching method in the field of structural damage detection is less, and the current research situation about the pattern matching method still has the following problems: (1) when the matching vector is related to the excitation factor, a pattern library cannot be established; (2) when the damage characteristic parameters in the time domain category are adopted, the calculated amount is very large; (3) when strain is used as a characteristic parameter, a large number of sensors are required. And the traditional method for identifying the structural damage based on the flexibility matrix can identify whether the damage exists or not, but can not quantify the damage degree.
Disclosure of Invention
The invention aims to overcome the defects existing when a mode matching method is applied to the field of structural damage detection, make up the defect that the damage degree cannot be quantified by the traditional damage detection method based on flexibility, provide a method for quickly identifying the structural damage after earthquake based on the flexibility change rate and mode matching, and realize quick identification of the damage after the earthquake of the structure.
The purpose of the invention can be achieved by adopting the following technical scheme:
a post-earthquake structural damage rapid identification method based on flexibility change rate and pattern matching comprises the following steps:
s1, establishing a finite element model of a structure for an identification object structure by using finite element software; all damage conditions in a damage mode library are formed by the damage conditions of the permutation and combination consisting of the damage positions and the damage degrees, and modal analysis is carried out on all the damage conditions to obtain modal vibration modes and natural frequencies of the identification object structure under various damage conditions;
s2, calculating the flexibility change rate of various damage working conditions, and establishing a damage mode library with damage positions and damage degree labels and using the flexibility change rate as a parameter, wherein the calculation process of the flexibility change rate is as follows:
wherein F is RouDegree matrix, f ij The physical meaning of (1) is the displacement generated at the measurement point at the position i when unit concentration force is applied to the measurement point at the position j, r is the modal order, omega r To identify the natural frequency of the r-th order of the object structure,
respectively representing the product of the r order modal shape value of the measurement point at the position i and the r order modal shape value of the measurement point at the position j, i =1,2, …, M, j =1,2, …, N;
calculating the flexibility matrix variation delta F of the lossless and damage working conditions, wherein the calculation formula is as follows:
ΔF＝F d -F u
in the formula, F u 、F d Flexibility matrixes of lossless and damaged working conditions are respectively;
calculating the change rate delta F of the compliance matrix through the diagonal elements of the compliance matrix, wherein the calculation formula is as follows:
wherein diag (·) is the diagonal element of the compliance matrix, f ii u 、f ii d The diagonal elements of the flexibility matrix of the nondestructive and damage working conditions are respectively expressed]' denotes the transpose of the row vector;
matching vectors for various lesions in a library of lesion patterns
The following were used:
wherein, δ F p Representing the flexibility change rate of the p damage working conditions in the damage mode library, wherein p =1,2, …, Q;
s3, mounting an acceleration sensor on the structure of the object to be identified, and measuring the acceleration response of the structure of the object to be identified;
s4, performing modal identification on the dynamic response of the measured identification object structure to obtain the r-th order actual measurement natural frequency omega of the identification object structure tr Harmonic mode phi t (r) ＝[φ t1 (r) φ t2 (r) … φ tj (r) … φ tN (r) ]', wherein phi tj (r) Measuring the real vibration mode value of the r order for the position j, wherein j =1,2, …, N;
s5, calculating the actually measured vibration mode and the inherent frequency according to the step S2 to obtain an actually measured flexibility matrix T of the structure of the recognition object:
wherein, ω is tr For identifying the natural frequency of the r-th order of the object structure, phi ti (r) 、φ tj (r) Expressing the product of the order of r modal vibration type value of the measurement point of the structure position i of the identified object and the order of r modal vibration type value of the measurement point of the position j, calculating the flexibility change rate vector to form a test matching vector set
Wherein, δ T k Representing the kth working condition to be tested in the test set, k =1,2, …, P;
s6, testing the matching vectors delta T in the matching vector set k Matching vectors delta F of various injuries in the injury mode library established in the step S2 in sequence p Carrying out similarity measurement;
and S7, determining the damage condition under the serial number in the damage mode library corresponding to the minimum value of the matching result of the similarity measurement as the damage of the actual measurement condition.
Further, in step S6, a euclidean distance method is used to measure the similarity, and a calculation formula is given as follows:
wherein, δ F p (a) The flexibility change rate vector of the a-th damage working condition in the damage mode library; delta T k (b) And concentrating the flexibility change rate vector of the b-th working condition to be tested for the test.
Further, in step S7, when two relatively close minimum values occur, it is determined that the two types of damage corresponding to the damage pattern library are both the damage of the actual measurement working condition.
Further, in step S4, a complex mode indication function CMIF is used to perform mode identification on the dynamic response of the measured identification object structure.
Compared with the prior art, the invention has the following advantages and effects:
1) The flexibility change rate is vector of dimension Nx 1 according to Euclidean distance algorithm formula
Therefore, the data matching calculation amount is small, the calculation speed is high, damage identification can be performed quickly, and the structural feature extraction process in the traditional identification method is avoided.
2) According to the formula of the flexibility change rate
Therefore, the flexibility change rate is only related to the modal information, and the modal information does not change along with the change of the external excitation and reflects the inherent attributes of the structure, so that the influence of eliminating the excitation can be realized by using the flexibility change rate as a matching vector, and the established damage mode library is only related to the inherent attributes of the structure and is not influenced by external environment factors;
3) The traditional method for identifying the structural damage based on the compliance matrix can identify whether the damage exists or not, but can not quantify the damage degree. The method provided by the invention combines the flexibility change rate with the mode matching, makes full use of the sensitivity of the flexibility change rate to the damage, and simultaneously, the mode matching method can quantify the damage degree, thereby making up the defects of the traditional method for identifying the structural damage based on the flexibility matrix.
Drawings
FIG. 1 is a flowchart illustrating the steps of a method for rapidly identifying post-earthquake structural damage based on flexibility change rate and pattern matching according to an embodiment of the present invention;
FIG. 2 is a diagram of a model of an experimental structure disclosed in an embodiment of the present invention;
fig. 3 is a comparison diagram of the first two orders of mode shape recognition results of the mode parameter recognition by using a complex mode indicating function CMIF in the embodiment of the present invention, where fig. 3 (a) is a diagram of the first order mode shape recognition results, and fig. 3 (b) is a diagram of the second order mode shape recognition results;
FIG. 4 is a diagram illustrating the results of matching lossless conditions in an embodiment of the present invention;
FIG. 5 is a graph illustrating the results of matched single loss operating conditions in an embodiment of the present invention;
FIG. 6 is a graph illustrating the results of the matched double loss condition in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
As shown in fig. 1, fig. 1 is a flowchart of steps of a damage fast identification method based on flexibility change rate and pattern matching disclosed in the embodiment of the present invention, where an experimental model in the embodiment is a four-layer centralized mass structure, a layer height is 0.2m, and a total height is 0.8m; the density is 7850kg/m ^3; a Poisson's ratio of 0.288; the elastic modulus is 210GPa; size of beam unit sectionThe width is 93mm; the thickness is 9.25mm; the mass of the one to four layers is 2.0444kg, 2.0449kg, 2.0538kg and 2.0445kg respectively. The damage is set according to the formula of the area moment of inertia I = bh 3 And K = EI, the structural stiffness is reduced by changing the value of b to achieve the desired damage level of the design, and the experimental structure and damage set are shown in fig. 2. The damage degree and the damage position form a damage mode library, and the damage mode library working condition formed by permutation and combination is shown in table 1, the damage working condition in the table respectively corresponds to one-layer to four-layer damage from left to right, for example, "20-20-0-0" indicates: one layer damaged by 20%, the second layer damaged by 20%, and so on.
TABLE 1 Damage Pattern library
| Serial number | Damage condition | Serial number | Damage condition | Serial number | Damage condition | Serial | Damage condition | |
| 1 | 0-0-0-0 | 21 | 20-0-0-40 | 41 | 0-40-20-0 | 61 | 0-60-60-0 | |
| 2 | 20-0-0-0 | 22 | 20-0-0-60 | 42 | 0-40-40-0 | 62 | 0-60-0-20 | |
| 3 | 40-0-0-0 | 23 | 0-20-20-0 | 43 | 0-40-60-0 | 63 | 0-60-0-40 | |
| 4 | 60-0-0-0 | 24 | 0-20-40-0 | 44 | 0-40-0-20 | 64 | 0-60-0-60 | |
| 5 | 0-20-0-0 | 25 | 0-20-60-0 | 45 | 0-40-0-40 | 65 | 0-0-60-20 | |
| 6 | 0-40-0-0 | 26 | 0-20-0-20 | 46 | 0-40-0-60 | 66 | 0-0-60-40 | |
| 7 | 0-60-0-0 | 27 | 0-20-0-40 | 47 | 0-0-40-20 | 67 | 0-0-60-60 | |
| 8 | 0-0-20-0 | 28 | 0-20-0-60 | 48 | 0-0-40-40 | 68 | 20-0-20-20 | |
| 9 | 0-0-40-0 | 29 | 0-0-20-20 | 49 | 0-0-40-60 | 69 | 40-40-0-40 | |
| 10 | 0-0-60-0 | 30 | 0-0-20-40 | 50 | 60-20-0-0 | 70 | 0-60-60-60 | |
| 11 | 0-0-0-20 | 31 | 0-0-20-60 | 51 | 60-40-0-0 | 71 | 20-0-40-60 | |
| 12 | 0-0-0-40 | 32 | 40-20-0-0 | 52 | 60-60-0-0 | 72 | 20-0-20-40 | |
| 13 | 0-0-0-60 | 33 | 40-40-0-0 | 53 | 60-0-20-0 | 73 | 20-0-40-40 | |
| 14 | 20-20-0-0 | 34 | 40-60-0-0 | 54 | 60-0-40-0 | |||
| 15 | 20-40-0-0 | 35 | 40-0-20-0 | 55 | 60-0-60-0 | |||
| 16 | 20-60-0-0 | 36 | 40-0-40-0 | 56 | 60-0-0-20 | |||
| 17 | 20-0-20-0 | 37 | 40-0-60-0 | 57 | 60-0-0-40 | |||
| 18 | 20-0-40-0 | 38 | 40-0-0-20 | 58 | 60-0-0-60 | |||
| 19 | 20-0-60-0 | 39 | 40-0-0-40 | 59 | 0-60-20-0 | |||
| 20 | 20-0-0-20 | 40 | 40-0-0-60 | 60 | 0-60-40-0 |
The specific implementation process is as follows:
s1, establishing a finite element model of a structure for an identified object structure by using finite element software; all damage conditions in a damage mode library are formed by the damage conditions of the permutation and combination consisting of the damage positions and the damage degrees, and modal analysis is carried out on all the damage conditions to obtain modal vibration modes and natural frequencies of the identification object structure under various damage conditions;
s2, calculating the flexibility change rate of various damage working conditions, and establishing a damage mode library with damage positions and damage degree labels and using the flexibility change rate as a parameter, wherein the formula derivation process of the flexibility change rate is as follows:
wherein F is a compliance matrix, F ij The physical meaning of (1) is the displacement generated at the measuring point at the position i when unit concentration force is applied to the measuring point at the position j, r is the modal order, omega r For identifying the natural frequency of the r-th order of the object structure, phi i (r) φ j (r) Represents the product of the r-th order modal shape value of the measurement point at position i and the r-th order modal shape value of the measurement point at position j, i =1,2, …, M, j =1,2, …, N.
Calculating the flexibility matrix variation delta F of the lossless and damage working conditions, wherein the calculation formula is as follows:
ΔF＝F d -F u
in the formula, F u 、F d Flexibility matrixes of lossless and damaged working conditions are respectively;
calculating the change rate delta F of the compliance matrix through the diagonal elements of the compliance matrix, wherein the calculation formula is as follows:
wherein diag (-) is a pair of compliance matricesAngle line element, f ii u 、f ii d The diagonal elements of the flexibility matrix of the nondestructive and damage working conditions are respectively expressed]' is the transpose of the row vector.
The matching vectors for various lesions in the lesion pattern library are as follows:
wherein, δ F p Representing the flexibility change rate of the p damage working conditions in the damage mode library, wherein p =1,2, …, Q; in this embodiment, the total number Q of damage conditions in the damage pattern library is 73.
S3, installing an acceleration sensor on the 3 to-be-identified object structures, and measuring acceleration response of the identified object structures; the experimental conditions are shown in table 2:
TABLE 2 Experimental condition table
| Working conditions | Lossless | Single loss | Double loss |
| Location and extent of injury | 0-0-0-0 | 60-0-0-0 | 20-40-0-0 |
In table 2, the damage conditions correspond to one-to-four-layer damage from left to right, for example, "20-40-0-0" indicates: one layer damaged 20%, the second 40%, and so on.
S4, performing modal identification on the dynamic response of the measured structure by using a complex modal indication function CMIF (measurement of frequency) to obtain the first two-order actual measurement natural frequency omega of the identified object structure tr Harmonic mode phi t (r) ＝[φ t1 (r) φ t2 (r) … φ tn (r) ]', wherein phi tn (r) The measured shape value of the r-th order is measured for position n as shown in fig. 3. First two-order actual measurement natural frequency omega tr As shown in Table 3
TABLE 3 inherent frequency identification results table
S5, calculating the actually measured vibration mode and the inherent frequency according to the step S2 to obtain a structure actually measured flexibility matrix T:
similarly, the obtained flexibility change rate vector delta T forms a test matching vector set
Wherein, δ T k And (3) representing the k-th working condition to be tested in the test set, wherein k =1,2, … and P. In this embodiment, the number P of the working conditions to be measured is 3.
S6, testing the matching vectors delta T in the matching vector set k The method is sequentially combined with the damage mode library delta F established in the step S2 p And (5) carrying out similarity measurement by adopting an Euclidean distance method. The calculation formula is given as follows:
wherein, δ F p (a) The flexibility change rate vector of the a-th damage working condition in the damage mode library; delta T k (b) And concentrating the flexibility change rate vector of the b-th working condition to be tested for the test.
S7, determining the damage condition under the serial number in the damage mode library corresponding to the minimum value of the matching result of the similarity measurement as the damage of the actual measurement condition; when two relatively close minimum values appear, the two corresponding damages in the damage mode library are both the damages of the actual measurement working condition. As shown in fig. 4, 5, and 6, the matching results are respectively shown for the lossless operating mode, the single-loss operating mode, and the double-loss operating mode.
To sum up, the embodiment provides a method for rapidly identifying structural damage based on flexibility change rate and pattern matching, the flexibility change rate is combined with the pattern matching, the sensitivity of the flexibility change rate to damage is fully utilized, meanwhile, the pattern matching method can quantify the damage degree, and the defects of the traditional method for identifying structural damage based on a flexibility matrix are overcome. On the other hand, the method takes the flexibility change rate as a matching vector, and eliminates the influence of excitation; rapidly completing the establishment of a mode library through modal analysis; and matching vectors obtained by processing the acceleration response signals with a pattern library in sequence according to an Euclidean distance algorithm, so that a large amount of calculation is avoided, and the quick identification of the damage position and the damage degree of the structure is realized.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (3)
1. A method for quickly identifying post-earthquake structural damage based on flexibility change rate and mode matching is characterized by comprising the following steps:
s1, establishing a finite element model of a structure for an identified object structure by using finite element software; all damage conditions in a damage mode library are formed by the damage conditions of the permutation and combination consisting of the damage positions and the damage degrees, and modal analysis is carried out on all the damage conditions to obtain modal vibration modes and natural frequencies of the identification object structure under various damage conditions;
s2, calculating the flexibility change rate of various damage working conditions, and establishing a damage mode library with damage positions and damage degree labels and using the flexibility change rate as a parameter, wherein the calculation process of the flexibility change rate is as follows:
wherein F is a compliance matrix, F ij The physical meaning of (1) is the displacement generated at the measurement point at the position i when unit concentration force is applied to the measurement point at the position j, r is the modal order, omega r For identifying the natural frequency of the r-th order of the object structure, phi i (r) 、φ j (r) Respectively representing the product of the r-th order modal shape value of the measurement point at the position i and the r-th order modal shape value of the measurement point at the position j, i =1,2, …, M, j =1,2, …, N;
calculating the flexibility matrix variation delta F of the lossless and damage working conditions, wherein the calculation formula is as follows:
ΔF＝F d -F u
in the formula, F u 、F d Flexibility matrixes of lossless and damage working conditions are respectively;
calculating the change rate delta F of the compliance matrix through the diagonal elements of the compliance matrix, wherein the calculation formula is as follows:
wherein diag (-) is a diagonal element of the compliance matrix, f ii u 、f ii d The diagonal elements of the flexibility matrix of the nondestructive and damage working conditions are respectively expressed]' denotes the transpose of the row vector;
matching vectors for various lesions in a library of lesion patterns
The following were used:
wherein, δ F p Representing the flexibility change rate of the p damage working conditions in the damage mode library, wherein p =1,2, …, Q;
s3, installing an acceleration sensor on the structure of the object to be identified, and measuring the acceleration response of the structure of the identified object;
s4, performing modal identification on the dynamic response of the measured identification object structure by using a complex modal indication function CMIF (constant amplitude frequency interface) method to obtain the r-th order actual measurement natural frequency omega of the identification object structure tr Harmonic mode phi t (r) ＝[φ t1 (r) φ t2 (r) … φ tj (r) … φ tN (r) ]', wherein phi tj (r) Measuring the real vibration mode value of the r order for the position j, wherein j =1,2, …, N;
s5, calculating the actually measured vibration mode and the inherent frequency according to the step S2 to obtain an actually measured flexibility matrix T of the structure of the recognition object:
wherein, ω is tr To identify the natural frequency of the r-th order of the object structure, phi ti (r) 、φ tj (r) Expressing the product of the order of r modal vibration type value of the measurement point of the structure position i of the identified object and the order of r modal vibration type value of the measurement point of the position j, calculating the flexibility change rate vector to form a test matching vector set
Wherein, δ T k The k-th working condition to be tested in the test set is represented, k =1,2, … and P;
s6, testing the matching vectors delta T in the matching vector set k Matching vectors delta F of various injuries in the injury mode library established in the step S2 in sequence p Carrying out similarity measurement;
and S7, determining the damage condition under the serial number in the damage mode library corresponding to the minimum value of the matching result of the similarity measurement as the damage of the actual measurement condition.
2. The method for rapidly identifying post-earthquake structural damage based on flexibility change rate and pattern matching as claimed in claim 1, wherein in the step S6, a euclidean distance method is adopted for similarity measurement, and a calculation formula is given as follows:
wherein, δ F p (a) The flexibility change rate vector of the a-th damage working condition in the damage mode library; delta T k (b) And concentrating the flexibility change rate vector of the b-th working condition to be tested for the test.
3. The method for rapidly identifying post-earthquake structural damage based on flexibility change rate and pattern matching as claimed in claim 1, wherein in step S7, when two relatively close minimum values occur, it is determined that the two damages corresponding to the damage pattern library are both damages of the measured working condition.
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| CN104462788A (en) * | 2014-11-21 | 2015-03-25 | 华中科技大学 | Finite element model correcting method based on reverse substructures |
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