CN115308054A - Railway bridge local damage diagnosis method using vehicle-induced strain response data - Google Patents

Railway bridge local damage diagnosis method using vehicle-induced strain response data Download PDF

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CN115308054A
CN115308054A CN202211069763.2A CN202211069763A CN115308054A CN 115308054 A CN115308054 A CN 115308054A CN 202211069763 A CN202211069763 A CN 202211069763A CN 115308054 A CN115308054 A CN 115308054A
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任鹏
袁宝军
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Abstract

The invention discloses a method for diagnosing local damage of a railway bridge by using vehicle-induced strain response data, which comprises the following steps of: acquiring strain response baseline data of a railway bridge structure train passing a bridge for multiple times to form a strain response baseline data set; extracting a strain response characteristic matrix of the strain response baseline data set; performing low-rank and sparse matrix separation on the strain response characteristic matrix to obtain a baseline low-rank matrix; acquiring new strain response monitoring data of the train passing through a bridge, and extracting a strain response characteristic vector to be diagnosed; constructing a strain response characteristic matrix to be diagnosed by using the strain response characteristic vector to be diagnosed and the baseline low-rank matrix; and (4) carrying out low-rank and sparse matrix separation on the strain response characteristic matrix to be diagnosed to obtain a sparse characteristic vector, and further carrying out local damage diagnosis on the railway bridge structure. The method combines the vehicle-induced vibration characteristic extraction and low-rank matrix recovery technology, eliminates the masking effect of monitoring data, and enhances the detectability of local damage of the railway bridge.

Description

Railway bridge local damage diagnosis method using vehicle-induced strain response data
Technical Field
The invention belongs to the technical field of structural health monitoring, and particularly relates to a method for diagnosing local damage of a railway bridge by using vehicle-induced strain response data.
Background
The railway bridge is an important carrier and key nodes for the safe operation of a railway transportation network. As the speed of the train is increased and the transportation volume is increased, the operating pressure of the infrastructure is increased; meanwhile, during the service period of dozens of years and hundreds of years, the infrastructures are continuously aged, and the damage accumulation and the performance degradation of the bridge structure are caused by the combined action of factors such as natural disasters, fatigue, corrosion and the like, so that the risk of failure and even collapse is increased. In the last two decades, structural health monitoring techniques have evolved rapidly with the goal of monitoring the operational state of the engineering infrastructure in real time and identifying damage before it has accumulated to a point where performance has degraded significantly to provide preventive maintenance strategies. These efforts make it possible to compensate for the deficiencies of visual inspection and in particular to facilitate the assessment of the condition of bridge structures whose operation is difficult to interrupt.
For railway bridges, especially old bridges in the middle and later stages of service, providing indexes representing the operation safety and stability of bridges and trains is a key task for implementing health monitoring. Currently, safety indexes based on monitoring information can be divided into two types: global indicators and local indicators. The overall indexes mainly comprise static and dynamic deflection of the bridge, modal frequency and the like; the indexes are suitable for evaluating the running stability of the vehicle-bridge coupling system, but the local damage of the structure is difficult to identify, and the indexes are interfered by the environment and the vehicle load factor, so that the caused masking effect covers the change of the original indexes, and further the practicability of the indexes is influenced. The local indexes mainly comprise stress, fatigue and the like of vulnerable parts mainly monitored by the bridge structure, and the indexes are generally obtained by calculating data measured by a stress/strain sensor which is more stable in test; although these indicators are more sensitive to damage to the component, they are still adversely affected by "masking effects" caused by environmental and vehicular loading factors, which can result in localized damage effects that are difficult to detect.
Disclosure of Invention
The invention provides a method for diagnosing local damage of a railway bridge by using vehicle-induced strain response data, which aims to solve the problems that health monitoring data of the railway bridge structure is easily influenced by environmental and vehicle load time-varying factors and the early damage detection of the structure is difficult to realize.
The invention provides a method for diagnosing local damage of a railroad bridge by using vehicle-induced strain response data, which comprises the following steps of:
step 1: acquiring strain response data of each strain measuring point under the action of multiple train passing bridges under the undamaged state of a railway bridge structure to form a strain response baseline data set;
step 2: extracting strain response characteristics corresponding to each strain measuring point under the action of each train passing a bridge in a strain response baseline data set to form a baseline strain response characteristic matrix;
and 3, step 3: carrying out low-rank and sparse matrix separation on the baseline strain response characteristic matrix to obtain a baseline low-rank matrix;
and 4, step 4: acquiring new strain response monitoring data under the action of train passing through a bridge, and extracting strain response characteristics corresponding to each strain measuring point by adopting the same method in the step 2 to form a strain response characteristic vector to be diagnosed;
and 5: constructing a strain response characteristic matrix to be diagnosed by using the strain response characteristic vector to be diagnosed and the baseline low-rank matrix;
step 6: and 3, performing low-rank and sparse matrix separation on the strain response characteristic matrix to be diagnosed by adopting the same method in the step 3 to obtain a sparse characteristic vector, and performing local damage diagnosis on the railway bridge structure according to the sparse characteristic vector.
The method for diagnosing the local damage of the railway bridge by using the vehicle-induced strain response data at least has the following beneficial effects:
1. aiming at the problems of full utilization of health monitoring data of a railway bridge structure and detectability of early damage, the method adopts an unsupervised learning paradigm, and realizes analysis and explanation of high-dimensional strain response monitoring data through a feature extraction and normalization algorithm. The algorithm does not depend on a physical model of the structure and time-varying load information and does not need label data of the structure damage state. In a specific embodiment, the method can eliminate the masking effect caused by the environment and the vehicle load in the strain response characteristic data, and realize the detection of the local small damage of the railway bridge structure.
2. The data required by the algorithm is the strain response of the vehicle-induced vibration, and can be measured by using strain sensors arranged at vulnerable parts of the bridge structure, and the strain measuring points are also compatible with a bridge dynamic weighing system; compared with global response data such as bridge modes and deflection, the strain response data are more suitable for local damage diagnosis.
3. The algorithm adopts a low-rank and sparse matrix separation technology to normalize the strain response characteristic matrix so as to eliminate the masking effect caused by the environment and the vehicle load in the characteristic data. Compared with unsupervised learning technologies such as clustering and the like, the low-rank matrix recovery technology does not need to traverse all possible structural states in training data.
4. Compared with dimensionality reduction technologies such as principal component analysis, the low-rank matrix recovery technology belongs to an unsupervised learning method, original information is completely separated into a low-rank part and a sparse part during low-dimensional projection, and the technologies such as principal component analysis need to intercept orthogonal projection, so that information loss is caused. The damage diagnosis result of the method provided by the invention is obviously superior to that of a principal component analysis method adopting the same baseline data set.
5. The low-rank and sparse matrix separation technology is essentially used for complementing a low-rank matrix containing noise, so that the algorithm is not influenced by missing data or detected outliers, and the robustness of the algorithm is enhanced.
6. The algorithm identifies the impairment based on non-zero detection of sparse features without performing the training phase and threshold calculations required for new anomaly detection.
7. The invention only needs a small amount of baseline data which are confirmed to be in an undamaged state, and does not need to process a large amount of training data from different structural states; after the sensor abnormity diagnosis is carried out on the train bridge crossing strain response data obtained by each monitoring, the local damage diagnosis can be automatically carried out, and the method is suitable for the online diagnosis of all types of railway bridges and has strong compatibility.
Drawings
FIG. 1 is a flow chart of a method of diagnosing localized damage to a railroad bridge using vehicle-induced strain response data in accordance with the present invention;
FIGS. 2 (a) - (b) are numerical calculations of a steel single span bowstring arch bridge according to an embodiment of the present invention; wherein, fig. 2 (a) is a three-dimensional finite element model diagram of a bridge, and fig. 2 (b) is a simplified schematic diagram of bridge bearing restraint;
FIGS. 3 (a) - (b) are schematic diagrams of strain sensor placement and lesion location in accordance with an embodiment of the present invention; wherein, fig. 3 (a) is a south side view of the bridge, and fig. 3 (b) is a north side view of the bridge;
FIG. 4 is the principal input data for the environmental and vehicular load effect simulation of an embodiment of the present invention;
FIGS. 5 (a) - (b) are exemplary strain response data under the influence of environmental and vehicle loading factors for embodiments of the present invention; wherein, fig. 5 (a) is the strain response of a strain measuring point s4 under the conditions of a Suburban type train, a bridge passing speed of 107km/h and a temperature of 18.2 ℃, and fig. 5 (b) is the strain response of a strain measuring point s6 under the conditions of an intersection type train, a bridge passing speed of 50km/h and a temperature of 26 ℃;
FIG. 6 is a graph of strain response characteristics corresponding to two of the strain gauges in an embodiment of the present invention;
FIG. 7 is a boxline graph of strain response characteristic data corresponding to all strain measurement points in an embodiment of the present invention;
FIG. 8 is sparse feature data corresponding to two of the strain measurement points in an embodiment of the present invention;
FIG. 9 is a boxline diagram of sparse feature data corresponding to all strain measurement points in an embodiment of the present invention;
FIGS. 10 (a) - (b) are graphs comparing the results of the diagnosis of lesions according to the method of the present invention and the principal component analysis; in fig. 10 (a) shows the diagnosis result of the method of the present invention, and fig. 10 (b) shows the diagnosis result of the Principal Component Analysis (PCA) method.
Detailed Description
Machine learning is a tool that classifies information according to learning patterns through different algorithms, and is believed to effectively enhance the capabilities of structural health monitoring systems. Compared with a supervised machine learning technology, the unsupervised learning technology does not need to provide label data from different structural states (including damage states), and can identify the abnormal state of the structure through the change pattern followed by long-term monitoring data under the influence of learning environment and vehicle load factors, so that the method is more suitable for health monitoring of a real bridge structure. Feature extraction and normalization are essential steps of the unsupervised learning paradigm. For railway bridges, response data excited by train passing bridges are strong in regularity and have large vibration amplitude, and the change of the amplitude is dominated by vehicle load. Therefore, the method for diagnosing the local damage of the railway bridge by using the vehicle induced strain response data is beneficial to realizing the detection of the early damage of the railway bridge structure by extracting the vehicle induced response characteristics obtained by long-term monitoring and eliminating the masking effect caused by the time-varying environment and the vehicle load in the characteristic data by adopting the unsupervised learning paradigm. The following description of the method according to the invention is given with reference to fig. 1.
The invention discloses a method for diagnosing local damage of a railroad bridge by using vehicle-induced strain response data, which comprises the following steps of:
step 1: acquiring strain response data of each strain measuring point under the action of multiple train passing bridges under the undamaged state of a railway bridge structure to form a strain response baseline data set, wherein the step 1 specifically comprises the following steps:
aiming at a railway bridge structure with m strain measurement points, according to the current operation state, the regular detection and the health monitoring history of the bridge, k acquired under the undamaged state of the bridge structure B And the strain response data of each measuring point excited by the secondary train passing bridge form a strain response baseline data set.
The strain measuring point for acquiring the strain response data is composed of a strain sensor arranged at a vulnerable part of the bridge structure; the strain sensors are in normal working states before and after the train passes through the bridge.
And 2, step: extracting strain response characteristics corresponding to each strain measuring point under the action of passing a bridge of the train each time in the strain response baseline data set to form a baseline strain response characteristic matrix, wherein the step 2 specifically comprises the following steps:
step 2.1: the strain response measured by the strain measuring point i is epsilon when the kth train passes a bridge i,k (t)，i＝1,2,…,m，k＝1,2,…,k B ，ε i,k (t) wavelet packet analysis the J-th decomposition layer decomposition gives 2 J Sub-band:
Figure BDA0003829238220000051
in the formula: the upper corner mark j represents the jth sub-band of the signal;
step 2.2: the first sub-band signal
Figure BDA0003829238220000052
The time history integral of the time history is used as the strain response characteristic SF of the strain measuring point i when the kth train passes the bridge i,k ：
Figure BDA0003829238220000061
In the formula: t is a unit of k The total time of the action of the load effect of the passing bridge of the kth train;
step 2.3: the strain response characteristics of the m strain measuring points obtained by passing the bridge of the kth train form a strain response characteristic vector SFV k ＝{SF 1,k SF 2,k … SF m-1,k SF m,k } T ；
Step 2.4: in the strain response baseline dataset, total k B Strain response characteristic matrix of m strain measuring points obtained by passing a secondary train through a bridge
Figure BDA0003829238220000062
Figure BDA0003829238220000063
And step 3: performing low-rank and sparse matrix separation on the baseline strain response characteristic matrix to obtain a baseline low-rank matrix, wherein the step 3 specifically comprises the following steps:
step 3.1: setting strain response characteristic matrix SFM B Is X as a baseline low rank matrix B Baseline sparse matrix of E B Then the optimization objective function is as follows:
Figure BDA0003829238220000064
in the formula: i | · | purple wind * Represents the kernel norm of the matrix, Ω represents the index set of the elements in the matrix except the non-number elements, P Ω (. To) is the matrix element corresponding to index set omega, | | | · | write 1 Representing the l1 norm of the matrix, wherein lambda is a weight factor, and lambda is more than or equal to 1;
step 3.2: solving the optimized objective function in the step 3.1 by adopting an alternative direction multiplier algorithm to obtain a base line low-rank matrix X B 。
And 4, step 4: acquiring new strain response monitoring data under the action of train passing through a bridge, extracting strain response characteristics corresponding to each strain measuring point by adopting the same method in the step 2 to form a strain response characteristic vector to be diagnosed, wherein the step 4 specifically comprises the following steps:
step 4.1: acquiring new strain response monitoring data under the action of train passing a bridge;
step 4.2: calculating z, z in turn>k B The strain response characteristics of the train passing bridge strain response monitoring data to be diagnosed of the m strain measuring points during the passing of the secondary train form a strain response characteristic vector SFV z ＝{SF 1,z SF 2,z … SF m-1,z SF m,z } T 。
And 5: constructing a strain response characteristic matrix to be diagnosed by using the strain response characteristic vector to be diagnosed and the baseline low-rank matrix;
wherein the strain response characteristic matrix to be diagnosed is represented as:
SFM z ＝[SFV z |X B ] (5)
in the formula:
Figure BDA0003829238220000071
is a strain response characteristic matrix to be diagnosed.
Step 6: performing low-rank and sparse matrix separation on the strain response characteristic matrix to be diagnosed by adopting the same method in the step 3 to obtain a sparse characteristic vector, and performing local damage diagnosis on the railway bridge structure according to the sparse characteristic vector, wherein the step 6 specifically comprises the following steps:
step 6.1: adopting the same method as the step 3 to treat the strain response characteristic matrix SFM to be diagnosed z Separating low-rank and sparse matrix to obtain sparse matrix
Figure BDA0003829238220000072
Let matrix E z Is a sparse feature vector SV z ∈R m×1 ；
Step 6.2: sequential detection of sparse feature vectors SV z Middle element SV i,z If SV i,z If the strain measuring point i is not damaged, indicating that the vulnerable part of the bridge structure where the strain measuring point i is located is damaged; on the contrary, if SV i,z If not equal to 0, indicating that the vulnerable part of the bridge structure where the strain measuring point i is likely to be damaged; and (4) repeating the steps 4 to 6 to implement online damage judgment and positioning every time new train bridge crossing strain response monitoring data in the operating state are obtained.
Examples
In the embodiment, the feasibility and the robustness of the proposed method are verified by performing a simulation test on an actual railway bridge. Fig. 2 (a) shows a finite element model of the single-span tied arch bridge, and fig. 2 (b) is a simplified schematic diagram of bridge abutment constraint. The bridge main body is a steel structure, the double-track bridge floor is a plane frame bridge floor system consisting of two main beams and 33 cross beams, the bridge floor system is hung on arch ribs at the north and south sides through 32 inclined support rods, and two ends of the bridge are respectively supported by two rubber support seats.
3 (a) - (b) are schematic diagrams of strain gage and deflection sensor placement and damage location for one embodiment of the present invention; FIG. 3 (a) is a south side view of the bridge and FIG. 3 (b) is a north side view of the bridge; as shown in the figure, each inclined strut is provided with a strain measuring point, and the axial strain response of the inclined strut is measured through a strain sensor; arranging displacement measuring points at the nodes of the main beam and the diagonal brace on the south side of the bridge, and measuring the vertical displacement response of the positions of the nodes of the main beam and the diagonal brace through a single-axis displacement meter; wherein the strain measuring points are numbered as s1-s32 in sequence.
When a real bridge is detected, the bolt connection between each inclined supporting rod of the bridge and the main beam and the arch is found to have construction defects, and then weak parts of the node connection are reinforced. Therefore, the embodiment considers the local damage of the end node position of the diagonal brace and the development evolution thereof in the simulation. Three Damage conditions (Damage Scenario, DS) were considered, representing three Damage states of the bridge: wherein DS1 is that the connecting parts of the diagonal brace 8 and the rod 9 and the main beam are damaged, and the connecting rigidity is reduced by 20%; the DS2 damage position is the same as DS1, but the damage degree, namely the connection rigidity is reduced by 50%; DS3 is that on the basis of DS2, the connecting part of the diagonal brace 17 and the main beam is damaged, and the connecting rigidity is reduced by 50%; in addition, DS0 represents the bridge undamaged state.
In order to fully verify the robustness of the data fusion algorithm under the influence of time-varying environment and vehicle load, 135 completely random train bridge-crossing events are simulated, as shown in fig. 4. The recorded temperature of each train passing through the bridge event is also uniformly distributed between-3 ℃ and 37 ℃ by randomly passing through two European trains of Suburban and Intercity along the direction B at the running speed which is uniformly distributed from 50km/h to 200km/h each time, see figure 2 (B). The bridge is in an undamaged state DS0 during the first 45 times of train passing, is in a damaged state DS1 during the 46 th to 75 th train passing, is in a damaged state DS2 during the 76 th to 105 th train passing, and is in a damaged state DS3 during the 106 th to 135 th train passing. 5 (a) - (b) are exemplary strain response data under the influence of environmental and vehicle loading factors for embodiments of the present invention; wherein, the figure 5 (a) is the strain response of a strain measuring point s4 under the conditions of a Suburban type train, a bridge passing speed of 107km/h and a temperature of 18.2 ℃, and the figure 5 (b) is the strain response of a strain measuring point s6 under the conditions of an intersection type train, a bridge passing speed of 50km/h and a temperature of 26 ℃.
Fig. 6 lists strain response characteristic data corresponding to the strain measuring points s9 and s17 extracted from 135 train bridge passing events. Some outliers exist in the strain response characteristic data, and analysis shows that the outliers are only response characteristics of the high-load interval train at the low-speed bridge crossing and are irrelevant to local damage. The connection parts of the inclined support rods and the main beams where the strain measuring points s9 and s17 are located are damaged, theoretically, response characteristics corresponding to the two strain measuring points are reflected, however, obvious changes of response characteristic data before and after damage are not seen in the drawing, which shows that damage is difficult to identify only by using the strain response characteristics of single strain measuring point, and the damage effect in the strain response characteristic data is covered by a masking effect caused by a time-varying environment and vehicle load.
Fig. 7 further shows the quantitative distribution of the response characteristic data corresponding to all strain measuring points in 135 train bridge crossing events by using a box plot, and it can be observed that the amplitude change of the response characteristic is dominated by the vehicle load, which results in local small damage, such as DS1 and DS3. And are difficult to detect directly.
Fig. 8 lists sparse characteristic data corresponding to strain measuring points s9 and s17 in 135 train bridge crossing events obtained by the damage diagnosis method provided by the invention. It can be seen that the sparse feature is zero before the adjacent nodes of the diagonal brace where the measuring points are located are damaged; after the lesion occurs, the sparse features are non-zero and change significantly. Therefore, the sparse features obtained based on the unsupervised learning method are feasible as the early damage detection indexes of the railway bridge structure.
The sparse features corresponding to all strain measurement points, namely damage diagnosis results, are shown in the form of a box plot in fig. 9. The damage diagnosis result shows that the invention fully utilizes the high-dimensional strain response monitoring data, eliminates the masking effect caused by the time-varying environment and vehicle load in the embodiment and enhances the detectability of local small damages (such as DS1 and DS 3).
This example also examines the results of a Principal Component Analysis (PCA) based method of lesion diagnosis using the same baseline data set as the proposed method. FIGS. 10 (a) - (b) are graphs comparing the results of the damage diagnosis by the method of the present invention and the principal component analysis method; in which, FIG. 10 (a) is the diagnosis result of the method of the present invention, and FIG. 10 (b) is the diagnosis result of the Principal Component Analysis (PCA) method. For simplifying the representation, the characteristic data of the strain measuring points s8, s9 and s17 corresponding to the damage position in each damage working condition are listed separately, and the characteristic data corresponding to the other measuring points adopt uniform marks. As can be seen from the figure, the sparse characteristic serving as the damage index of the invention can timely and accurately identify the rod piece with the damaged node connection, and the damage misjudgment is less; and the PCA characteristic is easy to cause damage misjudgment when identifying the damage position. Meanwhile, different from PCA (principal component analysis) characteristics, damage is identified by only adopting simple non-zero detection on sparse characteristics; therefore, the damage diagnosis method provided by the invention does not need to train an early warning threshold value, has strong sample expandability and can carry out online early warning by only using a small amount of reference data.
The above description is only a preferred embodiment of the present invention and should not be taken as limiting the scope of the invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.

Claims (8)

1. A method for diagnosing local damage of a railroad bridge by using vehicle-induced strain response data is characterized by comprising the following steps:
step 1: acquiring strain response data of each strain measuring point under the action of multiple train passing bridges under the undamaged state of a railway bridge structure to form a strain response baseline data set;
and 2, step: extracting strain response characteristics corresponding to each strain measuring point under the action of passing a bridge of the train each time in the strain response baseline data set to form a baseline strain response characteristic matrix;
and 3, step 3: carrying out low-rank and sparse matrix separation on the baseline strain response characteristic matrix to obtain a baseline low-rank matrix;
and 4, step 4: acquiring new strain response monitoring data under the action of train passing through a bridge, and extracting strain response characteristics corresponding to each strain measuring point by adopting the same method in the step 2 to form a strain response characteristic vector to be diagnosed;
and 5: constructing a strain response characteristic matrix to be diagnosed by using the strain response characteristic vector to be diagnosed and the baseline low-rank matrix;
and 6: and (4) performing low-rank and sparse matrix separation on the strain response characteristic matrix to be diagnosed by adopting the same method in the step (3) to obtain a sparse characteristic vector, and performing local damage diagnosis on the railway bridge structure according to the sparse characteristic vector.
2. The method for diagnosing the local damage of the railroad bridge by using the vehicle-induced strain response data according to claim 1, wherein the step 1 is specifically as follows:
aiming at a railway bridge structure with m strain measurement points, according to the current operation state, the regular detection and the health monitoring history of the bridge, k acquired under the undamaged state of the bridge structure B And the strain response data of each measuring point excited by the secondary train passing bridge form a strain response baseline data set.
3. The method for diagnosing the local damage of the railroad bridge by using the vehicle-induced strain response data as claimed in claim 2, wherein the strain measuring point for obtaining the strain response data is composed of a strain sensor arranged at a vulnerable part of the bridge structure; the strain sensors are in normal working states before and after the train passes through the bridge.
4. The method for diagnosing the local damage of the railroad bridge using the vehicle-induced strain response data according to claim 1, wherein the step 2 is specifically as follows:
step 2.1: the strain response measured by the strain measuring point i is epsilon when the kth train passes a bridge i,k (t)，i＝1,2,…,m，k＝1,2,…,k B ，ε i,k (t) wavelet packet analysis the J-th decomposition layer decomposition to 2 J Sub-band:
Figure FDA0003829238210000021
in the formula: the upper corner mark j represents the jth sub-band of the signal;
step 2.2: the first sub-band signal
Figure FDA0003829238210000022
The time history integral of the time history is used as the strain response characteristic SF of the strain measuring point i when the kth train passes the bridge i,k ：
Figure FDA0003829238210000023
In the formula: t is k The total time of the action of the load effect of the passing bridge of the kth train;
step 2.3: the strain response characteristics of the m strain measuring points obtained by passing the bridge of the kth train form a strain response characteristic vector SFV k ＝{SF 1,k SF 2,k …SF m-1,k SF m,k } T ；
Step 2.4: in the strain response baseline dataset, total k B Strain response characteristic matrix of m strain measuring points obtained by passing a secondary train through a bridge
Figure FDA0003829238210000026
Figure FDA0003829238210000024
5. The method for diagnosing the local damage of the railroad bridge by using the vehicle-induced strain response data as claimed in claim 4, wherein the step 3 of performing low rank and sparse matrix separation specifically comprises:
step 3.1: setting strain response characteristic matrix SFM B Is X as a baseline low rank matrix B The baseline sparse matrix is E B Then the optimization objective function is as follows:
Figure FDA0003829238210000025
in the formula: i | · | live through * Represents the kernel norm of the matrix, Ω represents the index set of the elements in the matrix except the non-number elements, P Ω (. One) is a matrix element corresponding to the index set omega, | | ·| purple wind 1 Representing the l1 norm of the matrix, wherein lambda is a weight factor and is more than or equal to 1;
step 3.2: solving the optimized objective function in the step 3.1 by adopting an alternative direction multiplier algorithm to obtain a base line low-rank matrix X B 。
6. The method for diagnosing the local damage of the railroad bridge by using the vehicle-induced strain response data as claimed in claim 4, wherein the step 4 is specifically as follows:
step 4.1: acquiring new strain response monitoring data under the action of train passing a bridge;
step 4.2: calculating z, z in turn>k B The strain response characteristics of the train passing bridge strain response monitoring data to be diagnosed of the m strain measuring points during the passing of the secondary train form a strain response characteristic vector SFV z ＝{SF 1,z SF 2,z …SF m-1,z SF m,z } T 。
7. The method for diagnosing the local damage of the railroad bridge using the vehicle-induced strain response data as claimed in claim 6, wherein the strain response characteristic matrix to be diagnosed in the step 5 is represented as:
SFM z ＝[SFV z |X B ] (5)
in the formula:
Figure FDA0003829238210000031
is a strain response characteristic matrix to be diagnosed.
8. The method for diagnosing the local damage of the railroad bridge using the vehicle induced strain response data as claimed in claim 7, wherein the step 6 is specifically as follows:
step 6.1: adopting the same method as the step 3 to treat the strain response characteristic matrix SFM to be diagnosed z Separating low-rank and sparse matrix to obtain sparse matrix
Figure FDA0003829238210000032
Let matrix E z Is a sparse feature vector SV z ∈R m×1 ；
Step 6.2: sequential detection of sparse feature vectors SV z Middle element SV i,z If SV i,z =0, indicates the strain measurement point iNo damage occurs to the vulnerable part of the bridge structure; on the contrary, if SV i,z If not equal to 0, indicating that the vulnerable part of the bridge structure where the strain measuring point i is likely to be damaged; and (4) repeating the steps 4 to 6 to implement online damage judgment and positioning every time new train bridge crossing strain response monitoring data in the operating state are obtained.
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