Steel structure health feature index extraction method and system based on multi-source data alignment
Patent Information
- Application Number
- CN202610874248.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-17
- Publication Date
- 2026-08-11
- Estimated Expiration
- 2046-06-17
AI Technical Summary
[0004]为了解决变电站钢结构健康监测中因多源数据时空关联性不足而导致健康特征提取准确性低下的技术问题,本发明的目的在于提供一种基于多源数据对齐的钢结构健康特征指标提取方法及系统,所采用的技术方案具体如下:
在本发明提供的基于多源数据对齐的钢结构健康特征指标提取方法及系统中,首先利用各测点的空间距离与应力波速常数对冲击事件下的应变数据和加速度数据进行时差补偿,生成因果次序严格对齐的时差补偿数据段集合,从源头上消除了因传感器空间高度差异导致的响应波形错位问题,为后续融合分析奠定了时空统一的可靠数据基础。在此基础上,将反映构件受力状态的第一指标与反映构件几何形变状态的第二指标引入图拓扑分析框架,通过构建拓扑传播关联矩阵并进行求逆解算,直接获得全网络各节点的拓扑风险积聚指数,实现了对局部病害在整体传力网络中引发连锁积聚效应的量化评估,突破了传统方法仅能孤立判断单一测点阈值的局限,同时规避了有限元迭代仿真带来的高昂算力消耗。进一步地,将提取自时差补偿数据段集合的节点振动特征与拓扑风险积聚指数进行乘法联合,生成动静联合异常指数,利用动态冲击能量对静态拓扑脆弱性进行交叉验证,使得仅有在结构薄弱节点实际遭遇瞬态强冲击时该指数才显著放大,有效抑制了纯几何偏斜引起的静态虚警和孤立高频干扰引起的动态误报,最终输出的包含联合异常指数的推送信息能够精准反映结构健康状态的真实威胁程度。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of data processing technology, specifically to a method and system for extracting health characteristic indicators of steel structures based on multi-source data alignment. Background Technology
[0002] Substations contain numerous tall steel structures that endure various external forces such as wind loads, temperature variations, and mechanical shocks during long-term service. Their structural health directly impacts the safe operation of the power system. To achieve continuous monitoring of the steel structure's health, a multi-source sensor network is typically deployed at measurement points on each component. This includes strain and acceleration sensors for acquiring high-frequency dynamic responses, and tilt and settlement sensors for acquiring low-frequency quasi-static deformations. This forms a multi-source heterogeneous monitoring data system encompassing both dynamic mechanical responses and static geometric deformations.
[0003] In existing technologies, feature extraction methods for steel structure health monitoring mostly rely on independent threshold judgments for data from each measuring point. When dealing with structures with wide spatial distribution and complex force transmission paths, these methods struggle to effectively reconstruct the true physical response order between different measuring points and cannot quantify the impact of local deformation or damage on the overall network force transmission state. As the dimensionality of monitoring data and the scale of the network increase, the analytical accuracy of traditional methods significantly decreases, making them unsuitable for the global health status assessment needs of substation steel structures under high spatial span conditions. Summary of the Invention
[0004] To address the technical problem of low accuracy in health feature extraction due to insufficient spatiotemporal correlation of multi-source data in substation steel structure health monitoring, this invention aims to provide a method and system for extracting steel structure health feature indicators based on multi-source data alignment. The specific technical solution adopted is as follows: Firstly, a method for extracting health characteristic indicators of steel structures based on multi-source data alignment is provided. This method includes: acquiring measurement data from corresponding measuring points of various components deployed on the steel structure of a substation; the measurement data includes strain data, acceleration data, tilt angle data, and settlement data; the steel structure includes multiple nodes connected by components; responding to the occurrence of an impact event, performing time-delay compensation on the strain and acceleration data collected from each measuring point based on the time delay of the impact event at different measuring points on the steel structure, generating a time-delay compensated data segment set; extracting a first indicator characterizing the stress state of the components from the time-delay compensated data segment set, and extracting a second indicator characterizing the geometric deformation state of the components from the tilt angle data and settlement data; constructing a topology propagation correlation matrix based on the first and second indicators, and inverting the topology propagation correlation matrix to obtain the topology risk accumulation index of each node; extracting the vibration characteristics of each node from the time-delay compensated data segment set, combining the topology risk accumulation index of each node to generate a joint anomaly index corresponding to each node, and outputting push information containing the joint anomaly index.
[0005] In one possible design, determining the time of occurrence of the impact event includes: identifying the first measuring point with the highest longitudinal coordinate value from the three-dimensional mesh model of the steel structure; extracting the strain data of the first measuring point within a first observation window and the strain data of the first measuring point within a second observation window, wherein the end times of the first and second observation windows are the same, and the time span of the first observation window is shorter than that of the second observation window; determining the first fluctuation degree of the strain data within the first observation window and the second fluctuation degree of the strain data within the second observation window; and determining that an impact event has occurred if the ratio of the first fluctuation degree to the second fluctuation degree is greater than a preset trigger threshold, and recording the end time of the first observation window as the time of occurrence of the impact event.
[0006] In one possible design, time-delay compensation is performed on the strain and acceleration data collected from different measuring points on the steel structure based on the time delay of the impact event. This includes: extracting the spatial distance between the first and second measuring points from the three-dimensional mesh model of the steel structure, where the second measuring point is any measuring point located below the first measuring point; determining the time delay of the second measuring point relative to the moment of the impact event based on the spatial distance and a preset stress wave velocity constant; and superimposing the moment of the impact event with the time delay to serve as the data extraction time reference for the second measuring point.
[0007] In one possible design, generating a time-difference compensation data segment set includes: extracting a first data segment from strain and acceleration data collected from a first measuring point, extending forward and backward by a preset time interval centered on the moment of the impact event; extracting a second data segment from strain and acceleration data collected from a second measuring point, extending forward and backward by a preset time interval centered on the data extraction time reference of a second measuring point; and merging the first and second data segments to obtain the time-difference compensation data segment set.
[0008] In one possible design, the first index characterizing the stress state of the component is extracted from the time-difference compensation data segment set, including: for each component, extracting the strain data sequence corresponding to the component from the time-difference compensation data segment set; taking the absolute value of all sampled values in the strain data sequence and determining the maximum absolute value as the strain peak value; obtaining the material elastic modulus and structural design yield strength corresponding to the component; determining the actual stress borne by the component based on the strain peak value and the material elastic modulus, and using the ratio of the actual stress to the structural design yield strength as the first index.
[0009] In one possible design, a second index characterizing the geometric deformation state of the component is extracted from the tilt angle data and settlement data. This includes: for each component, using the moment of the impact event as the retrieval anchor point, extracting the tilt angle value that is earlier in time and closest to the moment of the impact event from the tilt angle data, and taking the absolute value of the extracted tilt angle value to obtain the absolute value of the component's tilt angle; if the component is directly connected to the foundation, extracting the settlement data that is earlier in time and closest to the moment of the impact event from the settlement data, and determining the absolute difference between the extracted settlement data and the historical settlement benchmark value as the settlement change of the component; if the component is not directly connected to the foundation, setting the settlement change of the component to zero; obtaining preset tilt angle allowable limits and preset settlement allowable limits; and determining the second index based on the ratio of the absolute value of the tilt angle to the preset tilt angle allowable limit and the ratio of the settlement change to the preset settlement allowable limit.
[0010] In one possible design, a topological propagation correlation matrix is constructed based on the first and second indices, including: marking the foundation nodes with a longitudinal coordinate of zero in the 3D mesh model of the steel structure as absorbing nodes, and marking other nodes in the 3D mesh model besides the foundation nodes as suspended nodes; converting the undirected physical edges in the 3D mesh model into directed edges pointing from upstream nodes to downstream nodes according to a preset direction rule; for each suspended node, determining all downstream adjacent nodes directly connected to the suspended node through directed edges, with each directed edge corresponding to a component; for For each directed edge, the first index of the component corresponding to the directed edge is added to a preset constant, and then multiplied by the second index of the component corresponding to the directed edge. The reciprocal of the product is taken as the association weight of the directed edge. For each dangling node, the association weights of each directed edge pointing from the dangling node to its downstream neighbor are normalized to obtain the association distribution coefficients corresponding to each directed edge. The association distribution coefficients corresponding to each directed edge are filled into the corresponding positions of the preset matrix, and the association distribution coefficients from the dangling node to the absorbing node are not filled into the preset matrix, forming the topology propagation association matrix.
[0011] In one possible design, the topological risk accumulation index of each node is obtained by inverting the topological propagation correlation matrix. This includes: constructing an identity matrix with the same dimension as the topological propagation correlation matrix; calculating the difference matrix between the identity matrix and the topological propagation correlation matrix; inverting the difference matrix to obtain the expected matrix of the transmitted influence; and for each dangling node, extracting the row vector corresponding to the dangling node from the expected matrix of the transmitted influence, and summing the elements in the row vector to obtain the topological risk accumulation index of the dangling node.
[0012] In one possible design, vibration characteristics of each node are extracted from the time-difference compensation data segment set, and combined with the topological risk accumulation index of each node, a joint anomaly index corresponding to each node is generated. This includes: for each component, extracting the acceleration data sequence corresponding to the component from the time-difference compensation data segment set; performing high-pass filtering on the acceleration data sequence to obtain a processed acceleration data sequence; determining the root mean square value of the processed acceleration data sequence as the vibration characteristic of the component; for each node, determining the maximum value among the vibration characteristics of each component connected to the node as the vibration characteristic of the node; and multiplying the vibration characteristic of the node by the topological risk accumulation index of the node to obtain the joint anomaly index corresponding to the node.
[0013] Secondly, a system for extracting health characteristic indicators of steel structures based on multi-source data alignment is provided, comprising: a data acquisition unit for acquiring measurement data from corresponding measuring points of various components deployed on the steel structure of a substation, including strain data, acceleration data, tilt angle data, and settlement data; the steel structure includes multiple nodes connected by components; a time-difference compensation unit for compensating for the time delay of different measuring points on the steel structure in response to the occurrence of an impact event, generating a set of time-difference compensated data segments; a topology calculation unit for extracting a first indicator characterizing the stress state of the components from the set of time-difference compensated data segments, extracting a second indicator characterizing the geometric deformation state of the components from the tilt angle data and settlement data, constructing a topology propagation correlation matrix based on the first and second indicators, and inverting the topology propagation correlation matrix to obtain the topology risk accumulation index of each node; and a joint evaluation unit for extracting the vibration characteristics of each node from the set of time-difference compensated data segments, combining the topology risk accumulation index of each node to generate a joint anomaly index corresponding to each node, and outputting push information containing the joint anomaly index.
[0014] The present invention has the following beneficial effects: In the method and system for extracting health characteristic indicators of steel structures based on multi-source data alignment provided by this invention, the spatial distance between each measuring point and the stress wave velocity constant are first used to perform time difference compensation on strain and acceleration data under impact events, generating a set of time difference-compensated data segments with strict causal order alignment. This eliminates the problem of response waveform misalignment caused by differences in sensor spatial height from the source, laying a reliable data foundation for spatiotemporal unification for subsequent fusion analysis. On this basis, the first indicator reflecting the stress state of the component and the second indicator reflecting the geometric deformation state of the component are introduced into the graph topology analysis framework. By constructing the topology propagation correlation matrix and performing inverse calculation, the topology risk accumulation index of each node in the entire network is directly obtained. This realizes the quantitative assessment of the chain accumulation effect caused by local defects in the overall force transmission network, breaking through the limitation of traditional methods that can only judge the threshold of a single measuring point in isolation, while avoiding the high computational cost of finite element iterative simulation. Furthermore, the node vibration characteristics extracted from the time difference compensation data segment set are multiplied and combined with the topological risk accumulation index to generate a dynamic-static joint anomaly index. The dynamic impact energy is used to cross-validate the static topological vulnerability, so that the index is significantly amplified only when the weak nodes of the structure actually encounter transient strong impacts. This effectively suppresses static false alarms caused by pure geometric skew and dynamic false alarms caused by isolated high-frequency interference. The final output push information containing the joint anomaly index can accurately reflect the true threat level of the structural health status. Attached Figure Description
[0015] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0016] Figure 1 This is a flowchart illustrating a method for extracting health characteristic indicators of steel structures based on multi-source data alignment, provided in one embodiment of the present invention. Figure 2 This is a schematic diagram of a steel structure health feature index extraction system based on multi-source data alignment, provided as an embodiment of the present invention. Detailed Implementation
[0017] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a method and system for extracting health characteristic indicators of steel structures based on multi-source data alignment proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.
[0018] In embodiments of the present invention, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" or "for example" in embodiments of the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.
[0019] In the description of this invention, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The term "and / or" in this document is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, and B alone. Furthermore, "at least one" and "more than one" refer to two or more. The terms "first," "second," etc., do not limit the quantity or order of execution, and "first," "second," etc., do not necessarily imply differences.
[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.
[0021] The following description, in conjunction with the accompanying drawings, details the specific scheme of the method and system for extracting health characteristic indicators of steel structures based on multi-source data alignment provided by the present invention.
[0022] Please see Figure 1 The diagram illustrates a flowchart of a method for extracting health feature indicators of steel structures based on multi-source data alignment, provided by an embodiment of the present invention, including the following steps S101-S105.
[0023] S101. Obtain measurement data of the corresponding measuring points of each component deployed on the steel structure of the substation.
[0024] Optionally, the substation steel structure is a topological network structure composed of multiple nodes connected by components. The physical form of the steel structure is characterized by a three-dimensional mesh model, which records the spatial three-dimensional coordinates of each node and the connection topology between the nodes established by the components. Measurement points are deployed at corresponding positions of each component of the steel structure, and a sensor is installed at each measurement point to continuously collect measurement data at that location.
[0025] In some embodiments, measurement data collected by sensors at various measuring points is continuously received through an underlying data interface. This measurement data can be categorized into two main types based on the sampling method: high-frequency dynamic data and low-frequency quasi-static data. High-frequency dynamic data includes strain and acceleration data continuously sampled from each measuring point. Strain data characterizes the micro-strain response of each component under external loads, while acceleration data characterizes the acceleration response of each component under vibration excitation. Low-frequency quasi-static data includes tilt and settlement data sampled periodically from each measuring point. Tilt data characterizes the angular deviation of each component relative to its initial installation state, while settlement data characterizes the vertical displacement of the bottom support position of each component relative to its initial elevation.
[0026] In some embodiments, a fixed absolute benchmark and cold-start default value substitution mechanism is introduced for settlement data to prevent the true slow settlement characteristics from being smoothed out by short-term moving averages. Optionally, the duration of continuous fault-free operation is determined. When this duration does not meet a preset period (e.g., one week), the initial elevation survey values manually entered at the time of commissioning are read and stored in memory as a temporary absolute settlement benchmark. When this duration meets the preset period, all settlement data within the preset period are retrieved from the historical database, and an arithmetic average is performed to obtain a fixed settlement benchmark. This fixed settlement benchmark is then used to overwrite the temporary absolute settlement benchmark and stored as a fixed historical settlement benchmark value. This mechanism ensures that monitoring operations can be started immediately upon power-on and that the true absolute settlement relative to the initial commissioning state is retained during long-term service.
[0027] S102. In response to the occurrence of the impact event, based on the time delay of the impact event at different measuring points on the steel structure, time difference compensation is performed on the strain data and acceleration data collected at each measuring point to generate a set of time difference compensation data segments.
[0028] It should be noted that when the steel structure of a substation is subjected to transient strong impacts such as foreign object impacts or sudden mechanical vibrations, the impact oscillation characteristics are transmitted along the top solid steel to the bottom. Due to the differences in the spatial height distribution of each measuring point, there is a natural propagation delay in the time it takes for the shock wave peak to reach each measuring point. If data is directly intercepted according to the local clock of the sensor, the lower measuring points will truncate the force wave peak that has not yet fully arrived, thus disrupting the temporal consistency of multi-source data fusion. Therefore, this embodiment generates a set of time-difference-compensated data segments aligned in terms of physical causality by performing two stages of processing: transient strong impact event identification and time difference compensation.
[0029] As one possible approach, during the transient strong impact event identification phase, the measuring point with the highest longitudinal coordinate value is first located in the three-dimensional mesh model of the steel structure and defined as the first measuring point. Then, the strain data sequence corresponding to the first measuring point is retrieved, and strain data within the first and second observation windows are extracted from this strain data sequence.
[0030] The first observation window is a short-term observation window used to capture the intensity of fluctuations at the current instant; the second observation window is a long-term observation window used to characterize the average fluctuation level of environmental background noise over a longer period of time. The first and second observation windows end at the same time, and the time span of the first observation window is shorter than that of the second observation window. For example, the first observation window contains a duration of 1 second, while the second observation window contains a duration of 10 minutes.
[0031] Furthermore, the first fluctuation degree of the strain data within the first observation window and the second fluctuation degree of the strain data within the second observation window are determined respectively.
[0032] Optionally, in this embodiment, the first fluctuation level is the variance of the strain data within the first observation window, and the second fluctuation level is the variance of the strain data within the second observation window.
[0033] The ratio of the first fluctuation degree to the second fluctuation degree is then determined as the mutation coefficient. Furthermore, since the first observation window is contained within the second observation window, when the second fluctuation degree is zero, that is, when the variance of the strain data in the second observation window is zero, the variance of the strain data in the first observation window must also be zero, that is, the first fluctuation degree is zero. Therefore, the mutation coefficient is no longer determined by the ratio of the two, and can be directly determined as zero.
[0034] Under normal background oscillation conditions, the magnitudes of the first and second fluctuations are similar, and the mutation coefficient fluctuates around a constant of 1. However, when a transient strong impact event occurs, the magnitude of the first fluctuation increases sharply, while the magnitude of the second fluctuation lags behind, causing the mutation coefficient to amplify rapidly. Based on this, it is determined whether the mutation coefficient is greater than a preset trigger threshold (e.g., an empirical value of 5). When the mutation coefficient is greater than the preset trigger threshold, an impact event is determined to have occurred, and the end time of the first observation window is recorded as the time of occurrence of the impact event.
[0035] During the time difference compensation stage, based on the three-dimensional mesh model of the steel structure, any measuring point located below the first measuring point is defined as the second measuring point, and the spatial distance between the first measuring point and the second measuring point is extracted.
[0036] Optionally, the spatial distance between the first measuring point and the second measuring point can be the straight-line distance between the two measuring points in the three-dimensional mesh model, or it can be the shortest topological transmission distance based on the connecting path between the two measuring points in the three-dimensional mesh model, so as to ensure that the time delay is closer to the actual physical process of stress wave propagation along the solid medium.
[0037] Based on the spatial distance between the first and second measuring points, and combined with the preset stress wave velocity constant (the propagation speed of high-frequency stress waves in steel structures, such as the stress wave velocity constant corresponding to standard carbon structural steel material is 5100 m / s), the time delay of each second measuring point relative to the moment of the impact event is calculated. The calculation method is based on the logic that distance divided by velocity equals time, that is, the time delay is obtained by dividing the spatial distance by the preset stress wave velocity constant.
[0038] Then, the time of the impact event is added to the time delay of each second measuring point to obtain the data interception time reference for each second measuring point.
[0039] After completing the time delay calculation, data truncation and merging operations are performed to obtain a set of time difference compensation data segments.
[0040] Optionally, a first data segment is extracted from the strain and acceleration data collected at the first measuring point, extending a preset truncation time (e.g., 2 seconds) before and after the moment of the impact event. A second data segment is extracted from the strain and acceleration data collected at each second measuring point, extending a preset truncation time before and after the time reference. Finally, the first data segments are merged with all the second data segments to obtain a time-difference-compensated data segment set. All sampling data points in this time-difference-compensated data segment set have their physical causal relationships eliminated due to spatial propagation delays, ensuring that wave peaks under the same transient strong impact event are aligned in the analysis slices.
[0041] It should be noted that the method of determining the occurrence time of the impact event based on the first measuring point with the highest longitudinal coordinate value is applicable to typical working conditions where the shock wave source is located at or above the top of the steel structure and the stress wave mainly propagates in a top-down direction. For scenarios where the location of the impact event is random, such as when a vehicle hits the bottom or middle, causing the stress wave to propagate from bottom to top or to both ends, the mutation coefficient of each measuring point can be determined separately. Based on the mutation coefficient, it can be determined whether it is greater than a preset trigger threshold to determine the occurrence time corresponding to each measuring point. By comparing the occurrence times corresponding to all measuring points, the measuring point corresponding to the earliest occurrence time can be defined as the trigger measuring point, and this occurrence time is taken as the occurrence time of the impact event. The remaining measuring points are defined as influencing measuring points. The trigger measuring point replaces the first measuring point in the above processing, and the influencing measuring points replace the second measuring point in the above processing. Based on the above processing method, a time difference compensation data segment set is obtained, which will not be elaborated here.
[0042] S103. Extract the first index characterizing the stress state of the component from the time difference compensation data segment set, and extract the second index characterizing the geometric deformation state of the component from the tilt angle data and settlement data.
[0043] In the first index extraction stage, for each component, the strain data sequence corresponding to the component is extracted from the time difference compensation data segment set, and the absolute value operation is performed on all sampled values in the strain data sequence to eliminate the difference in positive and negative signs between tensile strain and compressive strain, and the maximum absolute value is selected as the strain peak value.
[0044] Then, the material elastic modulus corresponding to the component is obtained from the local configuration information (for example, for standard carbon steel, the material elastic modulus is taken as a value). Pa) and structural design yield strength (e.g., an empirical value can be taken as ). Based on the classical Hooke's law, the product of the peak strain and the material's elastic modulus is determined as the actual stress borne by the component, and the ratio of the actual stress to the structural design yield strength is further used as the primary indicator.
[0045] Understandably, the first indicator is a dimensionless value used to quantify the stress saturation degree of a component under transient strong impact. The larger the value, the closer the actual stress inside the component is to the material's yield limit, the smaller the remaining capacity of the component to continue to transmit external loads, and the higher the risk of stress saturation.
[0046] In the second indicator extraction stage, for each component, the moment of the impact event is used as the retrieval anchor point. The tilt angle value that is earlier in time and closest to the moment of the event is retrieved from the tilt angle data. The absolute value of the tilt angle value is taken to eliminate the difference in positive and negative signs caused by left or right deviation in the original sensor data, and the absolute value of the tilt angle is obtained.
[0047] A 3D mesh model of the steel structure is used to determine whether a component is directly connected to the foundation node. If the component is directly connected to the foundation, settlement data earlier than and closest to the time of the impact event is extracted from the settlement data. The absolute difference between the extracted settlement data and the historical settlement benchmark value is determined as the settlement change. If the component is not directly connected to the foundation, the settlement change of that component is set to zero.
[0048] Further obtain the preset allowable limit value of the tilt angle (e.g., an empirical value of 2 degrees) and the preset allowable limit value of settlement (e.g., an empirical value of 50 mm); and determine the second index based on the ratio of the absolute value of the tilt angle to the preset allowable limit value of the tilt angle, and the ratio of the amount of settlement change to the preset allowable limit value of settlement.
[0049] In some embodiments, the formula for calculating the second indicator is as follows: in, For the first The second metric for each component is used to quantify the degree to which geometric deformation hinders the transmission of anomalous features. For the first The absolute value of the tilt angle corresponding to each component. The preset allowable tilt angle limit is a non-zero constant. For the first The settlement change corresponding to each component The preset allowable settlement limit is a non-zero constant.
[0050] In the formula, The inclination ratio, which reflects the overall tilt and skewness of the component, The settlement ratio, which reflects the overall settlement degree of the component, is combined with the tilt ratio using arithmetic addition, unifying discrete defects with different physical dimensions into a dimensionless comprehensive evaluation value of geometric degradation. By taking the absolute value of the tilt data, it is ensured that the tilt deviation and settlement subsidence will not cancel each other out due to opposite signs when performing the summation; the outer term is added with a constant of 1 to ensure that even when the component is in an absolutely healthy state with no tilt and no settlement, the minimum value of the second index is always greater than zero.
[0051] Understandably, the second indicator is a dimensionless value used to quantify the degree to which the geometric deformation of a component caused by long-term service hinders the mechanical transmission path. The larger the value, the more serious the deviation of the component from the ideal vertical force transmission axis, and the greater the geometric resistance encountered when external loads are transmitted downward along the component, indicating a high risk of deformation degradation.
[0052] S104. Construct a topology propagation correlation matrix based on the first and second indicators, and invert the topology propagation correlation matrix to obtain the topology risk accumulation index of each node.
[0053] As one possible approach, firstly, the three-dimensional mesh model of the steel structure is read, and all nodes in the model are classified and labeled.
[0054] Optionally, nodes with a vertical coordinate of zero in the 3D mesh model can be extracted as foundation nodes. In subsequent steps, these foundation nodes can be designated as absorbing nodes, representing the fixed ends of the steel structure that are in contact with the ground. All other nodes in the 3D mesh model, excluding foundation nodes, are marked as suspended nodes, and the total number of suspended nodes is counted and denoted as a constant. .
[0055] In some embodiments, since the original physical connection relationships recorded by the 3D mesh model are undirected edges, before constructing directed edges, the undirected physical edges need to be converted into directed edges according to a preset direction rule. The preset direction rule involves reading the spatial 3D coordinates of the nodes at both ends of each undirected physical edge and extracting their respective longitudinal coordinates. If the longitudinal coordinates of the two ends differ, the undirected physical edge is determined as a directed edge pointing from the node with higher elevation to the node with lower elevation. If the longitudinal coordinates of the two ends are the same, the undirected physical edge is split into two directed edges with opposite directions.
[0056] For each suspended node, the three-dimensional mesh model is used to address and determine all downstream adjacent nodes directly connected to the suspended node through directed edges. Each directed edge corresponds to a component, and each directed edge is associated with the first and second indices calculated in the aforementioned step S103.
[0057] For a single directed edge pointing from the suspended node to the downstream adjacent node, the first index of the component corresponding to the single directed edge is added to a preset constant (such as taking an empirical value of 1), and then multiplied by the second index of the component corresponding to the directed edge. The reciprocal of the product is taken as the association weight of the directed edge.
[0058] The first index quantifies the stress saturation degree of a component under transient strong impact. A larger value indicates that the actual stress inside the component is closer to the material's yield limit, leading to a higher degree of transmission blockage. Adding this index to a preset constant prevents the weight calculation from going out of control when the first index is zero under no-load conditions. The second index represents the degree of obstruction caused by the geometric deformation of the component on the mechanical transmission path; a larger value indicates a higher degree of obstruction. Because the calculation uses the reciprocal, a larger first or second index corresponds to a smaller associated weight, indicating more severe structural damage to the directed connection and a more severe blockage of the pathway for transmitting abnormal characteristics downwards.
[0059] It should be noted that for directed edges generated by splitting edges with the same elevation, after calculating the association weight, it is multiplied by a preset bidirectional attenuation coefficient, which is used as the final association weight for the directed edge participating in the normalization process. The preset bidirectional attenuation coefficient has a value range of greater than 0 and less than 1, and an empirical value of 0.1 is used as an example to reduce the weight contribution of cross-connecting components at the same horizontal elevation in topology propagation, and to avoid the infinite oscillation of abnormal features between horizontal layers due to the introduction of bidirectional edges.
[0060] In some embodiments, the formula for calculating the association weight of a directed edge is as follows: In the formula, For the first The dangling node points to the first The association weight of the directed edges of each downstream adjacent node. For the first The dangling node points to the first The first indicator of directed edges connecting the next downstream neighboring node. For the first The dangling node points to the first The second indicator is the directed edges of the downstream adjacent nodes. , The denominator is not zero.
[0061] Further traverse all downstream adjacent nodes of the suspended node to obtain the association weight of the directed edges in each outflow direction. Then, normalize the association weight of each directed edge from the suspended node to the downstream adjacent node to obtain the association distribution coefficient corresponding to each directed edge.
[0062] The correlation distribution coefficient corresponding to each directed edge can be the correlation weight of that directed edge, which is the proportion of the total correlation weight of all directed edges in all outflow directions of the suspended node. The correlation distribution coefficient corresponding to the directed edge is always between 0 and 1, quantifying the non-equilibrium state of the steel structure caused by uneven deformation and different transmission tendencies.
[0063] In some embodiments, the formula for determining the correlation distribution coefficient corresponding to a directed edge can be expressed as follows: In the formula, For the first The dangling node points to the first The correlation distribution coefficient of the directed edges of each downstream adjacent node For the first The dangling node points to the first The association weight of the directed edges of each downstream adjacent node. For the first The total number of downstream adjacent nodes corresponding to each dangling node.
[0064] After determining the association distribution coefficients of each directed edge, fill them into the corresponding positions in the preset matrix. The preset matrix has dimensions of [missing information]. The matrix.
[0065] Among them, if the first The first dangling node If each of the downstream immediate neighboring nodes is a suspended node, then the correlation distribution coefficient... The first one that is effectively recorded in the preset matrix line, number In the column. If the first If a downstream neighboring node is an absorbing node, then the correlation distribution coefficient is discarded and not added to the preset matrix. After completing the iterative calculation of all dangling nodes, the dangling node pairs without directed edges and the elements at the corresponding positions from dangling nodes to absorbing nodes are all set to zero, resulting in a matrix with dimension [missing information]. A real matrix, denoted as the topological propagation incidence matrix. Topological propagation correlation matrix The directed weight distribution records the degree of correlation of abnormal feature propagation among all suspended nodes.
[0066] Furthermore, construct the correlation matrix with topological propagation. An identity matrix of the same dimension has all 1s on its diagonal and all 0s in the remaining positions. Then, subtract the topological propagation incidence matrix from the identity matrix. The difference matrix is obtained, and matrix inversion is performed on the difference matrix to obtain the expected matrix of the transmitted influence. The expected matrix of the transmitted influence This reflects the convergence of the overall structural correlation decay process.
[0067] Finally, for each dangling node, with the first... Taking a suspended node as an example, from the expected matrix of the transmitted influence... Extract the first The row vector corresponding to the nth dangling node is then summed by performing arithmetic summation on each element of the row vector to obtain the nth dangling node. The topological risk accumulation index of a dangling node.
[0068] Optionally, the absorbing node (i.e., the foundation node) represents the fixed end where the bottom of the steel structure contacts the ground. In the topology network, it serves as the final terminal for the propagation of anomalous features. After the impact load is transmitted to the absorbing node via the upper suspended node, it is completely absorbed by the ground foundation. There is no situation where the anomalous features are turned back and accumulated at this node due to the blockage of the downstream path. Therefore, the topological risk accumulation index of the absorbing node can be assigned a value of zero.
[0069] Understandable, if the first If a suspended node is severely deformed, or if several connecting components directly below it exhibit extremely high stress saturation and geometric bending, the abnormal features brought about by the impact cannot smoothly flow into the absorbing node. These abnormal features will then undergo a back-and-forth propagation within the suspended node and its immediate neighbors. Through repeated superposition and iteration of algebraic inversion operations, this is reflected in the macroscopic result as a sharply amplified abnormally large sum of elements in that row. The topological risk accumulation index is a positive dimensionless value greater than zero. The larger the value, the more vulnerable and congested the node's location has become in the network's force transmission channel due to localized obstruction of the force transmission path.
[0070] S105. Extract the vibration characteristics of each node from the time difference compensation data segment set, combine the topological risk accumulation index of each node, generate the joint anomaly index corresponding to each node, and output push information containing the joint anomaly index.
[0071] As one possible implementation, for each component, the acceleration data sequence corresponding to that component is extracted from the time difference compensation data segment set.
[0072] In some embodiments, due to potential changes in the physical installation angle of the sensor during long-term service, the acceleration data sequence often contains a non-zero gravity bias constant offset component. Simultaneously, the slow expansion of steel structural components due to temperature changes also introduces low-frequency drift signals. These low-frequency components do not reflect the structural vibration characteristics caused by transient impacts, and their direct inclusion in calculations would contaminate the vibration energy assessment results. Therefore, the acceleration data sequence is high-pass filtered to block all near-DC slowly varying waveform signals, including the constant gravity component and temperature gradients, thus removing the gravity bias component and low-frequency drift components, resulting in the processed acceleration data sequence.
[0073] Furthermore, the root mean square value of the processed acceleration data sequence is determined as the vibration characteristic of the component.
[0074] Understandably, the root mean square value is amplified by taking the square root of the sum of the squares of the instantaneous acceleration amplitudes at each point in the processed acceleration data sequence, thus amplifying the peak value of sudden high-frequency excitation with destructive potential. It is used to characterize the instantaneous mechanical kinetic energy scale that the component bears under impact events.
[0075] After obtaining the vibration characteristics of all components, for each node, the maximum value among the vibration characteristics of all components connected to that node is determined as the vibration characteristic of that node, in order to characterize the most severe vibration level experienced at that node.
[0076] It should be noted that the topology risk accumulation index calculated in step S104 essentially reflects the inherent vulnerability of the network topology at the current stage. In a static state without any external impact, this static vulnerability objectively exists but does not trigger immediate material collapse or damage. Therefore, the system needs to introduce real-time acquired vibration kinetic energy parameters to perform a joint scaling measure on this static index to filter out false alarms in static environments. For example, when isolated high-frequency vibration interference occurs due to a weak bird impact or localized loosening of the sensor, but the overall deformation of nearby components is slight and the force transmission path is intact, the topology risk accumulation index is extremely low. The combined anomaly index after multiplying the two numbers is still relatively small, thus eliminating false alarms. When no transient strong impact characteristics are detected, the vibration characteristics approach zero. Even if a base column exhibits severe static deformation over many years, resulting in a large topology risk accumulation index, the product result will be assimilated by a zero coefficient, thus avoiding continuous and frequent false alarms under conditions without strong excitation. Only when the weak points of the static topology are actually subjected to a sudden mechanical transient kinetic energy impact, the multiplication operation produces a multiplier effect amplification, and the joint anomaly index of the region shows a characteristic warning of multiplied amplification.
[0077] Based on the logic of this dynamic-static joint verification, the vibration characteristics of each node are multiplied by the topological risk accumulation index of that node to obtain the joint anomaly index corresponding to that node.
[0078] Optionally, before multiplying the vibration characteristics of a node by the topological risk accumulation index, the vibration characteristics of the node can be dimensionlessly processed, such as dividing the vibration characteristics by a preset reference value, which can be the gravitational acceleration or the root mean square reference value of vibration under normal operating conditions.
[0079] Finally, after traversing the joint anomaly index of all nodes, standardized encapsulation and push output are performed.
[0080] In some embodiments, the largest joint anomaly index is selected from all joint anomaly indices, and the location is traced back to extract the spatial coordinates of the node corresponding to the largest joint anomaly index, which is then identified as the target node identifier. Optionally, if multiple joint anomaly indices are all at their maximum values, the spatial coordinates of the nodes corresponding to these multiple joint anomaly indices are identified as the target node identifier. A one-dimensional continuous data cache vector is then constructed, with the occurrence time of the impact event inserted at the very beginning of this one-dimensional data vector as a timeline retrieval reference. The target node identifier and the largest joint anomaly index are pushed into the data vector to accurately pinpoint the physical location of the potential hazard and to quantify the degree of safety threat. Along the connected path of the target node in the three-dimensional mesh model, auxiliary state parameters such as the first index, second index, absolute value of the dip angle, and settlement change of each component along the connected path are extracted and encapsulated into the data vector to assist downstream decision-makers in tracing the classification of the dominant static deformation causes of topological obstruction. Finally, the one-dimensional data vector containing the time reference, node identifier, largest joint anomaly index, and auxiliary parameters is encapsulated into a standardized data vector. This push information is then reported to the remote comprehensive assessment server as a data stream through the device network communication interface.
[0081] Understandably, in the steel structure health characteristic index extraction method based on multi-source data alignment provided in this embodiment of the invention, the spatial distance of each measuring point and the stress wave velocity constant are first used to perform time difference compensation on the strain and acceleration data under impact events, generating a set of time difference-compensated data segments with strict causal order alignment. This eliminates the response waveform misalignment problem caused by the difference in spatial height of the sensors from the source, laying a reliable data foundation for spatiotemporal unification for subsequent fusion analysis. On this basis, the first index reflecting the stress state of the component and the second index reflecting the geometric deformation state of the component are introduced into the graph topology analysis framework. By constructing the topology propagation correlation matrix and performing inversion calculation, the topology risk accumulation index of each node in the entire network is directly obtained. This realizes the quantitative assessment of the chain accumulation effect caused by local defects in the overall force transmission network, breaking through the limitation of traditional methods that can only judge the threshold of a single measuring point in isolation, while avoiding the high computational cost brought by finite element iterative simulation. Furthermore, the node vibration characteristics extracted from the time difference compensation data segment set are multiplied and combined with the topological risk accumulation index to generate a dynamic-static joint anomaly index. The dynamic impact energy is used to cross-validate the static topological vulnerability, so that the index is significantly amplified only when the weak nodes of the structure actually encounter transient strong impacts. This effectively suppresses static false alarms caused by pure geometric skew and dynamic false alarms caused by isolated high-frequency interference. The final output push information containing the joint anomaly index can accurately reflect the true threat level of the structural health status.
[0082] Please see Figure 2 The diagram illustrates a structural schematic of a steel structure health feature index extraction system based on multi-source data alignment, according to an embodiment of the present invention. Figure 2 As shown, the steel structure health feature index extraction system 20 based on multi-source data alignment includes a data acquisition unit 21, a time difference compensation unit 22, a topology solution unit 23, and a joint evaluation unit 24.
[0083] The data acquisition unit 21 is used to acquire measurement data of corresponding measuring points of each component deployed on the steel structure of the substation. The measurement data includes strain data, acceleration data, tilt angle data and settlement data. The steel structure includes multiple nodes connected by components.
[0084] The time difference compensation unit 22 is used to respond to the occurrence of the impact event by compensating for the time difference of the strain data and acceleration data collected by each measuring point according to the time delay of the impact event at different measuring points on the steel structure, and generating a set of time difference compensation data segments.
[0085] The topology solution unit 23 is used to extract a first index characterizing the stress state of the component from the time difference compensation data segment set, extract a second index characterizing the geometric deformation state of the component from the tilt angle data and settlement data, construct a topology propagation correlation matrix based on the first index and the second index, and perform inversion solution on the topology propagation correlation matrix to obtain the topology risk accumulation index of each node.
[0086] The joint evaluation unit 24 is used to extract the vibration characteristics of each node from the time difference compensation data segment set, combine the topological risk accumulation index of each node, generate the joint anomaly index corresponding to each node, and output push information containing the joint anomaly index.
[0087] It should be noted that the steel structure health feature index extraction system 20 based on multi-source data alignment provided in the above embodiments is only an example of the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the computer equipment can be divided into different functional modules to complete all or part of the functions described above.
[0088] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
[0089] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.
Claims
1. A method for extracting health characteristic indicators of steel structures based on multi-source data alignment, characterized in that, The method includes: Acquire measurement data of corresponding measuring points of each component deployed on the steel structure of the substation. The measurement data includes strain data, acceleration data, tilt angle data and settlement data. The steel structure includes multiple nodes connected by components. In response to the moment of impact event, based on the time delay of the impact event at different measuring points on the steel structure, time difference compensation is performed on the strain data and acceleration data collected at each measuring point to generate a set of time difference compensated data segments. A first index characterizing the stress state of the component is extracted from the time difference compensation data segment set, and a second index characterizing the geometric deformation state of the component is extracted from the tilt angle data and settlement data. A topology propagation correlation matrix is constructed based on the first index and the second index, and the topology propagation correlation matrix is inverted to obtain the topology risk accumulation index of each node. The vibration characteristics of each node are extracted from the time difference compensation data segment set, and combined with the topological risk accumulation index of each node, a joint anomaly index corresponding to each node is generated, and push information containing the joint anomaly index is output. Construct a topology propagation correlation matrix based on the first and second indicators, including: In the three-dimensional mesh model of the steel structure, the foundation nodes with a longitudinal coordinate of zero are marked as absorbing nodes, and the other nodes in the three-dimensional mesh model other than the foundation nodes are marked as suspended nodes. The undirected physical edges in the three-dimensional mesh model are transformed into directed edges pointing from upstream nodes to downstream nodes according to a preset direction rule. For each suspended node, determine all downstream adjacent nodes directly connected to the suspended node through directed edges, with each directed edge corresponding to a component; For each directed edge, the first index of the component corresponding to the directed edge is added to a preset constant, and then multiplied by the second index of the component corresponding to the directed edge. The reciprocal of the product is taken as the association weight of the directed edge. For each dangling node, the association weights of each directed edge pointing from the dangling node to its downstream neighbor are normalized to obtain the association distribution coefficients corresponding to each directed edge. The correlation distribution coefficients corresponding to each directed edge are filled into the corresponding positions of the preset matrix, and the correlation distribution coefficients from dangling nodes to absorbing nodes are not filled into the preset matrix, thus forming the topology propagation correlation matrix. By inverting the topological propagation correlation matrix, the topological risk accumulation index of each node is obtained, including: Construct an identity matrix with the same dimensions as the topology propagation correlation matrix; Calculate the difference matrix between the identity matrix and the topology propagation correlation matrix; Inverting the difference matrix yields the expected matrix of the transmitted influence. For each dangling node, extract the row vector corresponding to the dangling node from the expected matrix of the transmitted influence, and sum the elements in the row vector to obtain the topological risk accumulation index of the dangling node.
2. The method for extracting health characteristic indicators of steel structures based on multi-source data alignment according to claim 1, characterized in that, Determining the timing of the impact event includes: Determine the first measuring point with the highest longitudinal coordinate value from the three-dimensional mesh model of the steel structure; Extract the strain data of the first measuring point within the first observation window and the strain data of the first measuring point within the second observation window. The first observation window and the second observation window end at the same time, and the time span of the first observation window is shorter than that of the second observation window. Determine the first degree of fluctuation of the strain data within the first observation window, and the second degree of fluctuation of the strain data within the second observation window; If the ratio of the first fluctuation level to the second fluctuation level is greater than a preset trigger threshold, an impact event is determined to have occurred, and the end time of the first observation window is recorded as the time of occurrence of the impact event.
3. The method for extracting health characteristic indicators of steel structures based on multi-source data alignment according to claim 2, characterized in that, Based on the time delay of the impact event at different measuring points on the steel structure, time-difference compensation is performed on the strain and acceleration data collected at each measuring point, including: From the three-dimensional mesh model of the steel structure, the spatial distance between the first measuring point and the second measuring point is extracted, where the second measuring point is any measuring point located below the first measuring point; Based on the spatial distance and the preset stress wave velocity constant, the time delay of the second measuring point relative to the moment of the impact event is determined; The time of occurrence of the impact event is superimposed with the time delay to serve as the data extraction time reference for the second measuring point.
4. The method for extracting health characteristic indicators of steel structures based on multi-source data alignment according to claim 3, characterized in that, Generate a set of time-difference compensation data segments, including: Centered on the moment of the impact event, a preset time segment is extracted forward and backward, and a first data segment is extracted from the strain data and acceleration data collected at the first measuring point. Using the data interception time reference of the second measuring point as the center, extend the preset interception time forward and backward, and extract the second data segment from the strain data and acceleration data collected from the second measuring point; The first data segment and the second data segment are merged to obtain the time difference compensation data segment set.
5. The method for extracting health characteristic indicators of steel structures based on multi-source data alignment according to claim 1, characterized in that, The first index characterizing the stress state of the component is extracted from the time difference compensation data segment set, including: For each component, extract the strain data sequence corresponding to that component from the time difference compensation data segment set; Take the absolute value of all sampled values in the strain data sequence, and determine the maximum absolute value as the strain peak value; Obtain the material elastic modulus and structural design yield strength of the component; The actual stress borne by the component is determined based on the peak strain and the elastic modulus of the material, and the ratio of the actual stress to the structural design yield strength is used as the first index.
6. The method for extracting health characteristic indicators of steel structures based on multi-source data alignment according to claim 1, characterized in that, A second index characterizing the geometric deformation state of the component is extracted from the dip angle data and settlement data, including: For each component, using the time of occurrence of the impact event as the retrieval anchor point, the tilt angle value that is earlier in time and closest to the time of occurrence is extracted from the tilt angle data, and the absolute value of the extracted tilt angle value is taken to obtain the absolute value of the tilt angle of the component. In the case where the component is directly connected to the foundation, the settlement data that is earlier in time and closest to the time of occurrence is extracted from the settlement data, and the absolute difference between the extracted settlement data and the historical settlement benchmark value is determined as the settlement change of the component. If the component is not directly connected to the foundation, the settlement change of the component is set to zero. Obtain the preset allowable tilt angle limit and the preset allowable settlement limit; The second index is determined based on the ratio of the absolute value of the inclination angle to the preset allowable inclination angle limit, and the ratio of the settlement change to the preset allowable settlement limit.
7. The method for extracting health characteristic indicators of steel structures based on multi-source data alignment according to claim 1, characterized in that, Vibration characteristics of each node are extracted from the time difference compensation data segment set, and combined with the topological risk accumulation index of each node, a joint anomaly index corresponding to each node is generated, including: For each component, an acceleration data sequence corresponding to that component is extracted from the time difference compensation data segment set; The acceleration data sequence is subjected to high-pass filtering to obtain the processed acceleration data sequence; The root mean square value of the processed acceleration data sequence is used to determine the vibration characteristics of the component. For each node, the maximum value among the vibration characteristics of each component connected to the node is determined as the vibration characteristic of the node. The joint anomaly index corresponding to the node is obtained by multiplying the vibration characteristics of the node with the topological risk accumulation index of the node.
8. A system for extracting health characteristic indicators of steel structures based on multi-source data alignment, characterized in that, include: The data acquisition unit is used to acquire measurement data of corresponding measuring points of each component deployed on the steel structure of the substation. The measurement data includes strain data, acceleration data, tilt angle data and settlement data. The steel structure includes multiple nodes connected by components. The time difference compensation unit is used to respond to the occurrence of an impact event by compensating for the time difference of strain and acceleration data collected at different measuring points on the steel structure based on the time delay of the impact event, and generating a set of time difference compensation data segments. The topology calculation unit is used to extract a first index characterizing the stress state of the component from the time difference compensation data segment set, extract a second index characterizing the geometric deformation state of the component from the tilt angle data and settlement data, construct a topology propagation correlation matrix based on the first index and the second index, and perform inversion calculation on the topology propagation correlation matrix to obtain the topology risk accumulation index of each node. The joint evaluation unit is used to extract the vibration characteristics of each node from the time difference compensation data segment set, combine the topological risk accumulation index of each node, generate the joint anomaly index corresponding to each node, and output push information containing the joint anomaly index. Construct a topology propagation correlation matrix based on the first and second indicators, including: In the three-dimensional mesh model of the steel structure, the foundation nodes with a longitudinal coordinate of zero are marked as absorbing nodes, and the other nodes in the three-dimensional mesh model other than the foundation nodes are marked as suspended nodes. The undirected physical edges in the three-dimensional mesh model are transformed into directed edges pointing from upstream nodes to downstream nodes according to a preset direction rule. For each suspended node, determine all downstream adjacent nodes directly connected to the suspended node through directed edges, with each directed edge corresponding to a component; For each directed edge, the first index of the component corresponding to the directed edge is added to a preset constant, and then multiplied by the second index of the component corresponding to the directed edge. The reciprocal of the product is taken as the association weight of the directed edge. For each dangling node, the association weights of each directed edge pointing from the dangling node to its downstream neighbor are normalized to obtain the association distribution coefficients corresponding to each directed edge. The correlation distribution coefficients corresponding to each directed edge are filled into the corresponding positions of the preset matrix, and the correlation distribution coefficients from dangling nodes to absorbing nodes are not filled into the preset matrix, thus forming the topology propagation correlation matrix. By inverting the topological propagation correlation matrix, the topological risk accumulation index of each node is obtained, including: Construct an identity matrix with the same dimensions as the topology propagation correlation matrix; Calculate the difference matrix between the identity matrix and the topology propagation correlation matrix; Inverting the difference matrix yields the expected matrix of the transmitted influence. For each dangling node, extract the row vector corresponding to the dangling node from the expected matrix of the transmitted influence, and sum the elements in the row vector to obtain the topological risk accumulation index of the dangling node.
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