A probabilistic anomaly early warning method for structural monitoring data fusion based on streaming over-threshold and evidence reasoning

Abstract

This invention discloses a probabilistic anomaly early warning method for structural monitoring data fusion based on streaming over-thresholding and evidence-based reasoning. The method includes: establishing historical datasets for each sensor as sample data; separating the sample data by temperature effects and extracting the response components after removing the temperature effects as the initial dataset for anomaly detection; determining the initial threshold; constructing an over-threshold dataset; fitting the over-threshold dataset and obtaining the posterior probability distributions of shape and scale parameters through Bayesian inference; calculating the probability distribution of early warning trigger values; calculating the anomaly certainty index; dynamically updating the probability distribution of early warning trigger values ​​using the streaming over-thresholding method; and synthesizing the results using the evidence fusion method to obtain the fused anomaly certainty index. This invention can form a fused anomaly certainty index, thereby better handling conflicts between indicators, avoiding false alarms caused by single sensor failures, and providing data support for structural maintenance.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring data technology, specifically relating to a probabilistic anomaly early warning method for structural monitoring data fusion based on streaming over-threshold and evidence reasoning. Background Technology

[0002] The primary function of structural health monitoring (SHM) is to monitor the condition of structures in real time or periodically through various sensing methods. With the development of intelligent technologies and the widespread application of monitoring and sensing methods, structural health monitoring data has become a crucial basis for the assessment and maintenance management of large infrastructure structures, leading to the widespread use of structural health monitoring systems. Taking bridge structural health monitoring as an example, effectively utilizing monitoring data to provide early warnings of abnormal bridge responses is of significant importance for ensuring the safe operation and timely maintenance of bridges.

[0003] Currently, early warning systems for abnormal bridge responses typically employ setting thresholds and issuing alarms for responses exceeding these thresholds. Methods for setting thresholds can be broadly categorized into those based on physical material properties and those based on data-driven approaches. Early threshold setting relied on analyses of the structure's ultimate limit state or serviceability limit state, often using material strength or design live load standards as warning thresholds. However, these thresholds essentially reflect the structure's ultimate limit state and are generally far higher than normal monitoring data levels. In practical applications, even if abnormal conditions occur in the bridge structure, the warning is difficult to trigger.

[0004] Building upon this, some scholars have proposed, from a statistical perspective, to construct thresholds based on statistical analysis of monitoring data, thereby determining early warning lines. Under normal operating conditions, the probability of monitored values ​​reaching the set early warning line is extremely small. Once the data touches the early warning line, it can be inferred that the structure is highly likely to be abnormal. Extreme Value Theory (EVT) in statistics is a technical model used to describe and study extreme random events. The EVT framework employs two different methods to model extreme values: the Block Maximum Model (BMM) and the Peak Overthreshold Model (POT). The BMM divides the data into blocks, focusing on analyzing the maximum value within each block, but this can lead to data waste. The Peak Overthreshold (POT) model aims to model data exceeding a given threshold. Non-maximum values ​​within a block are not discarded, thus improving data efficiency. Existing methods for setting early warning lines are often static, meaning that the early warning line cannot be updated with changes in the structural response level, and frequent manual updates of the threshold are inappropriate. Furthermore, the aforementioned early warning line settings remain at the level of deterministic methods, failing to consider uncertainties in the early warning process.

[0005] Furthermore, sensor failures can lead to data loss or errors, thus interfering with structural condition assessments. Researchers have proposed various methods, including statistical methods, signal processing, and machine learning, to diagnose and isolate sensor failures. However, these methods focus on fault diagnosis rather than classification, while distinguishing between sensor failures and structural condition anomalies is crucial. The simultaneous occurrence of actual structural anomalies and sensor failures is a real-world phenomenon with a certain probability, indicating a coupling between the two. In such cases, preventing false alarms and misleading conclusions hinges on accurately identifying and differentiating between structural and sensor anomalies, with a focus on higher-priority structural condition anomalies. In infrastructure health monitoring, introducing decision support methods suitable for handling information conflicts can provide an economical, efficient, and universally applicable technical means for anomaly identification and early warning. Summary of the Invention

[0006] Purpose of the invention: To overcome the shortcomings of existing technologies, this invention provides a probabilistic anomaly early warning method based on streaming over-threshold and evidence-based reasoning for structural monitoring data fusion. This method is a multi-sensor fusion anomaly early warning method with automatic update of early warning values ​​and quantification of structural response anomaly certainty in probabilistic form. It has the advantages of strong interpretability and good data adaptability. It can effectively utilize data streams to update anomaly early warning values ​​in a timely manner and synthesize the anomaly certainty of multiple individual sensors to form a fused anomaly certainty, thereby better handling conflicts between indicators, avoiding false alarms caused by single sensor failures, and providing certain data support for structural maintenance.

[0007] Technical Solution: To achieve the above objectives, this invention provides a probabilistic anomaly early warning method for structural monitoring data fusion based on streaming over-threshold and evidence reasoning, comprising the following steps:

[0008] S1: Based on the monitoring data of the sensors, establish historical datasets for each sensor as sample data;

[0009] S2: Perform temperature effect separation on the sample data and extract the response components after removing the temperature effect as the initial dataset D for anomaly detection;

[0010] S3: Determine the initial threshold based on the initial dataset D;

[0011] S4: Construct the over-threshold dataset based on the initial threshold;

[0012] S5: Fit the overthreshold dataset using a generalized Pareto distribution, and obtain the posterior probability distributions of the shape parameter γ and the scale parameter σ through Bayesian inference;

[0013] S6: Calculate the probability distribution of the warning trigger value based on the posterior probability distribution of the shape parameter γ and the scale parameter σ, and determine the specific form of the probability distribution of the warning trigger value by fitting the sample distribution;

[0014] S7: Calculate the anomaly certainty index based on the probability distribution of the warning trigger value;

[0015] S8: Dynamically update the probability distribution of early warning trigger values ​​using a streaming over-threshold method;

[0016] S9: The anomaly certainty indices of multiple selected individual sensors are synthesized using an evidence fusion method to obtain a fused anomaly certainty index.

[0017] Further, step S1 specifically includes: calculating the Pearson correlation coefficient among multiple sensors, selecting multiple individual sensors with good correlation, extracting the structural response recorded by the sensors as the basis for establishing the fusion probability anomaly determinism index; selecting monitoring data from all sensors within a certain time period, resampling the data, and establishing historical datasets for each sensor as sample data.

[0018] Furthermore, the specific method for separating the temperature effect in step S2 includes: establishing a Bayesian dynamic linear model, decomposing the obtained sample data into a superposition of trend components, periodic components and residual components, and using Kalman filtering to dynamically update the posterior probability of the state parameters of each component, thereby extracting the temperature effect.

[0019] The Bayesian dynamic linear model consists of observation equations and state equations. The observation equations are expressed through the state vector θ. t and observation matrix C t The generated observation value Y t At the same time, the observation error V is added. t The state equation represents the state vector θ. t The evolution over time is influenced by the state transition matrix A. t The influence of the state error W is also present. t ;

[0020] Y t =C t θ t +v t ,v t ~N(0,V) t )

[0021] θ t =A t θ t-1 +w t ,w t ~N(0,W t )

[0022] During the prediction phase, the Kalman filter estimates the prior probability distribution of the parameters at time T+1 based on the posterior distribution of the hidden state parameters at time T using the state equation; the posterior probability distribution of the hidden state parameters at time T is...

[0023] P(θ t |D t )~N(μ t|t ,∑ t|t )

[0024] Where, μ t|t and ∑ t|t Let T and T+1 be the mean and covariance matrices of the posterior probabilities of the state parameters at time t, respectively; and T+1 be the prior distribution of the parameters, obtained from the posterior distribution through the state equation transformation.

[0025] P(θ t+1 |D t )~N(μ t+1|t ,∑ t+1|t )

[0026] Where, μ t+1|t =A t+1 μ t|t ,Σ t+1|t =A t+1 ∑ t A' t+1 +W t+1 ;

[0027] The predicted value of the monitoring data at time T+1 is

[0028] P(Y t+1 |D t )~N(f t+1 Q t+1 )

[0029] Among them, E[Y t+1 |D t ] = C t+1 μ t+1|t ,Var[Y t+1 |D t ] = C t+1 ∑ t+1|t C' t+1 +V t+1 ;

[0030] After obtaining observation data through the monitoring system, the posterior probability distribution of the state parameters is updated using the predicted values ​​and the observed values.

[0031] P(θ t+1 |D t+1 )~N(μ t+1|t+1 ,∑ t+1|t+1 )

[0032] whereμ t+1|t+1 =μ t+1|t +K t+1 e t+1

[0033] ∑ t+1|t+1 =Σ t+1|t -K t+1 K′ t+1 Q t+1

[0034] e t+1 =Y t+1 -f t+1 ,K t+1 =∑ t+1|t C t+1 / Q t+1 .

[0035] Furthermore, the initial threshold in step S3 includes an initial upper bound threshold. and initial lower bound threshold The initial upper bound threshold is determined by calculating the mean transcendental function (MEF). and initial lower bound threshold

[0036] Initial upper bound threshold The calculations include:

[0037] A1: The probability density function of the generalized Pareto distribution is expressed as:

[0038]

[0039] in, σ>0 represents the shape and scale parameters, respectively, and u is a specific threshold; given a sufficiently large threshold u0, for any threshold u>u0, the average excess function MEF(u) is expressed as:

[0040]

[0041] The average excess function MEF(u) is linearly correlated with the threshold u, and its approximate expression is:

[0042]

[0043] Where, N u ={i|X i >u} is a sample X1,…,X n The number of observations exceeding a specific threshold u This corresponds to the excess sample; therefore, the following points will be considered:

[0044]

[0045] Depicted in a two-dimensional coordinate system, if Since u (u>u0) changes approximately linearly, u0 is a suitable threshold.

[0046] A2: The MEF function curve after linear fitting for each threshold u0, corresponding to Figure X;

[0047] A3: Calculate the root mean square error (RMES) between the linear fitting line and the MEF function curve, and use the RMES to quantify the linearity of the MEF function curve;

[0048] The root mean square error (RMSE) is expressed as:

[0049]

[0050] Among them, y i This represents the actual value of the average excess function MEF(u). This represents the linear fit value; the smaller the root mean square error (RMSE), the better the linearity of the MEF(u) function curve.

[0051] A4: Select the threshold at the MEF function curve with the smaller root mean square error as the initial upper bound threshold.

[0052] Initial lower bound threshold Calculation and Same.

[0053] Furthermore, the construction of the over-threshold dataset in step S4 includes:

[0054] Extract data from the initial dataset D that are greater than the initial upper bound threshold. The data forms the Peaks dataset. up ;

[0055] Extract data from the initial dataset D that are less than the initial lower bound threshold. The data forms the Peaks dataset. down .

[0056] Furthermore, in step S5, a generalized Pareto distribution is used to fit the peaks dataset. up and Peaks down The posterior probability distributions of shape parameter γ and scale parameter σ are obtained through Bayesian inference.

[0057] The core of Bayesian inference is Bayes' theorem, which describes how to update posterior probabilities based on existing prior knowledge. Its mathematical expression is:

[0058]

[0059] Here, θ is the unknown parameter to be inferred, namely the shape parameter γ and scale parameter σ of the generalized Pareto model; P(θ|Y) is the posterior distribution of the parameter θ; P(Y|θ) is the likelihood function, representing the probability of observing data X given that the parameter θ is known; P(θ) is the prior distribution of the parameter θ; and P(Y) is the marginal likelihood, which is also a normalization constant. In practice, the posterior distribution cannot be calculated analytically, so numerical methods (such as the Markov chain Monte Carlo method) are used to sample the posterior probability distribution of the parameter.

[0060] Further, step S6 specifically includes:

[0061] B1: Based on the posterior probability distribution of γ and the scale parameter σ according to the generalized Pareto distribution, the warning trigger value is sampled; the value of the warning trigger based on a certain extreme value level is calculated according to the following formula.

[0062]

[0063] Where p is the extreme value level corresponding to a certain return period. According to the design and operation period of the bridge, the quantile corresponding to the 95% guarantee rate within the 100-year operation period is usually taken as the value of p.

[0064] B2: After sampling the warning trigger values, the warning trigger value T is obtained by fitting a log-normal distribution. p The distribution f(T) p ; α,β), corresponding to Appendix X.

[0065] Furthermore, in step S7, the warning trigger value T is used as the basis for... p The distribution f(T) p ; α, β), calculate the normalized anomaly certainty index, the calculation formula is as follows:

[0066]

[0067] Where α and β are the probability distribution parameters of the parameterized trigger. The greater the anomaly certainty, the greater the probability that the point is considered an anomaly.

[0068] Furthermore, in step S8, the early warning trigger value T is dynamically updated using a streaming over-threshold method. p The distribution f(T) p ; α, β), specifically including:

[0069] C1: If the incoming data X new Less than the initial upper bound threshold Or greater than the initial lower bound threshold This value will be considered normal, and the warning trigger value will not be updated.

[0070] C2: If the incoming data X new Greater than the initial upper bound threshold Or less than the initial lower bound threshold Then, calculate the normalized anomaly certainty m according to step S7. i ;

[0071] C3: If the normalized outlier certainty m i Satisfying 0.05 <m i If the value is less than 0.98, then the future stream data X... new Add to Peaks dataset up Or Peaks down And recalculate and update the probability distribution of the warning trigger value through step S6;

[0072] C4: If the normalized outlier certainty m i Satisfy m i If the value is greater than 0.98, then the future stream data X new Add anomaly dataset A up Or A down .

[0073] Further, step S9 specifically includes:

[0074] D1: Determine the identification framework Θ = {C1, C2}, where C1 represents the data warning state and C2 represents the data normal state;

[0075] D2: Organize the anomaly certainty indices of the selected individual sensors into a body of evidence;

[0076] The evidence body, composed of the anomaly certainty indices of multiple individual sensors, is as follows:

[0077] E2:[m1(C1),m1(C2),m1(Θ)]

[0078] E2:[m2(C1),m2(C2),m2(Θ)]

[0079] …

[0080] E N :[m N (C1),m N (C2),m N (Θ)]

[0081] Where, m i (C k ) is assigned to proposition C k Reliability; using abnormal certainty as the basis for proposition C kThe reliability of the data is denoted as m(C1), which represents the certainty of the data warning state; m(C2) represents the certainty of the data normal state.

[0082] m(C1)=m i m(C2)=1-m i

[0083] D3: Calculate the correlation coefficients between each piece of evidence and determine the relationship between each piece of evidence and its corresponding m. i Credibility;

[0084] The evidence synthesis formula is used to synthesize the individual pieces of evidence in the evidence body, and the resulting synthesized evidence is used as the fusion anomaly certainty index.

[0085] The similarity factor between two pieces of evidence is defined as

[0086]

[0087] Where, N A To identify the number of focal elements in the frame; calculate the correlation coefficient r(m) between pairwise pieces of evidence. i ,m j And establish a correlation matrix between the evidence.

[0088]

[0089] Based on the correlation matrix, determine the relationship between each piece of evidence m. i The credibility is calculated using the following formula:

[0090]

[0091] Where R i The value range is [0,1];

[0092] D4: Introduce the credibility of evidence as a weight to modify the original evidence;

[0093] Credibility of Evidence R i It was used to modify the probability assignment function, taking into account ∑m(C k The condition ) = 1, the corrected formula is as follows:

[0094]

[0095] D5: Calculate the conflict coefficient between pieces of evidence;

[0096] Evidence E i and E j The conflict factor is

[0097]

[0098] The average conflict factor between pieces of evidence is

[0099]

[0100] Define the uncertainty of the evidence as in N is the number of pieces of evidence;

[0101] D6: Based on the uncertainty between pieces of evidence, the corrected evidence body is synthesized to obtain the fusion anomaly certainty index; the combination rule for the evidence body is as follows:

[0102]

[0103] Where q(A) is a subset C of the identification frame Θ. k The average support, and

[0104]

[0105] Beneficial Effects: Compared with existing technologies, this invention provides a multi-sensor fusion anomaly early warning method with automatic update of warning values ​​and quantification of structural response anomaly certainty in probabilistic form. It boasts advantages such as strong interpretability and good data adaptability. It effectively utilizes data streams to update anomaly warning values ​​in a timely manner and synthesizes the anomaly certainty of multiple individual sensors to form a fused anomaly certainty. When the fused anomaly certainty is high, it indicates that the abnormal response of the structure is caused by an abnormal event; when the anomaly certainty index of individual sensors is high, but the fused anomaly certainty is low, it indicates that the abnormal response of the structure is caused by sensor failure. Therefore, this invention can better handle conflicts between indices, avoid false alarms caused by single sensor failures, ensure the accuracy of early warnings, and provide certain data support for structural maintenance. Attached Figure Description

[0106] Figure 1 This is a schematic flowchart of the method of the present invention;

[0107] Figure 2 The result graph for linear fitting of each threshold;

[0108] Figure 3 This is the posterior probability distribution of the abnormal warning trigger;

[0109] Figure 4 This is a fitted distribution chart of the warning trigger values;

[0110] Figure 5 This is a diagram illustrating the dynamically updated early warning trigger values ​​obtained based on the method of this invention.

[0111] Figure 6 This is a diagram illustrating the anomaly determination of multi-sensor fusion based on the method of this invention;

[0112] Figure 7 This is a diagram illustrating the multi-sensor fusion anomaly certainty index obtained based on the method of this invention. Detailed Implementation

[0113] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0114] like Figure 1 As shown, this invention provides a probabilistic anomaly early warning method for structural monitoring data fusion based on streaming over-threshold and evidence reasoning, comprising the following steps:

[0115] S1: Based on the monitoring data of the sensors, establish historical datasets for each sensor as sample data;

[0116] The Pearson correlation coefficient among multiple sensors was calculated, and several individual sensors with good correlation were selected. The structural response recorded by the sensors was extracted as the basis for establishing the fusion probability anomaly determinism index. Monitoring data from all sensors within a certain time period were selected, resampled, and historical datasets of each sensor were established as sample data.

[0117] S2: Perform temperature effect separation on the sample data and extract the response components after removing the temperature effect as the initial dataset D for anomaly detection;

[0118] The specific methods for separating the temperature effect include: establishing a Bayesian dynamic linear model, decomposing the obtained sample data into a superposition of trend components, periodic components and residual components, and using Kalman filtering to dynamically update the posterior probability of the state parameters of each component, thereby extracting the temperature effect.

[0119] The Bayesian dynamic linear model consists of observation equations and state equations. The observation equations are expressed through the state vector θ. t and observation matrix C t The generated observation value Y t At the same time, the observation error V is added. t The state equation represents the state vector θ. t The evolution over time is influenced by the state transition matrix A. t The influence of the state error W is also present. t ;

[0120] Y t =C t θ t +v t ,vt ~N(0,V) t )

[0121] θ t =A t θ t-1 +w t ,w t ~N(0,W t )

[0122] During the prediction phase, the Kalman filter estimates the prior probability distribution of the parameters at time T+1 based on the posterior distribution of the hidden state parameters at time T using the state equation; the posterior probability distribution of the hidden state parameters at time T is...

[0123] P(θ t |D t )~N(μ t|t ,∑ t|t )

[0124] Where, μ t|t and ∑ t|t Let T and T+1 be the mean and covariance matrices of the posterior probabilities of the state parameters at time t, respectively; and T+1 be the prior distribution of the parameters, obtained from the posterior distribution through the state equation transformation.

[0125] P(θ t+1 |D t )~N(μ t+1|t ,∑ t+1|t )

[0126] Where, μ t+1|t =A t+1 μ t|t ,Σ t+1|t =A t+1 ∑ t A' t+1 +W t+1 ;

[0127] The predicted value of the monitoring data at time T+1 is

[0128] P(Y t+1 |D t )~N(f t+1 Q t+1 )

[0129] Among them, E[Y t+1 |D t ] = C t+1 μ t+1|t ,Var[Y t+1 |D t ] = C t+1 ∑ t+1|t C' t+1 +V t+1;

[0130] After obtaining observation data through the monitoring system, the posterior probability distribution of the state parameters is updated using the predicted values ​​and the observed values.

[0131] P(θ t+1 |D t+1 )~N(μ t+1|t+1 ,∑ t+1|t+1 )

[0132] whereμ t+1|t+1 =μ t+1|t +K t+1 e t+1

[0133] ∑ t+1|t+1 =∑ t+1|t -K t+1 K′ t+1 Q t+1

[0134] e t+1 =Y t+1 -f t+1 ,K t+1 =∑ t+1|t C t+1 / Q t+1 .

[0135] S3: Determine the initial threshold based on the initial dataset D;

[0136] The initial threshold includes the initial upper bound threshold. and initial lower bound threshold The initial upper bound threshold is determined by calculating the mean transcendental function (MEF). and initial lower bound threshold

[0137] Initial upper bound threshold The calculations include:

[0138] A1: The probability density function of the generalized Pareto distribution is expressed as:

[0139]

[0140] in, σ>0 represents the shape and scale parameters, respectively, and u is a specific threshold; given a sufficiently large threshold u0, for any threshold u>u0, the average excess function MEF(u) is expressed as:

[0141]

[0142] The average excess function MEF(u) is linearly correlated with the threshold u, and its approximate expression is:

[0143]

[0144] Where, N u ={i|X i >u} is a sample X1,…,X n The number of observations exceeding a specific threshold u This corresponds to the excess sample; therefore, the following points will be considered:

[0145]

[0146] Depicted in a two-dimensional coordinate system, if Since u (u>u0) changes approximately linearly, u0 is a suitable threshold.

[0147] A2: Linear fitting of the MEF function curve after each threshold u0, the specific fitting results are as follows. Figure 2 As shown;

[0148] A3: Calculate the root mean square error (RMES) between the linear fitting line and the MEF function curve, and use the RMES to quantify the linearity of the MEF function curve;

[0149] The root mean square error (RMSE) is expressed as:

[0150]

[0151] Among them, y i This represents the actual value of the average excess function MEF(u). This represents the linear fit value; the smaller the root mean square error (RMSE), the better the linearity of the MEF(u) function curve.

[0152] A4: Select the threshold at the MEF function curve with the smaller root mean square error as the initial upper bound threshold.

[0153] Initial lower bound threshold Calculation and Same.

[0154] S4: Construct the over-threshold dataset based on the initial threshold;

[0155] Extract data from the initial dataset D that are greater than the initial upper bound threshold. The data forms the Peaks dataset. up ;

[0156] Extract data from the initial dataset D that are less than the initial lower bound threshold. The data forms the Peaks dataset. down .

[0157] S5: Fit the overthreshold dataset using a generalized Pareto distribution, and obtain the posterior probability distributions of the shape parameter γ and the scale parameter σ through Bayesian inference;

[0158] Fit the Peaks dataset using a generalized Pareto distribution. up and Peaks down The posterior probability distributions of shape parameter γ and scale parameter σ are obtained through Bayesian inference.

[0159] The core of Bayesian inference is Bayes' theorem, which describes how to update posterior probabilities based on existing prior knowledge. Its mathematical expression is:

[0160]

[0161] Where θ is the unknown parameter to be inferred, namely the shape parameter γ and scale parameter σ of the generalized Pareto model; P(θ|Y) is the posterior distribution of the parameter θ; P(Y|θ) is the likelihood function, representing the probability of observing data X given that the parameter θ is known; P(θ) is the prior distribution of the parameter θ; and P(Y) is the marginal likelihood, which is also a normalization constant. Since the posterior distribution cannot be analytically calculated, numerical methods (such as the Markov chain Monte Carlo method) are used to sample the posterior probability distribution of the parameter, specifically as follows: Figure 3 As shown.

[0162] S6: Calculate the probability distribution of the warning trigger value based on the posterior probability distribution of the shape parameter γ and the scale parameter σ, and determine the specific form of the probability distribution of the warning trigger value by fitting the sample distribution;

[0163] Specifically, it includes:

[0164] B1: Based on the posterior probability distribution of γ and the scale parameter σ according to the generalized Pareto distribution, the warning trigger value is sampled; the value of the warning trigger based on a certain extreme value level is calculated according to the following formula.

[0165]

[0166] Where p is the extreme value level corresponding to a certain return period. According to the design and operation period of the bridge, the quantile corresponding to the 95% guarantee rate within the 100-year operation period is usually taken as the value of p.

[0167] B2: After sampling the warning trigger values, the warning trigger value T is obtained by fitting a log-normal distribution. p The distribution f(T) p ; α,β), specifically as Figure 4 As shown.

[0168] S7: Based on the warning trigger value T pThe distribution f(T) p ; α, β), calculate the normalized anomaly certainty index, the calculation formula is as follows:

[0169]

[0170] Where α and β are the probability distribution parameters of the parameterized trigger. The greater the anomaly certainty, the greater the probability that the point is considered an anomaly; the warning trigger value obtained in this embodiment is as follows: Figure 5 As shown;

[0171] S8: Dynamically update the warning trigger value T using a streaming over-threshold method. p The distribution f(T) p ; α, β), specifically including:

[0172] C1: If the incoming data X new Less than the initial upper bound threshold Or greater than the initial lower bound threshold This value will be considered normal, and the warning trigger value will not be updated.

[0173] C2: If the incoming data X new Greater than the initial upper bound threshold Or less than the initial lower bound threshold Then, calculate the normalized anomaly certainty m according to step S7. i ;

[0174] C3: If the normalized outlier certainty m i Satisfying 0.05 <m i If the value is less than 0.98, then the future stream data X... new Add to Peaks dataset up Or Peaks down And recalculate and update the probability distribution of the warning trigger value through step S6;

[0175] C4: If the normalized outlier certainty m i Satisfy m i If the value is greater than 0.98, then the future stream data X new Add anomaly dataset A up Or A down .

[0176] S9: The anomaly certainty indices of multiple selected individual sensors are synthesized using an evidence fusion method to obtain a fused anomaly certainty index, corresponding to the attached... Figure 6 and attached Figure 7Fusion anomaly certainty represents the probability that the structural response is caused by an anomalous event. When the fusion anomaly certainty is high, it indicates that the anomalous response of the structure is caused by an anomalous event; when the anomaly certainty index of individual sensors is high, while the fusion anomaly certainty is low, it indicates that the anomalous response of the structure is caused by sensor failure.

[0177] Specifically, it includes:

[0178] D1: Determine the identification framework Θ = {C1, C2}, where C1 represents the data warning state and C2 represents the data normal state;

[0179] D2: Organize the anomaly certainty indices of the selected individual sensors into a body of evidence;

[0180] The evidence body, composed of the anomaly certainty indices of multiple individual sensors, is as follows:

[0181] E2:[m1(C1),m1(C2),m1(Θ)]

[0182] E2:[m2(C1),m2(C2),m2(Θ)]

[0183] …

[0184] E N :[m N (C1),m N (C2),m N (Θ)]

[0185] Where, m i (C k ) is assigned to proposition C k Reliability; using abnormal certainty as the basis for proposition C k The reliability of the data is denoted as m(C1), which represents the certainty of the data warning state; m(C2) represents the certainty of the data normal state.

[0186] m(C1)=m i m(C2)=1-m i

[0187] D3: Calculate the correlation coefficients between each piece of evidence and determine the relationship between each piece of evidence and its corresponding m. i Credibility;

[0188] The evidence synthesis formula is used to synthesize the individual pieces of evidence in the evidence body, and the resulting synthesized evidence is used as the fusion anomaly certainty index.

[0189] The similarity factor between two pieces of evidence is defined as

[0190]

[0191] Where, NA To identify the number of focal elements in the frame; calculate the correlation coefficient r(m) between pairwise pieces of evidence. i ,m j And establish a correlation matrix between the evidence.

[0192]

[0193] Based on the correlation matrix, determine the relationship between each piece of evidence m. i The credibility is calculated using the following formula:

[0194]

[0195] Where R i The value range is [0,1];

[0196] D4: Introduce the credibility of evidence as a weight to modify the original evidence;

[0197] Credibility of Evidence R i It was used to modify the probability assignment function, taking into account ∑m(C k The condition ) = 1, the corrected formula is as follows:

[0198]

[0199] D5: Calculate the conflict coefficient between pieces of evidence;

[0200] Evidence E i and E j The conflict factor is

[0201]

[0202] The average conflict factor between pieces of evidence is

[0203]

[0204] Define the uncertainty of the evidence as in N is the number of pieces of evidence;

[0205] D6: Based on the uncertainty between pieces of evidence, the corrected evidence body is synthesized to obtain the fusion anomaly certainty index; the combination rule for the evidence body is as follows:

[0206]

[0207] Where q(A) is a subset C of the identification frame Θ. k The average support, and

[0208]

[0209] Based on the above scheme, in order to verify the effectiveness and effect of the method of the present invention, this embodiment uses the method of the present invention to perform anomaly early warning analysis on the structural monitoring data of a suspension bridge structure, as follows:

[0210] The structural health monitoring sensors for a suspension bridge selected based on the Pearson correlation index are shown in Table 1.

[0211] Table 1 Correlation coefficients of the selected sensors

[0212]

[0213]

[0214] To verify the effectiveness of the method of the present invention in fusing anomaly certainty indices, anomaly warnings were issued for monitoring data under the following two operating conditions:

[0215] Condition 1: Real structural anomaly (vehicle collision);

[0216] Operating Condition 2: Sensor Failure.

[0217] Numerical results analysis:

[0218] Operating Condition 1: In this embodiment, anomaly warnings are issued based on the monitoring data of the selected sensor on May 10, 2024. The method in steps S1-S9 is used to dynamically update the anomaly warning value and calculate the anomaly certainty index. The anomaly certainty index at the moment of vehicle collision is shown in Table 2.

[0219] Table 2 shows the anomaly certainty index of the selected volumetric sensors.

[0220]

[0221] Using the method in step 9, the anomaly certainty indices of multiple sensors were synthesized, resulting in a fused anomaly certainty index of 0.99. Figure 6 As can be seen from the data, the high degree of certainty in the fusion anomaly index indicates that a real anomaly event has occurred.

[0222] Scenario 2: In this implementation example, anomaly warnings are generated for the monitoring data of the selected sensor on March 1, 2024. The method from step S1 to step S9 is used to dynamically update the anomaly warning value and calculate the anomaly certainty index. The anomaly certainty index at the moment of sensor failure is shown in Table 3.

[0223] Table 3 shows the anomaly certainty index of the selected volumetric sensors.

[0224]

[0225] Using the method in step S9, the anomaly certainty indices of multiple sensors are synthesized, resulting in a fused anomaly certainty index of 0. Figure 7 It can be seen that although the anomaly certainty index of individual sensors is high, the anomaly certainty index of fusion is low, indicating that the abnormal response at this time is caused by sensor failure.

Claims

1. A structural monitoring data fusion probabilistic anomaly early warning method based on streaming super-threshold and evidential reasoning, characterized in that, The method comprises the following steps: S1: establishing a historical data set of each sensor as sample data according to the monitoring data of the sensors; S2: separating the temperature effect from the sample data to extract a response component after removing the temperature effect as an initial data set D for anomaly detection; S3: determining an initial threshold value according to the initial data set D; S4: constructing a super-threshold data set according to the initial threshold value; S5: Fit the super-threshold data set using a generalized Pareto distribution, obtaining posterior distributions of the shape parameter and scale parameter by Bayesian inference; S6: calculating the probability distribution of the early warning trigger value according to the posterior probability distribution of the shape parameter and the scale parameter and determining the specific form of the probability distribution of the early warning trigger value by fitting the sample distribution; S7: calculating an anomaly determination index based on the probability distribution of the early warning trigger value; S8: dynamically updating the probability distribution of the early warning trigger value through a streaming super-threshold method; S9: synthesizing the anomaly determination indexes of the selected multiple individual sensors through an evidence fusion method to obtain a fused anomaly determination index; Step S6 specifically comprises: B1 : sampling the early warning trigger value from the posterior probability distribution of the generalized Pareto distribution and scale parameter ​ The value of the early warning trigger based on a certain extreme value level is calculated according to the following formula ； wherein, is the extreme level corresponding to a certain return period; B2: after sampling the samples of the early warning trigger value, using the lognormal distribution to fit the distribution of the early warning trigger value ;​ The pre-alarm trigger value in step S7 of the distribution The normalized anomaly certainty index is calculated as follows: ； wherein, is a parameter of the probability distribution of the parameterized trigger; The pre-warning trigger value is dynamically updated by a flow threshold method in step S8 of distribution , specifically comprising: C1: If the incoming data is less than the initial upper threshold or greater than the initial lower threshold , it is considered normal and no update is made to the pre-alarm trigger value; C2: if the incoming data is greater than the initial upper threshold , or less than the initial lower threshold , then compute the normalized anomaly certainty according to step S7; C3: if the normalized anomaly certainty satisfies then the incoming data is added to the super-threshold data set Peaks up or Peaks down and the probability distribution of the early warning trigger value is recomputed and updated through step S6; C4: If the normalized anomaly certainty is satisfied , then the incoming data is added to the anomaly dataset A up or A down .

2. The structural monitoring data fusion probabilistic anomaly warning method based on streaming super-threshold and evidential reasoning according to claim 1, characterized in that, The step S1 specifically comprises: calculating the Pearson correlation coefficients between multiple sensors, selecting multiple individual sensors with good correlation, and extracting the structural response recorded by the sensors as the basis for establishing the fused probability anomaly determination index; resampling the monitoring data of all sensors in a selected time period, and establishing a historical data set of each sensor as sample data.

3. The structural monitoring data fusion probabilistic anomaly warning method based on streaming super-threshold and evidential reasoning according to claim 1, characterized in that, The specific method of temperature effect separation in the step S2 comprises: establishing a Bayesian dynamic linear model, decomposing the obtained sample data into the superposition of trend components, periodic components and residual components, and using Kalman filtering to dynamically update the posterior probability of the state parameters of each component, thereby extracting the temperature effect; The Bayesian dynamic linear model is composed of an observation equation and a state equation. The observation equation represents the generated observation value by a state vector and an observation matrix , while an observation error is added; the state equation represents the evolution of the state vector over time, which is affected by a state transition matrix , while a state error exists. ； ； In the prediction stage, the Kalman filter estimates the prior probability distribution of the parameter at T+1 time through the state equation according to the posterior probability distribution of the hidden state parameter at T time; the posterior probability distribution of the hidden state parameter at T time is ； where and are the mean and covariance matrix of the state parameter posterior at time t, respectively; the prior distribution of the parameters at time T+1, obtained from the posterior distribution by the state equation ； wherein ; The predicted value of the monitoring data at T+1 time is ； wherein ; When the observation data is obtained through the monitoring system, the posterior probability distribution of the state parameter is updated using the predicted value and the observation value ； ； ； 。 4. The structural monitoring data fusion probabilistic anomaly warning method based on streaming super-threshold and evidential reasoning according to claim 1, characterized in that, The initial threshold in the step S3 comprises an initial upper threshold and an initial lower threshold The initial upper threshold and the initial lower threshold are determined by calculating a mean exceedance function MEF, respectively. initial upper bound threshold The calculation of the initial upper bound threshold includes: A1: the probability density function of the generalized Pareto distribution is represented as: ； wherein, , denote shape, scale parameters, respectively, is a specific threshold value; given a threshold , for any threshold, the average excess function is denoted as: ； average excess function is linearly related to the threshold value with an approximate expression ； wherein, is the number of observations in the sample exceeding a certain threshold, is the corresponding excess sample; thus, the following points:​ ； Depicted in a two-dimensional coordinate system, if With respect to Approximately linearly varying, then is a suitable threshold value; A2: Linear fit of each threshold MEF function curve after A3: the root mean square error RMES between the linear fitting line and the MEF function curve is made, and the RMES is used to quantify the linearity of the MEF function curve; The root mean square error RMSE is represented as: ； wherein, represents the average excess function of the actual value, represents the linear fit value; A4: Select the threshold at the MEF function curve with smaller root mean square error as the initial upper threshold ; initial lower bound threshold the calculation of is the same.

5. The structural monitoring data fusion probabilistic anomaly warning method based on streaming super-threshold and evidential reasoning according to claim 4, characterized in that, The construction of the super-threshold data set in the step S4 comprises: extracting data from the initial data set D that is greater than an initial upper bound threshold to form a super-threshold data set Peaks up ; extracting data from the initial dataset D smaller than the initial lower bound threshold to form the super-threshold dataset Peaks down .

6. The structural monitoring data fusion probabilistic anomaly warning method based on streaming super-threshold and evidential reasoning according to claim 5, characterized in that, The step S5 uses a generalized Pareto distribution to fit the super-threshold data set Peaks up and Peaks down The posterior probability distributions of the shape parameter and the scale parameter are obtained by Bayesian inference; The core of Bayesian inference is the Bayesian formula, which describes how to update the posterior probability according to the existing prior knowledge, and its mathematical expression is: ； where θ is the unknown parameter to be inferred, i.e., the shape parameter of the generalized Pareto model and scale parameter , is the posterior distribution of the parameter ; is the likelihood function, representing the probability of observing the data given the parameter ; is the prior distribution of the parameter ; is the marginal likelihood, which is also a normalizing constant; the posterior probability distribution of the parameter is sampled using numerical methods.

7. The structural monitoring data fusion probabilistic anomaly warning method based on streaming super-threshold and evidential reasoning according to claim 6, characterized in that, The step S9 specifically comprises: D1: determining a recognition framework wherein representing a data warning state, representing a data normal state; D2: the anomaly determination indexes of the selected multiple individual sensors are arranged into an evidence body; The evidence body composed of the anomaly determination indexes of the multiple individual sensors is as follows: ； wherein, is the confidence assigned to the proposition ; the confidence of the proposition is determined using the anomaly certainty; is the certainty of the data alert state; is the certainty of the data normal state; ； D3: Calculate the correlation coefficient between each piece of evidence and determine the credibility of each piece of evidence to the evidence body ; The evidence in the evidence body is synthesized using the evidence synthesis formula, and the obtained synthesized evidence is taken as the fused anomaly determination index; The similarity factor between two evidences is defined as ； wherein, to identify the number of focal elements in the framework; to calculate the correlation coefficient between each pair of evidences and to establish a correlation matrix between the evidences ； Based on the correlation matrix, determine the relationship between each piece of evidence. The credibility is calculated using the following formula: ； wherein the value of r ranges from [0, 1]; D4: the evidence credibility is introduced as a weight to modify the original evidence body; Evidence credibility is used to modify the probability distribution function, taking into account the condition that the modified formula is ； D5: the conflict coefficient between the evidences is calculated; Evidence and the conflict factor for ； The average conflict factor between the evidences is ； The uncertainty of the evidence is defined as wherein N is the number of evidence. D6: the modified evidence body is synthesized based on the uncertainty between the evidences to obtain a fused anomaly determination index; The combination rule of the evidence body is ； in, To identify the frame subset of The average support, and ； 。

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