A vehicle-induced response identification method based on CEEMDAN-hierarchical clustering

Abstract

This application relates to the field of bridge monitoring technology and provides a vehicle-induced response identification method based on CEEMDAN-hierarchical clustering. The method includes: acquiring original bridge monitoring response data; decomposing the original bridge monitoring response data using the CEEMDAN method to obtain IMF components of various orders; extracting the fundamental frequency of the IMF components using power spectral density; identifying vehicle-induced response components based on frequency thresholds using the fundamental frequency; reconstructing the vehicle-induced response components to obtain vehicle-induced response data containing the vehicle-induced response components; identifying the vehicle-induced response data using an outlier test method to obtain identified vehicle-induced response data; and extracting the vehicle-induced response using a hierarchical clustering method to distinguish vehicle-induced responses. This application enables dynamic adaptive extraction of vehicle-induced responses without the need for fixed windows and fixed thresholds.

Description

Technical Field

[0001] This application relates to the field of bridge monitoring technology, specifically to a vehicle-induced response identification method based on CEEMDAN-hierarchical clustering. Background Technology

[0002] Vehicle load is the most important load component in conventional highway and municipal bridges. Assessing the dynamic response of bridges caused by vehicle load is crucial for understanding their service status. Analyzing the bridge response components under multiple coupled conditions is the first and most critical step in analyzing vehicle-induced effects. Due to the influence of wind load, temperature load, and random noise, accurately extracting vehicle-induced response components is extremely difficult. Furthermore, directly processing unanalyzed coupled responses can lead to significant biases in the evaluation results. Therefore, identifying and extracting vehicle-induced responses from the bridge response is a key step in ensuring the accuracy of the analysis and evaluation.

[0003] Conventional vehicle response identification and extraction typically involves using a fixed-width sliding window to traverse the response sequence and manually setting a threshold. Responses exceeding this threshold are considered vehicle-caused, and all responses within the window are extracted as those caused by that vehicle. The problem with this method is that threshold estimation is difficult, and the fixed window width limits the vehicle passage time, resulting in poor recognition performance. Summary of the Invention

[0004] To help solve the above-mentioned technical problems, this application provides a vehicle response recognition method based on CEEMDAN-hierarchical clustering, which adopts the following technical solution;

[0005] A vehicle-caused response recognition method based on CEEMDAN-hierarchical clustering is disclosed. The method employs a CEEMDAN-hierarchical clustering-based vehicle-caused response recognition system and includes the following steps:

[0006] Obtain raw bridge monitoring response data;

[0007] The original bridge monitoring response data was decomposed using the CEEMDAN method to obtain IMF components of each order.

[0008] The fundamental frequency of the IMF component is extracted by power spectral density, and the vehicle-induced response component is identified based on the fundamental frequency and frequency threshold. The vehicle-induced response component is then reconstructed to obtain vehicle-induced response data containing the vehicle-induced response component.

[0009] The vehicle-induced response data is identified by using the outlier test method to obtain the identified vehicle-induced response data;

[0010] Vehicle-induced responses are extracted using a hierarchical clustering method to distinguish vehicle-induced responses.

[0011] Preferably, the step of decomposing the original bridge monitoring response data using the CEEMDAN method to obtain IMF components of various orders includes:

[0012] Add adaptive white noise to the original response:

[0013] x j (t)=x(t)+εw j (t);

[0014] Where, x j (t) represents the original bridge monitoring response data, ε represents the white noise intensity, and w(t) represents the standard normally distributed white noise signal, j = 1, 2, ..., N. r , is used to represent the realized value.

[0015] Preferably, the step of decomposing the original bridge monitoring response data using the CEEMDAN method to obtain IMF components of various orders includes:

[0016] For each realized value, the EMD method is applied to extract the first-order IMF component:

[0017] IMF 1，j =EMD1[x j (t)];

[0018] Applying the first-order IMF components of CEEMDAN to all IMFs 1，j Mean:

[0019]

[0020] Preferably, the step of decomposing the original bridge monitoring response data using the CEEMDAN method to obtain IMF components of various orders includes:

[0021] Calculate the first-order residual:

[0022] r1(t) = x(t) - IMF1(t),

[0023] Further calculation of higher-order residuals to extract higher-order IMFs:

[0024] IMF s (t)=EMD1[r s (t)+εEMD1[w j (t)]],

[0025]

[0026] Repeat the above steps until the EMD termination condition is met. At this point, the original monitoring response can be expressed as:

[0027]

[0028] Where r k (t) represents the final residual. Treating the final residual as the last-order IMF component, the original monitoring response can be expressed as:

[0029]

[0030] Preferably, the step of extracting the fundamental frequency of the IMF component through power spectral density, identifying the vehicle-induced response component based on a frequency threshold using the fundamental frequency, and reconstructing the vehicle-induced response component to obtain vehicle-induced response data containing the vehicle-induced response component includes:

[0031]

[0032] Among them, IMF s [n] represents the time-domain signal of the IMF component, k is the frequency index, and N is the number of samples.

[0033] Preferably, the step of identifying the vehicle-induced response data using the outlier test method to obtain the identified vehicle-induced response data includes:

[0034] MAD = median(|X) i -median(X)|),

[0035] |X i -median(X)|>k×MAD,

[0036] Among them, X i For the identified vehicle response data, median(·) is the median operation, k is the coefficient, and MAD is the median absolute deviation. When X i Values ​​exceeding k times the MAD are considered outliers.

[0037] Preferably, vehicle-induced responses are extracted using hierarchical clustering methods to distinguish vehicle-induced responses:

[0038] Vehicle-induced responses are extracted using the Single Linkage hierarchical clustering method, where each cluster represents the response caused by a vehicle crossing the bridge.

[0039] Preferably, a vehicle response recognition system based on CEEMDAN-hierarchical clustering includes:

[0040] The bridge monitoring module is used to perform the acquisition of raw bridge monitoring response data;

[0041] The CEEMDAN decomposition module is used to perform the decomposition of the original bridge monitoring response data using the CEEMDAN method to obtain IMF components of each order.

[0042] The PSD analysis module is used to perform the extraction of the fundamental frequency of the IMF component through power spectral density, identify the vehicle-induced response component based on the fundamental frequency and frequency threshold, reconstruct the vehicle-induced response component, and obtain vehicle-induced response data containing the vehicle-induced response component.

[0043] The MAD outlier detection module is used to identify the vehicle-induced response data using the outlier detection method, and obtain the identified vehicle-induced response data.

[0044] The hierarchical clustering analysis module is used to extract vehicle-induced responses using the hierarchical clustering method to distinguish vehicle-induced responses.

[0045] In summary, compared with the prior art, the present invention discloses a vehicle-caused response recognition method based on CEEMDAN-hierarchical clustering, which can achieve dynamic adaptive extraction of vehicle-caused responses without the need for fixed windows and fixed thresholds. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the algorithm flow of the present invention;

[0047] Figure 2 To utilize the IMF components of each order obtained from CEEMDAN decomposition;

[0048] Figure 3 Spectral diagrams of IMF components of various orders analyzed using PSD;

[0049] Figure 4 The reconstructed noise components, trend components, and components containing vehicle-induced responses are used to reconstruct the noise components, trend components, and components.

[0050] Figure 5 To identify the extracted vehicle-induced response using the MAD outlier test and hierarchical clustering. Detailed Implementation

[0051] The present application will be further described below with reference to the accompanying drawings. The structure and principle of the present application are very clear to those skilled in the art. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.

[0052] Figure 1 This is a schematic diagram of the algorithm flow of the present invention. Figure 2 To utilize the IMF components of each order obtained from CEEMDAN decomposition, Figure 3 To utilize the spectrograms of IMF components of various orders analyzed by PSD, Figure 4 To reconstruct the noise components, trend components, and components containing vehicle-induced responses, Figure 5 To identify the extracted vehicle-induced response using the MAD outlier test and hierarchical clustering.

[0053] The case study uses dynamic deflection monitoring data from a real engineering project for analysis and demonstration. Figure 2 By utilizing the IMF components of each order obtained from CEEMDAN decomposition, it can be seen that different IMF components correspond to different frequency bands in the original response; Figure 3 Using the spectrum diagrams of IMF components of each order analyzed by PSD, it can be seen that the fundamental frequency of higher-order noise is higher, while the fundamental frequency of trend components and components containing vehicle-induced responses is lower. Figure 4 The reconstructed noise components, trend components, and components containing vehicle-induced responses show that the components containing vehicle-induced responses exhibit significant abrupt changes in response, corresponding to the transient changes in the bridge monitoring during vehicle movement. Figure 5 The vehicle-induced response extracted using the MAD outlier test and hierarchical clustering method can be seen to have high recognition accuracy.

[0054] Combination Figures 1 to 5 It is understood that the vehicle response recognition method based on CEEMDAN-PSD-MAD-hierarchical clustering in this application includes:

[0055] Obtain raw bridge monitoring response data.

[0056] The original bridge monitoring response data was decomposed using the CEEMDAN method to obtain IMF components of each order.

[0057] The fundamental frequency of the IMF component is extracted by power spectral density. The vehicle-induced response component is identified based on the fundamental frequency and a frequency threshold. The vehicle-induced response component is then reconstructed to obtain vehicle-induced response data containing the vehicle-induced response component.

[0058] The vehicle-induced response data is identified by outlier detection method to obtain identified vehicle-induced response data.

[0059] Vehicle-induced responses are extracted using a hierarchical clustering method to distinguish vehicle-induced responses.

[0060] Specifically, the original bridge monitoring response data is decomposed using the CEEMDAN method to obtain IMF components of various orders, including:

[0061] Add adaptive white noise to the original response:

[0062] x j (t)=x(t)+εw j (t);

[0063] Where, x j (t) represents the original bridge monitoring response data, ε represents the white noise intensity, and w(t) represents the standard normally distributed white noise signal, j = 1, 2, ..., N. r, is used to represent the realized value.

[0064] For each realized value, the EMD method is applied to extract the first-order IMF component:

[0065] IMF 1,j =EMD1[x j (t)];

[0066] Applying the first-order IMF components of CEEMDAN to all IMFs 1，j Mean:

[0067]

[0068] Calculate the first-order residual:

[0069] r1(t) = x(t) - IMF1(t),

[0070] Further calculation of higher-order residuals to extract higher-order IMFs:

[0071] IMF s (t)=EMD1[r s (t)+εEMD1[w j (t)],

[0072]

[0073] Repeat the above steps until the EMD termination condition is met. At this point, the original monitoring response can be expressed as:

[0074]

[0075] Where r k (t) represents the final residual. Treating the final residual as the last-order IMF component, the original monitoring response can be expressed as:

[0076]

[0077] Using the fundamental frequencies of each order of IMF components extracted by PSD analysis, the IMF components in the 0.1-3Hz range are selected to reconstruct a response containing vehicle-induced response components. All IMF components below 0.1Hz are considered trend components, and IMF components above 3Hz are considered noise components.

[0078]

[0079] Among them, IMF s [n] represents the time-domain signal of the IMF component, k is the frequency index, usually 3, and N is the number of samples.

[0080] The vehicle-induced response data was identified using an outlier test, resulting in the following identified vehicle-induced response data:

[0081] MAD = median(|X) i -median(X)|),

[0082] |X i -median(X)|>k×MAD,

[0083] Among them, X i For the identified vehicle response data, median(·) is the median operation, k is the coefficient, and MAD is the median absolute deviation. When X i Values ​​exceeding k times the MAD are considered outliers.

[0084] Vehicle-induced responses are extracted using hierarchical clustering methods to distinguish vehicle-induced responses, including:

[0085] Vehicle-induced responses are extracted using the Single Linkage hierarchical clustering method, where each cluster represents the response caused by a vehicle crossing the bridge.

[0086] This application also proposes a vehicle response recognition system based on CEEMDAN-PSD-MAD-hierarchical clustering using the above method, the system comprising:

[0087] The bridge monitoring module is used to perform the acquisition of raw bridge monitoring response data;

[0088] The CEEMDAN decomposition module is used to perform the decomposition of the original bridge monitoring response data using the CEEMDAN method to obtain IMF components of each order.

[0089] The PSD analysis module is used to perform the extraction of the fundamental frequency of the IMF component through power spectral density, identify the vehicle-induced response component based on the fundamental frequency and frequency threshold, reconstruct the vehicle-induced response component, and obtain vehicle-induced response data containing the vehicle-induced response component.

[0090] The MAD outlier detection module is used to identify the vehicle-induced response data using the outlier detection method, and obtain the identified vehicle-induced response data.

[0091] The hierarchical clustering analysis module is used to extract vehicle-induced responses using the hierarchical clustering method to distinguish vehicle-induced responses.

[0092] Single Linkage hierarchical clustering is a bottom-up hierarchical clustering method that determines cluster merging by calculating the distance between the nearest sample points in different clusters. In this application, this method is used to perform cluster analysis on vehicle-induced responses identified after MAD outlier testing, where each cluster represents the response caused by a vehicle crossing the bridge.

[0093] CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) is an improved ensemble empirical mode decomposition method used to decompose raw bridge monitoring response data to obtain intrinsic mode function (IMF) components of each order.

[0094] PSD (Power Spectral Density) is used to analyze the characteristics of a signal in the frequency domain. By calculating the power spectral density of each order IMF component, the fundamental frequency information is extracted, and the vehicle-induced response components are identified based on frequency thresholds. These components are then reconstructed to obtain vehicle-induced response data containing these components.

[0095] Median Absolute Deviation (MAD) is a robust statistic used to measure the dispersion of data points relative to the median. The MAD outlier test method is used to identify vehicle-induced response data, yielding the identified vehicle-induced response data.

[0096] Hierarchical clustering methods (such as Single Linkage hierarchical clustering) perform cluster analysis on the identified vehicle-induced response data to distinguish vehicle-induced responses caused by different vehicles, thereby achieving dynamic and adaptive extraction of vehicle-induced responses.

Claims

1. A vehicle-caused response recognition method based on CEEMDAN-hierarchical clustering, comprising a vehicle-caused response recognition system based on CEEMDAN-hierarchical clustering, characterized in that, include: Obtain raw bridge monitoring response data; The original bridge monitoring response data was decomposed using the CEEMDAN method to obtain IMF components of each order. The fundamental frequency of the IMF component is extracted by power spectral density, and the vehicle-induced response component is identified based on the fundamental frequency and frequency threshold. The vehicle-induced response component is then reconstructed to obtain vehicle-induced response data containing the vehicle-induced response component. The vehicle-induced response data is identified by using the outlier test method to obtain the identified vehicle-induced response data; Vehicle-induced responses are extracted using a hierarchical clustering method to distinguish vehicle-induced responses. The process of identifying the vehicle-induced response data using the outlier test method yields the following identified vehicle-induced response data: ， ， in, For the identified vehicle response data, the median operation is performed, k is a coefficient, and MAD is the median absolute deviation. When X i satisfy At that time, X i Consider it an outlier; The step of extracting vehicle-induced responses using hierarchical clustering to distinguish vehicle-induced responses includes: Vehicle-induced responses are extracted using the Single Linkage hierarchical clustering method, where each cluster represents the response caused by a vehicle crossing the bridge.

2. The vehicle response recognition method based on CEEMDAN-hierarchical clustering according to claim 1, characterized in that, The original bridge monitoring response data is decomposed using the CEEMDAN method to obtain IMF components of various orders, including: Add adaptive white noise to the original response: ； Where x(t) represents the original bridge monitoring response data. For white noise intensity, w j (t) represents a standard normally distributed white noise signal. x j (t) represents the realized value after adding noise for the jth time.

3. The vehicle response recognition method based on CEEMDAN-hierarchical clustering according to claim 2, characterized in that, The original bridge monitoring response data is decomposed using the CEEMDAN method to obtain IMF components of various orders, including: For each realized value, the EMD method is applied to extract the first-order IMF component: ； Applying the first-order IMF component of CEEMDAN to all Mean: 。 4. The vehicle response recognition method based on CEEMDAN-hierarchical clustering according to claim 3, characterized in that, The original bridge monitoring response data is decomposed using the CEEMDAN method to obtain IMF components of various orders, including: Calculate the first-order residual: ， Further calculation of higher-order residuals to extract higher-order IMFs: ， ， Repeat the above steps until the EMD termination condition is met. At this point, the original monitoring response can be expressed as: ， in As the final residual, which is also considered as the last-order IMF component, the original monitoring response can ultimately be expressed as: 。 5. The vehicle response recognition method based on CEEMDAN-hierarchical clustering according to claim 1, characterized in that, The process of extracting the fundamental frequency of the IMF component through power spectral density, identifying vehicle-induced response components based on a frequency threshold using the fundamental frequency, and reconstructing the vehicle-induced response components to obtain vehicle-induced response data containing the vehicle-induced response components includes: ， in Let k be the time-domain signal of the IMF component, k be the frequency index, and N be the number of samples.

6. The vehicle response recognition method based on CEEMDAN-hierarchical clustering according to claim 1, characterized in that, The vehicle response recognition system based on CEEMDAN-PSD-MAD-hierarchical clustering includes: The bridge monitoring module is used to perform the acquisition of raw bridge monitoring response data; The CEEMDAN decomposition module is used to perform the decomposition of the original bridge monitoring response data using the CEEMDAN method to obtain IMF components of each order. The PSD analysis module is used to perform the extraction of the fundamental frequency of the IMF component through power spectral density, identify the vehicle-induced response component based on the fundamental frequency and frequency threshold, reconstruct the vehicle-induced response component, and obtain vehicle-induced response data containing the vehicle-induced response component. The MAD outlier detection module is used to identify the vehicle-induced response data using the outlier detection method, and obtain the identified vehicle-induced response data. The hierarchical clustering analysis module is used to extract vehicle-induced responses using the hierarchical clustering method to distinguish vehicle-induced responses.

Images