Bridge frequency and damping identification method based on single position acceleration quadratic integration

Abstract

The invention discloses a bridge frequency and damping identification method based on single position acceleration quadratic integral, and relates to the technical field of bridge monitoring, and the method comprises the steps: reconstructing a displacement signal of a bridge through quadratic integral operation for an original acceleration signal of a single acceleration sensor; performing modeling analysis on the original acceleration signal by using a physical information neural network model, and subtracting the displacement signal to obtain a vibration signal; and analyzing the vibration signal by using a fourth-order autoregression model, extracting and selecting conjugate complex poles which conform to the main vibration mode characteristics of the bridge, and obtaining the inherent frequency and damping ratio of the bridge. Only a single acceleration sensor is needed, and the system cost is greatly reduced. Secondly, the signal quality is greatly improved through the physical information neural network model, the inherent frequency and the damping ratio of the inherent frequency can be accurately extracted even if the four-order autoregression model is applied to a single-point response signal, and the method has the advantages of being high in noise robustness, accurate in calculation and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge monitoring, in particular to a bridge frequency and damping identification method based on the quadratic integration of single position acceleration. Background Art

[0002] With the continuous advancement of bridge engineering technology, bridge health monitoring is becoming increasingly critical to ensuring long-term safe operation. Over their long service lives, bridges are inevitably subjected to the erosion of the natural environment and the repeated effects of traffic loads, leading to various types of damage such as cracks, corrosion, and fatigue. If these damages are not discovered and repaired promptly, they will seriously threaten the safety performance and service life of the bridge, and in extreme cases, may even cause catastrophic structural failure. Therefore, real-time monitoring of the actual working status and structural health of bridges, and ensuring their safe operation through effective health monitoring methods, has become a vital part of engineering practice.

[0003] Traditional bridge monitoring methods rely primarily on complex systems of densely deployed strain gauges, displacement sensors, and accelerometers. While these methods can provide relatively accurate data, their high cost and cumbersome data processing pose significant limitations. Especially for beam bridges, which make up the vast majority of bridges, the cost of deploying a comprehensive health monitoring system is prohibitive, making it difficult to implement in practice.

[0004] In contrast, accelerometers have been widely used in bridge monitoring and inspection due to their affordability, ease of installation, and convenient data acquisition. Existing technologies are already able to effectively identify the natural frequency of a bridge using acceleration signals from a single location. However, to simultaneously obtain the bridge's damping ratio, a key parameter, it is usually necessary to meet the basic requirements of modal identification with multi-channel output, that is, to install accelerometers at multiple locations. Although bridges generate free-decaying vibration signals under specific excitation, theoretically, the frequency and damping ratio can be simultaneously identified by searching for such free-decaying vibration signals in the acceleration signals at a single measuring point. However, the reality is that the probability of such free-decaying vibration events occurring in actual operating environments is low, and the number of signals is sparse, making it difficult to accurately capture and utilize them. Therefore, how to overcome technical bottlenecks and reliably and efficiently identify the frequency and damping ratio of a bridge simultaneously based solely on acceleration data from a single location remains a major challenge. Summary of the Invention

[0005] The purpose of the present invention is to provide a bridge frequency and damping identification method based on the quadratic integration of single position acceleration, which aims to overcome the above-mentioned problems existing in the prior art.

[0006] To achieve the purpose, the present invention provides the following technical solutions: A bridge frequency and damping identification method based on the quadratic integration of single-position acceleration includes the following steps: Step S1: a single acceleration sensor is installed only below the bridge, and the original acceleration signal collected by the acceleration sensor is used to reconstruct the displacement signal of the bridge at the detection position through a quadratic integration operation; Step S2: using a physical information neural network model to model and analyze the original acceleration signal, and subtract it from the reconstructed displacement signal to obtain a vibration signal; In step S3, the vibration signal obtained by subtraction is analyzed using a fourth-order autoregressive model, and conjugate complex poles that conform to the main vibration modal characteristics of the bridge are extracted and selected to obtain the natural frequency and damping ratio of the bridge.

[0007] Furthermore, the step S1 specifically includes: Step S101: When a vehicle passes a bridge to be tested at a constant speed along a straight line, the vertical acceleration of the bridge at the position of the acceleration sensor is measured and recorded. ; Vertical acceleration The sampling frequency is , the signal length is The discrete signal, let the discrete time point be , acceleration signal At discrete time points The value of ;in, ; Step S102: Acceleration signal Performing cumulative trapezoidal numerical integration, we obtain:

[0008] in, It's at the time The cumulative integral value of the bridge at the time point speed, , ; Step S103: accumulating the integral value Repeat step S102 to calculate the displacement signal of the bridge , .

[0009] Furthermore, the step S2 specifically includes: Step S201: Acceleration signal The displacement signal obtained by integrating Normalize them separately:

[0010] in, Speed ​​signal The maximum absolute value, To integrate the displacement signal The maximum absolute value; Step S202: construct a deep neural network, which contains three hidden layers, each with 100 neurons, and uses Activation function; at the same time, three learnable parameters are introduced: integral constant , initial velocity constant and the output scaling factor ; The form of the tentative solution is:

[0011] in, is the output of the neural network; Step S203: define the total loss function as:

[0012] in, For physical losses:

[0013] is the initial condition loss:

[0014] For data fidelity loss:

[0015] is the weight of the data fidelity item; Step S204: The displacement signal and Subtract and get the vibration signal of the bridge : .

[0016] Furthermore, the step S3 specifically includes: Step S301: Use the Yule-Walker method to fit a fourth-order autoregressive model to obtain model parameters. The fourth-order autoregressive model expression is:

[0017] in, is the white noise error term, 、 、 、 is the autoregressive coefficient, which reflects the linear relationship strength between the signal and its own value at several moments in the past; vibration signal is the time coefficient at time The value of Indicates in The vibration signal value at each sampling moment, The signal is The values ​​of 1, 2, 3, and 4 sampling moments before the sampling moment, ; Step S302, solve the roots of the characteristic polynomial corresponding to the fourth-order autoregressive model to obtain four discrete domain poles, and select a pair of conjugate complex poles from them, whose corresponding frequencies fall within the expected natural frequency range; Convert to continuous-time poles using the following formula :

[0018] in, is the sampling period; Step S303: Based on the continuous time extremes , calculate the natural frequency of the bridge and damping ratio :

[0019]

[0020] The present invention also discloses a bridge frequency and damping identification device based on the quadratic integration of single position acceleration. The identification device is used to implement any of the above-mentioned identification methods, and includes an acceleration sensor, an integral calculation module, a signal processing module and a parameter extraction module.

[0021] The acceleration sensor is installed below the main beam of the bridge and is used to convert the vibration acceleration of the bridge into a voltage signal, thereby measuring the original acceleration signal of the bridge vibration; The integral calculation module is used to perform a secondary integration on the original acceleration signal of the bridge to estimate the displacement signal of the bridge; The signal processing module is used to perform modeling and analysis on the measured original acceleration signal based on the physical information neural network model, and subtract the measured original acceleration signal from the reconstructed displacement signal to obtain a vibration signal; The parameter extraction module is based on a fourth-order autoregressive model and is used to extract and select conjugate complex poles that meet the main vibration modal characteristics of the bridge, thereby obtaining the natural frequency and damping ratio of the bridge.

[0022] Compared with the prior art, the present invention has the following beneficial effects: First, a breakthrough single-point measurement: The greatest advantage of this invention is that it can simultaneously identify frequency and damping ratio using only a single accelerometer, significantly reducing system cost, installation complexity, and maintenance. This approach is particularly suitable for large girder bridges where a comprehensive monitoring system is difficult to deploy. This approach successfully circumvents the bottlenecks of traditional methods that rely on rare free-decay vibration events or require the use of multiple sensors, providing a more universal and practical solution.

[0023] Second, physics guidance enhances robustness: This invention innovatively introduces the physical information neural network (PINN) model, integrating the basic physical laws of structural dynamics as strong constraints into the data processing process, effectively overcoming the inherent defects of calculating displacement by single-point acceleration integration (drift, noise amplification), and significantly improving the accuracy and robustness of subsequent modal identification (especially damping ratio identification).

[0024] Third, it effectively suppresses noise interference: The physical constraints of the Physical Information Neural Network (PINN) model provide powerful data cleaning and noise reduction capabilities, extracting "pure" vibration components that reflect the structure's true dynamic characteristics from noisy measured signals. Furthermore, the proposed method employs an analysis method based on a fourth-order autoregressive model to accurately extract the bridge's natural frequency and damping ratio, demonstrating high noise robustness and accurate calculations.

[0025] The entire recognition process does not require a large amount of manual intervention and can be automated, thereby improving work efficiency. In addition, the recognition method disclosed in the present invention is applicable to different types of bridge structures, does not require prior information, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a flow chart of the method for identifying bridge frequency and damping ratio in the present invention.

[0027] Figure 2 This is the acceleration time-history response curve (including simulated noise) of a simply supported beam bridge in the span.

[0028] Figure 3 Based on Figure 2 The acceleration time-history response curve shown is the response curve obtained by quadratic integration; among them, (a) is the velocity signal obtained by primary integration, and (b) is the displacement signal obtained by quadratic integration.

[0029] Figure 4 Based on Figure 2 The acceleration time-history response curve shown in the figure is used to model and analyze the vibration signal obtained by subtracting it from the displacement signal. (a) is the static displacement component extracted using the Physical Information Neural Network (PINN) model, and (b) is the free vibration component obtained by differentiating the static displacement component from the displacement signal.

[0030] Figure 5 Based on Figure 2 The acceleration time-history response curve shown is an impulse response diagram obtained based on fourth-order autoregressive model analysis.

[0031] Figure 6 This is a structural block diagram of the device for identifying bridge frequency and damping ratio in the present invention. DETAILED DESCRIPTION

[0032] The specific embodiments of the present invention are described below with reference to the accompanying drawings. In order to fully understand the present invention, many details are described below, but for those skilled in the art, the present invention can be implemented without these details.

[0033] like Figure 1 As shown, a method for identifying bridge frequency and damping ratio based on single-point acceleration is characterized by comprising the following steps: In step S1, a single acceleration sensor is installed only below the bridge, and the original acceleration signal collected by the acceleration sensor is used to reconstruct the displacement signal of the bridge at the detection position through a quadratic integration operation.

[0034] In a specific embodiment, the above step S1 specifically includes: Step S101: When a vehicle passes a bridge to be tested at a constant speed along a straight line, the vertical acceleration of the bridge at the position of the acceleration sensor is measured and recorded. ; Vertical acceleration The sampling frequency is , the signal length is The discrete signal, let the discrete time point be , acceleration signal At discrete time points The value of ;in, .

[0035] Step S102: Acceleration signal Performing cumulative trapezoidal numerical integration, we obtain:

[0036] in, It's at the time The cumulative integral value of the bridge at the time point speed, , .

[0037] Step S103: accumulating the integral value Repeat step S102 to calculate the displacement signal of the bridge .

[0038] Step S1 requires only data from a single-point acceleration sensor, eliminating the need for additional displacement sensors or measurement points, maintaining the solution's economy and portability. Furthermore, since displacement signals are typically more sensitive to low-frequency structural vibrations (such as the primary modes of a bridge), they contain more information about the bridge's overall stiffness and deformation. This provides a perspective beyond the acceleration signal for subsequent analysis and provides key physical constraints for the modeling of the physical information neural network in step S2.

[0039] In step S2, the original acceleration signal is modeled and analyzed using a physical information neural network (PINN) model, and the original acceleration signal is subtracted from the reconstructed displacement signal to obtain a vibration signal.

[0040] In a specific embodiment, the above step S2 specifically includes: Step S201: Acceleration signal The displacement signal obtained by integrating Normalize them separately:

[0041] in, Speed ​​signal The maximum absolute value, To integrate the displacement signal The absolute maximum value.

[0042] Step S202: construct a deep neural network, which contains three hidden layers, each with 100 neurons, and uses Activation function; at the same time, three learnable parameters are introduced: integral constant , initial velocity constant and the output scaling factor ; The form of the tentative solution is:

[0043] in, is the output of the neural network.

[0044] Step S203: define the total loss function as:

[0045] in, For physical losses:

[0046] is the initial condition loss:

[0047] For data fidelity loss:

[0048] is the weight of the data fidelity item; Step S204: The displacement signal and Subtract and get the vibration signal of the bridge : .

[0049] In step S2, the physical information neural network (PINN) model aims to learn a function that fits the observed acceleration data while also satisfying the fundamental physical laws of bridge dynamics. By subtracting the model's analysis of the original acceleration signal from the reconstructed displacement signal from step S1, a "pure" vibration signal is generated that better reflects the inherent vibration characteristics of the bridge structure, filtering out or attenuating noise, environmental interference, and errors that may be introduced by the integration process.

[0050] In step S3, the vibration signal obtained by subtraction is analyzed using the fourth-order autoregressive (AR(4)) model, and the conjugate complex poles that conform to the main vibration modal characteristics of the bridge are extracted and selected to obtain the natural frequency and damping ratio of the bridge.

[0051] In a specific embodiment, the above step S3 specifically includes: Step S301: Use the Yule-Walker method to fit a fourth-order autoregressive model to obtain model parameters. The fourth-order autoregressive model expression is:

[0052] in, is the white noise error term, 、 、 、 is the autoregressive coefficient, which reflects the linear relationship strength between the signal and its own value at several moments in the past; vibration signal is the time coefficient at time The value of Indicates in The vibration signal value at each sampling moment, The signal is The values ​​of 1, 2, 3, and 4 sampling moments before the sampling moment, .

[0053] Step S302, solve the roots of the characteristic polynomial corresponding to the fourth-order autoregressive model to obtain four discrete domain poles, and select a pair of conjugate complex poles from them, whose corresponding frequencies fall within the expected natural frequency range; Convert to continuous-time poles using the following formula :

[0054] in, is the sampling period.

[0055] Step S303: Based on the continuous time extremes , calculate the natural frequency of the bridge and damping ratio :

[0056] .

[0057] Because step S2 significantly improves signal quality through physical constraints, the fourth-order autoregressive (AR(4)) model can more reliably identify modal parameters (especially the damping ratio) even when applied to a single-point response signal. Traditional fourth-order autoregressive models are often ineffective at identifying the damping ratio of single-point signals because single-point signals typically contain multiple modes and have an insufficient signal-to-noise ratio. Step S2 of the present invention effectively alleviates this problem.

[0058] Practice Test like Figure 1-Figure 5 As shown in the figure, a finite element model of a bridge is created in Abaqus software. The model is a 40-meter simply supported beam bridge with a single span structure and a main span length of 40 meters. , moment of inertia , mass per unit length , elastic modulus . For bridge monitoring, only one accelerometer was set up in the mid-span, and the accelerometer collected 801 data at a sampling rate of 100 Hz. By converting the data in Abaqus software into mat format in MATLAB software, the acceleration time-history response curve of the measuring point in the mid-span of the bridge was obtained. Since the acceleration time-history response curve contains many typical free decay signals, the data collected by a single accelerometer can be used for damage identification, avoiding the complexity of installing multiple sensors. Through numerical simulation research, the natural frequency, vibration mode, damping ratio under bridge damage and structural modal parameter transformation caused by environmental factors are explored, which provides valuable data and experience for bridge health monitoring and damage identification, and has important practical significance.

[0059] First, 10% noise is added to the acceleration data monitored by the acceleration sensor to simulate the measurement error and the impact of factors such as road roughness on the original acceleration signal measured by the acceleration sensor in real situations. Figure 2 shown.

[0060] The original acceleration signal after adding noise is preprocessed to remove the trend term and noise in the signal. Then the acceleration signal is integrated once to obtain the velocity data. Then the velocity data is integrated twice to obtain the displacement data, i.e. the displacement signal. The result of the second integration is as follows: Figure 3 As shown in Figure 2, (a) is the velocity signal obtained by the first integration, and (b) is the displacement signal obtained by the second integration.

[0061] Next, the physical information neural network (PINN) model is used to model and analyze the measured acceleration signal, and the vibration signal is subtracted from the reconstructed displacement signal, such as Figure 4 shown.

[0062] Finally, based on the fourth-order autoregressive model analysis, the impulse response diagram is obtained, such as Figure 5 As shown in Table 1, the natural frequency and damping ratio of the bridge are accurately extracted.

[0063] The automatic identification results of the present invention are compared with the natural frequencies and damping ratios of the numerical simulation based on the reference, as shown in Table 1.

[0064] Table 1:

[0065] As can be seen from Table 1, in this simulation test, it is proved that the automatic identification method proposed in the present invention has strong robustness and is expected to be widely used in real-time health monitoring of bridges.

[0066] The present invention also discloses a bridge frequency and damping identification device based on the quadratic integration of single-position acceleration. The identification device is used to implement the above-mentioned identification method, and includes an interconnected acceleration sensor, an integral calculation module, a signal processing module and a parameter extraction module.

[0067] The acceleration sensor is installed under the main beam of the bridge and is used to convert the vibration acceleration of the bridge into a voltage signal, thereby measuring the original acceleration signal of the bridge vibration.

[0068] The integral calculation module is used to perform secondary integration on the original acceleration signal of the bridge to estimate the displacement signal of the bridge.

[0069] The signal processing module, based on the physical information neural network model, is used to model and analyze the measured original acceleration signal and subtract it from the reconstructed displacement signal to obtain the vibration signal.

[0070] The parameter extraction module, based on the fourth-order autoregressive model, is used to extract and select the conjugate complex poles that conform to the main vibration modal characteristics of the bridge, and then obtain the natural frequency and damping ratio of the bridge.

[0071] The above is only a specific implementation of the present invention, but the design concept of the present invention is not limited to this. Any non-substantial changes to the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.

Claims

1. A bridge frequency and damping identification method based on the quadratic integration of single-position acceleration, characterized by: The following steps are involved: Step S1: a single acceleration sensor is installed only below the bridge, and the original acceleration signal collected by the acceleration sensor is used to reconstruct the displacement signal of the bridge at the detection position through a quadratic integration operation; Step S2: using a physical information neural network model to model and analyze the original acceleration signal, and subtract it from the reconstructed displacement signal to obtain a vibration signal; In step S3, the vibration signal obtained by subtraction is analyzed using a fourth-order autoregressive model, and conjugate complex poles that conform to the main vibration modal characteristics of the bridge are extracted and selected to obtain the natural frequency and damping ratio of the bridge.

2. The bridge frequency and damping identification method based on the quadratic integration of single-position acceleration according to claim 1 is characterized by: The step S1 specifically includes: Step S101: When a vehicle passes a bridge to be tested at a constant speed along a straight line, the vertical acceleration of the bridge at the position of the acceleration sensor is measured and recorded. ; Vertical acceleration The sampling frequency is , the signal length is The discrete signal, let the discrete time point be , acceleration signal At discrete time points The value of ;in, ; Step S102: Acceleration signal Performing cumulative trapezoidal numerical integration, we obtain: in, It's at the time The cumulative integral value of the bridge at the time point speed, , ; Step S103: accumulating the integral value Repeat step S102 to calculate the displacement signal of the bridge , , .

3. The bridge frequency and damping identification method based on the quadratic integration of single-position acceleration according to claim 1 is characterized by: The step S2 specifically includes: Step S201: Acceleration signal The displacement signal obtained by integrating Normalize them separately: in, is the acceleration signal The maximum absolute value, To integrate the displacement signal The maximum absolute value; Step S202: construct a deep neural network, which contains three hidden layers, each with 100 neurons, and uses Activation function; at the same time, three learnable parameters are introduced: integral constant , initial velocity constant and the output scaling factor ; The form of the tentative solution is: in, is the output of the neural network; Step S203: define the total loss function as: in, For physical losses: is the initial condition loss: For data fidelity loss: is the weight of the data fidelity item; Step S204: The displacement signal and Subtract and get the vibration signal of the bridge : 。 4. The bridge frequency and damping identification method based on the quadratic integration of single-position acceleration according to claim 1 is characterized by: The step S3 specifically includes: Step S301: Use the Yule-Walker method to fit a fourth-order autoregressive model to obtain model parameters. The fourth-order autoregressive model expression is: in, is the white noise error term, 、 、 、 is the autoregressive coefficient, which reflects the linear relationship strength between the signal and its own value at several moments in the past; vibration signal is the time coefficient at time The value of Indicates in The vibration signal value at each sampling moment, The signal is The values ​​of 1, 2, 3, and 4 sampling moments before the sampling moment, ; Step S302, solve the roots of the characteristic polynomial corresponding to the fourth-order autoregressive model to obtain four discrete domain poles, and select a pair of conjugate complex poles from them, whose corresponding frequencies fall within the expected natural frequency range; Convert to continuous-time poles using the following formula : in, is the sampling period; Step S303: Based on the continuous time extremes , calculate the natural frequency of the bridge and damping ratio : 。 5. A bridge frequency and damping identification device based on the quadratic integration of single-position acceleration, characterized by: The recognition device is used to implement the recognition method according to any one of claims 1 to 4, and includes an acceleration sensor, an integral calculation module, a signal processing module and a parameter extraction module.

6. The acceleration sensor is installed below the main beam of the bridge and is used to convert the vibration acceleration of the bridge into a voltage signal, thereby measuring the original acceleration signal of the bridge vibration; The integral calculation module is used to perform a secondary integration on the original acceleration signal of the bridge to estimate the displacement signal of the bridge; The signal processing module is used to perform modeling and analysis on the measured original acceleration signal based on the physical information neural network model, and subtract the measured original acceleration signal from the reconstructed displacement signal to obtain a vibration signal; The parameter extraction module is based on a fourth-order autoregressive model and is used to extract and select conjugate complex poles that meet the main vibration modal characteristics of the bridge, thereby obtaining the natural frequency and damping ratio of the bridge.

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