A Bridge Damage Identification Method Based on Chaotic Phase Trajectory Evolution Law

Abstract

This invention discloses a bridge damage identification method based on the evolution law of chaotic phase trajectory, belonging to the field of bridge structural health monitoring. It solves the problem of poor sensitivity in identifying early, weak damage signals in existing technologies. The method includes: plotting the self-power spectrum of the bridge acceleration signal in a healthy state; constructing an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system; acquiring the phase trajectory diagram of the bridge acceleration signal in the healthy state; performing frequency / time scale transformation on the acceleration signal in the state to be diagnosed; comparing the phase trajectory diagram of the state to be diagnosed with that of the healthy state; and determining whether the phase trajectory diagram has entered a large-scale periodic state to identify whether the bridge structure has suffered damage. This invention can transform complex signal analysis into intuitive image comparison, possessing the potential for early bridge damage detection in complex actual operating environments and applicable to bridges with different natural frequencies, significantly enhancing its universality.

Description

Technical Field

[0001] This invention belongs to the field of bridge structural health monitoring, specifically relating to a bridge damage identification method based on the evolution law of chaotic phase trajectory. Background Technology

[0002] As a critical node in transportation networks, the long-term performance of bridges directly impacts the stability and safety of these networks. Over their extended operational cycles, bridge structures inevitably suffer from multiple adverse factors, including environmental erosion, material aging, fatigue load accumulation, and accidental damage. These factors lead to the gradual deterioration of the mechanical properties of bridge materials, weakening of component cross-sections, and continuous accumulation of damage, ultimately manifesting as changes in the overall dynamic characteristics of the structure (such as natural frequency, damping ratio, and mode shape). Since these dynamic characteristic parameters are sensitive indicators of structural stiffness, mass distribution, and connection status, their changes often foreshadow a decrease in load-bearing capacity and an increase in safety risks. Therefore, real-time monitoring and analysis of the evolution of structural dynamic characteristics are crucial for scientifically assessing bridge health, providing timely warnings of structural risks, and making reasonable maintenance decisions. This is a core element in ensuring the long-term safe operation and maintenance of infrastructure.

[0003] However, existing technologies for bridge health monitoring based on dynamic response characteristics still have significant shortcomings in identifying early damage. When a bridge structure experiences initial or minor damage, the resulting changes in dynamic characteristics are typically extremely weak, falling into the category of "small signals." These indicative features of early damage are easily obscured by strong interference factors such as environmental noise, inherent sensor measurement errors, and randomly changing traffic loads during daily operation. In this complex context of low signal-to-noise ratio, traditional damage detection methods mainly rely on frequency domain identification (such as peak picking to analyze the power spectrum) or conventional time domain analysis. However, traditional damage detection methods exhibit significant limitations: their sensitivity is insufficient to effectively separate and identify weak damage features from mixed background noise. This often prevents existing technologies from achieving true early damage warning and precise location, thus posing a potential threat to the long-term operational safety and service life of bridges.

[0004] In summary, existing damage detection methods have poor sensitivity to early, weak damage signals. Traditional methods generally suffer from insufficient sensitivity when strong noise interference and weak damage signals coexist. To address these issues, we propose a bridge damage identification method based on the evolution of chaotic phase trajectories. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a bridge damage identification method based on the evolution law of chaotic phase trajectories. This method solves the problems of poor sensitivity in identifying early weak damage signals and insufficient sensitivity in the presence of strong noise interference and weak damage signals.

[0006] This invention is implemented as follows: a bridge damage identification method based on the evolution law of chaotic phase trajectory, wherein the bridge damage identification method based on the evolution law of chaotic phase trajectory includes:

[0007] S10: Obtain the measured bridge acceleration signal under healthy conditions, plot the self-power spectrum based on the bridge acceleration signal under healthy conditions, analyze the self-power spectrum, and identify the bridge's natural frequency.

[0008] S20, constructing an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system;

[0009] S30 performs frequency / time scale transformation on the bridge acceleration signal, converts the bridge acceleration signal into a reconstructed signal that meets the requirements of the Lorenz system through a variable scaling method, and outputs the reconstructed signal in a healthy state.

[0010] S40, the reconstructed signal in the healthy state is added to the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, the system parameters are adjusted to make the system be in a critical chaotic state, and the phase trajectory diagram of the bridge acceleration signal in the healthy state is obtained.

[0011] S50, acquire the acceleration signal of the bridge structure under the condition to be diagnosed, and use the same parameters and steps as in step S30 to perform frequency / time scale transformation on the acceleration signal of the condition to be diagnosed to obtain the reconstructed signal to be diagnosed.

[0012] S60, input the reconstructed signal to be diagnosed into the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system to obtain the phase trajectory diagram of the bridge acceleration signal under the state to be diagnosed;

[0013] S70, compare the phase trajectory diagram of the state to be diagnosed with the phase trajectory diagram of the healthy state to determine whether the phase trajectory diagram has entered a large-scale periodic state, so as to identify whether the bridge structure has been damaged.

[0014] Preferably, the step of plotting the self-power spectrum based on the bridge acceleration signal under healthy conditions includes:

[0015] S101. Obtain the measured bridge acceleration signal x(t) under healthy conditions. The bridge acceleration signal x(t) under healthy conditions is equivalent to the discrete time-domain signal x[n]. Transform the discrete time-domain signal x[n] into the frequency domain through Discrete Fourier Transform (DFT) to obtain the complex spectrum. ;

[0016] S102, based on the complex spectrum Calculate the one-sided self-power spectral density;

[0017] S103, Identifying the natural frequencies of bridges using peak picking method and modal verification criteria. ;

[0018]

[0019] In the formula: The power spectrum is a function of frequency f. This indicates the natural frequency of the identified bridge (the frequency corresponding to the local peak value). This represents the first derivative of the power spectrum with respect to frequency. This represents the second derivative of the power spectrum with respect to frequency.

[0020] Preferably, the method for constructing an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system includes:

[0021] S201, Construct the initial state equations for an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, where the initial state equations of the system are expressed as:

[0022]

[0023] In the formula: These represent state variables, Indicates the magnitude of the driving force. This represents the angular frequency of the periodic forcing function. These represent the derivatives of the corresponding state variables with respect to time.

[0024] S202, detect signal Simultaneously inserting a sine function enhances the system's state variable response to the input signal, thereby amplifying the phase trajectory change caused by the signal, and adding a detection signal. The improved state equation of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system is expressed as:

[0025]

[0026] in, These represent state variables, Indicates the magnitude of the driving force. This represents the angular frequency of the periodic forcing function. These represent the derivatives of the corresponding state variables with respect to time. For detecting signals;

[0027] S203, Set the detection signal to empty, and adjust the system parameter driving amplitude. Angular frequency of the periodic forcing function This results in the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system being in a critical chaotic state when no detection signal is applied, as indicated by the phase trajectory diagrams drawn from the state variables x and z.

[0028] Preferably, when converting the bridge acceleration signal into a reconstructed signal that meets the requirements of the Lorenz system using a variable-scale method, the frequency / time scale transformation of the bridge acceleration signal is achieved by the following formula:

[0029]

[0030]

[0031] In the formula, f s This represents the sampling frequency of the bridge acceleration signal x(t). This represents the sampling time interval of x(t). This represents the time interval after time scale transformation. This represents the natural frequency of the bridge obtained by identifying the bridge acceleration signal x(t). This represents the reconstructed signal obtained after transforming the bridge acceleration signal x(t). The angular frequency, where R represents the variable scaling factor. The numerical value is determined based on the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, where, =11.527.

[0032] Preferably, when acquiring the phase trajectory diagram of the bridge acceleration signal under healthy conditions, the bridge acceleration signal after variable-scale reconstruction under healthy conditions is used as the detection signal and input into the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. In this case, the improved state equation is expressed as:

[0033]

[0034] In the improved state equation, the values ​​of the driving force amplitude and angular frequency parameters are taken as follows: , An improved four-dimensional hyperchaotic sinusoidal forced Lorenz system was run for analysis and calculation to obtain the phase trajectory diagram of the bridge acceleration signal under healthy conditions.

[0035] Preferably, in step S101, the complex spectrum The calculation formula is as follows:

[0036]

[0037] In the formula: x[n] represents the nth acceleration sample value after discretization, N represents the number of sampling points participating in the Fourier transform, j represents the imaginary unit, and k represents the frequency index, corresponding to the discrete frequency point. , This represents the complex spectrum value after the Fourier transform. Indicates the sampling frequency;

[0038] In step S102, the formula for calculating the one-sided self-power spectral density is as follows:

[0039]

[0040]

[0041]

[0042] In the formula: Indicates frequency The self-power spectral density value at that location, This represents the sampling time interval, and N represents the number of sampling points. Represents the spectrum The model, This represents the frequency value at the k-th frequency point.

[0043] Preferably, in step S103, the natural frequencies of the bridge are identified using the peak picking method and modal verification criteria. When using the modal verification criterion to identify the natural frequencies of a bridge, the MAC test is used to check the correlation between the identified mode shapes and the theoretical mode shapes. Based on the correlation, it is confirmed whether the identified mode shapes are the true natural frequencies of the structure.

[0044] The correlation formula between the mode shapes identified using the MAC test and the theoretical mode shapes is as follows:

[0045]

[0046] In the formula: This represents the correlation coefficient between the r-th and s-th mode shapes. The mode shape vector (column vector) represents the r-th mode. This represents the mode shape vector of the s-th mode. express Hermitian transpose. The modulus of a complex number Representing vectors The inner product of the two modes is its energy, where the closer the value is to 1, the higher the correlation between the identified mode shape and the theoretical mode shape.

[0047] Compared with the prior art, the embodiments of this application have the following main advantages:

[0048] In this embodiment of the invention, an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system is constructed and the signal injection method is optimized. Combined with the frequency / time scale transformation of the acceleration signal, the minute frequency changes caused by early damage to the bridge are mapped to the optimal sensitive frequency band of the chaotic system and significantly amplified. Utilizing the system's extremely high sensitivity to input signal changes in the critical chaotic state, the complex problem of identifying weak damage signals is transformed into an intuitive phase trajectory diagram comparison and analysis. This can overcome strong noise backgrounds and random traffic load interference, effectively identifying early weak damage characteristics that are difficult to detect using traditional methods. Thus, it enables accurate judgment of whether the bridge structure has entered a large-scale periodic state, significantly improving the early warning capability and reliability of the health monitoring system in complex actual operating environments.

[0049] This invention constructs an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. By embedding the detection signal into the phase of a sinusoidal function using nonlinear modulation, it significantly enhances the system's state variable response to input signals compared to traditional linear superposition signal injection methods. Simultaneously, it utilizes the complex dynamic characteristics of the four-dimensional hyperchaotic system, possessing multiple positive Lyapunov exponents, to provide more feature-carrying dimensions for weak signals. By adjusting the driving force amplitude and angular frequency, the system is brought to a critical chaotic state. At this point, the system is precisely located at the phase transition boundary between the chaotic attractor and the periodic orbit, exhibiting extreme sensitivity to frequency perturbations. This allows for the exponential amplification of minute frequency changes caused by early bridge damage through abrupt changes in phase trajectory morphology, achieving a dynamic microscopic detection effect. Furthermore, it can transform complex frequency domain analysis into intuitive image comparison. It not only possesses the capability for early bridge damage detection in high-noise and complex operating environments but also, through frequency / time scale transformation, is applicable to various bridge structures with different natural frequencies, significantly enhancing the method's universality and engineering practicality. Attached Figure Description

[0050] Figure 1 A schematic diagram of the implementation process of a bridge damage identification method based on the evolution law of chaotic phase trajectories is shown.

[0051] Figure 2 The phase trajectory diagram of the bridge acceleration signal in a healthy state is shown for the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system.

[0052] Figure 3 The phase trajectory diagram of the acceleration signal of a bridge under damage state is shown for the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. Detailed Implementation

[0053] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings of this application are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings of this application are used to distinguish different objects, not to describe a particular order.

[0054] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0055] Existing damage detection methods have poor sensitivity to early, weak damage signals. Traditional methods generally suffer from insufficient sensitivity when strong noise interference and weak damage signals coexist. To address these issues, we propose a bridge damage identification method based on the evolution of chaotic phase trajectories. In short, the method first constructs an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system by plotting the self-power spectrum of the bridge acceleration signal in a healthy state. Then, it obtains the phase trajectory diagram of the bridge acceleration signal in the healthy state. Next, it performs a frequency / time scale transformation on the acceleration signal in the state to be diagnosed, obtaining the reconstructed signal to be diagnosed. Finally, it compares the phase trajectory diagram of the state to be diagnosed with that of the healthy state to determine whether the phase trajectory diagram has entered a large-scale periodic state, thus identifying whether damage has occurred in the bridge structure. In this embodiment of the invention, an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system is constructed and the signal injection method is optimized. Combined with the frequency / time scale transformation of the acceleration signal, the minute frequency changes caused by early damage to the bridge are mapped to the optimal sensitive frequency band of the chaotic system and significantly amplified. Utilizing the system's extremely high sensitivity to input signal changes in the critical chaotic state, the complex problem of identifying weak damage signals is transformed into an intuitive phase trajectory diagram comparison and analysis. This can overcome strong noise backgrounds and random traffic load interference, effectively identifying early weak damage characteristics that are difficult to detect using traditional methods. Thus, it enables accurate judgment of whether the bridge structure has entered a large-scale periodic state, significantly improving the early warning capability and reliability of the health monitoring system in complex actual operating environments.

[0056] Example 1

[0057] This invention provides a bridge damage identification method based on the evolution law of chaotic phase trajectories. Figure 1 A schematic diagram illustrating the implementation process of a bridge damage identification method based on the evolution law of chaotic phase trajectories is shown. The bridge damage identification method based on the evolution law of chaotic phase trajectories specifically includes:

[0058] S10: Obtain the measured bridge acceleration signal under healthy conditions, plot the self-power spectrum based on the bridge acceleration signal under healthy conditions, analyze the self-power spectrum, and identify the bridge's natural frequency.

[0059] S20, constructing an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system;

[0060] S30 performs frequency / time scale transformation on the bridge acceleration signal, converts the bridge acceleration signal into a reconstructed signal that meets the requirements of the Lorenz system through a variable scaling method, and outputs the reconstructed signal in a healthy state.

[0061] Specifically, when converting the bridge acceleration signal into a reconstructed signal that meets the requirements of the Lorenz system using a variable-scale method, the frequency / time scale transformation of the bridge acceleration signal is achieved through the following formula, making... The signal requirements for the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system are met: the signal amplitude of x(t) remains constant, and the sampling time interval of x(t) is constant. Adjusted to :

[0062]

[0063]

[0064] In the formula, f s This represents the sampling frequency of the bridge acceleration signal x(t). This represents the sampling time interval of x(t). This represents the time interval after time scale transformation. This represents the natural frequency of the bridge obtained by identifying the bridge acceleration signal x(t). This represents the reconstructed signal obtained after transforming the bridge acceleration signal x(t). The angular frequency, where R represents the variable scaling factor. The numerical value is determined based on the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, where, =11.527.

[0065] S40, the reconstructed signal in the healthy state is added to the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, the system parameters are adjusted to make the system be in a critical chaotic state, and the phase trajectory diagram of the bridge acceleration signal in the healthy state is obtained.

[0066] In acquiring the phase trajectory diagram of the bridge acceleration signal under healthy conditions, the bridge acceleration signal after variable-scale reconstruction under healthy conditions is used as the detection signal and input into the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. The improved state equation is then expressed as:

[0067]

[0068] In the improved state equation, the values ​​of the driving force amplitude and angular frequency parameters are taken as follows: , An improved four-dimensional hyperchaotic sinusoidal forced Lorenz system was run for analysis and calculation to obtain the phase trajectory diagrams of variables x and z, thereby obtaining the phase trajectory diagram of the bridge acceleration signal under healthy conditions.

[0069] S50, acquire the acceleration signal of the bridge structure under the condition to be diagnosed, and use the same parameters and steps as in step S30 to perform frequency / time scale transformation on the acceleration signal of the condition to be diagnosed to obtain the reconstructed signal to be diagnosed.

[0070] In step S50, after acquiring the acceleration signal of the bridge structure under the condition to be diagnosed, the same variable scaling coefficient and transformation process as in step S30 are used to perform frequency / time scale transformation on the acceleration signal of the condition to be diagnosed to ensure the consistency and comparability of data processing between the healthy state and the condition to be diagnosed. Specifically, the variable scaling coefficient R determined based on the bridge's natural frequency identified in step S30 is kept unchanged, and the sampling time interval of the acceleration signal of the condition to be diagnosed is compressed or amplified by the same proportion so that its angular frequency is also mapped to the optimal sensitive frequency band of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, 11.527 rad / s, thereby outputting the reconstructed signal to be diagnosed. This signal only reflects the frequency difference between the condition to be diagnosed and the healthy state caused by structural damage, while excluding the interference caused by different data processing parameters, thus laying a strict basis for subsequent phase trajectory comparison analysis in the same chaotic system.

[0071] S60, input the reconstructed signal to be diagnosed into the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system to obtain the phase trajectory diagram of the bridge acceleration signal under the state to be diagnosed;

[0072] S70, compare the phase trajectory diagram of the state to be diagnosed with the phase trajectory diagram of the healthy state to determine whether the phase trajectory diagram has entered a large-scale periodic state, so as to identify whether the bridge structure has been damaged.

[0073] This invention constructs an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. By optimizing the signal injection method and the system's nonlinear characteristics, it significantly amplifies the minute frequency changes caused by early damage to the bridge structure. A frequency / time scale transformation is performed on the acceleration signal, mapping the original acceleration signal's detection frequency to the optimal sensitive frequency band of the chaotic system, thus achieving signal reconstruction. The reconstructed healthy signal is then added to the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, and the parameters are adjusted. and This method aims to bring the phase trajectory diagrams of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, plotted using variables x and z, into a critical chaotic state, thereby obtaining the phase trajectory diagrams of the bridge acceleration signals under healthy conditions. When analyzing the signals to be diagnosed under different bridge states, the same parameters are used to perform frequency / time scale transformations on the signals to be diagnosed, ensuring complete consistency in data processing before and after. The reconstructed signals to be diagnosed are then input into the same chaotic system to observe their phase trajectory evolution.

[0074] Furthermore, this invention compares the phase trajectory diagram of the acceleration signal of the bridge in the state to be diagnosed with that of the bridge in the healthy state to determine whether the phase trajectory has entered a large-scale periodic state, identifies whether there are slight changes in the natural frequency of the bridge contained in the acceleration signal of the bridge in the state to be diagnosed, and thus identifies whether the bridge structure has suffered structural damage. This method can transform complex signal analysis into intuitive image comparison, has the potential to detect early damage to bridges in complex actual operating environments, and is applicable to bridges with different natural frequencies, significantly enhancing its universality.

[0075] This invention provides a method for plotting a self-power spectrum based on bridge acceleration signals under healthy conditions. Specifically, the method includes:

[0076] S101. Obtain the measured bridge acceleration signal x(t) under healthy conditions. The bridge acceleration signal x(t) under healthy conditions is equivalent to the discrete time-domain signal x[n]. Transform the discrete time-domain signal x[n] into the frequency domain through Discrete Fourier Transform (DFT) to obtain the complex spectrum. ;

[0077]

[0078] In the formula: x[n] represents the nth acceleration sample value after discretization (time domain), N represents the number of sampling points participating in the Fourier transform, j represents the imaginary unit, and k represents the frequency index, corresponding to the discrete frequency point. , This represents the complex spectrum value (frequency domain) after the Fourier transform. Indicates the sampling frequency;

[0079] S102, based on the complex spectrum Calculate the one-sided self-power spectral density;

[0080]

[0081]

[0082]

[0083] In the formula: Indicates frequency The self-power spectral density value at that location, This represents the sampling time interval, and N represents the number of sampling points (the same as N in DFT). Represents the spectrum The magnitude (amplitude) This represents the frequency value of the k-th frequency point;

[0084] S103, Identifying the natural frequencies of bridges using peak picking method and modal verification criteria. ;

[0085]

[0086] In the formula: The power spectrum is a function of frequency f. This indicates the natural frequency of the identified bridge (the frequency corresponding to the local peak value). This represents the first derivative of the power spectrum with respect to frequency. This represents the second derivative of the power spectrum with respect to frequency.

[0087] When using the modal verification criterion to identify the natural frequencies of a bridge, the MAC test is used to check the correlation between the identified mode shapes and the theoretical mode shapes. Based on the correlation, it is confirmed whether the identified mode shapes are the true natural frequencies of the structure.

[0088] The correlation formula between the mode shapes identified using the MAC test and the theoretical mode shapes is as follows:

[0089]

[0090] In the formula: This represents the correlation coefficient between the r-th and s-th mode shapes. The mode shape vector (column vector) represents the r-th mode. This represents the mode shape vector of the s-th mode. express Hermitian transpose. The modulus of a complex number Representing vectors The inner product of the two modes is its energy, where the closer the value is to 1, the higher the correlation between the identified mode shape and the theoretical mode shape.

[0091] This invention provides a method for constructing an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. The method specifically includes:

[0092] S201, Construct the initial state equations for an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, where the initial state equations of the system are expressed as:

[0093]

[0094] In the formula: These represent state variables, Indicates the magnitude of the driving force. This represents the angular frequency of the periodic forcing function. These represent the derivatives of the corresponding state variables with respect to time.

[0095] It should be noted that the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system is a four-dimensional multi-parameter nonlinear dynamic system constructed on the basis of the classical Lorenz system by introducing new state variables and periodic external forces. When improving the Lorenz system in this invention, a fourth state variable u is added on the basis of the three-dimensional Lorenz system (x, y, z), and a four-dimensional space is constructed, which gives it the basis to generate more complex dynamic behaviors (hyperchaos).

[0096] S202, detect signal Simultaneously inserting a sine function enhances the system's state variable response to the input signal, thereby amplifying the phase trajectory change caused by the signal, and adding a detection signal. The improved state equation of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system is expressed as:

[0097]

[0098] in, These represent state variables, Indicates the magnitude of the driving force. This represents the angular frequency of the periodic forcing function. These represent the derivatives of the corresponding state variables with respect to time. For detecting signals;

[0099] In this embodiment of the invention, the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system introduces a periodic forcing function. Unlike traditional systems, the improvement of this invention lies in simultaneously inserting the structural response signal s(t) to be detected into the sine function, so that the external input signal s(t) can be deeply coupled into the nonlinear terms of the system.

[0100] S203, Set the detection signal to empty, and adjust the system parameter driving amplitude. Angular frequency of the periodic forcing function This results in the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system being in a critical chaotic state when no detection signal is applied, as indicated by the phase trajectory diagrams drawn from the state variables x and z.

[0101] In this embodiment, when , At that time, the phase trajectory diagrams drawn by variables x and z are in a critical chaotic state.

[0102] In this embodiment of the invention, the bridge acceleration signal s(t) is added as an input perturbation to the nonlinear term of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system through a signal injection mechanism. Since the system itself is in a critical chaotic state, it is extremely sensitive to minute perturbations, exponentially amplifying minute frequency changes (weak signals) caused by structural damage, thereby producing visible morphological abrupt changes on the phase trajectory diagram. This allows for the effective extraction of early damage features that were previously submerged by noise, thus achieving an intuitive visual representation of the signal characteristics.

[0103] This invention constructs an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. By embedding the detection signal into the phase of a sinusoidal function using nonlinear modulation, it significantly enhances the system's state variable response to input signals compared to traditional linear superposition signal injection methods. Simultaneously, it utilizes the complex dynamic characteristics of the four-dimensional hyperchaotic system, possessing multiple positive Lyapunov exponents, to provide more feature-carrying dimensions for weak signals. By adjusting the driving force amplitude and angular frequency, the system is brought to a critical chaotic state. At this point, the system is precisely located at the phase transition boundary between the chaotic attractor and the periodic orbit, exhibiting extreme sensitivity to frequency perturbations. This allows for the exponential amplification of minute frequency changes caused by early bridge damage through abrupt changes in phase trajectory morphology, achieving a dynamic microscopic detection effect. Furthermore, it can transform complex frequency domain analysis into intuitive image comparison. It not only possesses the capability for early bridge damage detection in high-noise and complex operating environments but also, through frequency / time scale transformation, is applicable to various bridge structures with different natural frequencies, significantly enhancing the method's universality and engineering practicality.

[0104] Example 2

[0105] To verify the effectiveness of the bridge damage identification method based on the chaotic phase trajectory evolution law provided by this invention, acceleration data in healthy and damaged states were obtained using bridge models under different states for verification. The effectiveness of the method (i.e., the bridge damage identification method based on the chaotic phase trajectory evolution law) was verified by analyzing whether the bridge acceleration response phase trajectory evolution in the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system was consistent with the damage simulation in the actual experiment.

[0106] Specifically, acceleration data under different conditions was obtained using a laboratory model of a long-span cable-stayed bridge. The widely accepted method of adding a lumped mass was employed to simulate local stiffness loss, thereby simulating the bridge's structural damage state. A 2kg weight was added at the mid-span of the main span. Acceleration response data was collected for 10 minutes. Based on the bridge acceleration signal measured in the healthy state, the self-power spectrum of the acceleration signal was plotted, identifying the bridge's natural frequency as 9.8877Hz.

[0107] According to the method flow of this invention, the measured acceleration signal is transformed by time-frequency scale, and the acceleration signal of the bridge is transformed by frequency / time scale into a reconstructed signal that meets the usage conditions of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. The amplitude of the driving force of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system parameters is then adjusted. The angular frequency of the periodic forcing function is 1. It is 11.527 rad / s. Figure 2 The figure shows the phase trajectory of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system under healthy conditions, specifically the phase trajectory of the bridge acceleration signal. At this point, the phase trajectory of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system with variables x and z is in a critical state. Figure 2 As shown.

[0108] The acceleration signal simulating the damage state of the bridge structure is transformed by frequency / time scale to preserve the dynamic amplitude of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system parameters. angular frequency constant, Figure 3 The figure shows the phase trajectory of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system under bridge acceleration signal in the damaged state. At this point, the phase trajectory of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system with variables x and z is in a large-scale periodic state, as shown in the figure. Figure 3As shown in the figure. Experimental results demonstrate that combining the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system with bridge acceleration signal analysis provides a novel and sensitive approach for detecting minute frequency changes in structures. The core advantage of this invention lies in utilizing the state abrupt change characteristics of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system to amplify the effects caused by weak damage signals. The improved four-dimensional hyperchaotic sinusoidal forced Lorenz system constructed in this invention exhibits extremely high state resolution and sensitivity. Even extremely small frequency drifts (weak stiffness changes) caused by a 2kg added mass can be captured by the system and amplified into a macroscopic phase trajectory evolution from "chaos" to "period". This result confirms that this method can effectively overcome the technical bottleneck of traditional methods being insensitive to weak damage in strong noise backgrounds, providing a novel, intuitive, and highly sensitive technical approach for early damage detection in bridges.

[0109] In summary, this invention provides a bridge damage identification method based on the evolution law of chaotic phase trajectories. In this embodiment, by constructing an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system and optimizing the signal injection method, combined with frequency / time scale transformation of the acceleration signal, the minute frequency changes caused by early bridge damage are mapped to the optimal sensitive frequency band of the chaotic system and significantly amplified. Utilizing the system's extremely high sensitivity to input signal changes in a critical chaotic state, the complex problem of identifying weak damage signals is transformed into intuitive phase trajectory diagram comparison and analysis. This method can overcome strong noise backgrounds and random traffic load interference, effectively identifying early weak damage features that are difficult to detect using traditional methods. Thus, it achieves accurate judgment on whether the bridge structure has entered a large-scale periodic state, significantly improving the early warning capability and reliability of the health monitoring system in complex actual operating environments.

[0110] It should be noted that, for the sake of simplicity, the foregoing embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to the present invention. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0111] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on these embodiments, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still combine, add, delete, or otherwise adjust the features of the various embodiments of the present invention according to the circumstances without conflict or creative effort, thereby obtaining different technical solutions that do not fundamentally depart from the concept of the present invention. These technical solutions also fall within the scope of protection of the present invention.

Claims

1. A bridge damage identification method based on the evolution law of chaotic phase trajectories, characterized in that, The method includes: S10: Obtain the measured bridge acceleration signal under healthy conditions, plot the self-power spectrum based on the bridge acceleration signal under healthy conditions, analyze the self-power spectrum, and identify the bridge's natural frequency. S20, constructing an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system; S30 performs frequency / time scale transformation on the bridge acceleration signal, converts the bridge acceleration signal into a reconstructed signal that meets the requirements of the Lorenz system through a variable scaling method, and outputs the reconstructed signal in a healthy state. S40, the reconstructed signal in the healthy state is added to the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, the system parameters are adjusted to make the system be in a critical chaotic state, and the phase trajectory diagram of the bridge acceleration signal in the healthy state is obtained. S50, acquire the acceleration signal of the bridge structure under the condition to be diagnosed, and use the same parameters and steps as in step S30 to perform frequency / time scale transformation on the acceleration signal of the condition to be diagnosed to obtain the reconstructed signal to be diagnosed. S60, input the reconstructed signal to be diagnosed into the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system to obtain the phase trajectory diagram of the bridge acceleration signal under the state to be diagnosed; S70, compare the phase trajectory diagram of the state to be diagnosed with the phase trajectory diagram of the healthy state to determine whether the phase trajectory diagram has entered a large-scale periodic state, so as to identify whether the bridge structure has been damaged.

2. The bridge damage identification method based on the chaotic phase trajectory evolution law as described in claim 1, characterized in that: The method of plotting the self-power spectrum based on the bridge acceleration signal under healthy conditions includes: S101. Obtain the measured bridge acceleration signal x(t) under healthy conditions. The bridge acceleration signal x(t) under healthy conditions is equivalent to the discrete time-domain signal x[n]. Transform the discrete time-domain signal x[n] into the frequency domain through Discrete Fourier Transform (DFT) to obtain the complex spectrum. ; S102, according to the complex spectrum Calculate the one-sided self-power spectral density; S103, Identifying the natural frequencies of bridges using peak picking method and modal verification criteria. .

3. The bridge damage identification method based on the chaotic phase trajectory evolution law as described in claim 1, characterized in that: Methods for constructing improved four-dimensional hyperchaotic sinusoidal forced Lorenz systems include: S201, Construct the initial state equations for an improved four-dimensional hyperchaotic sinusoidal forced Lorenz system, where the initial state equations of the system are expressed as: In the formula: These represent state variables, Indicates the magnitude of the driving force. This represents the angular frequency of the periodic forcing function. These represent the derivatives of the corresponding state variables with respect to time. S202, detect signal Simultaneously insert a sine function and add a detection signal. The improved state equation of the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system is expressed as: in, These represent state variables, Indicates the magnitude of the driving force. This represents the angular frequency of the periodic forcing function. These represent the derivatives of the corresponding state variables with respect to time. For detecting signals; S203, Set the detection signal to empty, and adjust the system parameter driving amplitude. Angular frequency of the periodic forcing function This results in the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system being in a critical chaotic state when no detection signal is applied, as indicated by the phase trajectory diagrams drawn from the state variables x and z.

4. The bridge damage identification method based on the chaotic phase trajectory evolution law as described in claim 3, characterized in that: When converting the bridge acceleration signal into a reconstructed signal that meets the requirements of the Lorenz system using a variable-scale method, the frequency / time scale transformation of the bridge acceleration signal is achieved by the following formula: In the formula, f s This represents the sampling frequency of the bridge acceleration signal x(t). This represents the sampling time interval of x(t). This represents the time interval after time scale transformation. This represents the natural frequency of the bridge obtained by identifying the bridge acceleration signal x(t). This represents the reconstructed signal obtained after transforming the bridge acceleration signal x(t). The angular frequency, where R represents the variable scaling factor.

5. The bridge damage identification method based on the chaotic phase trajectory evolution law as described in claim 4, characterized in that: When acquiring the phase trajectory diagram of the bridge acceleration signal under healthy conditions, the bridge acceleration signal after variable-scale reconstruction under healthy conditions is used as the detection signal and input into the improved four-dimensional hyperchaotic sinusoidal forced Lorenz system. The improved state equation is then expressed as: In the improved state equation, the values ​​of the driving force amplitude and angular frequency parameters are taken as follows: , An improved four-dimensional hyperchaotic sinusoidal forced Lorenz system was run for analysis and calculation to obtain the phase trajectory diagram of the bridge acceleration signal under healthy conditions.

6. The bridge damage identification method based on the chaotic phase trajectory evolution law as described in claim 2, characterized in that: In step S101, the complex spectrum The calculation formula is as follows: In the formula: x[n] represents the nth acceleration sample value after discretization, N represents the number of sampling points participating in the Fourier transform, j represents the imaginary unit, and k represents the frequency index, corresponding to the discrete frequency point. , Represents the complex spectrum value after Fourier transform. Indicates the sampling frequency; In step S102, the formula for calculating the one-sided self-power spectral density is as follows: In the formula: Indicates frequency The self-power spectral density value at that location, This represents the sampling time interval, and N represents the number of sampling points. Represents the spectrum The model, This represents the frequency value at the k-th frequency point.

7. The bridge damage identification method based on the chaotic phase trajectory evolution law as described in claim 6, characterized in that: In step S103, the natural frequencies of the bridge are identified using the peak picking method and modal verification criteria. When using the modal verification criterion to identify the natural frequencies of a bridge, the MAC test is used to check the correlation between the identified modal modes and the theoretical modal modes. Based on the correlation, it is confirmed whether the identified modal modes are the true natural frequencies of the structure.

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