Two-dimensional micro-damage localization method and device based on Duffing oscillator

Abstract

The invention discloses a two-dimensional micro-damage positioning method and device based on Duffing oscillator, including: arranging a group of PZT piezoelectric sensors on a uniform structural part to form an exciter-sensor monitoring channel; collecting structural nonlinear Lamb wave response signals of all monitoring channels; inputting the nonlinear Lamb wave signals of all monitoring channels into the adjusted Duffing chaotic oscillator and reconstructing the phase space to calculate the maximum Lyapunov index; according to the maximum Lyapunov index in the healthy state and the maximum Lyapunov index in the damaged state of the same path, calculating the damage index under this path and performing normalization processing; using the calculated damage positioning index to perform two-dimensional plane positioning evaluation on micro-damage. The method of the invention can monitor the nonlinear signal caused by structural nonlinearity to a certain extent, improve the monitoring efficiency of nonlinear signals, evaluate its current damage degree, and complete the preliminary positioning of early micro-damage of the structure, thereby improving the accuracy of the monitoring results.

Description

Technical Field

[0001] The present invention relates to a two-dimensional micro-damage positioning method and device based on a Duffing oscillator, and in particular to a method for monitoring nonlinear signals in nonlinear Lamb wave damage monitoring and extracting and quantifying damage features, thereby completing micro-damage positioning in a two-dimensional plane. Background Art

[0002] With the continuous development of nonlinear Lamb wave damage monitoring technology, the application of nonlinear Lamb wave damage monitoring technology is increasing. Different from the traditional linear Lamb wave damage monitoring technology, nonlinear Lamb wave is more sensitive to early micro-damage and other damage forms, and is very sensitive to changes in structural nonlinearity and body elasticity nonlinear effects, thereby realizing damage assessment of early micro-damage and early fatigue. In order to obtain more effective damage assessment results and more accurate damage location information, it is necessary to accurately detect the nonlinear Lamb wave signal and extract efficient features, and based on this, to achieve damage location.

[0003] Linear Lamb wave detection technology plays an important role in the field of nondestructive testing due to its high stability, relatively simple propagation process, easy signal analysis, and high energy transfer efficiency. It is regarded as one of the most efficient detection methods. However, the linear Lamb wave detection method shows a weak trend when facing early micro-damage, early fatigue and other forms of damage. It has low sensitivity to micro-damage and cannot even detect the existence of damage. This is a disadvantage that cannot be ignored for engineering applications. The development of materials science and engineering applications has led to the increasing complexity of material structures, and at the same time has put forward high requirements and high standards for structural health monitoring. The current Lamb wave detection technology cannot meet the detection function of micro-damage. In addition, with the rapid development of nonlinear ultrasonic detection technology in recent years, nonlinear Lamb wave detection technology has entered the field of vision of researchers, and scientific researchers have explored its possibility of being used in the field of micro-damage detection. Since the generation and propagation process of nonlinear signals is very complicated, although it is highly sensitive to the changes in the material property parameters of the composite material itself, various noise interferences and environmental factors have become the key to affecting the degree of damage and location determination. Therefore, research on sensor network layout, signal acquisition, signal amplification, signal processing, and data analysis is also the key to promoting the progress of nonlinear Lamb detection technology. At present, the method of using nonlinear Lamb wave technology for two-dimensional damage location is mainly based on the traditional nonlinear parameter β, which is closely related to the amplitude of the second harmonic part of the nonlinear signal. The double frequency signal is easily interfered by the noise signal and submerged, losing signal accuracy. Therefore, the method of completing two-dimensional plane micro-damage location based on the nonlinear parameter β is unreliable. At present, the existing research on nonlinear Lamb wave damage monitoring technology lacks results in nonlinear signal detection, quantitative analysis and two-dimensional micro-damage location. Summary of the invention

[0004] The technical problem to be solved by the present invention is: to provide a two-dimensional micro-damage positioning method based on Duffing oscillator, utilizing the characteristics that the damage indicators σ under different paths when micro-damage occurs in the piezoelectric array are different, and proposing a damage positioning index σ′-location based on the maximum Lyapunov index to realize the two-dimensional plane micro-damage positioning of the structural parts.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A two-dimensional micro-damage localization method based on Duffing oscillator, comprising:

[0007] Obtain the structural nonlinear Lamb wave response signals of all monitoring channels under the healthy and damaged states of the structural parts;

[0008] Input the structural nonlinear Lamb wave response signals of all monitoring channels into the Duffing chaotic oscillator system adjusted to the critical state. The system will undergo a state transition to a large-scale periodic state, and then adjust the chaotic oscillator from the large-scale periodic state back to the critical state, and obtain the time series x(t) about the time parameter t.

[0009] According to the obtained time series x(t), the phase space is reconstructed by determining the time delay parameter τ and the embedding dimension m to obtain a new time series x′(t);

[0010] The maximum Lyapunov exponent of the structural nonlinear Lamb wave response signal of all monitoring channels is calculated in the new time series x′(t), including the maximum Lyapunov exponent of each path in the healthy state and the maximum Lyapunov exponent of each path in the damaged state;

[0011] According to the maximum Lyapunov index Lya0 in the healthy state and the maximum Lyapunov index Lya1 in the damaged state of the same path, the damage index σ of this path is calculated to be Lya1 / Lya0;

[0012] Using the damage index σ, the damage location index σ′-location is calculated to realize the location of two-dimensional micro-damage.

[0013] In some embodiments, the method for acquiring the structural nonlinear Lamb wave response signals of all monitoring channels in the healthy state and damaged state of the structural component includes:

[0014] Arrange PZT sensors on the uniform structural member to be detected to form a piezoelectric excitation / sensing array;

[0015] In the piezoelectric excitation / sensing array, different sensors are selected as excitation elements and sensing elements respectively to form an excitation-sensing monitoring channel to collect the structural nonlinear Lamb wave response signals of all monitoring channels under the healthy and damaged states of the structural parts.

[0016] Further, it specifically includes:

[0017] In the piezoelectric excitation / sensing array, sensor i is selected as the excitation element, and the Lamb wave ultrasonic excitation signal is loaded onto sensor i, i = 1, 2, ..., N, where N is the number of exciters, to excite the excitation signal in the structural member;

[0018] Select sensor j as the sensing element in turn, j = 1, 2, ..., M, M = the number of receivers, collect the nonlinear Lamb wave response signal of the structure under excitation, and obtain the monitoring path L with the excitation element i and the sensing element j ij Structural nonlinear Lamb wave response signal under .

[0019] In some embodiments, before inputting the structural nonlinear Lamb wave response signals of all monitoring channels into the Duffing chaotic oscillator system, the nonlinear Lamb wave response signals are preprocessed, and the preprocessing includes:

[0020] The nonlinear Lamb wave response signal is subjected to high-pass filtering, period extension processing and Gaussian white noise component addition.

[0021] In some embodiments, the Duffing chaotic oscillator system is essentially a differential equation for detecting weak signals of a specific frequency, and the expression is as follows:

[0022] x (2) (t)+kx (1) (t)-3x 3 (t)+5x 5 (t)=Fcos(ωt)+f(t)

[0023] Among them, x (2) (t) represents the second-order derivative of the time series x(t), x (1) (t) represents the first-order derivative of the time series x(t), k represents the damping ratio, the right side of the equation is the driving force term, which includes the internal driving force and the signal to be detected, F is the driving force amplitude, ω is the frequency of the signal to be detected, and f(t) is the signal to be detected;

[0024] When the signal to be detected is not added, that is, f(t) is 0, the driving force amplitude F is adjusted according to the change of the phase trajectory diagram, so that the system enters the critical state. Then the nonlinear Lamb wave signal to be detected is introduced into the right side of the Duffing chaotic oscillator equation, that is, f(t). At this time, the system will transition to a large-scale periodic state, and the driving force amplitude F is adjusted to return to the critical state. For the adjusted Duffing chaotic oscillator, the differential equation is solved and the phase trajectory diagram is drawn. From the phase trajectory diagram, the motion trajectory and subsequent motion state of the kinematic system can be preliminarily judged, and the time series x(t) about the time parameter t can be obtained.

[0025] In some embodiments, according to the obtained time series x(t), the CC method is used to determine the time delay parameter τ and the embedding dimension m, and the phase space is reconstructed to obtain a new time series x′(t):

[0026] x′(t)=(x(t),x(t-τ),...,x(t-(m-1)τ)),t=(m-1)τ-1,...,T

[0027] Where T represents the length of time in phase space.

[0028] In some embodiments, the damage index σ=Lya1 / Lya0 of the path is calculated based on the maximum Lyapunov index Lya0 in the healthy state and the maximum Lyapunov index Lya1 in the damaged state of the same path;

[0029] The sensor network consists of a row of actuators and a row of receivers, i = 1, 2, ..., N, N is the number of actuators, j = 1, 2, ..., M, M is the number of receivers, and any sensor path is composed of L ij express.

[0030] In some embodiments, the damage index σ is used to calculate the damage location index σ′-location, including:

[0031] The damage index σ is normalized to obtain the normalized damage index σ′:

[0032]

[0033] where σ max and σ min Indicates the maximum and minimum values ​​of the damage index;

[0034] According to the normalized damage index σ′, the damage location index σ′-location is calculated:

[0035]

[0036] Where n represents the total number of all sensor paths in the sensor network, and y represents any one of the sensor paths. represents the mean value of the normalized damage index of each path under the damage state, represents the mean value of the normalized damage index of each path in the healthy state, σ′ y Represents the normalized damage index of each path under the damage state.

[0037] The excitation signal is a narrowband signal.

[0038] In a second aspect, a two-dimensional micro-damage localization device based on a Duffing vibrator is provided, including a processor and a storage medium;

[0039] The storage medium is used to store instructions;

[0040] The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 8.

[0041] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0042] 1. The present invention eliminates the influence of external noise signals on nonlinear signals, especially the second harmonic, to a certain extent, and improves the accuracy of nonlinear Lamb wave two-dimensional plane micro-damage positioning.

[0043] 2. The method of the present invention does not require any changes or additions to equipment and parameters during implementation and can be implemented using existing hardware systems.

[0044] 3. The implementation method of the present invention is simple. It only needs to extract the nonlinear Lamb wave damage response signal under each path for analysis, extract the damage characteristics and perform quantification processing to complete the two-dimensional plane micro-damage positioning work without performing other operations on the system.

[0045] 4. The present invention has strong portability and can be applied to the micro-damage location assessment of thin plate structures made of different materials. At the same time, the method has high reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a diagram of the experimental specimen and piezoelectric wire array in the present invention.

[0047] Figure 2 It is a waveform time domain diagram of the narrow-band excitation signal in the present invention.

[0048] Figure 3 It is a schematic diagram of signal processing and damage feature extraction in the present invention.

[0049] Figure 4 It is the partial verification test result of the present invention. DETAILED DESCRIPTION

[0050] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0051] In the description of the present invention, "several" means more than one, "many" means more than two, "greater than", "less than", "exceed", etc. are understood to exclude the number itself, and "above", "below", "within", etc. are understood to include the number itself. If there is a description of "first" or "second", it is only used for the purpose of distinguishing the technical features, and cannot be understood as indicating or implying the relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0052] In the description of the present invention, the description with reference to the terms "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0053] Example 1

[0054] A two-dimensional micro-damage localization method based on Duffing oscillator, comprising:

[0055] Obtain the structural nonlinear Lamb wave response signals of all monitoring channels under the healthy and damaged states of the structural parts;

[0056] Input the structural nonlinear Lamb wave response signals of all monitoring channels into the Duffing chaotic oscillator system adjusted to the critical state. The system will undergo a state transition to a large-scale periodic state, and then adjust the chaotic oscillator from the large-scale periodic state back to the critical state, and obtain the time series x(t) about the time parameter t.

[0057] According to the obtained time series x(t), the CC method is used to determine the time delay parameter τ and the embedding dimension m, reconstruct the phase space, and obtain the new time series x′(t);

[0058] In the new time series x′(t), the wolf method is used to calculate the maximum Lyapunov exponent of the structural nonlinear Lamb wave response signal of all monitoring channels, including the maximum Lyapunov exponent of each path in the healthy state and the maximum Lyapunov exponent of each path in the damaged state.

[0059] According to the maximum Lyapunov index Lya0 in the healthy state and the maximum Lyapunov index Lya1 in the damaged state of the same path, the damage index σ of this path is calculated to be Lya1 / Lya0;

[0060] Using the damage index σ, the damage location index σ′-location is calculated to realize the location of two-dimensional micro-damage.

[0061] In some embodiments, a two-dimensional micro-damage localization method based on a Duffing oscillator comprises the following steps:

[0062] (1) Arranging PZT sensors on the uniform structure to be detected to form a piezoelectric excitation / sensing array and an excitation-sensing channel;

[0063] In this embodiment, an epoxy resin thin plate structure is used as the experimental object, and its size is 600mm*600mm*4mm. Seven piezoelectric sensors are installed on the structure, such as Figure 1 As shown in Figure 1, the linear array of 7 piezoelectric sensors forms multiple excitation-sensing channels.

[0064] (2) Collect all excitation-sensing monitoring channels L of the engineering structure in healthy and damaged states ij The structural nonlinear Lamb wave response signal, where i = 1, 2, ..., N, j = 1, 2, ..., M, N is the number of excitation sensors, M is the number of receivers;

[0065] The detailed steps of step (2) are:

[0066] (21) When the structure is in a healthy state or in a damaged state, a Lamb wave ultrasonic excitation signal is loaded onto i as an excitation element through a function generator and a power amplifier to excite the excitation signal in the structure;

[0067] The above Lamb wave ultrasonic excitation signal is a narrow-band signal, such as Figure 2 shown.

[0068] (22) Select piezoelectric element j as the receiving element in turn, and sense, amplify and collect the Lamb wave structure response signal under excitation into the control computer through the charge amplifier to obtain the monitoring channel L with the excitation element i and the receiving element j. ij The structural nonlinear Lamb wave response signal under the condition of

[0069] (23) Repeat steps (21) and (22) until the nonlinear Lamb wave response signals under all excitation / sensing channels are acquired.

[0070] In some embodiments, the collected nonlinear Lamb wave response signal is also preprocessed: high-pass filtering is performed to remove the fundamental frequency signal wave component, and the nonlinear signal wave mainly composed of the second harmonic is retained for detection; the Duffing chaotic oscillator is more sensitive to periodic signals, so the above-mentioned signal to be detected is processed by period extension to ensure that the original signal is not changed and the damage characteristics contained in the nonlinear Lamb wave are retained. In order to simulate noise signal interference, Gaussian white noise components are added to the nonlinear Lamb wave signal;

[0071] (3) Set all monitoring channels L ij The structural nonlinear Lamb wave response signal is input into the Duffing chaotic oscillator adjusted to the critical state, and the system will undergo a state transition to a large-scale periodic state. At this time, the chaotic oscillator is adjusted again to return from the large-scale periodic state to the critical state.

[0072] The essence of Duffing chaotic oscillator is a differential equation for detecting weak signals of a specific frequency. The differential equation expression is as follows:

[0073] x (2) (t)+kx (1) (t)-3x 3 (t)+5x 5 (t)=Fcos(ωt)+f(t)

[0074] Among them, x (2) (t) represents the second-order derivative of the time series x(t), x (1) (t) represents the first-order derivative of the time series x(t), k represents the damping ratio, the right side of the equation is the driving force term, which includes the internal driving force and the signal to be detected, F is the driving force amplitude, ω is the frequency of the signal to be detected, and f(t) is the signal to be detected;

[0075] Set the frequency ω of the signal to be detected, for example, 480KHz. When the signal to be detected is not added, that is, f(t) is 0, adjust the driving force amplitude F according to the change of the phase trajectory diagram, so that the system enters the critical state, and then introduce the nonlinear Lamb wave signal to be detected to the right side of the Duffing chaotic oscillator equation, that is, f(t). At this time, the system will transition to a large-scale periodic state, and the driving force amplitude F needs to be adjusted to return to the critical state. For the adjusted Duffing chaotic oscillator, solve the differential equation and draw its phase trajectory diagram. From the phase trajectory diagram, the motion trajectory and subsequent motion state of the kinematic system can be preliminarily determined, and the time series x(t) about the time parameter t can be obtained;

[0076] (4) According to the time series x(t) obtained in step (3), select a suitable time delay parameter τ and embedding dimension m to complete the reconstruction of the phase space, and calculate the maximum Lyapunov exponent of the structural nonlinear Lamb wave response signal of all monitoring channels in the reconstructed phase space;

[0077] The sensor network consists of a row of actuators and a row of receivers, i = 1, 2, ..., N, N = the number of actuators, j = 1, 2, ..., M, M = the number of receivers, and any sensor path is composed of L ij It means that the damage index σ of any sensing path is obtained by comparing the maximum Lyapunov index in the healthy state with the maximum Lyapunov index in the damaged state of the same path, that is, σ = Lya1 / Lya0;

[0078] The detailed steps of step (4) are:

[0079] (41) Use the time series x(t) to solve the optimal delay parameter τ and embedding dimension m. The most common method is the CC method.

[0080] (42) Using the optimal time delay parameter τ and embedding dimension m, the phase space is reconstructed. The reconstructed phase space can describe the kinematic characteristics of the original system and obtain a new time series x′(t);

[0081] (43) Using the wolf method in the new phase space time series x′(t), the maximum Lyapunov exponent extracted from the nonlinear Lamb wave signal under the state path is calculated;

[0082] (44) By comparing the maximum Lyapunov exponents in the damaged state and the healthy state, the damage index σ = Lya1 / Lya0 is obtained;

[0083] (5) Using the damage index σ, the damage index σ is normalized to obtain the normalized damage index σ′, and then the damage location index σ′-location is solved to realize the location of two-dimensional plane micro-damage.

[0084] The damage index σ is normalized to obtain the normalized damage index σ′:

[0085]

[0086] where σ max and σ min Indicates the maximum and minimum values ​​of the damage index;

[0087] According to the normalized damage index σ′, the damage location index σ′-location is calculated:

[0088]

[0089] Where n represents the total number of all sensor paths in the sensor network, and y represents any one of the sensor paths. represents the mean value of the normalized damage index of each path under the damage state, represents the mean value of the normalized damage index of each path in the healthy state, σ′ y Represents the normalized damage index of each path under the damage state.

[0090] When damage occurs on the sensing path, the nonlinear effect changes significantly, including the increase in the second harmonic amplitude and energy. The maximum Lyapunov index reflects the state change of the Duffing chaotic oscillator. Such state change is positively correlated with the change in the driving force amplitude, and the driving force amplitude directly reflects the input signal, that is, the magnitude of the second harmonic amplitude in the nonlinear Lamb wave signal, which also maintains a positive correlation. Therefore, the normalized damage index σ′ can accurately reflect the nonlinear material changes caused by micro-damage to the structural parts, and the damage location index σ′-location can complete the location of micro-damage.

[0091] In some embodiments, a method for verifying the accuracy of positioning micro-damages can be accomplished by using the damage location index σ′-location, including:

[0092] In L 26 and L 17 Damage is created at the intersection, and the damage index σ is calculated using the same signal acquisition and analysis method;

[0093] Observe all paths L ij The change of the damage index σ under the sensor path can be more intuitive by making a bar graph. When the damage occurs on a certain sensing path, the damage index under the path will show a significant increasing trend. Mainz can determine the sensing path where the damage occurs.

[0094] Then, the damage localization index σ′-location is used to determine the specific location of the sensing path where the damage occurs in the two-dimensional plane.

[0095] In L 25 and L 17 Damage is created at the intersection to verify the feasibility of using damage indicators for two-dimensional damage location.

[0096] Example 2

[0097] In a second aspect, a two-dimensional micro-damage localization device based on a Duffing vibrator is provided, including a processor and a storage medium;

[0098] The storage medium is used to store instructions;

[0099] The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 8.

[0100] The present invention can effectively eliminate the problem that the traditional nonlinear parameter β is easily affected by noise signals, resulting in inaccurate micro-damage positioning, which is beneficial to improving the accuracy of nonlinear signal detection and the precision of micro-damage positioning, and promoting the promotion and application of structural nonlinear Lamb wave damage monitoring technology.

[0101] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0102] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0103] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0104] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0105] The above embodiments are only for illustrating the technical idea of ​​the present invention, and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A two-dimensional micro-damage localization method based on Duffing oscillator, characterized in that: include: Obtain the structural nonlinear Lamb wave response signals of all monitoring channels under the healthy and damaged states of the structural parts; Input the structural nonlinear Lamb wave response signals of all monitoring channels into the Duffing chaotic oscillator system adjusted to the critical state. The system will undergo a state transition to a large-scale periodic state, and then adjust the chaotic oscillator from the large-scale periodic state back to the critical state, and obtain the time series x(t) about the time parameter t. According to the obtained time series x(t), the phase space is reconstructed by determining the time delay parameter τ and the embedding dimension m to obtain a new time series x′(t); The maximum Lyapunov exponent of the structural nonlinear Lamb wave response signal of all monitoring channels is calculated in the new time series x′(t), including the maximum Lyapunov exponent of each path in the healthy state and the maximum Lyapunov exponent of each path in the damaged state; According to the maximum Lyapunov index Lya0 in the healthy state and the maximum Lyapunov index Lya1 in the damaged state of the same path, the damage index σ of this path is calculated to be Lya1 / Lya0; Using the damage index σ, the damage location index σ′-location is calculated to achieve the location of two-dimensional micro-damage. The essence of the Duffing chaotic oscillator system is a differential equation for detecting weak signals of a specific frequency, which is expressed as follows: x (2) (t)+kx (1) (t)-3x 3 (t)+5x 5 (t)=Fcos(ωt)+f(t) Among them, x (2) (t) represents the second-order derivative of the time series x(t), x (1) (t) represents the first-order derivative of the time series x(t), k represents the damping ratio, the right side of the equation is the driving force term, which includes the internal driving force and the signal to be detected, F is the driving force amplitude, ω is the frequency of the signal to be detected, and f(t) is the signal to be detected; When the signal to be detected is not added, that is, f(t) is 0, the driving force amplitude F is adjusted according to the change of the phase trajectory diagram, so that the system enters the critical state, and then the nonlinear Lamb wave signal to be detected is introduced into the right side of the Duffing chaotic oscillator equation, that is, f(t). At this time, the system will transition to a large-scale periodic state, and the driving force amplitude F is adjusted to return to the critical state; for the adjusted Duffing chaotic oscillator, the differential equation is solved and the phase trajectory diagram is drawn. From the phase trajectory diagram, the motion trajectory and subsequent motion state of the kinematic system can be preliminarily determined, and the time series x(t) about the time parameter t can be obtained; According to the obtained time series x(t), the CC method is used to determine the time delay parameter τ and the embedding dimension m, reconstruct the phase space, and obtain the new time series x′(t): x′(t)=(x(t),x(t-τ),...,x(t-(m-1)τ)),t=(m-1)τ-1,...,T Where T represents the time length in phase space; Using the damage index σ, the damage location index σ′-location is calculated, including: The damage index σ is normalized to obtain the normalized damage index σ′: where σ max and σ min Indicates the maximum and minimum values ​​of the damage index; According to the normalized damage index σ′, the damage location index σ′-location is calculated: Where n represents the total number of all sensor paths in the sensor network, and y represents any one of the sensor paths. represents the mean value of the normalized damage index of each path under the damage state, represents the mean value of the normalized damage index of each path in the healthy state, σ′ y Represents the normalized damage index of each path under the damage state.

2. According to claim 1, the two-dimensional micro-damage localization method based on Duffing oscillator is characterized in that: The method for acquiring the structural nonlinear Lamb wave response signals of all monitoring channels in the healthy state and damaged state of the structural component includes: Arrange PZT sensors on the uniform structural member to be detected to form a piezoelectric excitation / sensing array; In the piezoelectric excitation / sensing array, different sensors are selected as excitation elements and sensing elements respectively to form an excitation-sensing monitoring channel to collect the structural nonlinear Lamb wave response signals of all monitoring channels under the healthy and damaged states of the structural parts.

3. According to claim 2, the two-dimensional micro-damage localization method based on Duffing oscillator is characterized in that: In the piezoelectric excitation / sensing array, different sensors are selected as excitation elements and sensing elements respectively to form an excitation-sensing monitoring channel to collect the structural nonlinear Lamb wave response signals of all monitoring channels in the healthy and damaged states of the structural parts, including: In the piezoelectric excitation / sensing array, sensor i is selected as the excitation element, and the Lamb wave ultrasonic excitation signal is loaded onto sensor i, i = 1, 2, ..., N, where N is the number of exciters, to excite the excitation signal in the structural member; Select sensor j as the sensing element in turn, j = 1, 2, ..., M, M = the number of receivers, collect the nonlinear Lamb wave response signal of the structure under excitation, and obtain the monitoring path L with the excitation element i and the sensing element j ij Structural nonlinear Lamb wave response signal under .

4. According to claim 1, the two-dimensional micro-damage localization method based on Duffing oscillator is characterized in that: Before inputting the structural nonlinear Lamb wave response signals of all monitoring channels into the Duffing chaotic oscillator system, the nonlinear Lamb wave response signals are preprocessed, and the preprocessing includes: The nonlinear Lamb wave response signal is subjected to high-pass filtering, period extension processing and Gaussian white noise component addition.

5. The two-dimensional micro-damage localization method based on Duffing oscillator according to claim 1 is characterized in that: According to the maximum Lyapunov index Lya0 in the healthy state and the maximum Lyapunov index Lya1 in the damaged state of the same path, the damage index σ of this path is calculated to be Lya1 / Lya0; The sensor network consists of a row of actuators and a row of receivers, i = 1, 2, ..., N, N is the number of actuators, j = 1, 2, ..., M, M is the number of receivers, and any sensor path is composed of L ij express.

6. The two-dimensional micro-damage localization method based on Duffing oscillator according to claim 3 is characterized in that: The excitation signal is a narrowband signal.

7. A two-dimensional micro-damage localization device based on Duffing oscillator, characterized in that: including processor and storage medium; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 6.

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