Multi-modal dynamic strain monitoring method and system based on blade tip acceleration

Abstract

This application provides a multimodal dynamic strain monitoring method and system based on blade tip acceleration, belonging to the field of aero-engine technology. The method includes recording the vibration arrival time series under multimodal vibration states of the blade, establishing a vibration acceleration calculation model, calculating the blade tip vibration acceleration, and acquiring an undersampled blade tip vibration acceleration signal. Based on this signal, a sparse identification model of the blade's multimodal vibration parameters is established, the acceleration response is reconstructed, the blade's multimodal vibration acceleration parameters are obtained, and the full-time domain response of the blade tip vibration acceleration is calculated. A finite element model of the rotor blade is established to obtain the blade's multimodal acceleration and strain mode shapes, and the transformation relationship between blade tip vibration acceleration and dynamic strain at any point on the blade is constructed. Based on the full-time domain response and transformation relationship of the blade tip vibration acceleration, the dynamic strain at any point on the blade is calculated and monitored. This application can accurately capture the dynamic strain changes under multimodal blade vibration, improving monitoring accuracy and real-time performance.

Description

Technical Field

[0001] This application relates to the field of aero-engine technology, and in particular to a multimodal dynamic strain monitoring method and system based on blade tip acceleration. Background Technology

[0002] Aero-engine rotor blades are prone to multimodal vibration under complex multi-source excitation, exhibiting wide vibration bandwidths and frequencies ranging from hundreds of hertz to kilohertz. This is especially true for hot-end components of the engine, where turbine rotor blades are typically short and thick, with small tip amplitudes and high vibration frequencies. Existing contact methods, such as strain gauge measurements, are difficult to operate for extended periods in high-temperature environments, have limited ability to capture multimodal time- and spatial strain changes in the blades, and are prone to failure due to detachment under thermal and vibrational conditions. Tip timing, as a non-contact measurement system, can acquire blade arrival time information without intruding on the blade structure itself. Combined with real-time rotor speed information, it can obtain tip vibration information. Tip timing has advantages in measuring high-frequency multimodal vibrations of blades, but the following problems need to be addressed: 1) Traditional methods of converting arrival time to vibration displacement are difficult to use for monitoring high-frequency vibrations; 2) The blade vibration information acquired through tip timing needs to be effectively converted into stress / strain. Summary of the Invention

[0003] To address the problems existing in the prior art, this application provides a multimodal dynamic strain monitoring method and system based on blade tip acceleration. By using vibration acceleration sparse regularization identification, the multimodal dynamic strain at any point on the blade is reconstructed, thereby realizing real-time monitoring of multimodal vibration and dynamic strain of engine rotor blades.

[0004] In a first aspect, embodiments of this application provide a multimodal dynamic strain monitoring method based on blade tip acceleration, the method comprising:

[0005] While the blade is rotating, the vibration arrival time sequence under multimodal vibration is recorded based on the blade tip timing sensor;

[0006] Based on the blade vibration arrival time series, a vibration acceleration calculation model is established. Based on the vibration acceleration calculation model, the blade tip vibration acceleration is calculated, and the undersampled blade tip vibration acceleration signal is obtained.

[0007] Based on the undersampled blade tip vibration acceleration signal, a sparse identification model of blade multimodal vibration parameters is established, the acceleration response is reconstructed, the blade multimodal vibration acceleration parameters are obtained, and the blade tip vibration acceleration full-time domain response is calculated based on the blade multimodal vibration acceleration parameters.

[0008] A finite element model of the rotor blade was established, and modal analysis of the rotating blade was carried out to obtain the multimodal acceleration mode shape and strain mode shape of the blade.

[0009] Based on multimodal acceleration mode shapes and strain mode shapes, the transformation relationship between tip vibration acceleration and dynamic strain at any point on the blade is constructed, forming a transformation matrix to decouple the multimodal vibration of the blade;

[0010] Based on the full-time domain response and transformation matrix of blade tip vibration acceleration, the dynamic strain at any point on the blade is calculated in real time, and the multi-modal dynamic strain of the blade is monitored.

[0011] According to a specific implementation of an embodiment of this application, the recording of the vibration arrival time sequence under the multimodal vibration state of the blade includes:

[0012] Set the number of blade tip timing sensors The K blade tip timing sensors are installed at the following angles in the casing: , Let K be the mounting angle of the Kth blade tip timing sensor in the casing, and let the mounting interval angle between two adjacent sensors be denoted by . , The rotor blade rotation frequency, The highest recognizable target frequency in the multimodal analysis of the blade;

[0013] The vibration arrival time series under multimodal vibration states of the blade are recorded and represented by the blade tip vibration arrival time matrix. The expression of the blade tip vibration arrival time matrix is ​​as follows:

[0014] ,

[0015] T N This is the tip vibration arrival time matrix, where N is the total number of rotations of the rotor blade within the measurement time, and t is the time matrix. N,K Let be the arrival time of the blade tip vibration as measured by the Kth blade tip timing sensor during the Nth revolution.

[0016] According to a specific implementation of an embodiment of this application, the step of establishing a vibration acceleration calculation model based on the blade vibration arrival time series includes:

[0017] The rotor blades vibrate during rotation until the first... The first leaf tip timing sensor, the first The installation angles of the leaf tip timing sensor and its two adjacent leaf tip timing sensors are as follows: , and ,in, , ; the blade in the first The vibration reaches the first cycle. The, the The and the first The timing of each blade tip timing sensor is as follows: , and ;

[0018] Based on the blade vibration arrival time series, establish the blade in the first... The ring vibration reaches the first The vibration acceleration calculation model for a single blade tip timing sensor is expressed as follows:

[0019] ,

[0020] in, For the blade in the first The ring vibration reaches the first Vibration acceleration at the timer sensor of the blade tip Radius of gyration For the blade in the first The ring vibration reaches the first The time interval between the first and (i+2)th leaf tip timing sensors ; For the blade in the first The time interval between the arrival of the loop vibration at the (i+1)th blade tip timing sensor and the (i+2)th blade tip timing sensor. ; For the blade in the first The time interval between the arrival of the loop vibration at the i-th blade tip timing sensor and the (i+1)-th blade tip timing sensor. ; Let be the installation interval angle between the (i+1)th and (i+2)th blade tip timing sensors. ; Let be the installation interval angle between the i-th blade tip timing sensor and the (i+1)-th blade tip timing sensor. ;

[0021] corresponding time The expression is: .

[0022] According to a specific implementation of an embodiment of this application, the step of calculating the blade tip vibration acceleration based on a vibration acceleration calculation model and obtaining the undersampled blade tip vibration acceleration signal includes:

[0023] Based on the vibration acceleration calculation model, the blade tip vibration acceleration is calculated, forming a multimodal acceleration matrix. The expression for the multimodal acceleration matrix is ​​as follows:

[0024] ,

[0025] Where A is the multimodal acceleration matrix. The time interval between the blade's vibration on the Nth cycle reaching the Kth tip timing sensor and the (K-2)th tip timing sensor is given. The time interval between the blade's vibration on the Nth cycle reaching the Kth tip timing sensor and the (K-1)th tip timing sensor is given. The time interval between the blade's vibration reaching the (K-1)th blade tip timing sensor and the (K-2)th blade tip timing sensor during the Nth rotation is given. The installation interval angle between the (K-1)th blade tip timing sensor and the Kth blade tip timing sensor is... The installation interval angle between the (K-2)th blade tip timing sensor and the (K-1)th blade tip timing sensor;

[0026] The multimodal acceleration matrix corresponding to the tip multimodal acceleration acquisition time matrix T a The expression is:

[0027] .

[0028] According to a specific implementation of an embodiment of this application, the step of establishing a sparse identification model of multimodal vibration parameters of the blade based on the undersampled blade tip vibration acceleration signal includes:

[0029] The tip acceleration response of the rotor blade in multimodal vibration is expressed as:

[0030] ,

[0031] in, The tip acceleration response of the rotor blade is shown as the multimodal vibration of the rotor blade, where t is the moment of the vibration acceleration response. The first vibration acceleration coefficient of the y-th order at the blade tip. The coefficient of the second vibration acceleration of the blade tip in the y-th order is... y is the yth vibrational frequency of the multimodal vibration at the blade tip, and h is the number of modes;

[0032] Based on compressed sensing sparse regularization theory, a sparse identification model for multimodal vibration parameters of a blade is constructed. The expression for the sparse identification model of multimodal vibration parameters of a blade is as follows: ,in, Represents the q-norm. ;a is the undersampled acceleration vector formed by column expansion of the multimodal acceleration matrix A during continuous blade rotation. Here, S is the regularization parameter; S is the coefficient vector. ,in, Representing the For the first and second vibration acceleration coefficient pairs, D is a static constant; H is a sparse transformation matrix, and the expression for the sparse transformation matrix is:

[0033] ,

[0034] Among them, t p For the p-th moment of undersampling of the blade tip vibration acceleration, To achieve sparse spectrum reconstruction resolution; and to meet the frequency identification requirements of multimodal broadband response of blades, the upper limit of the sparse matrix identification bandwidth must satisfy: , This is the highest frequency of the multimodal vibration of the blade.

[0035] According to a specific implementation of an embodiment of this application, the reconstructing of the acceleration response to obtain the multimodal vibration acceleration parameters of the blade, and the calculation of the full-time domain response of the blade tip vibration acceleration based on the multimodal vibration acceleration parameters of the blade, includes:

[0036] Solve the sparse identification model of the multimodal vibration parameters of the blade, reconstruct the response spectrum, and obtain the response frequency, amplitude, and phase of the multimodal vibration acceleration at the blade tip. The expressions for the amplitude and phase of the y-th order vibration acceleration are as follows:

[0037] ,

[0038] in, Let y be the amplitude of the y-th order vibration acceleration. The phase of the y-th order vibration acceleration;

[0039] Based on the multimodal vibration acceleration parameters of the blade, the full-time response of the blade tip vibration acceleration is calculated, and the expression is as follows:

[0040] ,

[0041] Where a(t) is the full-time response of the blade tip vibration acceleration.

[0042] According to a specific implementation of an embodiment of this application, the expression for the multimodal acceleration mode shape of the blade is:

[0043] ,

[0044] The expression for the strain mode shape is:

[0045] ,

[0046] Where C is the multimodal acceleration mode shape of the blade, C h Let Φ be the tip acceleration mode shape of the h-th vibration, and Φ be the strain mode shape. Let h be the strain mode shape at any point of order h.

[0047] According to a specific implementation of an embodiment of this application, the expression of the transformation matrix is:

[0048] ,

[0049] Where T is the transformation matrix.

[0050] According to a specific implementation of an embodiment of this application, the expression for the arbitrary point-motion strain of the blade is:

[0051] ,

[0052] in, This represents the dynamic strain at any point and in any dimension of the blade under full-time multimodal vibration.

[0053] Secondly, embodiments of this application also provide a multimodal dynamic strain monitoring system based on tip acceleration, used to implement the multimodal dynamic strain monitoring method based on tip acceleration as described in any embodiment of the first aspect, the system comprising:

[0054] The rotor blade tip timing measurement module is used to record the vibration arrival time sequence of the blade under multimodal vibration state based on the blade tip timing sensor while the blade is rotating.

[0055] The undersampled vibration acceleration calculation module is used to establish a vibration acceleration calculation model based on the blade vibration arrival time series, calculate the blade tip vibration acceleration based on the vibration acceleration calculation model, and obtain the undersampled blade tip vibration acceleration signal.

[0056] The sparse regularization identification module for acceleration vibration parameters is used to establish a sparse identification model of multimodal vibration parameters of the blade based on the undersampled blade tip vibration acceleration signal, reconstruct the acceleration response, obtain the multimodal vibration acceleration parameters of the blade, and calculate the full-time domain response of the blade tip vibration acceleration based on the multimodal vibration acceleration parameters of the blade.

[0057] The rotor blade finite element analysis module is used to establish a finite element model of the rotor blade, carry out modal analysis of the rotating blade, and obtain the multimodal acceleration mode shape and strain mode shape of the blade.

[0058] The multimodal acceleration and dynamic strain conversion module is used to construct the conversion relationship between the tip vibration acceleration and the dynamic strain at any point on the blade based on the multimodal acceleration mode shape and the strain mode shape, forming a conversion matrix to decouple the multimodal vibration of the blade;

[0059] The dynamic strain monitoring module is used to calculate the dynamic strain at any point on the blade in real time based on the full-time domain response and transformation matrix of the blade tip vibration acceleration, and to monitor the multi-modal dynamic strain of the blade.

[0060] Beneficial effects:

[0061] The multimodal dynamic strain monitoring method and system based on blade tip acceleration in this application fundamentally breaks through the traditional dynamic strain response monitoring mode that relies on blade tip vibration displacement. This method fully utilizes the sensitivity of acceleration signals to high-frequency vibration responses and the sparse all-time-domain sensing characteristics to construct a transmission relationship from the rotor blade tip acceleration to the multimodal dynamic strain response at any position on the blade surface. Thus, even under complex vibration conditions with multimodal coupling (synchronous vibration of higher and lower orders), it can still achieve high-precision calculation and real-time monitoring of blade dynamic strain. This invention uses a blade tip timing system to capture the blade tip arrival time series, thereby calculating undersampled acceleration. Furthermore, it effectively identifies high-frequency vibration components by constructing a sparse canonical acceleration model, ensuring that low-frequency strong responses and high-frequency weak vibration signals are synchronously preserved. Based on the acceleration mode shapes and strain mode shapes of the blade system, a sensing matrix from multimodal blade tip acceleration to dynamic strain at any point is constructed, forming a monitoring mechanism capable of real-time dynamic strain sensing. This method is particularly suitable for capturing high- and low-frequency coupled dynamic strain responses that are prone to causing blade fatigue. It enables comprehensive monitoring of multimodal dynamic strain of rotor blades in a non-contact manner, which is of great value for promoting the development of blade health monitoring systems towards non-invasive, high-sensitivity, and vibration decoupling. Attached Figure Description

[0062] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0063] Figure 1 This is a flowchart illustrating a multimodal dynamic strain monitoring method based on tip acceleration according to an embodiment of the present invention.

[0064] Figure 2 This is a schematic diagram of a multimodal dynamic strain monitoring system based on tip acceleration according to an embodiment of the present invention;

[0065] Figure 3 A rotor blade model according to an embodiment of the present invention;

[0066] Figure 4(a) shows the first-order acceleration mode shape of a rotor blade according to an embodiment of the present invention;

[0067] Figure 4(b) shows the first strain mode shape of a rotor blade according to an embodiment of the present invention;

[0068] Figure 4(c) shows the second-order acceleration mode shape of a rotor blade according to an embodiment of the present invention;

[0069] Figure 4(d) shows the second-order strain mode shape of a rotor blade according to an embodiment of the present invention;

[0070] Figure 4(e) shows the third-order acceleration mode shape of a rotor blade according to an embodiment of the present invention;

[0071] Figure 4(f) shows the third strain mode shape of a rotor blade according to an embodiment of the present invention. Detailed Implementation

[0072] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0073] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0074] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0075] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0076] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0077] In a first aspect, embodiments of this application provide a multimodal dynamic strain monitoring method based on tip acceleration, referring to... Figure 1 The method includes:

[0078] Step S100: While the blade is rotating, record the vibration arrival time sequence under the multimodal vibration state of the blade based on the blade tip timing sensor;

[0079] Step S200: Based on the blade vibration arrival time series, establish a vibration acceleration calculation model, calculate the blade tip vibration acceleration based on the vibration acceleration calculation model, and obtain the undersampled blade tip vibration acceleration signal;

[0080] Step S300: Based on the undersampled blade tip vibration acceleration signal, establish a sparse identification model of blade multimodal vibration parameters, reconstruct the acceleration response, obtain blade multimodal vibration acceleration parameters, and calculate the full-time domain response of blade tip vibration acceleration based on the blade multimodal vibration acceleration parameters.

[0081] Step S400: Establish a finite element model of the rotor blade, conduct modal analysis of the rotating blade, and obtain the multimodal acceleration mode shape and strain mode shape of the blade;

[0082] Step S500: Based on the multimodal acceleration mode shape and strain mode shape, construct the transformation relationship from the tip vibration acceleration to the dynamic strain at any point on the blade, form a transformation matrix, and decouple the multimodal vibration of the blade;

[0083] Step S600: Based on the full-time domain response and transformation matrix of the blade tip vibration acceleration, calculate the dynamic strain at any point on the blade in real time and monitor the multi-modal dynamic strain of the blade.

[0084] In this embodiment, to address problem 1 in the background art, an acceleration sparsity regularization identification method is provided, which can effectively identify high-frequency multimodal vibration parameters of the blade; to address problem 2 in the background art, a method for reconstructing vibration acceleration into dynamic strain is provided, which can realize real-time monitoring of dynamic strain at any point on the blade, forming a monitoring system. Therefore, this embodiment provides a multimodal dynamic strain monitoring method and system based on blade tip acceleration to realize dynamic strain monitoring under multimodal vibration of aero-engine rotor blades.

[0085] This embodiment proposes a multimodal dynamic strain monitoring method for blade tip acceleration in multimodal coupling (high- and low-order synchronous vibration). It reconstructs the dynamic strain of multimodal blade vibration and proposes a sparse regularization identification method for acceleration parameters to ensure the accuracy of amplitude and phase parameters, enabling non-contact measurement of multimodal dynamic strain under complex blade vibration. Specifically, this method constructs a transformation matrix between acceleration mode shapes and strain mode shapes, effectively transferring tip vibration acceleration information to any position on the blade, thereby achieving accurate calculation of dynamic strain. In practical applications, this method can significantly improve the sensitivity and reliability of blade health monitoring, and is particularly suitable for blade condition assessment in high-speed rotating machinery such as aero-engines. The non-contact measurement method avoids the additional mass effects and signal drift problems caused by traditional strain gauge bonding, while also reducing maintenance costs. Furthermore, this method supports synchronous decoupling analysis of multimodal vibration components, accurately capturing high- and low-frequency coupled vibration characteristics, providing crucial data support for blade fatigue life prediction and fault diagnosis. Experimental results show that the proposed technical solution maintains high-precision monitoring while possessing excellent noise resistance and environmental adaptability, and can meet the long-term stable operation requirements under complex working conditions.

[0086] Furthermore, in step S100, recording the vibration arrival time series under the multimodal vibration state of the blade includes:

[0087] The arrival time of blade tip vibration is measured using a blade tip timing sensor, and the number of blade tip timing sensors is set. The K blade tip timing sensors are installed at the following angles in the casing: , Let K be the mounting angle of the Kth blade tip timing sensor in the casing, and let the mounting interval angle between two adjacent sensors be denoted by . , The rotor blade rotation frequency, The highest recognizable target frequency in the multimodal analysis of the blade;

[0088] The vibration arrival time series under multimodal vibration states of the blade are recorded and represented by the blade tip vibration arrival time matrix. The expression of the blade tip vibration arrival time matrix is ​​as follows:

[0089] ,

[0090] T N This is the tip vibration arrival time matrix, where N is the total number of rotations of the rotor blade within the measurement time, and t is the time matrix. N,K Let be the arrival time of the blade tip vibration as measured by the Kth blade tip timing sensor during the Nth revolution.

[0091] Furthermore, the establishment of a vibration acceleration calculation model based on the blade vibration arrival time series includes:

[0092] The rotor blades vibrate during rotation until the first... The first leaf tip timing sensor, the first The installation angles of the leaf tip timing sensor and its two adjacent leaf tip timing sensors are as follows: , and ,in, , ; the blade in the first The vibration reaches the first cycle. The, the The and the first The timing of each blade tip timing sensor is as follows: , and ;

[0093] Based on the blade vibration arrival time series, establish the blade in the first... The ring vibration reaches the first The vibration acceleration calculation model for a single blade tip timing sensor is expressed as follows:

[0094] ,

[0095] in, For the blade in the first The ring vibration reaches the first Vibration acceleration at the timer sensor of the blade tip Radius of gyration For the blade in the first The ring vibration reaches the first The time interval between the first and (i+2)th leaf tip timing sensors ; For the blade in the first The time interval between the arrival of the loop vibration at the (i+1)th blade tip timing sensor and the (i+2)th blade tip timing sensor. ; For the blade in the first The time interval between the arrival of the loop vibration at the i-th blade tip timing sensor and the (i+1)-th blade tip timing sensor. ; Let be the installation interval angle between the (i+1)th and (i+2)th blade tip timing sensors. ; Let be the installation interval angle between the i-th blade tip timing sensor and the (i+1)-th blade tip timing sensor. ;

[0096] corresponding time The expression is: .

[0097] Furthermore, the calculation of blade tip vibration acceleration based on the vibration acceleration calculation model to obtain the undersampled blade tip vibration acceleration signal includes:

[0098] Based on the vibration acceleration calculation model, the blade tip vibration acceleration is calculated, forming a multimodal acceleration matrix. The expression for the multimodal acceleration matrix is ​​as follows:

[0099] ,

[0100] Where A is the multimodal acceleration matrix. The time interval between the blade's vibration on the Nth cycle reaching the Kth tip timing sensor and the (K-2)th tip timing sensor is given. The time interval between the blade's vibration on the Nth cycle reaching the Kth tip timing sensor and the (K-1)th tip timing sensor is given. The time interval between the blade's vibration reaching the (K-1)th blade tip timing sensor and the (K-2)th blade tip timing sensor during the Nth rotation is given. The installation interval angle between the (K-1)th blade tip timing sensor and the Kth blade tip timing sensor is [angle missing]. The installation interval angle between the (K-2)th blade tip timing sensor and the (K-1)th blade tip timing sensor;

[0101] The multimodal acceleration matrix corresponding to the tip multimodal acceleration acquisition time matrix T a The expression is:

[0102] .

[0103] Furthermore, the step of establishing a sparse identification model for multimodal vibration parameters of the blade based on the undersampled blade tip vibration acceleration signal includes:

[0104] The tip acceleration response of the rotor blade in multimodal vibration is expressed as:

[0105] ,

[0106] in, The tip acceleration response to the multimodal vibration of the rotor blade is given by t, where t is the moment of the vibration acceleration response. The first vibration acceleration coefficient of the y-th order at the blade tip. The coefficient of the second vibration acceleration of the blade tip in the y-th order is... y is the yth vibrational frequency of the multimodal vibration at the blade tip, and h is the number of modes;

[0107] Based on compressed sensing sparse regularization theory, a sparse identification model for multimodal vibration parameters of a blade is constructed. The expression for the sparse identification model of multimodal vibration parameters of a blade is as follows: ,in, Represents the q-norm. ;a is the undersampled acceleration vector formed by column expansion of the multimodal acceleration matrix A during continuous blade rotation. Here, S is the regularization parameter; S is the coefficient vector. ,in, Representing the For the first and second vibration acceleration coefficient pairs, D is a static constant; H is a sparse transformation matrix, and the expression for the sparse transformation matrix is:

[0108] ,

[0109] Among them, t p For the p-th moment of undersampling of the blade tip vibration acceleration, To achieve sparse spectrum reconstruction resolution; and to meet the frequency identification requirements of multimodal broadband response of blades, the upper limit of the sparse matrix identification bandwidth must satisfy: , This is the highest frequency of the multimodal vibration of the blade.

[0110] In practical implementation, the optimization of the sparse identification model (regular model) for multimodal vibration parameters of the blade employs convex optimization, non-convex optimization, and greedy algorithms to adjust the regularization parameters and solve the model. In this embodiment, by constructing a sparse identification model for multimodal vibration parameters of the blade, the multimodal characteristic parameters in the blade vibration can be accurately extracted, including the vibration frequency, amplitude, and phase information of each mode. These parameters are crucial for accurately assessing the vibration state and health of the blade. In the actual solution process, convex optimization algorithms can utilize their global convergence to find the optimal solution in a large parameter space, ensuring the accuracy of the identification results; non-convex optimization algorithms can gradually optimize the model parameters through iterative approximation for some complex nonlinear problems, improving the model's adaptability and accuracy; greedy algorithms, with their efficient local search capabilities, select the currently optimal parameter adjustment direction in each iteration, thereby quickly converging to a better solution.

[0111] By adjusting the regularization parameter, a balance can be struck between model complexity and fitting ability. A smaller regularization parameter makes the model focus more on fitting the data, but may lead to overfitting, where the model performs well on training data but poorly on new test data. Conversely, an excessively large regularization parameter makes the model too simple, failing to capture the complex features of the data, resulting in underfitting. Therefore, by appropriately adjusting the regularization parameter, the model can achieve an optimal balance between fitting the data and generalization ability.

[0112] After solving the sparse identification model of the constructed blade multimodal vibration parameters, the obtained blade multimodal vibration parameters can be further used for subsequent dynamic strain calculation and health monitoring.

[0113] Furthermore, the reconstructed acceleration response obtains the multimodal vibration acceleration parameters of the blade, and based on these parameters, the full-time response of the blade tip vibration acceleration is calculated, including:

[0114] Solve the sparse identification model of the multimodal vibration parameters of the blade, reconstruct the response spectrum, and obtain the response frequency, amplitude, and phase of the multimodal vibration acceleration at the blade tip. The expressions for the amplitude and phase of the y-th order vibration acceleration are as follows:

[0115] ,

[0116] in, Let y be the amplitude of the y-th order vibration acceleration. The phase of the y-th order vibration acceleration;

[0117] Based on the multimodal vibration acceleration parameters of the blade, the full-time response of the blade tip vibration acceleration is calculated, and the expression is as follows:

[0118] ,

[0119] Where a(t) is the full-time response of the blade tip vibration acceleration.

[0120] In one embodiment, a finite element model of the rotor blade is established based on finite element analysis, referring to... Figure 3 The finite element material parameters of the blade, including density and Young's modulus, are set based on the physical blade material parameters. Rotational modal analysis is performed on the blade to obtain the first h-order mode shapes, including multimodal acceleration mode shapes and strain mode shapes. The mode shapes for the first three orders are shown in Figures 4(a) to 4(f). The expression for the multimodal acceleration mode shape of the blade at the blade tip measuring point is:

[0121] ,

[0122] The expression for the strain mode shape is:

[0123] ,

[0124] Where C is the multimodal acceleration mode shape of the blade, C h Let Φ be the tip acceleration mode shape of the h-th vibration, and Φ be the strain mode shape. Let h be the strain mode shape at any point of order h.

[0125] In one embodiment, the blade vibration acceleration response expression in modal space is established as follows: The expression for the vibration strain response is: C y Let y be the tip acceleration mode shape of the y-th order vibration. Let y be the strain mode shape at any point of order y. Let y be the vibration mode response of the yth order.

[0126] Based on the blade modal response and mode shape, a transformation relationship between tip vibration acceleration and strain at any point is established. The expression for the transformation matrix is ​​as follows:

[0127] ,

[0128] Where T is the transformation matrix.

[0129] Furthermore, based on the conversion relationship between tip vibration acceleration and strain at any point, the dynamic strain is calculated. The relationship between the strain response at any point on the blade at any time and the tip vibration acceleration response, i.e., the expression for the dynamic strain at any point on the blade, is:

[0130] ,

[0131] in, The dynamic strain of the blade at any point in any dimension (X direction, Y direction, Z direction, XY direction, YZ direction, XZ direction) under full-time multimodal vibration.

[0132] This application's method fundamentally breaks through the traditional dynamic strain response monitoring mode that relies on tip vibration displacement. It fully utilizes the sensitivity of acceleration signals to high-frequency vibration responses and their sparse, full-time-domain sensing characteristics to construct a transmission relationship from rotor blade tip acceleration to multimodal dynamic strain responses at any position on the blade surface. This allows for high-precision calculation and real-time monitoring of blade dynamic strain even under complex multimodal coupling vibration conditions (synchronous high-order and low-order vibrations). By capturing the tip arrival time series using a tip timing system, undersampled acceleration is calculated. Furthermore, a sparse, canonical acceleration model is constructed to effectively identify high-frequency vibration components, ensuring that strong low-frequency responses and weak high-frequency vibration signals are synchronously preserved. Based on the acceleration and strain mode shapes of the blade system, a sensing matrix from multimodal tip acceleration to dynamic strain at any point is constructed, forming a real-time dynamic strain monitoring mechanism. This method is particularly suitable for capturing high- and low-frequency coupled dynamic strain responses that are prone to causing blade fatigue. It enables comprehensive monitoring of multimodal dynamic strain of rotor blades in a non-contact manner, which is of great value for promoting the development of blade health monitoring systems towards non-invasive, high-sensitivity, and vibration decoupling.

[0133] Secondly, embodiments of this application also provide a multimodal dynamic strain monitoring system based on blade tip acceleration, referring to... Figure 2 The system is used to implement the multimodal dynamic strain monitoring method based on tip acceleration as described in any embodiment of the first aspect, the system comprising:

[0134] The rotor blade tip timing measurement module is used to record the vibration arrival time sequence of the blade under multimodal vibration state based on the blade tip timing sensor while the blade is rotating.

[0135] The undersampled vibration acceleration calculation module is used to establish a vibration acceleration calculation model based on the blade vibration arrival time series, calculate the blade tip vibration acceleration based on the vibration acceleration calculation model, and obtain the undersampled blade tip vibration acceleration signal.

[0136] The sparse regularization identification module for acceleration vibration parameters is used to establish a sparse identification model of multimodal vibration parameters of the blade based on the undersampled blade tip vibration acceleration signal, reconstruct the acceleration response, obtain the multimodal vibration acceleration parameters of the blade, and calculate the full-time domain response of the blade tip vibration acceleration based on the multimodal vibration acceleration parameters of the blade.

[0137] The rotor blade finite element analysis module is used to establish a finite element model of the rotor blade, carry out modal analysis of the rotating blade, and obtain the multimodal acceleration mode shape and strain mode shape of the blade.

[0138] The multimodal acceleration and dynamic strain conversion module is used to construct the conversion relationship between the tip vibration acceleration and the dynamic strain at any point on the blade based on the multimodal acceleration mode shape and the strain mode shape, forming a conversion matrix to decouple the multimodal vibration of the blade;

[0139] The dynamic strain monitoring module is used to calculate the dynamic strain at any point on the blade in real time based on the full-time domain response and transformation matrix of the blade tip vibration acceleration, and to monitor the multi-modal dynamic strain of the blade.

[0140] The embodiments provided by this invention offer a method and system for monitoring multimodal dynamic strain based on blade tip acceleration. By comprehensively utilizing various techniques such as blade tip timing measurement, vibration acceleration calculation, parameter sparsity identification, finite element analysis, and multimodal acceleration-dynamic strain conversion, it achieves accurate monitoring of multimodal dynamic strain of the blade. This method can not only effectively extract multimodal characteristic parameters from blade vibration, such as the vibration frequency, amplitude, and phase information of each mode, but also calculate the dynamic strain at any point on the blade in real time based on these parameters, thereby comprehensively assessing the vibration state and health of the blade. Compared with traditional monitoring methods, this invention has higher accuracy and wider applicability, providing more reliable technical support for blade maintenance and management. Furthermore, this method further improves the adaptability and accuracy of the model by constructing a multimodal vibration parameter sparsity identification model of the blade and using convex optimization, non-convex optimization, and greedy algorithms for optimization, ensuring the accuracy and reliability of the identification results. In addition, the present invention provides a multimodal dynamic strain monitoring system based on blade tip acceleration. This system, in conjunction with the monitoring method, can automatically complete the monitoring task of multimodal dynamic strain of the blade, greatly improving the monitoring efficiency and convenience.

[0141] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multimodal dynamic strain monitoring method based on blade tip acceleration, characterized in that, The method includes: While the blade is rotating, the vibration arrival time sequence under multimodal vibration is recorded based on the blade tip timing sensor; Based on the blade vibration arrival time series, a vibration acceleration calculation model is established. Based on the vibration acceleration calculation model, the blade tip vibration acceleration is calculated, and the undersampled blade tip vibration acceleration signal is obtained. Based on the undersampled blade tip vibration acceleration signal, a sparse identification model of blade multimodal vibration parameters is established, the acceleration response is reconstructed, the blade multimodal vibration acceleration parameters are obtained, and the blade tip vibration acceleration full-time domain response is calculated based on the blade multimodal vibration acceleration parameters. A finite element model of the rotor blade was established, and modal analysis of the rotating blade was carried out to obtain the multimodal acceleration mode shape and strain mode shape of the blade. Based on multimodal acceleration mode shapes and strain mode shapes, the transformation relationship between tip vibration acceleration and dynamic strain at any point on the blade is constructed, forming a transformation matrix to decouple the multimodal vibration of the blade; Based on the full-time domain response and transformation matrix of blade tip vibration acceleration, the dynamic strain at any point on the blade is calculated in real time, and the multi-modal dynamic strain of the blade is monitored. The vibration acceleration calculation model established based on the blade vibration arrival time series includes: The rotor blades vibrate during rotation until the first... The first leaf tip timing sensor, the first The installation angles of the leaf tip timing sensor and its two adjacent leaf tip timing sensors are as follows: , and ,in, , ; the blade in the first The vibration reaches the first cycle. The, the The and the first The timing of each blade tip timing sensor is as follows: , and ; Based on the blade vibration arrival time series, establish the blade in the first... The ring vibration reaches the first The vibration acceleration calculation model for a single blade tip timing sensor is expressed as follows: ， in, For the blade in the first The ring vibration reaches the first Vibration acceleration at the timer sensor of the blade tip Radius of gyration For the blade in the first The ring vibration reaches the first The time interval between the first and (i+2)th leaf tip timing sensors ; For the blade in the first The time interval between the arrival of the loop vibration at the (i+1)th blade tip timing sensor and the (i+2)th blade tip timing sensor. ; For the blade in the first The time interval between the arrival of the loop vibration at the i-th blade tip timing sensor and the (i+1)-th blade tip timing sensor. ; Let be the installation interval angle between the (i+1)th and (i+2)th blade tip timing sensors. ; Let be the installation interval angle between the i-th blade tip timing sensor and the (i+1)-th blade tip timing sensor. ; corresponding time The expression is: .

2. The multimodal dynamic strain monitoring method based on tip acceleration according to claim 1, characterized in that, The recording of the vibration arrival time series under the multimodal vibration state of the blade includes: Set the number of blade tip timing sensors The K blade tip timing sensors are installed at the following angles in the casing: , Let K be the mounting angle of the Kth blade tip timing sensor in the casing, and let the mounting interval angle between two adjacent sensors be denoted by . , The rotor blade rotation frequency, The highest recognizable target frequency in the multimodal analysis of the blade; The vibration arrival time series under multimodal vibration states of the blade are recorded and represented by the blade tip vibration arrival time matrix. The expression of the blade tip vibration arrival time matrix is ​​as follows: ， T N This is the tip vibration arrival time matrix, where N is the total number of rotations of the rotor blade within the measurement time, and t is the time matrix. N,K Let be the arrival time of the blade tip vibration as measured by the Kth blade tip timing sensor during the Nth revolution.

3. The multimodal dynamic strain monitoring method based on tip acceleration according to claim 1, characterized in that, The method for calculating blade tip vibration acceleration based on the vibration acceleration calculation model and obtaining undersampled blade tip vibration acceleration signals includes: Based on the vibration acceleration calculation model, the blade tip vibration acceleration is calculated, forming a multimodal acceleration matrix. The expression for the multimodal acceleration matrix is ​​as follows: ， Where A is the multimodal acceleration matrix. The time interval between the blade's vibration on the Nth cycle reaching the Kth tip timing sensor and the (K-2)th tip timing sensor is given. The time interval between the blade's vibration on the Nth cycle reaching the Kth tip timing sensor and the (K-1)th tip timing sensor is given. The time interval between the blade's vibration reaching the (K-1)th blade tip timing sensor and the (K-2)th blade tip timing sensor during the Nth rotation is given. The installation interval angle between the (K-1)th blade tip timing sensor and the Kth blade tip timing sensor is [angle missing]. The installation interval angle between the (K-2)th blade tip timing sensor and the (K-1)th blade tip timing sensor; The multimodal acceleration matrix corresponding to the tip multimodal acceleration acquisition time matrix T a The expression is: 。 4. The multimodal dynamic strain monitoring method based on tip acceleration according to claim 3, characterized in that, The establishment of a sparse identification model for multimodal vibration parameters of the blade based on undersampled blade tip vibration acceleration signals includes: The tip acceleration response of the rotor blade in multimodal vibration is expressed as: ， in, The tip acceleration response to the multimodal vibration of the rotor blade is given by t, where t is the moment of the vibration acceleration response. The first vibration acceleration coefficient of the y-th order at the blade tip. The coefficient of the second vibration acceleration of the blade tip in the y-th order is... y is the yth vibrational frequency of the multimodal vibration at the blade tip, and h is the number of modes; Based on compressed sensing sparse regularization theory, a sparse identification model for multimodal vibration parameters of a blade is constructed. The expression for the sparse identification model of multimodal vibration parameters of a blade is as follows: ,in, Represents the q-norm. ;a is the undersampled acceleration vector formed by column expansion of the multimodal acceleration matrix A during continuous blade rotation. S is the regularization parameter; S is the coefficient vector. ,in, Representing the For the first and second vibration acceleration coefficient pair, D is a static constant; H is a sparse transformation matrix, and the expression for the sparse transformation matrix is: ， Among them, t p For the p-th moment of undersampling of the blade tip vibration acceleration, To achieve sparse spectrum reconstruction resolution; and to meet the frequency identification requirements of multimodal broadband response of blades, the upper limit of the sparse matrix identification bandwidth must satisfy: , This is the highest frequency of the multimodal vibration of the blade.

5. The multimodal dynamic strain monitoring method based on tip acceleration according to claim 4, characterized in that, The reconstructed acceleration response obtains the multimodal vibration acceleration parameters of the blade. Based on these parameters, the full-time response of the blade tip vibration acceleration is calculated, including: Solve the sparse identification model of the multimodal vibration parameters of the blade, reconstruct the response spectrum, and obtain the response frequency, amplitude, and phase of the multimodal vibration acceleration at the blade tip. The expressions for the amplitude and phase of the y-th order vibration acceleration are as follows: ， in, Let y be the amplitude of the y-th order vibration acceleration. The phase of the y-th order vibration acceleration; Based on the multimodal vibration acceleration parameters of the blade, the full-time response of the blade tip vibration acceleration is calculated, and the expression is as follows: ， Where a(t) is the full-time response of the blade tip vibration acceleration.

6. The multimodal dynamic strain monitoring method based on tip acceleration according to claim 5, characterized in that, The expression for the multimodal acceleration mode shape of the blade is: ， The expression for the strain mode shape is: ， Where C is the multimodal acceleration mode shape of the blade, C h Let Φ be the tip acceleration mode shape of the h-th vibration, and Φ be the strain mode shape. Let h be the strain mode shape at any point of order h.

7. The multimodal dynamic strain monitoring method based on tip acceleration according to claim 6, characterized in that, The expression for the transformation matrix is: ， Where T is the transformation matrix.

8. The multimodal dynamic strain monitoring method based on tip acceleration according to claim 7, characterized in that, The expression for the arbitrary point strain of the blade is: ， in, This represents the dynamic strain of any point and any dimension of the blade under full-time multimodal vibration.

9. A multimodal dynamic strain monitoring system based on blade tip acceleration, used to implement the multimodal dynamic strain monitoring method based on blade tip acceleration as described in any one of claims 1-8, characterized in that, The system includes: The rotor blade tip timing measurement module is used to record the vibration arrival time sequence of the blade under multimodal vibration state based on the blade tip timing sensor while the blade is rotating. The undersampled vibration acceleration calculation module is used to establish a vibration acceleration calculation model based on the blade vibration arrival time series, calculate the blade tip vibration acceleration based on the vibration acceleration calculation model, and obtain the undersampled blade tip vibration acceleration signal. The sparse regularization identification module for acceleration vibration parameters is used to establish a sparse identification model of multimodal vibration parameters of the blade based on the undersampled blade tip vibration acceleration signal, reconstruct the acceleration response, obtain the multimodal vibration acceleration parameters of the blade, and calculate the full-time domain response of the blade tip vibration acceleration based on the multimodal vibration acceleration parameters of the blade. The rotor blade finite element analysis module is used to establish a finite element model of the rotor blade, carry out modal analysis of the rotating blade, and obtain the multimodal acceleration mode shape and strain mode shape of the blade. The multimodal acceleration and dynamic strain conversion module is used to construct the conversion relationship between the tip vibration acceleration and the dynamic strain at any point on the blade based on the multimodal acceleration mode shape and the strain mode shape, forming a conversion matrix to decouple the multimodal vibration of the blade; The dynamic strain monitoring module is used to calculate the dynamic strain at any point on the blade in real time based on the full-time domain response and transformation matrix of the blade tip vibration acceleration, and to monitor the multimodal dynamic strain of the blade.

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