Non-contact multi-order dynamic strain reconstruction method and system based on tip speed

Abstract

This application provides a non-contact multi-order dynamic strain reconstruction method and system based on blade tip velocity, belonging to the field of aero-engine technology. Specifically, it includes calculating the blade Campbell diagram, obtaining multi-order vibration information of the rotor blade, and determining the number and installation angle of the blade tip timing sensors; acquiring the sensor measurement time series, obtaining undersampled time-domain data of blade tip vibration velocity under all operating conditions, constructing a sparse canonical model based on this undersampled data, identifying vibration velocity parameters, and obtaining the reconstructed vibration velocity response of the blade tip at any time; acquiring the blade vibration velocity and strain mode shapes, and calculating the dynamic strain and vibration velocity transformation matrix; and calculating the dynamic strain at any point on the blade based on the reconstructed vibration velocity response and transformation matrix, thus realizing non-contact measurement of multi-order, multi-dimensional vibration and dynamic strain of the blade under all operating conditions. This application has the advantages of non-contact, all-operating-condition, and multi-order, multi-dimensional vibration and dynamic strain measurement, improving the accuracy and efficiency of dynamic strain measurement.

Description

Technical Field

[0001] This application relates to the field of aero-engine technology, and in particular to a non-contact multi-stage dynamic strain reconstruction method and system based on blade tip velocity. Background Technology

[0002] As a core component of an engine, rotor blades endure complex loads from high-temperature, high-pressure, high-speed environments and unsteady airflow excitation, making them highly susceptible to vibration. Within the operating speed range, blade vibrations induced by complex excitations often exhibit multi-order or even complexly coupled states. The high-level stress / strain generated by high- and low-order vibrations can easily cause cracks to initiate at stress concentration points, leading to fatigue failure and seriously threatening the operational safety of the engine. Therefore, conducting rotor blade vibration stress / strain monitoring is of great significance to ensure the operational safety of aero-engines. Traditional strain gauges are widely used in blade strain measurement, but due to their contact-based measurement method and short service life, they can only measure the strain at a fixed point on the blade for a limited time. However, during multi-order blade vibration, the point of maximum dynamic strain on the blade is not fixed, and the single-point measurement method of strain gauges cannot meet the dynamic strain sensing requirements of multi-order blade vibration. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention proposes a non-contact multi-order dynamic strain reconstruction method and system based on blade tip velocity. By identifying vibration velocity sparse regularity, the multi-order dynamic strain at any point on the blade is reconstructed, thereby realizing non-contact dynamic strain sensing of multi-order vibration of engine rotating blades.

[0004] In a first aspect, embodiments of this application provide a non-contact multi-order dynamic strain reconstruction method based on blade tip velocity, the method comprising:

[0005] A finite element model of the rotor blade was established, rotational modal analysis was performed, the Campbell diagram of the blade was calculated, and multi-order vibration information of the rotor blade was obtained.

[0006] The number of tip timing sensors is determined based on the modal order of interest, and the sensor layout is optimized by combining multi-order vibration information of the rotor blades to determine the sensor installation angle.

[0007] Acquire sensor measurement time series, calculate blade tip vibration velocity, and obtain time-domain undersampled data of blade tip vibration velocity under all operating conditions;

[0008] Based on the time-domain undersampled data of blade tip vibration velocity under all operating conditions, a sparse regular model is constructed to reconstruct the blade tip vibration velocity response, identify the vibration velocity parameters, and obtain the reconstructed blade tip vibration velocity response at any time.

[0009] Based on the modal analysis of the blade finite element model, the vibration velocity mode shape and strain mode shape of the blade are obtained, and the transformation matrix of dynamic strain at any point on the blade and vibration velocity at the blade tip measuring point is calculated.

[0010] Based on the reconstructed vibration velocity response and transformation matrix of the blade tip at any time, the dynamic strain at any point on the blade is calculated, realizing non-contact measurement of multi-order and multi-dimensional vibration and dynamic strain of the blade under all working conditions.

[0011] According to a specific implementation of an embodiment of this application, the step of establishing a finite element model of the rotor blade, performing rotational modal analysis, calculating the blade Campbell diagram, and obtaining multi-order vibration information of the rotor blade includes:

[0012] Mesh generation was performed on the 3D model of the rotating blade to establish a finite element model of the rotor blade;

[0013] Set material parameters, perform rotational modal analysis, and set the rotor blade speed range from zero to the maximum operating speed, with a speed interval of no more than 1000 r / min.

[0014] Based on the modal analysis results, the multi-order natural frequency values ​​of the blade at different speeds are obtained. Combined with the rotational frequency, the Campbell diagram of the blade within the set speed range is plotted. Through the Campbell diagram, the multi-order vibration information of the rotor blade within the operating speed range is estimated.

[0015] According to a specific implementation of an embodiment of this application, the step of determining the number of tip timing sensors based on the modal order of interest, optimizing the sensor layout in conjunction with multi-order vibration information of the rotor blades, and determining the sensor installation angle includes:

[0016] Based on the modal order of interest and experimental requirements, the number of sensors that can be installed circumferentially in the casing and the limited angle range are determined, and the sensing matrix of the sensor layout is constructed.

[0017] Optimize the number of sensing matrix conditions within the limited angle range. When the number of sensing matrix conditions reaches its minimum value, the sensor installation angles obtained are the sensor installation angles under the optimized layout.

[0018] According to a specific implementation of an embodiment of this application, the expression of the perception matrix is:

[0019] ,

[0020] in, For the perception matrix, f k Let θ be the k-th natural frequency of the leaf tip. l Let be the installation angle of the l-th sensor, where sin is the sine function and cos is the cosine function;

[0021] The expression for the condition number of the perception matrix is:

[0022] ,

[0023] Where cond is the condition number of the perception matrix.

[0024] According to a specific implementation of an embodiment of this application, the step of acquiring the sensor measurement time series, calculating the blade tip vibration velocity, and acquiring the undersampled time-domain data of the blade tip vibration velocity under all operating conditions includes:

[0025] Acquire sensor measurement time series to form a full-condition arrival time matrix;

[0026] Based on the arrival time matrix under all operating conditions, the blade tip vibration velocity is calculated to form the time domain matrix of blade tip vibration velocity under all operating conditions.

[0027] Based on the arrival time matrix under all operating conditions, the acquisition time corresponding to the blade tip vibration velocity under all operating conditions is calculated, forming the blade tip vibration velocity acquisition time matrix under all operating conditions.

[0028] According to a specific implementation of an embodiment of this application, the expression for the full-condition arrival time matrix is:

[0029] ,

[0030] Where T is the arrival time matrix under all operating conditions, t n,l This represents the moment when the blade reaches the l-th sensor after rotating to the nth revolution;

[0031] The expression for the time-domain matrix of the blade tip vibration velocity under all operating conditions is as follows:

[0032] ,

[0033] Where V is the time-domain matrix of the blade tip vibration velocity under all operating conditions, f n,w R is the rotor frequency on the nth revolution, and R is the blade tip gyration radius;

[0034] The expression for the time matrix of blade tip vibration velocity acquisition under all operating conditions is:

[0035] ,

[0036] Among them, T v This is a time matrix for collecting blade tip vibration velocity data under all operating conditions.

[0037] According to a specific implementation of an embodiment of this application, the steps of constructing a sparse regularized model, reconstructing the blade tip vibration velocity response, identifying vibration velocity parameters, and obtaining the reconstructed blade tip vibration velocity response at any time include:

[0038] The time-domain expression for the multi-modal vibration velocity response of the blade tip is as follows:

[0039] ,

[0040] in, This refers to the multi-mode vibration velocity response of the blade tip. The first vibration velocity coefficient of the i-th order at the blade tip. is the second vibration velocity coefficient of the i-th order at the blade tip, t is the sampling time of vibration velocity, and k represents that the highest order vibration of the blade is the k-th order vibration.

[0041] Construct a sparse regularized model, the expression is: ,

[0042] Where v is the velocity vector formed by expanding the time-domain matrix of the blade tip vibration velocity under all operating conditions according to the time series, and λ is the regularization parameter. Represents the q-norm, where P is the coefficient vector. ,in, Representing the For the first and second vibration velocity coefficient pair, C is a static constant; D is the constructed sparse transformation matrix, and the expression for D is:

[0043] ,

[0044] Among them, t h Let h be the time of undersampling of the blade tip vibration velocity; Δf is the frequency identification resolution to be reconstructed. To meet the requirements of multi-order identification, it should satisfy: ;

[0045] The sparse regular model is solved using a non-convex sparse solution method. The blade tip vibration velocity response spectrum is reconstructed, and multi-order vibration velocity parameters of the blade tip are identified. These parameters include the k-th order vibration velocity frequency, vibration velocity amplitude, and vibration velocity phase. The expressions for the i-th order vibration velocity amplitude and phase are:

[0046] ,

[0047] in, To identify the amplitude and phase parameters of the i-th order vibration velocity, The phase of the i-th order vibration velocity is to be identified;

[0048] Based on the identified multi-order vibration velocity parameters of the blade, the reconstructed vibration velocity response of the blade tip at any time is obtained, expressed as: ,

[0049] in, This represents the vibration velocity response of the blade tip at any given moment in the reconstructed image.

[0050] According to a specific implementation of an embodiment of this application, the step of obtaining the blade vibration velocity mode shape and strain mode shape based on the blade finite element model modal analysis, and calculating the transformation matrix between the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point, includes:

[0051] Based on finite element modal analysis, the multi-order vibration velocity mode shape S at the blade tip measuring point and the multi-order strain mode shape at any point on the blade body were obtained. S and The expressions are as follows:

[0052] ,

[0053] ,

[0054] Among them, S k For the first measuring point at the leaf tip First-order vibration velocity mode shape quantity For any point on the leaf body First strain mode shape;

[0055] Based on the mode shape, the transformation matrix F is calculated for the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point. The expression for the transformation matrix F is:

[0056] .

[0057] According to a specific implementation of an embodiment of this application, the expression for the arbitrary point-motion strain of the blade is:

[0058] ,

[0059] in, This refers to the dynamic strain of any point and any dimension of the blade under all operating conditions and in all time domains.

[0060] Secondly, embodiments of this application also provide a non-contact multi-order dynamic strain reconstruction system based on blade tip velocity, used to implement the non-contact multi-order dynamic strain reconstruction method based on blade tip velocity as described in any embodiment of the first aspect, the system comprising:

[0061] The rotor blade modal analysis module is used to establish a finite element model of the rotor blade, perform rotational modal analysis, calculate the blade Campbell diagram, and obtain multi-order vibration information of the rotor blade.

[0062] The blade tip timing sensor layout module is used to determine the number of blade tip timing sensors based on the order of the mode of interest, and to optimize the sensor layout by combining multi-order vibration information of the rotor blades, and to determine the sensor installation angle.

[0063] The undersampled vibration velocity calculation module is used to acquire the sensor measurement time series, calculate the blade tip vibration velocity, and acquire the time-domain undersampled data of blade tip vibration velocity under all operating conditions.

[0064] The blade tip vibration velocity sparse reconstruction module is used to construct a sparse regular model based on the time-domain undersampled data of blade tip vibration velocity under all operating conditions, reconstruct the blade tip vibration velocity response, identify vibration velocity parameters, and obtain the reconstructed blade tip vibration velocity response at any time.

[0065] The vibration velocity and dynamic strain conversion module is used to obtain the vibration velocity mode shape and strain mode shape of the blade based on the modal analysis of the blade finite element model, and to calculate the conversion matrix between the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point.

[0066] The dynamic strain calculation module is used to calculate the dynamic strain at any point on the blade based on the reconstructed vibration velocity response and transformation matrix at any moment of the blade tip, realizing non-contact measurement of multi-order and multi-dimensional vibration dynamic strain of the blade under all working conditions.

[0067] Beneficial effects:

[0068] The non-contact multi-order dynamic strain reconstruction method and system based on blade tip velocity in this application focuses on calculating the broadband multi-order dynamic strain of rotor blades using non-contact velocity measurement. Unlike strain reconstruction based on displacement signals, this method uses the blade tip arrival time series as input. By accurately identifying blade vibration velocity parameters, it establishes a direct mapping relationship from multi-order vibration velocities to dynamic strain responses, thereby reconstructing the multi-order vibration dynamic strain of rotor blades. A key breakthrough of this method lies in employing non-convex sparse regularization technology to identify vibration velocity parameters, significantly improving the amplitude recognition accuracy for multi-order vibrations (especially higher-order vibration components). Simultaneously, by establishing a transformation matrix between the blade's multi-order velocity mode shapes and strain mode shapes, an explicit reconstruction mechanism from blade tip vibration velocity to dynamic strain at any point within the field is formed. This innovative multi-order velocity sparse regularization identification strategy and velocity-dynamic strain conversion model have significant engineering value for the accurate perception of dynamic strain in aero-engine rotor blades, especially blades that easily induce broadband multi-order vibrations within their operating envelope. Attached Figure Description

[0069] 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.

[0070] Figure 1This is a flowchart illustrating a non-contact multi-stage dynamic strain reconstruction method based on tip velocity provided in one embodiment of the present invention.

[0071] Figure 2 This is a schematic diagram of the structure of a non-contact multi-stage dynamic strain reconstruction system based on tip velocity provided in one embodiment of the present invention;

[0072] Figure 3 This is a layout diagram of a rotor blade tip timing measurement system provided in one embodiment of the present invention;

[0073] Figure 4 This is a vibration velocity response diagram of a rotor blade calculated based on tip timing undersampling in one embodiment of the present invention;

[0074] Figure 5(a) is a waterfall plot of the reconstructed vibration velocity spectrum of a first-order rotor blade in an embodiment of the present invention.

[0075] Figure 5(b) is a waterfall plot of the reconstructed vibration velocity spectrum of a second-order rotor blade in one embodiment of the present invention;

[0076] Figure 5(c) is a waterfall plot of the reconstructed vibration velocity spectrum of a third-order rotor blade in one embodiment of the present invention. Detailed Implementation

[0077] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0078] 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.

[0079] 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.

[0080] 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.

[0081] 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.

[0082] Tip timing, as a non-contact rotor blade vibration measurement system, can measure the arrival time of rotor blade rotational vibration. Based on the measured arrival time and parameters such as the blade's real-time rotational speed and radius of gyration, undersampled vibration data such as blade tip displacement and velocity can be further obtained. Vibration velocity is more sensitive to the mid-to-high frequency response of the blade than vibration displacement. Parameter identification based on vibration velocity can improve the accuracy of multi-order blade response reconstruction. Therefore, this invention provides a method and system for vibration velocity parameter identification and strain response reconstruction at any point on the blade based on tip timing measurement, to achieve non-contact dynamic strain sensing of multi-order vibration of rotating blades, which will be described in detail below.

[0083] In a first aspect, embodiments of this application provide a non-contact multi-order dynamic strain reconstruction method based on blade tip velocity, referring to... Figure 1 The method includes:

[0084] Step S100: Establish a finite element model of the rotor blade, perform rotational modal analysis, calculate the blade Campbell diagram, and obtain multi-order vibration information of the rotor blade.

[0085] Step S200: Determine the number of tip timing sensors based on the order of the modes of interest, optimize the sensor layout by combining the multi-order vibration information of the rotor blades, and determine the sensor installation angle.

[0086] Step S300: Obtain the sensor measurement time series, calculate the blade tip vibration velocity, and obtain the time-domain undersampled data of the blade tip vibration velocity under all working conditions;

[0087] Step S400: Based on the undersampled time-domain vibration velocity data of the blade tip under all operating conditions, construct a sparse regular model, reconstruct the blade tip vibration velocity response, identify the vibration velocity parameters, and obtain the reconstructed vibration velocity response of the blade tip at any time.

[0088] Step S500: Based on the modal analysis of the blade finite element model, obtain the vibration velocity mode shape and strain mode shape of the blade, and calculate the transformation matrix of dynamic strain at any point on the blade and vibration velocity at the blade tip measuring point.

[0089] Step S600: Based on the reconstructed vibration velocity response and transformation matrix of the blade tip at any time, calculate the dynamic strain at any point on the blade to realize non-contact measurement of multi-order and multi-dimensional vibration dynamic strain of the blade under all working conditions.

[0090] In this embodiment, non-contact, precise measurement of multi-order, multi-dimensional vibration dynamic strain of rotor blades under all operating conditions is achieved, providing strong support for the health monitoring of rotor blades in critical equipment such as aero-engines. This method, through non-contact tip-timed measurement technology combined with a sparse canonical model and a non-convex sparse solution method, accurately identifies the multi-order vibration velocity parameters of the blade. Then, by constructing a velocity-dynamic strain transformation matrix, a direct mapping from tip vibration velocity to dynamic strain at any point on the blade is achieved. This innovative method not only improves the accuracy of amplitude identification for higher-order vibration components but also forms an explicit reconstruction mechanism, making the measurement of dynamic strain more accurate and reliable. In practical applications, this method can be widely used for dynamic strain monitoring of rotor blades in various rotating machinery, which is of great significance for preventing blade fatigue fracture and improving equipment operational safety.

[0091] In one embodiment, establishing a finite element model of the rotor blade, performing rotational modal analysis, calculating the blade Campbell diagram, and obtaining multi-order vibration information of the rotor blade includes:

[0092] Mesh generation was performed on the 3D model of the rotating blade to establish a finite element model of the rotor blade;

[0093] Set material parameters, including material elastic modulus and density, and perform rotational modal analysis. The rotor blade speed setting range includes zero to the maximum operating speed, and the speed interval is no more than 1000 r / min.

[0094] Based on the modal analysis results, the multi-order natural frequencies of the blade at different rotational speeds were obtained. Combined with the rotational frequency, a Campbell diagram of the blade within a set rotational speed range was plotted, with the multi-order natural frequencies of the blade being... , where f kLet be the k-th natural frequency of the blade tip. Using Campbell's plot, we can predict the multi-order vibration information of the rotor blade within the operating speed range.

[0095] In this embodiment, multi-order vibration information of the rotor blades within the operating speed range was acquired, providing accurate basic data for subsequent sensor layout optimization and vibration velocity parameter identification. Through detailed finite element model establishment and rotating modal analysis, a comprehensive understanding of the blade vibration characteristics can be ensured, thereby enabling more accurate capture of the blade's vibration response under different operating conditions.

[0096] In one embodiment, determining the number of tip timing sensors based on the modal order of interest, optimizing the sensor layout by combining multi-order vibration information of the rotor blades, and determining the sensor installation angle includes:

[0097] Based on the modal order of interest and experimental requirements, the number of sensors that can be installed circumferentially in the casing and the limited angle range are determined, and the sensing matrix of the sensor layout is constructed.

[0098] Optimize the number of sensing matrix conditions within the limited angle range. When the number of sensing matrix conditions reaches its minimum value, the sensor installation angles obtained are the sensor installation angles under the optimized layout.

[0099] Furthermore, the expression for the perception matrix is:

[0100] ,

[0101] in, For the perception matrix, f k Let θ be the k-th natural frequency of the leaf tip. l Let be the installation angle of the l-th sensor, where sin is the sine function and cos is the cosine function;

[0102] The expression for the condition number of the perception matrix is:

[0103] ,

[0104] Where cond is the condition number of the perception matrix.

[0105] In this embodiment, by constructing a sensing matrix for the sensor layout and optimizing the sensor layout based on the condition number of the sensing matrix, the rationality and measurement accuracy of the sensor layout are effectively improved. This optimization method ensures that the distribution of sensors in the circumferential direction of the casing captures multi-order vibration information of the blades to the maximum extent, while reducing redundant data and improving the accuracy of subsequent vibration velocity parameter identification. In practical applications, the optimized sensor layout can significantly reduce the measurement error of higher-order vibration components, providing a more reliable data foundation for the subsequent reconstruction of sparse regularized models. In addition, this method clarifies the calculation method of the sensing matrix and its condition number through mathematical expressions, providing a quantitative basis for sensor layout design in engineering practice and enhancing the operability and repeatability of the method. At the same time, this optimization method has a certain degree of universality and can be applied to rotor blades of different types and sizes, providing strong technical support for vibration monitoring of rotating machinery.

[0106] In one embodiment, acquiring the sensor measurement time series, calculating the blade tip vibration velocity, and acquiring undersampled time-domain data of the blade tip vibration velocity under all operating conditions includes:

[0107] Acquire sensor measurement time series to form a full-condition arrival time matrix;

[0108] Based on the arrival time matrix under all operating conditions, the blade tip vibration velocity is calculated to form the time domain matrix of blade tip vibration velocity under all operating conditions.

[0109] Based on the arrival time matrix under all operating conditions, the acquisition time corresponding to the blade tip vibration velocity under all operating conditions is calculated, forming the blade tip vibration velocity acquisition time matrix under all operating conditions.

[0110] Furthermore, the expression for the arrival time matrix under all operating conditions is as follows:

[0111] ,

[0112] Where T is the arrival time matrix under all operating conditions, t n,l This represents the moment when the blade reaches the l-th sensor after rotating to the nth revolution;

[0113] The expression for the time-domain matrix of the blade tip vibration velocity under all operating conditions is as follows:

[0114] ,

[0115] Where V is the time-domain matrix of the blade tip vibration velocity under all operating conditions, f n,w R is the rotor frequency on the nth revolution, and R is the blade tip gyration radius;

[0116] The expression for the time matrix of blade tip vibration velocity acquisition under all operating conditions is:

[0117] ,

[0118] Among them, T v This is a time matrix for collecting blade tip vibration velocity data under all operating conditions.

[0119] In this embodiment, a time-domain matrix of blade tip vibration velocity and a time-domain matrix of blade tip vibration velocity acquisition under all operating conditions were obtained, providing comprehensive data support for subsequent vibration velocity parameter identification and dynamic strain reconstruction. The construction of the arrival time matrix under all operating conditions ensures that the time information of the blade tip arriving at each sensor under different speeds and operating conditions is completely recorded, providing a foundation for subsequent velocity calculations. The generation of the time-domain matrix of blade tip vibration velocity under all operating conditions, by combining rotational frequency and blade tip gyration radius, transforms time information into vibration velocity information, intuitively reflecting the vibration state of the blade at different times. The determination of the acquisition time matrix of blade tip vibration velocity under all operating conditions further clarifies the acquisition time points corresponding to each velocity data point, providing accurate time references for subsequent data processing and analysis. The construction of this series of matrices not only improves the efficiency and accuracy of data processing but also lays a solid foundation for subsequent sparse regularized model construction and vibration velocity parameter identification. In practical applications, this matrix data can be widely used for rotor blade vibration monitoring in various rotating machinery, providing strong support for equipment health management and fault prevention.

[0120] In one embodiment, the construction of a sparse regularized model, the reconstruction of the blade tip vibration velocity response, the identification of vibration velocity parameters, and the acquisition of the reconstructed blade tip vibration velocity response at any given time include:

[0121] The time-domain expression for the multi-modal vibration velocity response of the blade tip is as follows:

[0122] ,

[0123] in, This refers to the multi-mode vibration velocity response of the blade tip. The first vibration velocity coefficient of the i-th order at the blade tip. is the second vibration velocity coefficient of the i-th order at the blade tip, t is the sampling time of vibration velocity, and k represents that the highest order vibration of the blade is the k-th order vibration.

[0124] Construct a sparse regularized model, the expression is: ,

[0125] Where v is the velocity vector formed by expanding the time-domain matrix of the blade tip vibration velocity under all operating conditions according to the time series, and λ is the regularization parameter. Represents the q-norm, where P is the coefficient vector. ,in, Representing the For the first and second vibration velocity coefficient pair, C is a static constant; D is the constructed sparse transformation matrix, and the expression for D is:

[0126] ,

[0127] Among them, t h Let h be the time of undersampling of the blade tip vibration velocity; Δf is the frequency identification resolution to be reconstructed. To meet the requirements of multi-order identification, it should satisfy: ;

[0128] The sparse regular model is solved using a non-convex sparse solution method. The blade tip vibration velocity response spectrum is reconstructed, and multi-order vibration velocity parameters of the blade tip are identified. These parameters include the k-th order vibration velocity frequency, vibration velocity amplitude, and vibration velocity phase. The expressions for the i-th order vibration velocity amplitude and phase are:

[0129] ,

[0130] in, To identify the amplitude and phase parameters of the i-th order vibration velocity, The phase of the i-th order vibration velocity is to be identified;

[0131] Based on the identified multi-order vibration velocity parameters of the blade, the reconstructed vibration velocity response of the blade tip at any time is obtained, expressed as: ,

[0132] in, This represents the vibration velocity response of the blade tip at any given moment in the reconstructed image.

[0133] In this embodiment, a sparse regularized model for reconstructing the blade tip vibration velocity response was constructed. A non-convex sparse solution method was used to solve the sparse regularized model, reconstructing the blade tip vibration velocity response spectrum. Referring to the waterfall plots of the rotor blade's non-convex sparse regularized vibration velocity reconstruction spectrum shown in Figures 5(a) to 5(c), multi-order vibration velocity parameters at the blade tip were identified. Based on these identified multi-order vibration velocity parameters, the vibration velocity response at any given time at the blade tip was obtained. This process effectively improved the accuracy and reliability of vibration velocity parameter identification. The construction of the sparse regularized model fully considered the sparsity characteristics of the blade vibration velocity response. By introducing regularization parameters, the model was effectively constrained, avoiding overfitting. Simultaneously, the application of the non-convex sparse solution method further improved the accuracy of parameter identification, enabling precise capture of multi-order vibration velocity information of the blade. In practical applications, this method can accurately identify the vibration velocity parameters of the blade under different operating conditions, including frequency, amplitude, and phase, providing an accurate data foundation for subsequent dynamic strain reconstruction. Furthermore, this method exhibits strong robustness, effectively addressing interference factors such as measurement noise and ensuring the stability and reliability of the identification results. By reconstructing the vibration velocity response of the blade tip at any given moment, the vibration state of the blade at different times can be intuitively reflected, providing strong support for equipment health monitoring and fault diagnosis.

[0134] In one embodiment, the modal analysis based on the blade finite element model, obtaining the blade vibration velocity mode shape and strain mode shape, and calculating the transformation matrix between the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point, includes:

[0135] Based on finite element modal analysis, the multi-order vibration velocity mode shape S at the blade tip measuring point and the multi-order strain mode shape at any point on the blade body were obtained. S and The expressions are as follows:

[0136] ,

[0137] ,

[0138] Among them, S k For the first measuring point at the leaf tip First-order vibration velocity mode shape quantity For any point on the leaf body First strain mode shape;

[0139] Based on the mode shape, the transformation matrix F is calculated for the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point. The expression for the transformation matrix F is:

[0140] .

[0141] In practical implementation, based on the principle of modal superposition, the spatial-temporal response of the blade tip vibration velocity modes can be expressed as: , among which, S i Let W be the mode shape of the i-th vibration velocity at any point on the blade tip. i (t) represents the i-th modal response at any point on the leaf tip.

[0142] The space-time response of the strain mode at any point on the blade can be expressed as: .

[0143] Calculate the blade modal response based on the blade vibration velocity response expression. , can be represented as:

[0144] .

[0145] Based on the mode shape, the relationship between the tip vibration velocity and the strain at any point on the blade is constructed and expressed as: .

[0146] In this embodiment, multi-order vibration velocity mode shapes at the blade tip and multi-order strain mode shapes at any point on the blade were successfully obtained through finite element modal analysis. These mode shape data provide a solid foundation for subsequent calculations. Based on these mode shapes, the transformation matrix between the dynamic strain at any point on the blade and the vibration velocity at the blade tip was further calculated. The establishment of this transformation matrix achieves an accurate conversion from blade tip vibration velocity to dynamic strain at any point on the blade, providing crucial technical support for subsequent dynamic strain reconstruction. In practical applications, this transformation matrix can accurately reflect the strain distribution of the blade under different vibration modes, contributing to a deeper understanding of the blade's vibration characteristics and their impact on structural safety.

[0147] Furthermore, the expression for the arbitrary point-motion strain of the blade is:

[0148] ,

[0149] in, The dynamic strain of any point on the blade in any dimension (X direction, Y direction, Z direction, XY direction, YZ direction, XZ direction) under all working conditions and in the entire time domain is given.

[0150] Secondly, embodiments of this application also provide a non-contact multi-order dynamic strain reconstruction system based on blade tip velocity, used to implement the non-contact multi-order dynamic strain reconstruction method based on blade tip velocity as described in any embodiment of the first aspect, referring to... Figure 2 The system includes:

[0151] The rotor blade modal analysis module is used to establish a finite element model of the rotor blade, perform rotational modal analysis, calculate the blade Campbell diagram, and obtain multi-order vibration information of the rotor blade.

[0152] The blade tip timing sensor layout module is used to determine the number of blade tip timing sensors based on the order of the mode of interest, and to optimize the sensor layout by combining multi-order vibration information of the rotor blades, and to determine the sensor installation angle.

[0153] The undersampled vibration velocity calculation module is used to acquire the sensor measurement time series, calculate the blade tip vibration velocity, and acquire the time-domain undersampled data of blade tip vibration velocity under all operating conditions.

[0154] The blade tip vibration velocity sparse reconstruction module is used to construct a sparse regular model based on the time-domain undersampled data of blade tip vibration velocity under all operating conditions, reconstruct the blade tip vibration velocity response, identify vibration velocity parameters, and obtain the reconstructed blade tip vibration velocity response at any time.

[0155] The vibration velocity and dynamic strain conversion module is used to obtain the vibration velocity mode shape and strain mode shape of the blade based on the modal analysis of the blade finite element model, and to calculate the conversion matrix between the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point.

[0156] The dynamic strain calculation module is used to calculate the dynamic strain at any point on the blade based on the reconstructed vibration velocity response and transformation matrix at any moment of the blade tip, realizing non-contact measurement of multi-order and multi-dimensional vibration dynamic strain of the blade under all working conditions.

[0157] The embodiments provided by this invention firstly acquire undersampled time-domain data of blade tip vibration velocity under all operating conditions by obtaining sensor measurement time series and calculating blade tip vibration velocity, providing a comprehensive and accurate foundation for subsequent data processing and analysis. Secondly, by constructing a sparse canonical model and employing a non-convex sparse solution method, the blade tip vibration velocity response spectrum is effectively reconstructed, and multi-order vibration velocity parameters at the blade tip, including frequency, amplitude, and phase, are accurately identified, providing accurate data support for subsequent dynamic strain reconstruction. Furthermore, based on modal analysis of the blade finite element model, the blade vibration velocity mode shape and strain mode shape are successfully obtained, and the transformation matrix between dynamic strain at any point on the blade and vibration velocity at the blade tip measurement point is calculated, realizing accurate conversion from blade tip vibration velocity to dynamic strain at any point on the blade. Finally, by comprehensively applying the above methods and technologies, this invention successfully achieves non-contact measurement of multi-order, multi-dimensional vibration and dynamic strain of blades under all operating conditions, providing strong support for health monitoring and fault diagnosis of rotating machinery. In addition, the present invention has the advantages of high computational efficiency, high identification accuracy and strong robustness, and can be widely applied to the field of rotor blade vibration monitoring of various rotating machinery.

[0158] 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 non-contact multi-order dynamic strain reconstruction method based on blade tip velocity, characterized in that, The method includes: A finite element model of the rotor blade was established, rotational modal analysis was performed, the Campbell diagram of the blade was calculated, and multi-order vibration information of the rotor blade was obtained. The number of tip timing sensors is determined based on the modal order of interest, and the sensor layout is optimized by combining multi-order vibration information of the rotor blades to determine the sensor installation angle. The process involves acquiring sensor measurement time series, calculating blade tip vibration velocity, and obtaining undersampled time-domain data of blade tip vibration velocity under all operating conditions. This includes: acquiring sensor measurement time series to form a full-condition arrival time matrix; calculating blade tip vibration velocity based on the full-condition arrival time matrix to form a full-condition blade tip vibration velocity time-domain matrix; and calculating the acquisition time corresponding to the full-condition blade tip vibration velocity based on the full-condition arrival time matrix to form a full-condition blade tip vibration velocity acquisition time matrix. The expression for the arrival time matrix under all operating conditions is: ， Where T is the arrival time matrix under all operating conditions, t n,l This represents the moment when the blade reaches the l-th sensor after rotating to the nth revolution; The expression for the time-domain matrix of the blade tip vibration velocity under all operating conditions is as follows: ， Where V is the time-domain matrix of the blade tip vibration velocity under all operating conditions, f n,w Let R be the rotor's rotational frequency on the nth revolution, R be the blade tip gyration radius, and θ be the rotational frequency. l The installation angle for the l-th sensor; The expression for the time matrix of blade tip vibration velocity acquisition under all operating conditions is: ， Among them, T v This is a time matrix for collecting blade tip vibration velocity data under all operating conditions. Based on the time-domain undersampled data of blade tip vibration velocity under all operating conditions, a sparse regular model is constructed to reconstruct the blade tip vibration velocity response, identify the vibration velocity parameters, and obtain the reconstructed blade tip vibration velocity response at any time. Based on the modal analysis of the blade finite element model, the vibration velocity mode shape and strain mode shape of the blade are obtained, and the transformation matrix of dynamic strain at any point on the blade and vibration velocity at the blade tip measuring point is calculated. Based on the reconstructed vibration velocity response and transformation matrix of the blade tip at any time, the dynamic strain at any point on the blade is calculated, realizing non-contact measurement of multi-order and multi-dimensional vibration dynamic strain of the blade under all working conditions. The process of constructing a sparse regularized model, reconstructing the blade tip vibration velocity response, identifying vibration velocity parameters, and obtaining the reconstructed blade tip vibration velocity response at any given time includes: The time-domain expression for the multi-modal vibration velocity response of the blade tip is as follows: ， in, This refers to the multi-mode vibration velocity response of the blade tip. The first vibration velocity coefficient of the i-th order at the blade tip. is the second vibration velocity coefficient of the i-th order at the blade tip, t is the sampling time of vibration velocity, and k represents that the highest order vibration of the blade is the k-th order vibration. Construct a sparse regularized model, the expression is: , Where v is the velocity vector formed by expanding the time-domain matrix of the blade tip vibration velocity under all operating conditions according to the time series, and λ is the regularization parameter. Represents the q-norm, where P is the coefficient vector. ,in, Representing the For the first and second vibration velocity coefficient pair, C is a static constant; D is the constructed sparse transformation matrix, and the expression for D is: ， Among them, t h Let h be the time of undersampling of the blade tip vibration velocity; Δf is the frequency identification resolution to be reconstructed. To meet the requirements of multi-order identification, it should satisfy: ; The sparse regular model is solved using a non-convex sparse solution method. The blade tip vibration velocity response spectrum is reconstructed, and multi-order vibration velocity parameters of the blade tip are identified. These parameters include the k-th order vibration velocity frequency, vibration velocity amplitude, and vibration velocity phase. The expressions for the i-th order vibration velocity amplitude and phase are: ， in, To identify the amplitude and phase parameters of the i-th order vibration velocity, The phase of the i-th order vibration velocity is to be identified; Based on the identified multi-order vibration velocity parameters of the blade, the reconstructed vibration velocity response of the blade tip at any time is obtained, expressed as: , in, This represents the vibration velocity response of the blade tip at any given moment in the reconstructed image.

2. The non-contact multi-order dynamic strain reconstruction method based on tip velocity according to claim 1, characterized in that, The process of establishing a finite element model of the rotor blade, performing rotational modal analysis, calculating the blade Campbell diagram, and obtaining multi-order vibration information of the rotor blade includes: Mesh generation was performed on the 3D model of the rotating blade to establish a finite element model of the rotor blade; Set material parameters, perform rotational modal analysis, and set the rotor blade speed range from zero to the maximum operating speed, with a speed interval of no more than 1000 r / min. Based on the modal analysis results, the multi-order natural frequency values ​​of the blade at different speeds are obtained. Combined with the rotational frequency, the Campbell diagram of the blade within the set speed range is plotted. Through the Campbell diagram, the multi-order vibration information of the rotor blade within the operating speed range is estimated.

3. The non-contact multi-order dynamic strain reconstruction method based on tip velocity according to claim 1, characterized in that, The process of determining the number of tip timing sensors based on the modal order of interest, optimizing the sensor layout by combining multi-order vibration information of the rotor blades, and determining the sensor installation angle includes: Based on the modal order of interest and experimental requirements, the number of sensors that can be installed circumferentially in the casing and the limited angle range are determined, and the sensing matrix of the sensor layout is constructed. Optimize the number of sensing matrix conditions within the limited angle range. When the number of sensing matrix conditions reaches its minimum value, the sensor installation angles obtained are the sensor installation angles under the optimized layout.

4. The non-contact multi-order dynamic strain reconstruction method based on tip velocity according to claim 3, characterized in that, The expression for the perception matrix is: ， in, For the perception matrix, f k Let θ be the k-th natural frequency of the leaf tip. l Let be the installation angle of the l-th sensor, where sin is the sine function and cos is the cosine function; The expression for the condition number of the perception matrix is: ， Where cond is the condition number of the perception matrix.

5. The non-contact multi-order dynamic strain reconstruction method based on tip velocity according to claim 1, characterized in that, The modal analysis based on the finite element model of the blade obtains the vibration velocity mode shape and strain mode shape of the blade, and calculates the transformation matrix between the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point, including: Based on finite element modal analysis, the multi-order vibration velocity mode shape S at the blade tip measuring point and the multi-order strain mode shape at any point on the blade body were obtained. S and The expressions are as follows: ， ， Among them, S k For the first measuring point at the leaf tip First-order vibration velocity mode shape quantity For any point on the leaf body First strain mode shape; Based on the mode shape, the transformation matrix F is calculated for the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point. The expression for the transformation matrix F is: 。 6. The non-contact multi-order dynamic strain reconstruction method based on tip velocity according to claim 5, characterized in that, The expression for the arbitrary point strain of the blade is: ， in, This refers to the dynamic strain of any point and any dimension of the blade under all operating conditions and in all time domains.

7. A non-contact multi-order dynamic strain reconstruction system based on blade tip velocity, used to implement the non-contact multi-order dynamic strain reconstruction method based on blade tip velocity as described in any one of claims 1-6, characterized in that, The system includes: The rotor blade modal analysis module is used to establish a finite element model of the rotor blade, perform rotational modal analysis, calculate the blade Campbell diagram, and obtain multi-order vibration information of the rotor blade. The blade tip timing sensor layout module is used to determine the number of blade tip timing sensors based on the order of the mode of interest, and to optimize the sensor layout by combining multi-order vibration information of the rotor blades, and to determine the sensor installation angle. The undersampled vibration velocity calculation module is used to acquire the sensor measurement time series, calculate the blade tip vibration velocity, and acquire the time-domain undersampled data of blade tip vibration velocity under all operating conditions. The blade tip vibration velocity sparse reconstruction module is used to construct a sparse regular model based on the time-domain undersampled data of blade tip vibration velocity under all operating conditions, reconstruct the blade tip vibration velocity response, identify vibration velocity parameters, and obtain the reconstructed blade tip vibration velocity response at any time. The vibration velocity and dynamic strain conversion module is used to obtain the vibration velocity mode shape and strain mode shape of the blade based on the modal analysis of the blade finite element model, and to calculate the conversion matrix between the dynamic strain at any point on the blade and the vibration velocity at the blade tip measuring point. The dynamic strain calculation module is used to calculate the dynamic strain at any point on the blade based on the reconstructed vibration velocity response and transformation matrix at any moment of the blade tip, realizing non-contact measurement of multi-order and multi-dimensional vibration dynamic strain of the blade under all working conditions.

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