Blade Natural Frequencies Research Articles

A recursive calculation method of vibration displacements using blade tip timing in angular domain

Blade tip timing (BTT) is a non-contact measurement technique that can be used to monitor blade vibration in turbomachinery. The raw data measured by BTT is the arrival time of all blades at the same stage. However, most blade vibration monitoring methods based on BTT require the use of blade vibration displacements, which are derived from the raw arrival time data, the blade rotation radius and speed. Conventional BTT methods calculate blade tip displacements by comparing the measured arrival time with the ideal arrival time. The ideal arrival time is obtained by assuming that the rotational speed is constant in a revolution, which is inconsistent with the fact, especially when the rotational speed changes rapidly. In this paper, a recursive calculation method called recursive BTT is proposed to reduce the influence of rotational speed fluctuation on the accuracy of blade tip displacement calculation. Recursive BTT calculates the displacements in the angular domain instead of the time domain. A recursive formula is constructed in the angular domain to calculate the blade vibration displacement by using the angle between the vibrating blades. Compared with the conventional BTT method, which relies on the once-per-revolution (OPR) signal, recursive BTT makes full use of the arrival time of all blades at the same stage to calculate the displacements. The advantage of recursive BTT is illustrated through a simulation, a laboratory test and a full-scale aeroengine test. To evaluate the reliability of the calculated displacements, strain signals are resampled to compare with the calculated displacements in the laboratory test. In the full-scale aeroengine test, due to the lack of strain signals, BTT displacements are used to track the blade natural frequency to qualitatively indicate the influence of displacements on blade vibration monitoring. The results of finite element analysis and modal test are used for verification in the full-scale aeroengine test. Simulation and experimental results demonstrate that compared with existing methods, recursive BTT is robust for calculating blade vibration displacements.

Vibration characteristics of pre-twisted rotating Ti-SiC composite airfoil blade

In this paper, a pre-twisted blade model is established based on the FSDT (first-order shear deformation theory), where the Ti-SiC fiber reinforced composite and NACA 4-digit airfoil are innovatively proposed. Rayleigh-Ritz method is utilized to deduce the pre-twisted blade natural frequencies and mode shapes where the exponential polynomials satisfying the cantilever boundary conditions are taken as admissible functions. Comparing with the existing literature, the precision of the model and the method is verified. The material properties of Ti-SiC fiber reinforced composites are calculated by the M-T (Mori-Tanaka) method and FE (Finite Element) method to guarantee the reliability of the calculation method. In addition, the parameters affecting blade vibration, such as rotating speed and aspect ratio, are studied in detail. The research findings indicate that the addition of SiC fibers enhances the properties of the composite blade, and then improves the frequency of the rotating blade. Additionally, the pre-twisted angle, rotating speed, aspect ratio and blade shape significantly affect the natural frequency of Ti-SiC composite airfoil blade. The well-established model accurately predicts the dynamic behaviors of the rotating blade, which has certain guiding value for the optimization of blade material and geometric size.

A Single Probe Blade Tip Timing Method for Fast Extraction of Blade Natural Frequency

A Single Probe Blade Tip Timing Method for Fast Extraction of Blade Natural Frequency

Comparative analysis of the dynamic characteristics of all-metal, composite and composite blades with the same profile, taking into account the influence of the connection of elements and aerodynamic loads

The paper presents a comparative analysis of the dynamic properties of the blades of one rotary machine which have the same airfoil shape, but are made of three different materials, namely aluminum alloy, a complex material combining aluminum alloy and steel, and a composite material which is unidirectional fiberglass. In the case of an all-metal blade, its airfoil and root are made of aluminum alloy. In the case of complex blade airfoil material, the root is made of steel which is also a component of the airfoil material. In the case of a composite blade, the root is steel and is connected at the root section to its composite airfoil. The main attention when comparing models of the mechanical behavior of three types of blades is paid to the influence of the connection of complex and composite elements with the root on the dynamic characteristics of the blade as a whole which is achieved by considering the contact interactions of the elements under the action of centrifugal and aerodynamic loads and the subsequent transfer of the prestressed state of the blades to the modal analysis for determination of the dynamic characteristics of samples and their comparison. In order to correctly display the fixation of elements in the fan impeller in the case of an aluminum blade, the sector of cyclic symmetry of the rotor is considered which makes it possible to draw a conclusion about the possibility of further separate consideration of the blade for determination of its dynamic characteristics due to the much greater stiffness of the connection of the blade with the impeller in comparison with stiffness of the blade airfoil, and to generalize this conclusion in the case of a complex blade by considering a steel root with an aluminum profile with rigid clamping of the model on the contact shelves of the root, and in the case of a composite blade by considering an airfoil with rigid clamping in the root section, where the fastening to the steel root of the blade takes place. The results of a comparative analysis of the dynamic behavior of three types of blades with the same airfoil shape are presented in the form of a study of the blade natural frequencies and mode shapes.

Mistuning identification and model updating of a blisk with piezoelectric excitation components

Integrally bladed disks (blisks) are extensively used in military and commercial aircraft engines. There are inevitable deviations between blades called mistuning, leading to the vibration localization of blisks, which potentially results in high cycle fatigue (HCF). Furthermore, the dynamic performance is sensitive to mistuning patterns. Hence, to predict the vibration response of mistuned blisks accurately, the mistuning pattern needs to be identified experimentally and verified under traveling wave excitation (TWE). Piezoelectric TWE is a promising testing technique for blisk dynamics in a non-rotating state, offering advantages such as high excitation force, wide bandwidth, and a simple setup. However, piezoelectric materials are generally arranged on blades forming an electromechanically coupled structure, which challenges the existing mistuning identification methods. In this paper, an integral mistuning identification and model updating method with traveling wave excitation verification is developed. The detuning strategy is used to split natural frequencies of blades, whereupon the response is measured blade by blade. Measured response functions of isolated blades can be retrieved by data reconstruction. Then, the mistuning patterns of elastic modulus and damping ratio are identified by Kirchhoff-plate theory and half-power bandwidth method, respectively. Experimental studies are carried out to validate the method. A dummy blisk with piezoelectric patches is designed and the dynamic properties are calculated. Blade-by-blade measurement and TWE test are conducted. Results show that natural frequencies of the updated model are in excellent agreement with the measured ones. Under TWE, the deviations of natural frequencies for all blades are less than 0.25%. The response deviation of the updated model is decreased by 89.4% on average compared with the original model and the average response deviation of the updated model is 7.4%.

Damping and Stiffness Mistuning Effects in a Bladed Disk With Varied Disk Coupling

Abstract Component mode mistuning (CMM) is a well-known, well documented reduced order modeling technique that effectively models small variations in blade-to-blade stiffness for bladed disks. In practice, bladed disks always have variations, referred to as mistuning, and are a focus of a large amount of research. One element that is commonly ignored from small mistuning implementations is the variation within the blade-to-blade damping values. This work seeks to better understand the effects of damping mistuning by utilizing both structural and proportional damping formulations. This work builds from previous work that implemented structural damping mistuning reduced order models formulated based on CMM. A similar derivation was used to create reduced order models with a proportional damping formulation. The damping and stiffness mistuning values investigated in this study were derived using measured blade natural frequencies and damping ratios from high-speed rotating experiments on freestanding blades. The two separate damping formulations that are presented give very similar results, enabling the user to select their preferred method for a given application. A key parameter investigated in this work is the significance of blade-to-blade coupling. The blade-to-blade coupling study investigates how the level of coupling impacts damping mistuning effects versus applying average damping to the bladed disk model. Also, the interaction of stiffness and damping mistuning is studied. Monte Carlo simulations were carried out to determine amplification factors, or the ratio of mistuned blade responses to tuned blade responses, for various mistuning levels and patterns.

Multi-Actuator Full-Scale Fatigue Test of a Tidal Blade

Fatigue testing for tidal turbine blades involves the application of cyclic loads without matching the blade's natural frequency, which is challenging due to their high stiffness and associated thermal issues of composite materials at those frequencies (typically around 18Hz cycles). An auxiliary system is required to load the blades to address this challenge. However, traditional hydraulic systems tend to be highly energy-demanding and inefficient.
 To solve this problem, researchers utilized real on-site data to define a series of equivalent target loads and implemented them in FastBlade, which proved an efficient way to perform fatigue testing. They used a regenerative digital displacement hydraulic pump system and achieved a remarkable 75% energy savings compared to a standard hydraulic system. During the testing, they utilized a system of 3 actuators instead of the traditional single actuator system, which produced more realistic and complex loads. We also address such changes in temperature along large composite structures during the test and mechanisms to address these issues. 
 Throughout the test, a series of measurements were taken on the blade response and FastBlade itself, which revealed exciting results on the mechanical behaviour of the blade and best testing practices for FastBlade. Impressively, the blade withstood 40 years' worth of accelerated fatigue loading without catastrophic failure.

Effects of film cooling holes on vibration characteristics of aeroengine turbine blades

PurposeThe purpose of this paper is to evaluate the effect of film cooling holes on the vibration characteristics of a turbine blade, and provide the design basis for the blade, which may reduce computing costs.Design/methodology/approachModal analysis of the blades with and without film cooling holes is performed to evaluate the effect of film cooling holes on its natural frequency. Harmonic analysis of the blade is performed to calculate the stress concentration factors of film cooling holes for different modes.FindingsThe frequency differences between two blades with and without film cooling holes are insignificant, while the differences of the vibration stress cannot be neglected. For the first three modes of the blades, the stress concentration factor is sensitive to the hole’s shape and position on the blade. With the help of the stress concentration factor defined in this work, the concentration of stresses induced by different film cooling holes can be accurately described when evaluating HCF life of the turbine blade.Originality/valueThe effect of film cooling holes on a turbine blade's natural frequencies was confirmed to be insignificant and the stress concentration factors around the holes are calculated. Therefore, the simplified model of the blade without film cooling holes can be used to evaluate the natural frequencies and vibration stress, which saves a lot of time and cost.

Research on 3D Modeling and Dynamic characteristics of wind turbine blade

In order to prevent blade resonance, reduce blade deflection, improve wind turbine power generation efficiency and wind energy utilization rate, the blade model of 3 kW wind turbine is established, and the natural frequency of wind turbine blade is analyzed. Based on the vibration theory, the effects of dynamic stiffening and rotational softening on the natural frequencies of blades are analyzed. Study the change rule of blade vibration mode under rotating speed of 0~300rpm, and analyze the influence of two effects on blade frequency. The results show that at low speed, the rotating softening effect of the blade is obvious, and the vibration frequency decreases; At high speed, the stress stiffening effect is more obvious, the vibration frequency increases, and the coupling vibration has greater destructiveness.

Single-sensor-based dynamic response reconstruction of blades under base excitation

Blades in the turbo-machinery are inevitably excited by base excitation in addition to unbalanced excitation of the rotor during operation. Accurate measurements of the dynamic response under base excitation are especially critical, which feasibly provides essential guidance on vibration fatigue analysis and remaining life prediction of blades. However, due to some practical factors such as the restriction of the sensor installation position and the inability to directly obtain the external load information, there are still significant challenges in obtaining dynamic response of blades at critical positions under base excitation. In this paper, a novel method is proposed to reconstruct the dynamic response of blades under base excitation, where the measurement of only one sensor is adopted. The method comprises mostly of two steps. The measured signal is first divided into single-frequency response components using empirical mode decomposition with intermittency criteria (EMDIC), and the response components are then classified into two groups depending on whether the frequency is the blade's natural frequency. Then, by combing the time-domain and frequency-domain response transmissibility matrices under base excitation (RTMBE) derived in this paper, the dynamic response of the blade can be reconstructed, whether the blade is in the resonant or non-resonant state. This paper presents numerical simulation and experimental research on a titanium alloy fan blade. The effects of single-and multi-frequency excitation, measurement noise, and measuring point selection on the results of response reconstruction are all investigated. The results demonstrate the feasibility of the response reconstruction method presented in this work for the dynamic response reconstruction of blades under base excitation.

Biprobes Blade Tip Timing Method for Frequency Identification Based on Active Aliasing Time-Delay Estimation and Dealiasing

Rotating blades are key turbomachinery components with high failure risk due to harsh working conditions. Thus, monitoring the running state of blades is urgently required. Blade tip timing (BTT) is regarded as a potential technology for blade vibration monitoring owing to its noncontact nature and low cost. However, severe undersampling and strict probe layout hinder the application of BTT. As a result of severe undersampling, aliasing and its suppression are the main research topics in BTT. However, in this article, a biprobes method for BTT based on the utilization of aliasing is proposed to identify the natural frequencies of blades. Active aliasing is used in this method to produce aliasing findings at various equivalent sampling frequencies, and the closed-form robust Chinese remainder theorem is used for dealiasing. Unlike the conventional multirate sampling systems for BTT that use a multiprobe configuration or varied speed, the suggested method utilizes varying delay durations to obtain varying equivalent sample frequencies. Furthermore, to ensure that active aliasing and dealiasing form a closed loop, an included angle coprime layout is proposed. Finally, the robustness and effectiveness of the proposed method are verified through numerical and experimental validation.

Mechanical Behavior of Variable Nozzle Guide Vane Systems Based on Full-Scale Testing

Abstract A full-scale test bench for the analysis of frictional and modal behavior of nozzle guide vanes (NGV) is an advanced tool enabling high design accuracy for these components equipped with an increasing number of turbo-expanders. This subassembly is a key feature enabling operational flexibility for the expander. During the NGVs design, great attention must be paid to the natural frequencies of its kinematic chain, which are influenced by internal clearances and by friction. In this paper, the results of a testing campaign performed on an NGV assembly employing realistic blade geometry are presented together with details concerning the test bench commissioning and setup procedure. The testing campaign involves three different combinations of blade orientation and preload corresponding to typical design conditions of the expander. In addition, two bushing clearance values corresponding to different worn-out conditions were investigated. The measurements of the global friction coefficient based on actuator force detection are summarized. After that, the reconstruction of mode shapes based on experimental modal analysis is explained. The results highlight the importance of loading conditions on the actual value of friction force and their influence on blade natural frequencies. The testing campaign was used to properly validate finite element models to be used for further investigations.

An improved mistuning identification and dynamic strain prediction method for rotating blades with application of blade tip timing technology

Blade tip timing (BTT) is the most effective technique for vibration monitoring of rotating blades. The research of dynamic characteristics and forced responses of the blisk is crucial to the matters of blade vibration with far-reaching significance. The general mistuning identification techniques require experimental tests and numerical solutions of the whole bladed disk. Since the feature of the BTT technique can identify the modal properties of blades, this paper proposed a blade natural frequency deviation-based mistuning identification method, which achieves the mistuning quantitative evaluation and the model online update of mistuned blisk. Numerical analysis and experimental investigations prove that the improved mistuning identification method can reach accurate and reasonable results, especially in the mode dominated by blade vibration. Furthermore, based on the three assumptions of the fundamental mistuning model (FMM), an additional condition was defined: The mode strain energy proportions of the blade in the isolated modal family can be believed identical. This study revealed the relationship between blade strain and blade vibration, and an improved dynamic strain prediction method for the implementation of non-contact measurement of blade strain was proposed. The numerical analysis shows the prediction error of dynamic strain is less than 3%. Two experimental tests reported that the prediction results of dynamic strain are consistent with the FMM and BTT-based non-contact dynamic stress measurement (FB-NDSM) method, and the maximum error of prediction results is less than 2% about a FB-NDSM method reference, which is acceptable in practical applications. Improved mistuning identification and dynamic strain prediction method with the application of BTT technology are attractive for the dynamic characteristic study and health management of the bladed disk, which significantly promotes the application of BTT technology in blade vibration monitoring of large-scale rotating machinery.

On the submerged low-Cauchy-number canopy dynamics under unidirectional flows

The unsteady dynamics and induced turbulence associated with flow development of a fully-submerged canopy with relatively low flexibility were explored experimentally under small Cauchy numbers Ca≲9 using particle image velocimetry (PIV) and particle tracking velocimetry (PTV). Inspection of the flow around a rigid canopy supported the identification of significant modulation of the flow dynamics due to minor blade reconfiguration and oscillations within the first rows. The canopies consisted of relatively short arrays of rectangular blades of height h=37.5mm placed in a staggered layout and extending Δx/h=5 in the streamwise direction. The results show a downstream shift in the onset of the internal boundary layer. Canopy top friction velocity was lower than its rigid counterpart, even where blades undergo negligible deflection, evidencing the impact of the leading structure dynamics on flow adjustment. A transition from vortex-induced blade motions to dominance by natural blade frequency occurs with distance from the canopy edge. A frequency synchronization occurs several rows into the canopy, resulting in peak displacement intensity of the blades. The relationship between flow-induced and blade natural frequencies is described through a developed transfer function, enabling the determination of the characteristic vortex frequency. Natural and flow-induced frequencies dominate the flow-structure interaction near the leading edge region, resulting in increased small-scale turbulence.

Rotating blade frequency identification by single-probe blade tip timing

The rotating blade is a key turbomachinery component with a high failure risk. Therefore, monitoring the rotating blade is urgently required. Blade tip timing (BTT) is regarded as an efficient technique for blade vibration monitoring as it reflects the condition of blades. However, the identification process from under-sampled data and probe layout optimization hinder the application of BTT. Most of the existing parameter identification methods have strict probe layout requirements; thus, an inappropriate probe layout may fail BTT measurements. An increased number of probes and optimal probe positions are considered essential for frequency identification. However, an optimal probe layout is usually restricted by arrangement. In this work, a novel frequency identification method via a single BTT probe is proposed by considering arrangement, cost, and safety restrictions. The proposed method focuses on the relationship between sampling and aliasing frequencies, which can be summarized in two steps: obtaining a Sampling–Aliasing Frequency (SAFE) map and identifying the resonance center and corresponding engine order (EO). Obtaining the SAFE map of the BTT signal recorded by a single probe is difficult because of low and variable sampling frequency. To overcome this problem, the adaptive window length short-time Fourier transform is proposed. Based on the SAFE and EO, the natural frequency can be accurately extracted from a single BTT measurement. Uniformly and nonuniformly variable speed conditions were investigated, and the results were compared with those obtained using multiple probes. The proposed method has been verified to provide blade natural frequency from a single-probe BTT measurement.

Vibration Response of Steam Turbine Healthy and Cracked Blade under the Stress Stiffening and Spin Softening Effects

In the present paper, vibration responses of the healthy and cracked blade under the influence of stress-stiffening and spin-softening have been studied. The three-dimensional finite element-based numerical analysis is carried out to study the blade's mode shape and natural frequencies and are validated with the experimental modal analysis test results. In the case of spin softening, for healthy blade at the turbine’s speed over 1000 RPM, natural frequencies increase significantly in both first flap-wise and chordwise bending modes. In both cases of STF and SOF, for the cracked blade, the deviation from the healthy blade in the natural frequency increases with increasing crack size, maximal in a crack size of 90%. It is also observed that irrespective of crack size, deviation in natural frequencies as compared to healthy blade increases as spin speed increases in the cases of chordwise bending mode (Mode II) and higher-order overlapped mode IV, and in the case of fundamental torsion mode (Mode III), higher-order overlapped mode V and VI natural frequencies decrease in both STF and SOF cases.

Mistuning and Damping of a Radial Turbine Wheel. Part 1: Fundamental Analyses and Design of Intentional Mistuning Pattern

Abstract The radial turbine impeller of an exhaust turbocharger is analyzed in view of both free vibration and forced response. Due to random blade mistuning resulting from unavoidable inaccuracies in manufacture or material inhomogeneities, localized modes of vibration may arise, which involve the risk of severely magnified blade displacements and inadmissibly high-stress levels compared to the tuned counterpart. Contrary, the use of intentional mistuning (IM) has proved to be an efficient measure to mitigate the forced response. Independently, the presence of aerodynamic damping is significant with respect to limit the forced response since structural damping ratios of integrally bladed rotors typically take extremely low values. Hence, detailed knowledge of respective damping ratios would be desirable while developing a robust rotor design. For this, far-reaching experimental investigations are carried out to determine the damping of a comparative wheel within a wide pressure range by simulating operation conditions in a pressure tank. Reduced-order models are built up for designing suitable intentional mistuning patterns by using the subset of nominal system modes approach introduced by Yang and Griffin (2001, “A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes,” J. Eng. Gas Turbines Power, 123(4), pp. 893–900), which conveniently allows for accounting both differing mistuning patterns and the impact of aeroelastic interaction by means of aerodynamic influence coefficients. Further, finite element analyses are carried out in order to identify appropriate measures of how to implement intentional mistuning patterns, which are featuring only two different blade designs. In detail, the impact of specific geometric modifications on blade natural frequencies is investigated. The first part of this three-part paper is focused on designing the IM pattern. The second and third part following, later on, will address the topics (i) experimental validation after implementation of the IM pattern at rest and under rotation, and (ii) the development of an approach for fast estimating damping ratios in the design phase.

Analytical and numerical study on centrifugal stiffening effect for large rotating wind turbine blade based on NREL 5 MW and WindPACT 1.5 MW models

To pursue high efficiency for wind turbine and harness more energy from wind, the wind power generation system has been designed larger and larger. With length scale increasing, the natural frequency of blade will be lower and changing dramatically with rotational speed, which will threaten the stability of the blade and turbine. However, in the previous research, the parametric, analytical, and quantitative study of centrifugal stiffening effect is rare to see. As a result, the current research has comprehensively studied the centrifugal stiffening effect on the structural characteristics of large wind turbine blade. Specifically, the equivalent rotating wedge beam model has been proposed for composite wind turbine blade. Based on the proposed wedge beam model and Rayleigh-Ritz method, the natural frequency variation curve has been derived and verified by ANSYS 3D simulation results. The parameters, including blade length, stiffness-mass ratio, and aspect ratio, affecting the natural frequency curve have been uncovered and analysed. It was found that the centrifugal stiffening effect has a great impact on the fundamental frequency of blade, e.g. 10% for NREL 5 MW, while it has less impact on other modal frequencies. The variation curve of fundamental natural frequency can be approximated by parabola. The product of the parabola curvature and fundamental frequency is found to be approximately constant for both NREL 5 MW and WindPACT 1.5 MW turbine blades. This research will provide guidelines for the resonance avoidance design of large wind turbine blade in the future.

Development of a Modal-Based Turbomachine Blade-Disk Attachment Inspection Technique

Turbine blade failures are among the leading causes of steam turbine failure. Failure types typically include cracking, rubbing, blade fouling, and foreign object damage. There is currently a range of non-destructive testing methods used to detect damage at the blade-disk attachment zone, all of which involve disassembling of the blade from the disk for periodic inspection. Evidence indicate that a method to detect damage at the blade-disk attachment zone using a non-contact, non-destructive in-situ off-line modal-based structural health monitoring technique could be useful under some circumstances. Such a technique would have the advantage of eliminating the necessity to disassemble blades during inspection. This would result in significant cost savings. Also, defects associated with the disassembly and reassembly of blades would be avoided. Thus, the aim of this study was to develop a modal-based turbomachinery blade disk attachment inspection technique. Modal parameters were acquired from a robust experimental modal analysis of freely supported low-pressure steam turbine blade-disk segment assemblies. Artificial single-location cracks were intentionally introduced into the turbine blades by cutting a 1 mm thickness notch at three probable damage locations, namely, at the upper pinhole on the leading-edge pressure side, above the root at the base of the aerofoil on the leading-edge and on the trailing-edge. In this work, a finite element analysis of the bladed disk segment assemblies was carried out with and without damage. To validate the reliability of the numerical models, the numerical results were correlated with the measured values, the results of which showed a strong correlation. Finally, a parametric study was conducted in which various healthy and damaged blade-disk cases were systematically investigated. This was done to examine the sensitivity of the blade natural frequency to damage. The artificial damage above the root was found to cause the largest changes in natural frequency. These changes were even more pronounced for assemblies with two blades. Receiver operating characteristic curves were used to assess the discriminatory ability of the results. Each damage case was found to be unique and therefore identifiable from its corresponding healthy case.

Sparse reconstruction for blade tip timing signal using generalized minimax-concave penalty

Rotor blade health monitoring based on the non-contact blade tip timing (BTT) technique has already been proved to be an alternative method to the classical contact strain measurement method. However, the signal sampled by the BTT system is usually undersampled due to the limited BTT sensors. Sparse regularization in the framework of ℓ1-norm has been introduced to identify the blade vibration parameter from the undersampled BTT data. However, the standard sparse regularization based onℓ1-norm penalty generally generates an underestimated solution. Compared with ℓ1-norm penalty, generalized minimax-concave (GMC) penalty as a non-convex penalty has the promising property of amplitude improvement. In this paper, a non-convex optimization model based on GMC penalty is developed for reconstructing the undersampled BTT signal to obtain the accurate blade-tip displacement and blade natural frequency. The optimization model based on GMC penalty is presented to find the global optimal solution for the sparse representation of the BTT signal even if GMC penalty turns out to be a non-convex regularizer. Additionally, the strategy of regularization parameter selection is provided through the blade tip timing simulator. The relationship between the noise level and the regularization parameter is established to provide the strategy of regularization parameter selection in experiment. Finally, the blade spin testing is carried out for measuring the blade vibration by BTT and strain gauge systems. Amplitudes and frequencies of reconstructed BTT signals are compared with the measurements of the strain gauge, which are transferred from the strain at the blade root to the displacement at the blade tip by using the conversion coefficient obtained from the finite element model. Both simulation and experiment demonstrate that compared with the ℓ1-norm penalty, GMC penalty can reconstruct the blade-tip displacement and blade natural frequency with high accuracy.