Modal Identification Method Research Articles

Output-only time-varying modal parameter online identification method and engineering application based on TARMA model

Abstract The modal parameters of long-range cruise weapon systems are typically obtained through finite element analysis and ground vibration testing. However, due to the inability to simulate the system’s time-varying characteristics under flight conditions, it is customary to conduct finite element modelling or ground vibration testing based on several representative operating scenarios. Subsequently, the flight modal frequency of the system is derived through numerical interpolation. This repetitive modelling, analysis, and ground testing process is both time-consuming and resource-intensive. This paper delves into the data-driven output-only identification approach, developing a recursive identification method solely based on the output, which incorporates a time-varying auto-regressive moving average (TARMA) model. By introducing a forgetting factor, the method effectively tracks the system’s time-varying characteristics, enabling rapid and accurate acquisition of the time-varying mode of long-range guided missiles even under unknown excitation conditions. Focusing specifically on the time-varying modal identification challenge posed by a long-range cruise missile, this study performs a frequency spectrum analysis of flight telemetry data. By comparing this analysis with ground vibration experimental data, the disparities between the in-flight and ground modes are elucidated. Leveraging the recursive identification method, the time-varying modal parameters of the flight telemetry data are successfully identified. The alignment between the identified results and the spectral analysis outcomes validates the effectiveness of the proposed online identification technique for time-varying modal parameters, thereby serving the engineering requirements for finite element model refinement and attitude control system design in long-range cruise missiles.

Operational Modal Analysis of Civil Engineering Structures with Closely Spaced Modes Based on Improved Hilbert-Huang Transform.

In long-span bridges and high-rise buildings, closely spaced modes are commonly observed, which greatly increases the challenge of identifying modal parameters. Hilbert-Huang transform (HHT), a widely used method for modal parameter identification, first applies empirical mode decomposition (EMD) to decompose the acquired response and then uses the Hilbert transform (HT) to identify the modal parameters. However, the problem is that the deficiency of mode separation of EMD in HHT limits its application for structures with closely spaced modes. In this study, an improved HHT based on analytical mode decomposition (AMD) is proposed and is used to identify the modal parameters of structures with closely spaced modes. In the improved HHT, AMD is first employed to replace EMD for decomposing the measured response into several mono-component modes. Then, the random decrement technique is applied to the decomposed mono-component modes to obtain the free decay responses. Furthermore, the resulting free decay responses are analyzed by HT to estimate the modal parameters of structures with closely spaced modes. Examples of a simple three-degree-of-freedom system with closely spaced modes, a high-rise building under ambient excitation, and the Ting Kau bridge under typhoon excitations are adopted to validate the accuracy, effectiveness, and applicability of the proposed method. The results demonstrate that the proposed method can efficiently and accurately identify the natural frequencies and damping ratios of structures with closely spaced modes. Moreover, its identification results are more precise compared to those obtained using existing methods.

Modal Parameter Identification of Jacket-Type Offshore Wind Turbines Under Operating Conditions

Operational modal analysis (OMA) is essential for long-term health monitoring of offshore wind turbines (OWTs), helping identifying changes in structural dynamic characteristics. OMA has been applied under parked or idle states for OWTs, assuming a linear and time-invariant dynamic system subjected to white noise excitations. The impact of complex operating environmental conditions on structural modal identification therefore requires systematic investigation. This paper studies the applicability of OMA based on covariance-driven stochastic subspace identification (SSI-COV) under various non-white noise excitations, using a DTU 10 MW jacket OWT model as a basis for a case study. Then, a scaled (1:75) 10 MW jacket OWT model test is used for the verification. For pure wave conditions, it is found that accurate identification for the first and second FA/SS modes can be achieved with significant wave energy. Under pure wind excitations, the unsteady servo control behavior leads to significant identification errors. The combined wind and wave actions further complicate the picture, leading to more scattered identification errors. The SSI-COV based modal identification method is suggested to be reliably applied for wind speeds larger than the rated speed and with sufficient wave energy. In addition, this method is found to perform better with larger misalignment of wind and wave directions. This study provides valuable insights in relation to the engineering applications of in situ modal identification techniques under operating conditions in real OWT projects.

Efficacy of modal curvature damage detection in various pre-damage data assumptions and modal identification techniques

The efficacy of modal curvature approach for damage localization is discussed in the paper in the context of input data. Three modal identification methods, i.e., Eigensystem Realization Algorithm (ERA), Natural Excitation Technique with ERA (NExT-ERA) and Covariance Driven Stochastic Subspace Identification (SSI-Cov), and four methods of determining baseline data, i.e., real measurement of the undamaged state, analytical function, Finite Element (FE) model and approximation of current experimental mode shape, are considered. Practical conclusions are formulated based on analysis of two cases. The first is a laboratory beam with a notch and the second is a stonemasonry historic lighthouse with modern restoration in its upper part. The analysis shows that NExT-ERA and SSI-Cov in combination with approximation of current mode shape provide high efficacy in damage localization alongside relatively straightforward determination of baseline data. It proves that the construction of advanced FE models of a structure can be replaced with a much simpler method of baseline data acquisition. Furthermore, the research shows the structural mode shapes identified with ERA may not always indicate the presence of damage.

Dynamic Testing and Finite Element Model Adjustment of the Ancient Wooden Structure Under Traffic Excitation

In situ dynamic testing is conducted to study the dynamic characteristics of the wooden structure of the North House main hall. The velocity response signals on the measurement points are obtained and analyzed using the self-interaction spectral method and stochastic subspace method, yielding natural frequencies, mode shapes, and damping ratios. This study reveals that the natural frequencies and damping ratios are highly consistent between the two methods. Therefore, to eliminate errors, the average of the results from both modal identification methods is taken as the final measured modal parameters of the structure. The natural frequencies of the first and second order in the X direction were 2.097 Hz and 3.845 Hz and in the Y direction were 3.955 Hz and 5.701 Hz. The modal frequency in the Y direction of the structure exceeds that in the X direction. Concurrently, a three-dimensional finite element model was established using ANSYS 2021R1, considering the semi-rigid properties of mortise–tenon connections, and validated based on in situ dynamic testing. The sensitivity analysis indicates adjustments to parameters such as beam–column elastic modulus, tenon–mortise joint stiffness, and roof mass for finite element model refinement. Modal parameter calculations from the corrected finite element model closely approximate the measured modal results, with maximum errors of 9.41% for the first two frequencies, both within 10% of the measured resonant frequencies. The adjusted finite element model closely matches the experimental results, serving as a benchmark model for the wooden structure of North House main hall. The validation confirms the rationality of the benchmark finite element model, providing valuable insights into ancient timber structures along transportation routes.

Exploration on flutter mechanism of a damaged transonic rotor blade using high-fidelity fluid–solid coupling method

Structural damage in turbomachinery is a primary origin of aeronautic accidents, which is receiving increased attention. This study is thus focused on the aeroelastic analysis of damaged blades, including the onset of flutter and underlying mechanisms. First, a high-fidelity fluid–solid coupling system is established with computational fluid dynamics (CFD) and computational structural dynamics (CSD) technologies, via which the dynamic aeroelastic analysis is conducted based on static aeroelastic deformation. Second, a damaged rotor blade is parametrically modelled with variable damage levels, extents, and positions. Finally, the modal identification method of spectral proper orthogonal decomposition (SPOD) is applied to observe flow details and provide physical insight into the flutter mechanism for damaged blades. Numerical analysis finds that there is a critical damage level below which the aeroelastic stability is positively improved with increasing damage level; otherwise, a significant loss of stability is induced. The damage location and extent further affect this critical damage level and the change rate crossing the threshold. The simulation with CFD/CSD finds that the high pressure near the trailing edge induced from boundary layer separation suppresses vibrations in stable conditions, but motivates vibrations during flutter, which is because of the high-pressure spread to nearing blades. SPOD modes reveal that high-frequency disturbances with large scale are primary factors inducing flutter, which is further stimulated by the high-order disturbances with small scale. This study provides a crucial foundation for the fatigue prediction for rotor blades in service and the optimisation design for high-performance turbomachinery in the near future.

Modal identification of wind turbine tower based on optimal fractional order statistical moments

AbstractIn vibration testing of civil engineering structures, the first two vibration modes are crucial in representing the global dynamic behavior of the structure measured. In the present study, a comprehensive method is proposed to identify the first two vibration modes of wind turbine towers, which is based on the analysis of fractional order statistical moments (FSM). This study offers novel contributions in two key aspects: (1) theoretical derivations of the relationship between FSM and vibration mode; and (2) successful use of 32/7‐order displacement statistical moment as the optimal FSM to identify wind turbine tower modes, by combining with noise resistance analysis, sensitivity analysis, and stability analysis, respectively. Using the proposed method, the FSM was first used to identify the modal vibration of wind turbine towers. By obtaining the response of the structure on the same vertical line, FSM was then calculated to estimate the corresponding structural modal vibration. Considering other influencing factors in the field test, the modal identification results of this index under different excitation forms and noise conditions were analyzed based on numerical simulation and verified with field wind tower test data. The results of the evaluation show that the proposed statistical moments of can accurately identify the first two vibration modes of wind turbine towers. This presents a new robust method for modal vibration identification, that is, simple and effective in its implementation.

Automatic High-Resolution Operational Modal Identification of Thin-Walled Structures Supported by High-Frequency Optical Dynamic Measurements.

High-frequency optical dynamic measurement can realize multiple measurement points covering the whole surface of the thin-walled structure, which is very useful for obtaining high-resolution spatial information for damage localization. However, the noise and low calculation efficiency seriously hinder its application to real-time, online structural health monitoring. To this end, this paper proposes a novel high-resolution frequency domain decomposition (HRFDD) modal identification method, combining an optical system with an accelerometer for measuring high-accuracy vibration response and introducing a clustering algorithm for automated identification to improve efficiency. The experiments on the cantilever aluminum plate were carried out to evaluate the effectiveness of the proposed approach. Natural frequency and damping ratios were obtained by the least-squares complex frequency domain (LSCF) method to process the acceleration responses; the high-resolution mode shapes were acquired by the singular value decomposition (SVD) processing of global displacement data collected by high-speed cameras. Finally, the complete set of the first nine order modal parameters for the plate within the frequency range of 0 to 500 Hz has been determined, which is closely consistent with the results obtained from both experimental modal analysis and finite element analysis; the modal parameters could be automatically picked up by the DBSCAN algorithm. It provides an effective method for applying optical dynamic technology to real-time, online structural health monitoring, especially for obtaining high-resolution mode shapes.

Identification of Sub-Synchronous Oscillation Mode Based on HO-VMD and SVD-Regularized TLS-Prony Methods

To reduce errors in sub-synchronous oscillation (SSO) modal identification and improve the accuracy and noise resistance of the traditional Prony algorithm, this paper focuses on SSOs caused by the integration of doubly fed induction generators (DFIGs) with series compensation into the grid. A novel SSO modal identification method based on the hippopotamus optimization–variational mode decomposition (HO-VMD) and singular value decomposition–regularized total least squares–Prony (SVD-RTLS-Prony) algorithms is proposed. First, the energy ratio function is used for real-time monitoring of the system to identify oscillation signals. Then, to address the limitations of the VMD algorithm, the HO algorithm’s excellent optimization capabilities were utilized to improve the VMD algorithm, leading to preliminary denoising. Finally, the SVD-RTLS-improved Prony algorithm was employed to further suppress noise interference and extract oscillation characteristics, allowing for the accurate identification of SSO modes. The performance of the proposed method was evaluated using theoretical and practical models on the Matlab and PSCAD simulation platforms. The results indicate that the algorithms effectively perform denoising and accurately identify the characteristics of SSO signals, confirming its effectiveness, accuracy, superiority, and robustness against interference.

An Adaptive Chirp Mode Decomposition-Based Method for Modal Identification of Time-Varying Structures

Modal parameters are inherent characteristics of civil structures. Due to the effect of environmental factors and ambient loads, the physical and modal characteristics of a structure tend to change over time. Therefore, the effective identification of time-varying modal parameters has become an essential topic. In this study, an instantaneous modal identification method based on an adaptive chirp mode decomposition (ACMD) technique was proposed. The ACMD technique is highly adaptable and can accurately estimate the instantaneous frequencies of a structure. However, it is important to highlight that an initial frequency value must be selected beforehand in ACMD. If the initial frequency is set incorrectly, the resulting instantaneous frequencies may lack accuracy. To address the aforementioned problem, the Welch power spectrum was initially developed to extract a high-resolution time–frequency distribution from the measured signals. Subsequently, the time–frequency ridge was identified based on the maximum energy position in the time–frequency distribution plot, with the frequencies associated with the time–frequency ridge serving as the initial frequencies. Based on the initial frequencies, the measured signals with multiple degrees of freedom could be decomposed into individual time-varying components with a single degree of freedom. Following that, the instantaneous frequencies of each time-varying component could be calculated directly. Subsequently, a sliding window principal component analysis (PCA) method was introduced to derive instantaneous mode shapes. Finally, vibration data collected under various operational scenarios were used to validate the proposed method. The results demonstrated the effective identification of time-varying modal parameters in real-world civil structures, without missing modes.

Synchronous LoRa sensor nodes for modal identification in footbridge vibration monitoring

AbstractThis article aims at presenting a preliminary investigation of using long-range and low-cost LoRa (Long Range) technology and two synchronous LoRa sensor nodes for cost-effective footbridge structural health monitoring (SHM). Two sensor nodes with LoRa modules and accelerometers were employed for vibration monitoring and a new attempt was made to use synchronous LoRa nodes for modal identification. In this article, a modal identification method based on a lightweight synchronization concept was proposed. This method is able to identify the fundamental mode of vibrating beam structures. Meanwhile, maximum accelerations can also be tracked periodically from the simultaneously recorded acceleration data by the synchronous LoRa nodes. Specifically, synchronization was achieved through the wireless peer-to-peer (P2P) communication between the two LoRa nodes, with the aim of initializing simultaneous acceleration recordings. The fundamental frequency and the phase information derived from the on-board calculation of the synchronized nodes can then be used to effectively identify the vertical bending mode and torsion mode. A series of laboratory tests were also conducted on a beam structure for the purpose of validation. The test results showed that the fundamental mode of the vibrating beam can be obtained rapidly and accurately using the synchronized LoRa nodes, with an average synchronization accuracy of 4.45 ms. The maximum acceleration data recorded by the LoRa nodes also showed high accuracy when compared with the raw acceleration data collected from a commercial Bluetooth accelerometer node. The fundamental frequencies obtained from both types of nodes also compare reasonably. The proposed modal identification method using two synchronous LoRa sensor nodes provides a basis for the development of a low-cost footbridge SHM system with the integration of IoT techniques. An attempt has been made to perform a preliminary field test on a cable-stayed footbridge, where the fundamental frequency and the mode shape type of the footbridge were successfully identified and its serviceability condition was also found to satisfy the code requirements.

Silicone Rubber-Packaged FBG Sensing Information and SSI-COV-Recognized Modal Parameters Motivated Damage Identification in Pipe Structures

Pipes are the main structures serving as the lifeline for oil and gas transportation. However, they are prone to cracks, holes and other damages due to harsh working environments, which can lead to leakage incidents and result in significant economic losses. Therefore, the development of structural health monitoring systems with advanced online diagnostic methods is of great importance for identifying local damages and assessing the safety state of pipe structures. These efforts can guide rapid repairs and ensure the continuous, efficient and cost-effective transportation of oil and gas resources. To address this problem, this paper proposes the development of a pipe monitoring system based on quasi-distributed fiber Bragg grating (FBG) sensing technology. The SSI-COV method is employed to process the sensor responses and extract the modal parameters of the structure. Based on this foundation, an enhanced damage identification index is proposed, which mitigates the effects of support and excitation positions on damage identification. The pipe structure can be regarded as a continuous super-statical beam, and based on its structural symmetry, a unit structure, specifically a stainless-steel pipe with fixed ends, is regarded as the experimental subject. Impact experiments have been conducted to analyze its behavior in both undamaged and damaged states. The research indicates that by using the proposed modal parameter identification method and the ASMDI damage index, ASMDI exhibits peak values at damage locations of the pipe structure. This allows for the identification of structural damage with high accuracy, fast processing efficiency and strong robustness. The study provides an effective and reliable damage diagnosis method, which can contribute to the refinement and visualization of pipe structural health monitoring systems.

Bridge modal identification method based on adaptive VMD-HT algorithm

ABSTRACT Bridge engineering structures play a crucial role in transportation. Traditional methods of road and bridge closures for inspection and evaluation, while effective, increase bridge inspection costs and disrupt normal traffic flow. Therefore, a rapid detection and evaluation method for bridge structural modal parameters in the operational state is more suitable for practical engineering applications. However, under real operating conditions, bridge vibration signals typically contain a large amount of noise and interference, and modal identification must overcome issues of non-stationarity and non-linearity in the vibration signals caused by vehicle loads and environmental changes to ensure the accuracy of the identification. This study replaces the traditional Empirical Mode Decomposition algorithm in the Hilbert-Huang Transform with the Variational Mode Decomposition algorithm. It proposes a new method that combines the VMD algorithm with the Hilbert Transform, referred to as the Variational Mode Decomposition-Hilbert Transform method. Compared to the EMD algorithm, it offers significant improvements in suppressing mode mixing and endpoint effects. A vehicle-bridge coupling model was constructed, and the bridge’s natural modal information was successfully extracted from the vibration response signals. The research results indicate that the improved algorithm offers higher accuracy and faster computational speed compared to traditional identification algorithms.

Operating modal parameter identification of railway vehicle bogie based on k-value optimization variational mode decomposition and second-order blind identification method

Due to the variable operating conditions and strong background noise, the accuracy of modal parameter identification of the railway vehicle bogie is low. This paper proposes a method for identifying operational modal parameters by combining the K-value optimization variational mode decomposition (KVMD) and second-order blind identification (SOBI) method (KVMD–SOBI method). Firstly, the variational mode decomposition (VMD) algorithm is used to adaptively decompose a single-channel vibration signal into intrinsic mode function (IMF) components with different scale characteristics. The feature IMF components are selected through the K-value optimization method based on energy ratio and stability graph. Then, the SOBI algorithm is used to separate the matrix composed of the feature IMF components. And the mode shape and single-mode signal are obtained. Finally, the natural frequency and damping ratio of each order mode are extracted by the single-mode parameter recognition method. Through simulation and experimental verification, it is shown that the proposed method has good noise robustness and can effectively identify the first three modal parameters of railway vehicle bogies in variable-speed operation. At the same time, the feature IMF components extracted by KVMD algorithm eliminate the sensitivity of sensor installation positions and operating conditions to detection results. Therefore, this method is an excellent operational mode identification method based on a single-channel signal with good noise and working condition robustness.

Dynamic mode decomposition based Doppler monitoring of de novo cavitation induced by pulsed HIFU: an in vivo feasibility study

Pulsed high-intensity focused ultrasound (pHIFU) has the capability to induce de novo cavitation bubbles, offering potential applications for enhancing drug delivery and modulating tissue microenvironments. However, imaging and monitoring these cavitation bubbles during the treatment presents a challenge due to their transient nature immediately following pHIFU pulses. A planewave bubble Doppler technique demonstrated its potential, yet this Doppler technique used conventional clutter filter that was originally designed for blood flow imaging. Our recent study introduced a new approach employing dynamic mode decomposition (DMD) to address this in an ex vivo setting. This study demonstrates the feasibility of the application of DMD for in vivo Doppler monitoring of the cavitation bubbles in porcine liver and identifies the candidate monitoring metrics for pHIFU treatment. We propose a fully automated bubble mode identification method using k-means clustering and an image contrast-based algorithm, leading to the generation of DMD-filtered bubble images and corresponding Doppler power maps after each HIFU pulse. These power Doppler maps are then correlated with the extent of tissue damage determined by histological analysis. The results indicate that DMD-enhanced power Doppler map can effectively visualize the bubble distribution with high contrast, and the Doppler power level correlates with the severity of tissue damage by cavitation. Further, the temporal characteristics of the bubble modes, specifically the decay rates derived from DMD, provide information of the bubble dissolution rate, which are correlated with tissue damage level—slower rates imply more severe tissue damage.

Modal analysis and frequency matching study of subway bogie frame under ambient excitation

A wealth of practical cases indicates that the fatigue failure of subway bogies primarily stems from the modal resonance of the structure. If the modal characteristics of the entire vehicle, including equipment and bogies, are mismatched, rail vehicles may experience abnormal vibrations and noise. Therefore, it is imperative to conduct modal analysis and matching design for subway vehicle bogies to ensure smooth operation, reduce structural vibrations and noise, and enhance vehicle safety and ride comfort. Modal identification methods under the ambient l excitations during vehicle operation were employed to identify the modal parameters of the bogie structure before and after wheel reprofiling and under different load conditions. According to the test results, wheel reprofiling has minimal impact on the modal parameters of the structure, but with an increase in load, the modal frequencies of each order generally increase. This is associated with boundary constraint states, such as the increased stiffness of the bogie air spring with an increase in vehicle load. By comparing the test results with simulation analysis results of the bogie structure under free and constrained states, it is evident that simulating realistic boundary constraint conditions is crucial to ensure the accuracy of the finite element model. Based on frequency isolation criteria and vibration isolation theory, a frequency planning basis for the bogie structure was established. The study found that as the vehicle load increases, changes in the boundary conditions of the bogie affecting the elastic modal frequencies of the structure may have a certain impact on matching design, and may even better comply with the requirements of frequency management equations. This provides a new direction for subsequent scholars researching modal matching design.

A computer vision–aided methodology for bridge flexibility identification from ambient vibrations

AbstractThis paper presents the implementation of a novel monitoring system in which video images and conventional sensor network data are simultaneously analyzed to identify the structural flexibility from the ambient vibrations. The magnitude ratio between the flexibility estimated from known/unknown input force are theoretically derived and decomposed into two parts: and . The first scale factor related to basic modal parameters can be acquired using the general modal identification methods. Aiming to tackle the difficulty in identifying the second scale factor related to the force intensity, a video stream of traffic is processed to detect and classify vehicles to determine the vehicle's location while displacement measurements are simultaneously collected. By integrating the toll station data, the vehicle loads are assigned to the vehicle on the bridge deck through the uniqueness of the license plate number. Thus, a structural input–output relationship is established to solve the second scale factor . Finally, the flexibility estimated from the ambient vibration are scaled by and , respectively to obtain the exact flexibility , which are same as the analytical ones . Both numerical example and a laboratory test are performed to demonstrate the accuracy of the proposed methodology. The algorithms, approaches, and results given in the paper demonstrate its effectiveness and shows great potential for its application on a real‐life bridge's condition assessment.

Mode identification method of long span steel bridge based on CEEMDAN and SSI algorithm

AbstractStochastic subspace identification (SSI) stands as one of the most extensively employed algorithms for modal parameter identification within the domain of bridge structural health monitoring. However, when confronted with nonstationary signals, it often generates numerous false modes in the stability graph, consequently impeding the accuracy of modal parameter identification. To address this challenge, an algorithm combining the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and covariance‐driven SSI (COV‐SSI) has been proposed in this research, referred to as the CEEMDAN‐SSI algorithm. The CEEMDAN‐SSI algorithm first decomposes the structural vibration acceleration into intrinsic mode functions (IMFs) and then selects the pertinent IMF component for signal reconstruction using the Pearson correlation coefficient. Subsequently, the reconstructed signal undergoes analysis using the COV‐SSI algorithm, effectively mitigating the occurrence of false modes. Furthermore, the research focuses on a large‐span continuous rigid frame bridge with elevated piers situated in Toutunhe, Xinjiang Province, currently under construction. Modal parameters of the rigid frame bridge under various wind speed conditions are compared and analyzed using both COV‐SSI and CEEMDAN‐SSI algorithms. The findings reveal that the CEEMDAN‐SSI algorithm markedly diminishes false modes while enhancing the strength of stability axes for each mode, thus affirming the feasibility and robustness of the CEEMDAN‐SSI algorithm.

An Enhanced Failure Mode and Effects Analysis Risk Identification Method Based on Uncertainty and Fuzziness

An Enhanced Failure Mode and Effects Analysis Risk Identification Method Based on Uncertainty and Fuzziness

Structural modal parameter identification with the Power-Exponential window function

In view of the demand for accurate modal identification, and based on the characteristics of free vibration response, this paper introduces a new window function for Fourier Transform called the Power–Exponential window. The Power–Exponential window addresses the characteristics of free vibration response. It significantly enhances the accuracy of modal identification by improving the spectral properties of structural response. The proposed window function consists of exponential and power terms. This study focuses on the additional damping and frequency-domain differentiation introduced by the Power–Exponential window function. The exponential term weakens the boundary effect related to the time-domain truncation and suppresses the spectral leakage. Moreover, it can be interpreted in clear physical terms as providing additional damping to the signal. The power term in the window function corresponds to frequency domain differentiation, and it alleviates the spectral broadening that arises due to the additional damping. Furthermore, the analytical expression for the response spectrum confirms that the Power–Exponential window not only aligns the peak response frequency with the damped natural frequency but also establishes an explicit linear relationship between the actual structural damping ratio and the identification result from the half power bandwidth method. Both contribute to an improved accuracy and usability of certain frequency-domain modal identification methods. The influence of the Power–Exponential window parameters on modal parameter identification is analyzed, and the optimal selection principle and suggested parameter values are proposed. Finally, numerical simulations and an experimental frame model test are conducted to verify the accuracy and validity of modal parameter identification based on the Power–Exponential window.