Periodic Components Research Articles

Wind Power Scenario Synthesis With Smoothing Effect Through Spectral Decomposition and Its Application to Flexible Resource Adequacy

We synthesize future scenarios of total wind power generation (WPG) of future wind farms by considering the smoothing effect, in which mid-term variability fades out, but periodicity and short-term variability remain as more geographically distributed wind farms are aggregated. First, we decompose the WPG into a periodic component (PC) and non-periodic component (NC). We design the future PC by modifying the standard deviation and mean of the current PC. Then, we assume that the NC can be decomposed into a variable component (VC), which is a source of mid-term variability, and an uncertain component (UC), which is a source of short-term variability. We separate the VC and UC in the frequency domain. We design the VC by modifying the slope of power spectral density (PSD) to represent the smoothing effect and the UC by synthesizing the PSD distribution to represent randomness. Based on our scenarios, we develop a new flexibility index and a novel recursive algorithm to calculate the required amount of future flexible resources and the value of the smoothing effect to maintain the flexible resource adequacy. Finally, we verify the smoothing effect and the amount of flexible resources by simulating the IEEE test network based on actual WPG in Texas and Australia.

Lateral Circulation in an Elongated Curved Tidal Channel

Abstract The dynamic theory of curvature-induced lateral circulation has been developed for open channel flows but not for oscillatory tides. A linear three-dimensional analytical model was developed to investigate the lateral circulation in an elongated tidal channel with mildly curved bends of which the radius of curvature is larger than the width. The curvature-induced lateral circulation has two components with the same amplitude, namely, a periodic component having an overtide frequency and a steady component. The combination of the two components allows the strength of the lateral circulation to vary periodically and the rotation direction to be unchanged during a tidal period. Friction modifies the strength and structure of the lateral circulation. The phase between the lateral flow and streamwise tidal flow decreases with increasing friction, indicating that the two flows are not necessarily in phase unless friction is strong. The lateral circulations driven by the Coriolis and curvature centrifugal forces augment each other during one phase and compete in the opposite phase, and the relative importance of the two circulations is determined by the Rossby number and friction. The adaptation time is the same for spinup and spindown of the curvature-induced lateral circulation and is determined by water depth and vertical eddy viscosity. The estimation of the adaptation time depends on the leading modes because the transition solution of the curvature-induced lateral circulation comprises a series of cosine modes. These results provide a theoretical basis for interpreting curvature-induced lateral circulation in tidal channels and coastal headlands. Significance Statement The dynamic theory of curvature-induced lateral circulation in a tidal flow remains unexplored. The purpose of this study is to understand the essentials of curvature-induced lateral circulation in an elongated tidal channel using a three-dimensional analytical model. The results showed that the curvature-induced lateral circulation has two components with the same amplitude: a periodic component having an overtide frequency and a steady component. This is significantly different from the curvature-induced lateral circulation associated with open channel flows, which is steady and in phase with the streamwise flow. Future work may show the role of curvature-induced lateral circulation in streamwise dynamics and mass transport.

Decomposing age effects in EEG alpha power

Increasing life expectancy is prompting the need to understand how the brain changes during healthy aging. Research utilizing electroencephalography (EEG) has found that the power of alpha oscillations decrease from adulthood on. However, non-oscillatory (aperiodic) components in the data may confound results and thus require re-investigation of these findings. Thus, the present report analyzed a pilot and two additional independent samples (total N = 533) of resting-state EEG from healthy young and elderly individuals. A newly developed algorithm was utilized that allows the decomposition of the measured signal into periodic and aperiodic signal components. By using multivariate sequential Bayesian updating of the age effect in each signal component, evidence across the datasets was accumulated. It was hypothesized that previously reported age-related alpha power differences will largely diminish when total power is adjusted for the aperiodic signal component.First, the age-related decrease in total alpha power was replicated. Concurrently, decreases of the intercept and slope (i.e. exponent) of the aperiodic signal component were observed. Findings on aperiodic-adjusted alpha power indicated that this general shift of the power spectrum leads to an overestimation of the true age effects in conventional analyses of total alpha power. Thus, the importance of separating neural power spectra into periodic and aperiodic signal components is highlighted. However, also after accounting for these confounding factors, the sequential Bayesian updating analysis provided robust evidence that aging is associated with decreased aperiodic-adjusted alpha power. While the relation of the aperiodic component and aperiodic-adjusted alpha power to cognitive decline demands further investigation, the consistent findings on age effects across independent datasets and high test-retest reliabilities support that these newly emerging measures are reliable markers of the aging brain. Hence, previous interpretations of age-related decreases in alpha power are reevaluated, incorporating changes in the aperiodic signal.

Natural Exponential and Three-Dimensional Chaotic System.

Existing chaotic system exhibits unpredictability and nonrepeatability in a deterministic nonlinear architecture, presented as a combination of definiteness and stochasticity. However, traditional two-dimensional chaotic systems cannot provide sufficient information in the dynamic motion and usually feature low sensitivity to initial system input, which makes them computationally prohibitive in accurate time series prediction and weak periodic component detection. Here, a natural exponential and three-dimensional chaotic system with higher sensitivity to initial system input conditions showing astonishing extensibility in time series prediction and image processing is proposed. The chaotic performance evaluated theoretically and experimentally by Poincare mapping, bifurcation diagram, phase space reconstruction, Lyapunov exponent, and correlation dimension provides a new perspective of nonlinear physical modeling and validation. The complexity, robustness, and consistency are studied by recursive and entropy analysis and comparison. The method improves the efficiency of time series prediction, nonlinear dynamics-related problem solving and expands the potential scope of multi-dimensional chaotic systems.

Productivity change of airlines: A global total factor productivity index with network structure

Airlines require more effective utilization of resources and pursuit of innovation in their operations in order to meet the challenges of rising competition, increased costs of operation, and reduced profit margins. Competitive advantage can be better understood through productivity analysis. The popular technique utilized in airline productivity literature, the geometric mean Malmquist productivity index, is non-circular, sensitive to infeasibility, and for adjacent period components it provides different measurements of change in productivity. Moreover, the network structure of an airline's internal operation arises because of the unstorable nature of airline services. This internal structure should be accounted for while assessing the productivity changes of airlines. To eschew the limitations of the geometric mean Malmquist productivity index and open the black box of an airline's process of operation, this paper develops a novel network data envelopment analysis-based global Malmquist productivity index to evaluate the change in productivity of global airlines based on the individual internal stages. The proposed method further decomposes the productivity change in two ways. One way decomposes the productivity change into efficiency change and technological change assuming constant returns to scale. Another way decomposes the productivity change into the pure technical efficiency change, pure technological change, and the contribution of economies of scale based on the variable returns to scale. The empirical results indicate that improvement in efficiency is the key source of the productivity gains of the overall system, the first stage, as well as the second stage. Furthermore, the productivity improvement of the first and second stages simultaneously drives the overall productivity progress. Most airlines experience productivity growth in the sample period.

Periodic component pursuit-based kurtosis deconvolution and its application in roller bearing compound fault diagnosis

As an effective roller bearing fault diagnosis method, Adaptive Periodic Mode Decomposition (APMD) method has excellent capability of repeated transient extraction. In APMD, the Maximum Likelihood Estimation (MLE) method is used to calculate the projection energy, and the period corresponding to the maximum projection energy is taken as the main period of the present signal. When the noise is large, the noise energy will greatly interfere with the projection energy, thereby affecting the accuracy of the period estimation. To solve this problem, a Periodic Component Pursuit-based Kurtosis Deconvolution (PCPKD) method is proposed, which uses Maximum Reweighted Kurtosis Deconvolution (MRKD) to de-noise the signals that need to estimate the main periods, so as to reduce the influence of noise energy on the periodic estimation to the greatest extent. The proposed method is applied to roller bearing compound fault diagnosis, and the experimental results show that PCPKD has a good ability of signal period enhancement and can effectively segment multi frequency components.

Prediction method of pipe joint opening-closing deformation of immersed tunnel based on singular spectrum analysis and SSA-SVR

In order to predict the joint opening-closing deformation of immersed tunnel in operation, a comprehensive prediction model combining time series decomposition, least square method, sparrow search algorithm (SSA) and support vector regression (SVR) is proposed, which is verified by the monitoring data of E13-E14 and E17-E18 joints opening-closing deformation of immersed tunnel in Hong Kong-Zhuhai-Macao Bridge. Firstly, on the basis of summarizing and analyzing the characteristics of joint opening-closing deformation, the monitoring sequence of joint opening-closing is decomposed into trend component, periodic component and residual component by using time series decomposition singular spectrum analysis method, which clearly shows the composition of each component. Secondly, the least square method is used to fit and predict the trend component; Combining the commonly used RBF kernel function, Sigmoid kernel function and Ploy kernel function with SVR respectively, the SSA algorithm is used to globally optimize the penalty factors and kernel function parameters of the three models, and the optimized three coupling models are used to predict the periodic component and residual component. The results show that the prediction effect of the SVR model optimized by SSA algorithm is better than that of the traditional SVR model, The prediction result of SSA-SVR model constructed by RBF kernel function is the best. Finally, the time series addition model is applied to superimpose the optimal predicted values to obtain the predicted opening-closing amount. The mean square errors of the total predicted values of the opening-closing amount of the two joints are 0.1900mm and 0.2291mm respectively, the average errors are 0.1587mm and 0.2156mm respectively, and the correlation coefficients are 0.9792 and 0.9695 respectively. A satisfactory prediction effect is obtained, which proves the reliability and accuracy of this method, and provides a new way for the prediction of the opening-closing deformation of the pipe joint of immersed tunnel during the operation period.

Prediction of Landslide Displacement Based on the Variational Mode Decomposition and GWO-SVR Model

Accurate prediction of landslide displacement is an effective way to reduce the risk of landslide disaster. Under the influence of periodic precipitation and reservoir water level, many landslides in the Three Gorges Reservoir area underwent significant displacement deformation, showing a similar step-like deformation curve. Given the nonlinear characteristics of landslide displacement, a prediction model is established in this study according to the variational mode decomposition (VMD) and support vector regression (SVR) optimized by gray wolf optimizer (GWO-SVR). First, the original data are decomposed into trend, periodic and random components by VMD. Then, appropriate influential factors are selected using the grey relational degree analysis (GRDA) method for constructing the input training data set. Finally, the sum of the three displacement components is superimposed as the total displacement of the landslide, and the feasibility of the model is subsequently tested. Taking the Shuizhuyuan landslide in the Three Gorges Reservoir area as an example, the accuracy of the model is verified using the long time-series monitoring data. The results indicate that the newly proposed model achieves a relatively good prediction accuracy with data decomposition and parameter optimization. Therefore, this model can be used for the predict the accuracy of names and affiliations ion of landslide displacement in the Three Gorges Reservoir area.

Glutamatergic and GABAergic Receptor Modulation Present Unique Electrophysiological Fingerprints in a Concentration-Dependent and Region-Specific Manner.

Brain function depends on complex circuit interactions between excitatory and inhibitory neurons embedded in local and long-range networks. Systemic GABAA-receptor (GABAAR) or NMDA-receptor (NMDAR) modulation alters the excitatory-inhibitory balance (EIB), measurable with electroencephalography (EEG). However, EEG signatures are complex in localization and spectral composition. We developed and applied analytical tools to investigate the effects of two EIB modulators, MK801 (NMDAR antagonist) and diazepam (GABAAR modulator), on periodic and aperiodic EEG features in freely-moving male Sprague Dawley rats. We investigated how, across three brain regions, EEG features are correlated with EIB modulation. We found that the periodic component was composed of seven frequency bands that presented region-dependent and compound-dependent changes. The aperiodic component was also different between compounds and brain regions. Importantly, the parametrization into periodic and aperiodic components unveiled correlations between quantitative EEG and plasma concentrations of pharmacological compounds. MK-801 exposures were positively correlated with the slope of the aperiodic component. Concerning the periodic component, MK-801 exposures correlated negatively with the peak frequency of low-γ oscillations but positively with those of high-γ and high-frequency oscillations (HFOs). As for the power, θ and low-γ oscillations correlated negatively with MK-801, whereas mid-γ correlated positively. Diazepam correlated negatively with the knee of the aperiodic component, positively to β and negatively to low-γ oscillatory power, and positively to the modal frequency of θ, low-γ, mid-γ, and high-γ. In conclusion, correlations between exposures and pharmacodynamic effects can be better-understood thanks to the parametrization of EEG into periodic and aperiodic components. Such parametrization could be key in functional biomarker discovery.

Wavelet Analysis for Studying Rainfall Variability and Regionalizing Data: An Applied Study of the Moulouya Watershed in Morocco

This study analyzes the spatiotemporal variability of precipitation at the scale of the Moulouya watershed in eastern Morocco, which is very vulnerable to the increasing water shortage. For this purpose, we opted for wavelet transformation, a method based on the spectral analysis of data which allows for periodic components of a rainfall time series to change with time. The results obtained from this work show spectral power across five frequency ranges of variability: 1 to 2 years, 2 to 4 years, 4 to 8 years, 8 to 16 years, and 16 to 32 years. The duration of significant power at these frequencies is generally not homogeneous and varies from station to station. The most widespread frequency over the entire study area was found in the 4- to 8-year range. This mode of variability can last up to 27 consecutive years. In most of the basin, this mode of variability was observed around the period between 1990 and 2010. Oscillations at 8 to 16 years in frequency appear in only five series and over different time periods. The 16- to 32-year mode of variability appears in 15 stations and extends over the period from 1983 to 2008. At this level, signal strength is very weak compared to other higher-frequency modes of variability. On the other hand, the mode of variability at the 1- to 2-year frequency range appeared to be continuous in some stations and intermittent in others. This allowed us to regionalize our study basin into two homogeneous clusters that only differ in variability and rainfall regime.

Time–frequency signal analysis of flow pulsation in siphon outlet conduit based on HHT considering the pump‐conduit interaction

AbstractThe unsteady three‐dimensional numerical simulation calculation of the vertical axial flow pump device is performed based on CFD to examine the pressure pulsation and energy distribution features of the water flow within the siphon outlet conduit (SOC) under the hydraulic coupling of the pump and the flow conduit. The pressure pulsation signals (PPS) of monitoring points are decomposed using the Hilbert–Huang approach via empirical mode decomposition (EMD) and Hilbert spectrum analysis. The results show that the PPS of monitoring points of the SOC has no obvious periodicity. The low‐frequency range below 20 Hz serves as the primary frequency, and the energy ratio of the high‐frequency signal above 700 Hz is less than 1%. Under the condition of a small flow rate 0.3Qbep, there is obvious high‐frequency pulsation above 500 Hz at the inlet of the upstream section of the SOC, and there are periodic components distributed around 200 Hz. The energy of the pressure pulsation is primarily focused in the low‐frequency range below 40 Hz at the SOC outlet section. The PPS at the top and bottom monitoring points of the hump section are consistent, and the pressure pulsation energy (PPE) is mainly concentrated in the low frequency below 40 Hz. In both the big flow condition (1.2Qbep) and the optimal flow condition (1.0Qbep), the PPE of the monitoring points at the top of the hump section is distributed in the middle and low‐frequency band below 40 Hz, and the energy of monitoring points at the bottom of the hump section is concentrated in the low‐frequency band below 20 Hz, accounting for more than 70%. When the flow rate increases from 0.3Qbep to 1.2Qbep, the peak value of the pressure pulsation coefficient at the main frequency of each monitoring point at the top of the hump section changes little, and the peak value of the pressure pulsation coefficient at the main frequency of each monitoring point at the bottom increases first and then decreases. From the upstream section to the hump section of the SOC, the average frequency of each intrinsic mode function (IMF) of the PPS under different flow conditions shows an overall increasing trend. From the hump section of the SOC to its outlet, the average frequency of each IMF of the PPS decreases under the conditions of 1.0Qbep and 1.2Qbep, and there is no obvious change under the condition of 0.3Qbep.

A Novel Joint Time-Frequency Spectrum Resources Sustainable Risk Prediction Algorithm Based on TFBRL Network for the Electromagnetic Environment

To protect the electromagnetic environment and understand its current state in a timely manner, monitoring the electromagnetic environment has great practical significance, while massive amounts of data are generated. It is crucial to utilize data mining technology to extract valuable information from these massive amounts of data for effective spectrum management. Traditional spectrum prediction methods do not integrate the prior information of spectrum resource occupancy, so that the prediction of the channel state of a single frequency point is of limited significance. To address these issues, the paper describes a dynamic threshold algorithm which mines bottom noise and spectrum resource occupancy from massive electromagnetic environment data. Moreover, the paper describes a joint time-frequency spectrum resource prediction algorithm based on the time-frequency block residual LSTM (TFBRL) network, which utilizes hourly time closeness, daily period, and annual trend as prior knowledge of spectrum resources. The TFBRL network comprises three main parts: (1) a residual convolution network with a squeeze-and-excitation (SE) attention mechanism, (2) a long short term memory (LSTM) model with memory ability to capture sequence latent information, and (3) a feature fusion module based on a matrix to combine time closeness, daily period, and annual trend feature components. Experimental results demonstrate that the TFBRL network outperforms the baseline networks, improving by 31.37%, 16.00% and 13.06% compared with the best baseline for MSE, RMSE and MAE, respectively. Thus, the TFBRL network has good risk prediction performance and lays the foundation for subsequent frequency scheduling.

Natural resource rent, financial globalization, and environmental degradation: Evidence from a resource rich country

This paper examines the role of financial globalization and natural resource rents on carbon emissions in the case of Nigeria from 1970 to 2020 using Breitung-Candelin Spectral Granger-causality and wavelet coherence analysis. The spectral analysis decomposes variability in a time series into its periodic components, which is preferable for series that are short-spanned, nonlinear, or are characterized by seasonal and economic episodes, while the wavelet coherence analysis could produce localized decompositions both in time and frequency domains. Using these techniques, we find a one-way causal effect running from financial globalization and natural resource rents to carbon emissions within the specified scale and time. Financial globalization and natural resource rents are useful for predicting environmental degradation in Nigeria. Thus, policymakers should factor in financial globalization and natural resource rent when formulating environmental policies to mitigate climate change effect for the immediate and future generations. Financial penetration should be channeled toward green investment. The deposit money banks should provide and prioritize credit only to firms and individuals that consider investing in modern and clean technologies, while the policy on exploration and exploitation of natural resources should review to attract foreign investors that would improve the existing technologies or bring in energy-efficient and energy-saving ones.

Enhanced weight symplectic geometry decomposition based on maximum periodic kurtosis deconvolution

To enhance the periodic impact component and improve the accuracy of planetary gear fault detection, an enhanced weighted symplectic geometry decomposition based on maximum periodic kurtosis deconvolution (MPKD-EWSGD) is proposed in the paper. On the one hand, MPKD-EWSGD adopts the MPKD method for noise reduction preprocessing to highlight the periodic impulse component. On the other hand, MPKD-EWSGD introduces the periodic impulse intensity (PII) to choose components with fault information, avoiding the disadvantages of denoising methods that use the component energy as the measurement standard. Emulation and experimental signals show that MPKD-EWSGD can effectively reduce noise and is an effective method for planetary gearbox fault detection.

Wind power prediction based on periodic characteristic decomposition and multi-layer attention network

Aiming at the wind power characteristics of temporality, periodicity and complexity, the periodic law of short-term and long-term repetitive patterns is studied, and an integrated dual-channel prediction model is proposed. A practical periodic characteristic extracting strategy is designed to show the hidden periodic law of the original signal. Combining the grid search algorithm with the variation trend of amplitude/period, the optimal periodic step is determined. Based on the above analysis, the original signal is decomposed into temporal and periodic components. Then the temporal attention network and the encoder-decoder attention network are schemed out to dispose the two components respectively. Finally, the linear regression attention network is adopted to realize data fitting. The integrated forecasting framework can deal with the long-term and short-term dependencies of the original data at the same time, and ensure the rapid convergence of training process, thereby improve the prediction accuracy and stability. The multi-dimensional experimental verification is carried out through the comparison of evaluation indicators, prediction trends, scatter plots and box plots.

AutoMSNet: Multi-Source Spatio-Temporal Network via Automatic Neural Architecture Search for Traffic Flow Prediction

Recently the research of traffic flow prediction with deep learning framework has be largely developed, whereas most current methods are still faced with the following shortcomings. For spatial feature extraction, studies have shown that both local and non-local correlations exist on traffic networks. Considering the temporal dependencies, short-term impending and longer periodic components are two most critical patterns of traffic data, which further provide different information for the prediction task. Furthermore, multi-source heterogeneous external data, which naturally holds semantic gap with traffic data, also have impact on traffic flow. To solve the above problems, this paper proposes an AutoMSNet (Multi-Source Spatio-Temporal Network via Automatic neural architecture search). The AutoMSNet is composed of an encoder-decoder structure. The encoder takes neighboring data as inputs, while the decoder captures long-term periodic patterns. Thus, different functions of two temporal features are simultaneously extracted. Moreover, a neural architecture search space is designed for spatial feature extraction. Through architecture search technique, graph convolutions with different receptive fields are automatically selected and combined to form an optimal module structure. Therefore, both local and non-local spatial features can be adaptively captured. Besides, a meta learning feature fusion strategy is proposed to integrate external data, which can alleviate the semantic gap between different data sources. Extensive experiments on three real-world traffic datasets evaluate the superiority of the proposed model.

Estimation of Respiratory Rate through Breathing Audio

Abstract: To overcome the major obstacle posed by a lack of access to physical examination, which includes inexpensive and accurate remote measurements of vital signs. Here, we use audio to estimate the patient's respiratory rate using machine learning. There are other strategies (non-learning based), but their precision is restricted, and the research we realize about utilizing ML is either not straightforwardly valuable or non-public datasets are used. There is only one accessible dataset that is public, hence it is used for the evaluation of the Proposed methods. Considering the above, we propose a novel data augmentation technique to increase its effective size to avoid the overfitting issue. Our calculation utilizes the depiction of the spectrum of frequencies and the need for names for relaxing cycles, which are used to make a repetitive neural network that can see the cycles. Using only the breathing audio of the patient, our augmentation technique makes use of the independence of the majority of the spectrogram's periodic frequency components and their order is calculated for generating multiple signals representing it. The smartphone is used to collect those signals allowing doctors to accurately and automatically determine the respiratory rate of patients from a distance.

Compartmental Unpredictable Functions

There is a huge family of recurrent functions, which starts with equilibria and ends with Poisson stable functions. They are fundamental in theoretical and application senses, and they admit a famous history. Recently, we have added the unpredictable functions to the family. The research has been performed in several papers and books. Obviously, theoretical and application merits of functions increase if one provides rigorously approved efficient methods of construction of concrete examples, as well as their numerical simulations. In the present study, we met the challenges for unpredictability by considering functions of two variables on diagonals. Algorithms have been created, and they are both deterministic and random. Characteristics are introduced to evaluate contributions of periodic and unpredictable components to the dynamics, and they are clearly illustrated in graphs of the functions. Definitions of non-periodic compartmental functions are provided as suggestions for the research in the future.

Determination of periodic deformation from InSAR results using the FFT time series analysis method in Gediz Graben.

Permanent Scatterers (PS) point velocities obtained by the interferometric synthetic aperture radar (InSAR) method are generally determined using the linear regression model, which ignores periodic and seasonal effects. In this study, software was developed that can detect periodic effects by applying fast Fourier transformation (FFT) time series analysis to InSAR results. Using the FFT time series analysis, the periodic components of the surface movements at the PS points were determined, and then the annual velocity values free from periodic effects were obtained. The study area was chosen as the Gediz Graben, a tectonically active region where aseismic surface deformations have been observed in recent years. As a result, using the developed method, seasonal effects were successfully determined with the InSAR method at the PS points in the study area with a period of 384days and an average amplitude of 19mm. In addition, groundwater level changes of a water well in the region were modeled, and 0.93 correlation coefficient values were calculated between seasonal InSAR displacement values and water level changes. Thus, using the developed methodology, the relationship between the tectonic movement in the Gediz Graben in Turkey and the seasonal movements and the change in the groundwater level was determined.

Structural Modal Parameter Identification Method Based on the Delayed Transfer Rate Function under Periodic Excitations

The dynamic response transfer rate function (TRF) is increasingly used in the field of structural modal parameter identification because it does not depend on the white noise assumption of the excitation. In this paper, the interference of periodic excitation on structural modal parameter identification using TRF is analyzed theoretically for a class of civil engineering structures with obvious periodic components in excitation, and then an identification method of structural real modal parameters is proposed. First, a delayed TRF is constructed, and the pseudo-frequency response function is further obtained to identify the periodic spurious poles of the whole system. Then, the effective identification of the real modal parameters of the structure is achieved by comparing the system poles identified via conventional TRF. Finally, the feasibility and robustness of the proposed method were verified using a calculation example with four-degrees-of-freedom system. In addition, the modal parameters of a structure under periodic excitation were effectively identified by taking a pumping station as an example, and the results show that the method accurately identified the structural modal parameters when the excitation contained periodic components, which has wider prospects for technical applications.