Frequency Spectrum Characteristics Research Articles

Vibration transmission model of buildings based on virtual spring model and energy functional variation principle

In recent years, the “metro depot + over-track buildings” development model has witnessed rapid growth in China, driven by its advantages of high land utilization and investment return rate. However, the issue of vibration and noise caused by trains entering and exiting the depot has become a major impediment to its sustainable development. To predict the vibration of over-track buildings induced by trains, this paper presented a vibration transmission model of buildings based on the virtual spring model and the energy functional variation principle. The model was then applied to an actual engineering project at a metro depot in Guangzhou, China, and its accuracy was validated by comparing the results with finite element analysis and field measurements. Additionally, the vibration transmission characteristics of the over-track building were studied. The results indicated that the vibration transmission model of buildings presented in this paper aligns well with the results obtained through finite element analysis and field measurements. This approach eliminates the need to disassemble structural members, and the introduced virtual spring model effectively simulates non-ideal connections and boundary conditions. Consequently, it offers convenient structural connection and boundary condition settings, as well as high computational efficiency. Due to the edge effects on the top floor of the buildings, vibration waves in the higher floors experience a combination of reflected and incident waves, resulting in slow attenuation and, in some cases, amplification of vibrations as they propagate from the middle floors to the top floor. The vibration of the over-track building is closely related to the natural vibration characteristics of the floor and the frequency spectrum characteristics of the vibration source. When the natural frequency of a building's floor aligns with the main frequency of the vibration source, significant vibration amplification occurs due to local resonance.

Breast ultrasound image despeckling using multi-filtering DFrFT and adaptive fast BM3D

Improving the quality of breast ultrasound images is of great significance for clinical diagnosis which can greatly boost the diagnostic accuracy of ultrasonography. However, due to the influence of ultrasound imaging principles and acquisition equipment, the collected ultrasound images naturally contain a large amount of speckle noise, which leads to a decrease in image quality and affects clinical diagnosis. To overcome this problem, we propose an improved denoising algorithm combining multi-filter DFrFT (Discrete Fractional Fourier Transform) and the adaptive fast BM3D (Block Matching and 3D collaborative filtering) method. Firstly, we provide the multi-filtering DFrFT method for preprocessing the original breast ultrasound image so as to remove some speckle noise early in fractional transformation domain. Based on the fractional frequency spectrum characteristics of breast ultrasound images, three types of filters are designed correspondingly in low, medium, and high frequency domains. And by integrating filtered images, the enhanced images are obtained which not only remove some speckle noise in background but also preserve the details of breast lesions. Secondly, for further enhancing the image quality on the basis of multi-filter DFrFT, we propose the adaptive fast BM3D method by introducing the DBSCAN-based super pixel segmentation to block matching process, which utilizes super pixel segmentation labels to provide a reference on how similar it is between target block and retrieval blocks. It reduces the number of blocks to be retrieved and make the matched blocks with more similar features. At last, the local noise parameter estimation is also adopted in the hard threshold filtering process of traditional BM3D algorithm to achieve local adaptive filtering and further improving the denoising effect. The synthetic data and real breast ultrasound data examples show that this combined method can improve the speckle suppression level and keep the fidelity of structure effectively without increasing time cost.

Simulation method and spectrum modulation characteristic analysis of typical fault signals of inter-shaft bearing

In order to study the frequency spectrum characteristics of the vibration signal of the inter-shaft bearing defect fault in the aero-engine dual-rotor system, a vibration signal mathematical model is established based on the fault characteristic frequency of the inner and outer ring defects of the inter-shaft bearing, and the mutual modulation law of the signals during transmission is analyzed. A test bench for signal transmission path analysis is built to verify the calculation results. The results indicate that the fault signal of the inter-shaft bearing defect significantly attenuates during transmission, and the characteristic frequency of the inter-shaft bearing fault is modulated with the rotor rotation frequency. There are corresponding characteristic frequencies and modulation frequency components in the envelope spectrum of the inter-shaft bearing. The error between the experimental and simulation results is less than 1%, which verifies the accuracy of the simulation calculation results. After being transmitted to the rotor through the inter-shaft bearing, the rotor frequency includes the modulation frequency of bearing varying compliance frequency and rotation frequency, as well as the fault characteristic frequency of the inter-shaft bearing.

Investigation of micro spill in RF KO extraction using tailored excitation signals

Radio Frequency Knock Out (RF KO) extraction is used to extract stored particle beams from synchrotrons through transverse excitation, delivering spills of particles for experiments and medical therapy. Minimizing the fluctuations of spill intensity is vital to prevent detector pile-up and interlocks while making most efficient use of the extracted beam. To improve the spill quality, different excitation signals with characteristic frequency spectra are explored. Results of experimental studies at the Heidelberg Ion Beam Therapy Center (HIT) are presented. These demonstrate the possible improvements by tuning multi-band spectra at different harmonics. Particle tracking simulations of the slow extraction process at HIT are used to understand how different excitation signals influence the spill quality.

Unsupervised Learning-Based Plant Pipeline Leak Detection Using Frequency Spectrum Feature Extraction and Transfer Learning

Unsupervised Learning-Based Plant Pipeline Leak Detection Using Frequency Spectrum Feature Extraction and Transfer Learning

Cumulative damage evolution of jointed slopes subject to continuous earthquakes: Influence of joint type on dynamic amplification effect and failure mode of slopes

This work investigates the dynamic response characteristics and cumulative damage evolution of jointed slopes under continuous earthquakes. Three jointed slope discrete-element models were created using a new fracture formation method to avoid particle overlap. The effects of joint types on dynamic amplification and failure mode are investigated. The results show that joints amplify the seismic response, with bedded jointed slopes exhibiting the highest magnification effect, followed by parallel jointed slopes and anti-dip jointed slopes. Cracks gradually increase under continuous earthquakes, with an increasing rate characterized by increase–decrease-increase–decrease. The failure scale of the bedded jointed slopes is the largest, followed by the parallel jointed slopes, and the anti-dip jointed slopes have the smallest failure scale. Seismic cumulative damage evolution encompasses stages of local damage (priming effect), expansion of local damage (accumulative effect), slip body formation, and instability (acceleration effect). Discontinuous joints affect the damage characteristics and instability modes of slopes by controlling fracture initiation and expansion. They have minimal impact on intrinsic frequency and frequency spectrum characteristics but significantly affect marginal spectrum characteristics. This work provides insights into the behaviour of jointed slopes under continuous earthquakes and the influence of joint types on their cumulative damage evolution process.

Effect of excitation frequency and joint density on the dynamic amplification effect of slope surface on jointed rock slopes

This paper presents the slope dynamic response of jointed rock slopes containing three groups of typical joints and analyzes the effect of input harmonic frequency and joint density on the peak horizontal acceleration (PGA) of the slope surface under vertically impinging SV wave (shear vertical wave) excitation. First, the dynamic response of the slope surface of the bedding slope was investigated with a large-scale shaking table test, and the reliability of the numerical model was verified by the physical modeling. Then, a series of jointed rock slope models with different joint densities were established based on the three-dimensional discrete element software 3DEC. It is found that the natural frequency fn of the jointed slope decreases with the increase of joint density. The effect of excitation frequency f on the slope surface dynamic response of the jointed slope is stronger than that of joint density. The closer the f is to the fn, the stronger the slope surface and slope crest dynamic response is. Notably, taking fn as the critical value of f, the slope surface dynamic amplification mode of jointed slope can be divided into two types: when f ≤ fn, the acceleration amplification factor of X-direction (AAF-X) of the slope surface amplifies monotonically with increasing elevation; when f >fn, the AAF-X of the slope surface shows a fluctuated amplification pattern with the increase of elevation. The results of this paper show that in the seismic design of slope engineering, the influence of site conditions on the frequency spectrum characteristics of ground motion should be considered, and then the optimal design should be carried out.

High-time resolution PM2.5 source apportionment assisted by spectrum-based characteristics analysis

Characteristics extraction and anomaly analysis based on frequency spectrum can provide crucial support for source apportionment of PM2.5 pollution. In this study, an effective source apportionment framework combining the Fast Fourier Transform (FFT)- and Continuous Wavelet Transform (CWT)-based spectral analyses and Positive Matrix Factorization (PMF) receptor model is developed for spectrum characteristics extraction and source contribution assessment. The developed framework is applied to Beijing during the winter heating period with 1-h time resolution. The spectrum characteristics of anomaly frequency, location, duration and intensity of PM2.5 pollution can be captured to gain an in-depth understanding of source-oriented information and provide necessary indicators for reliable PMF source apportionment. The combined analysis demonstrates that the secondary inorganic aerosols make relatively high contributions (50.59 %) to PM2.5 pollution during the winter heating period in Beijing, followed by biomass burning, vehicle emission, coal combustion, road dust, industrial process and firework emission sources accounting for 15.01 %, 11.00 %, 10.70 %, 5.31 %, 3.88 %, and 3.51 %, respectively. The source apportionment result suggests that combining frequency spectrum characteristics with source apportionment can provide consistent rationales for understanding the temporal evolution of PM2.5 pollution, identifying the potential source types and quantifying the related contributions.

Anti-motion imaging photoplethysmography via self-adaptive multi-ROI tracking and selection

Objective. The imaging photoplethysmography (IPPG) technique allows people to measure heart rate (HR) from face videos. However, motion artifacts caused by rigid head movements and nonrigid facial muscular movements are one of the key challenges. Approach. This paper proposes a self-adaptive region of interest (ROI) pre-tracking and signal selection method to resist motion artifacts. Based on robust facial landmark detection, we split the whole facial skin (including the forehead, cheeks, and chin) symmetrically into small circular regions. And two symmetric sub-regions constitute a complete ROI. These ROIs are tracked and the motion state is simultaneously assessed to automatically determine the visibility of these ROIs. The obscured or invisible sub-regions will be discarded while the corresponding symmetric sub-regions will be retained as available ROIs to ensure the continuity of the IPPG signal. In addition, based on the frequency spectrum features of IPPG signals extracted from different ROIs, a self-adaptive selection module is constructed to select the optimum IPPG signal for HR calculation. All these operations are updated per frame dynamically for the real-time monitor. Results. Experimental results on the four public databases show that the IPPG signal derived by our proposed method exhibits higher quality for more accurate HR estimation. Compared with the previous method, metrics of the evaluated HR value on our approach demonstrates superior or comparable performance on PURE, VIPL-HR, UBFC-RPPG and MAHNOB-HCI datasets. For instance, the RMSEs on PURE, VIPL-HR, and UBFC-RPPG datasets decrease from 4.29, 7.62, and 3.80 to 4.15, 3.87, and 3.35, respectively. Significance. Our proposed method can help enhance the robustness of IPPG in real applications, especially given motion disturbances.

Study on the Influence of a Rubber-Modified Soil Isolation Layer on the Isolation Performance of Frame Structures with Different Foundation Forms

In order to investigate the seismic performance of a rubber-modified soil isolation layer, a three-dimensional finite element model was constructed using finite element analysis software, utilizing a two-story frame structure as the engineering background. Nonlinear dynamic time history analysis and comparisons were performed against the seismic performance of the structure. The evaluation was based on several parameters, including the contact area of the base, the thickness of the rubber-particle-modified soil isolation layer, ground motion records with varying amplitudes, and seismic frequency spectrum characteristics. The research findings indicate that the implementation of a rubber-modified soil isolation layer effectively mitigates the peak acceleration, horizontal displacement, and shear stress of the frame structure. This not only enhances the seismic performance of the structure but also enlarges the contact area of the base. Increasing the thickness of the rubber-modified soil isolation layer will effectively decrease the peak acceleration, horizontal displacement, and shear stress of the structure during seismic events. The effectiveness of the isolation provided by the rubber-modified soil layer improves as the intensity of the ground motion record increases.

Сравнительная характеристика частотных диапазонов ээг и церебрального энергообмена при низком уровне психофизиологической адаптации у работников ядерно-опасных предприятий и производств

Purpose: Comparative assessment of the functional state and energy processes of the brain in workers of nuclear hazardous enterprises and industries with high and low levels of psychophysiological adaptation (PPA). The parameters of the spectral power of the EEG frequency ranges and cerebral energy exchange at low and high levels of PPA, low and high functional activity (FA) of conditionally isolated structural and functional formations (SFF) characterizing: mental level of functioning − SFF-1, psychophysiological level − SFF-2, physiological − SFF-3 were compared. Material and methods: 311 archived EEG – 159 individuals with a low level of PPA (50.8±4.6; 13 women); 152 EEG individuals with a high level of PPA (48.8±1.5; 12 women). The power of the frequency ranges of the EEG was evaluated by computer analysis using the fast Fourier transform algorithm; cerebral energy exchange using the value of the hemispheric differences in the power of biopotentials of EEG homologous leads. Results: At a low level of PPA, higher activity of cortical structures and higher cerebral energy exchange were revealed. In the SFF the changes manifested themselves in different ways. Increased activity of cortical structures was noted in SFF-1 and SFF-3 (in all areas of the cortex, including temporal, associated with the limbic-reticular complex). In SFF-2, the activity of cortical structures weakened both in the anterior and posterior parts of the cortex, the activity of the temporal zones did not change. Increased cerebral energy exchange was noted in SFF-1 and SFF-2. It was detected in the anterior parts of the cortex, and was not detected in the posterior. In SFF-3, the cerebral energy exchange did not change – neither in the anterior nor posterior parts of the cortex. Conclusion: Various SFF of the brain take part in ensuring brain activity at a low level of PPA, which is reflected in the characteristics of EEG frequency spectra and indicators of cerebral energy exchange of the brain regions concerned. The processes associated with the participation of structural and functional education reflecting the mental level of functioning (SFF-1) are characterized at a low level of PPA by increased activity of the anterior cortex, which is accompanied by increased cerebral energy exchange. The deepening of research in this direction may contribute to the identification of additional compensatory mechanisms of the brain aimed at ensuring the functional activity required for the exercise of professional activity by persons with a low level of PPA.

Steady state prediction model and spectrum characteristics analysis of cutting force for CNC lathe considering variable machining parameters

This paper presents a steady state cutting force prediction model for CNC lathe considering feed displacement. The frequency spectrum characteristics of the cutting force in principal direction are analyzed. The turning test for 12Cr18Ni9 stainless steel workpiece is carried out by CNC machine tool ETC1625P firstly, and the real-time displacement data of worktable in the turning process are obtained. The cutting force data varying with the displacement of the worktable under different cutting parameters are obtained by cubic spline interpolation. The mechanical force model including metal shearing force and plowing force is established, so as to predict the steady state cutting force accurately corresponding to different displacement of the worktable. The influence of different cutting parameters on the amplitude frequency characteristics for the low frequency part of the cutting force in principal direction is studied by using wavelet packet decomposition and fast Fourier transform. The results show that the method can predict the steady cutting force accurately and reflect the amplitude frequency characteristics of the low frequency part for the cutting force in principal direction under different cutting parameters.

An effective source number detection method for single-channel signals based on signal reconstruction and deep learning at low SNR

Determining the number of sources under low signal-to-noise ratio (SNR) and signal interference with the same frequency and modulation presents a significant challenge. To address this challenge, we propose a novel method for detecting the number of signal sources from single-channel that leverages signal reconstruction and deep learning. The method employs subspace projection based on the Hankel matrix to reconstruct the measured single-channel signals, effectively suppressing noise. Furthermore, we incorporate the correlation of information and the integrity of feature in the signal, by fusing the in-phase component, quadrature component, and frequency spectrum feature of the reconstructed complex signal into a one-dimensional feature suitable for convolutional neural network (CNN). To address the source number detection task, we design a one-dimensional CNN based on convolutional block attention module, transforming it into a classification problem. Finally, experimental measurements demonstrate the effectiveness of our proposed method, with an detection accuracy of 94% even at an SNR of −10 dB.

Frequency spectrum characteristics of blast-induced vibration with electronic detonators in ground blasting

With the wide application of electronic detonators in blasting engineering, further study of frequency spectrum characteristics under precise delay time is essential for blasting design and safety evaluation. In this paper, the frequency spectra induced by blasting vibration under different delay times and distances are calculated, the frequency distribution and energy characteristics of various frequency bands are then investigated, and the demonstration is conducted using numerical simulation and electronic detonator blasting experiments. The results show that the low-frequency vibration proportion increases, and the dominant frequency shifts to a lower frequency compared with the vibration frequency distribution of single-hole blasting when using a very short delay time (≤5 ms). However, when a short delay time (6–12 ms) is used, the low-frequency shift to high frequency, reducing the energy ratio of low-frequency bands. And there are certain differences in the delay time to reduce PPV at different blasting center distances. A shorter delay time (6–8 ms) in the nearer region and a longer delay time (10–20 ms) in the intermediate and farther regions better reduce blasting vibration. Finally, considering multiple influencing factors, the 7–12 ms delay time is recommended to protect structures in the blasting area factors.

Títul Automatic Extraction and Discrimination of Vocal Theme Based on Quadratic Wave Equation

Abstract Tune is the essential music component. Melody extraction is a crucial technique in music retrieval. The pitching order of polyphonic music is the main feature of vocal music. This paper presents an improved method of extracting vocal themes based on the quadratic wave equation. This paper presents a new algorithm based on the frequency spectrum characteristics of verbal signals. This method can effectively reduce the amount of computation and shorten the time of the primary melody extraction. This paper proposes a new fundamental frequency recognition model based on BP neural network, which has a good ability for secondary wave transformation. This method can improve the recognition accuracy of the primary melody model while reducing the error of melody location. This can improve the overall vocal music of the leading melody extraction precision. The analysis results of MIR-1K data show that the overall recognition accuracy of the improved theme is 2.13% higher than that of the original method. Compared with the traditional way, the average time of theme extraction is shortened by 0.06 seconds.

Pipeline Leakage Detection Using Acoustic Emission and Machine Learning Algorithms.

Pipelines play a significant role in liquid and gas resource distribution. Pipeline leaks, however, result in severe consequences, such as wasted resources, risks to community health, distribution downtime, and economic loss. An efficient autonomous leakage detection system is clearly required. The recent leak diagnosis capability of acoustic emission (AE) technology has been well demonstrated. This article proposes a machine learning-based platform for leakage detection for various pinhole-sized leaks using the AE sensor channel information. Statistical measures, such as kurtosis, skewness, mean value, mean square, root mean square (RMS), peak value, standard deviation, entropy, and frequency spectrum features, were extracted from the AE signal as features to train the machine learning models. An adaptive threshold-based sliding window approach was used to retain the properties of both bursts and continuous-type emissions. First, we collected three AE sensor datasets and extracted 11 time domain and 14 frequency domain features for a one-second window for each AE sensor data category. The measurements and their associated statistics were transformed into feature vectors. Subsequently, these feature data were utilized for training and evaluating supervised machine learning models to detect leaks and pinhole-sized leaks. Several widely known classifiers, such as neural networks, decision trees, random forests, and k-nearest neighbors, were evaluated using the four datasets regarding water and gas leakages at different pressures and pinhole leak sizes. We achieved an exceptional overall classification accuracy of 99%, providing reliable and effective results that are suitable for the implementation of the proposed platform.

Acoustics demonstration extravaganza

The Education in Acoustics and Physical Acoustics committees are pleased to present an Acoustics Demonstration Extravaganza - a showcase of demonstrations and apparatus to inspire and challenge your understanding of acoustics and vibration phenomena. In the spirit of the “Circus of Acoustics” demonstration show from the June 2002 ASA 143 Pittsburgh meeting [J. Acoust. Soc., Am., 111, 5, Pt2, p. 2451, (2002) session 4pPAb] this session will consist of several short demonstrations covering a wide variety of acoustics and vibration topics. Among the demonstrations intended to be shown are the following (there may be some last-minute additions or substitutions depending on equipment and presenter availability): Simple Sound Sources: Directory patterns and frequency spectrum characteristics of monopole, dipole, and quadrupole sources, the pressure doubling effect of a baffle, and a beam-forming array. Radiation of Sound from Plates: Demonstration of the radiated intensity from various vibrational modes of a simply supported thin plate. Strings of Pearls: Modes of vibration for a N-DOF mass-spring system and standing waves on a compound string comprised of a two string segments with different densities. Burning Wire of Death: Standing waves on a nichrome wire carrying a high current so it glows red at nodes. The Song of the Singing Rod: The singing rod demonstration is commonly used to describe longitudinal waves in a free-free rod. However, if the length of the rod is adjusted just right, a nonlinear pulsating effect is observed resulting from modal coupling of transverse bending modes and either subharmonic longitudinal modes or torsional modes. Nonlinear Oscillations in a Membrane: A membrane is driven with a large amplitude, so the vibration becomes nonlinear. As the frequency sweeps up and then down, the amplitude jumps and follows a hysteresis loop characteristic of a stiffening nonlinear spring. Demonstration apparatus of the Cochlea (designed by Robert Keolian): A mechanical hydrodynamic analog model of the basilar membrane in the cochlea illustrating von Békésy's classical passive tonotopic traveling wave as an explanation of how the ear responds to different frequencies. Acoustic Resonator Rockets: A pair of lightweight Helmholtz Resonators, balanced on a pivot, will rotate when exposed to a loud amplitude sound at their resonance frequency. Acoustic Filters: An audible and visual demonstration of low-pass, high-pass, and band-stop acoustic filters using PVC pipes. Vocal Tract Models: A collection of short pipes with varying cross-sectional areas (designed by Takayuki Arai) that produce vowel sounds and may be used to model the acoustics of speech. Speed of Sound: A series of short demonstrations that illustrate the effect of temperature on the speed of sound in air, sound speed dependence on gas composition, and the effect of bubbles on the speed of sound in water. Fluid Loading of a Plate: A comparison of the vibration response of a vibrating plate, and the audibly radiated sound, when the plate is in air versus submerged in water. Rectangular Waveguide: Plane waves will propagate down a waveguide without decay at all frequencies, but non-plane wave modes will propagate only if driven above the cut-on frequency. When driven below the cut-on frequency, non-plane modes become evanescent and decay exponentially. Baseball Bat Piano: The hollow cylindrical barrels of metal and composite softball bats exhibit cylindrical shell vibrational modes. A collection of softball bats with hoop-mode frequencies corresponding to a musical scale may be played like a xylophone.

Non-Fermi-Liquid Behavior from Cavity Electromagnetic Vacuum Fluctuations at the Superradiant Transition.

We study two-dimensional materials where electrons are coupled to the vacuum electromagnetic field of a cavity. We show that, at the onset of the superradiant phase transition towards a macroscopic photon occupation of the cavity, the critical electromagnetic fluctuations, consisting of photons strongly overdamped by their interaction with electrons, can in turn lead to the absence of electronic quasiparticles. Since transverse photons couple to the electronic current, the appearance of non-Fermi-Liquid behavior strongly depends on the lattice. In particular, we find that in a square lattice the phase space for electron-photon scattering is reduced in such a way to preserve the quasiparticles, while in a honeycomb lattice the latter are removed due to a nonanalytical frequency dependence of the damping ∝|ω|^{2/3}. Standard cavity probes could allow us to measure the characteristic frequency spectrum of the overdamped critical electromagnetic modes responsible for the non-Fermi-liquid behavior.

Edge-Enabled Heart Rate Estimation from Multisensor PPG Signals.

Heart rate (HR) estimation from multisensor PPG signals suffers from the dilemma of inconsistent computation results, due to the prevalence of bio-artifacts (BAs). Furthermore, advancements in edge computing have shown promising results from capturing and processing diversified types of sensing signals using the devices of Internet of Medical Things (IoMT). In this paper, an edge-enabled method is proposed to estimate HRs accurately and with low latency from multisensor PPG signals captured by bilateral IoMT devices. First, we design a real-world edge network with several resource-constrained devices, divided into collection edge nodes and computing edge nodes. Second, a self-iteration RR interval calculation method, at the collection edge nodes, is proposed leveraging the inherent frequency spectrum feature of PPG signals and preliminarily eliminating the influence of BAs on HR estimation. Meanwhile, this part also reduces the volume of sent data from IoMT devices to compute edge nodes. Afterward, at the computing edge nodes, a heart rate pool with an unsupervised abnormal detection method is proposed to estimate the average HR. Experimental results show that the proposed method outperforms traditional approaches which rely on a single PPG signal, attaining better results in terms of the consistency and accuracy for HR estimation. Furthermore, at the designed edge network, our proposed method processes a 30 s PPG signal to obtain an HR, consuming only 4.24 s of computation time. Hence, the proposed method is of significant value for the low-latency applications in the field of IoMT healthcare and fitness management.

Frequency spectrum analysis of the rotor system with bolted joint: Numerical and experimental verification

The bolted joint is commonly used to connect several parts of aero-engine rotor system. Several papers have studied the nonlinear vibration responses of bolted rotor systems. However, the frequency spectrum characteristics of bolted rotor systems are not fully revealed. Aiming at this issue, this study develops a dynamic model of the bolted rotor system, where the piecewise stiffness characteristic is considered. A solution methodology is presented by incorporating the piecewise stiffness into the incremental harmonic balance method. The effects of unbalance and preload on the dynamic characteristics are discussed. Moreover, the stiffness and damping of the support structure and bolted joint are identified based on the particle swarm optimization algorithm and experimental results. Furthermore, the experimental study on a bolted rotor test rig is conducted to verify the accuracy of the identified parameters and the model. The simulation and experimental results indicate that 3X and 5X of the rotating frequency can be observed. Besides, the rotating speed corresponding to 5X's peak is different from the critical speed, and the peak of 5X precedes the primary resonance peak.