Time-varying Natural Frequencies Research Articles

Hybrid coupling rules for leaderless heterogeneous oscillators: Uniform global asymptotic and finite-time synchronization

We investigate the engineering scenario where the objective is to synchronize heterogeneous oscillators in a distributed fashion. The internal dynamics of each oscillator are general enough to capture their time-varying natural frequency as well as physical couplings and unknown bounded terms. A communication layer is set in place to allow the oscillators to exchange synchronizing coupling actions through a tree-like leaderless network. In particular, we present a class of hybrid coupling rules depending only on local information to ensure uniform global practical or asymptotic synchronization, which is impossible to obtain by using the Kuramoto model customarily used in the literature. We further show that the synchronization set can be made uniformly globally prescribed finite-time stable by selecting the coupling function to be discontinuous at the origin. Novel mathematical tools on non-pathological functions and set-valued Lie derivatives are developed to carry out the stability analysis. The effectiveness of the approach is illustrated in simulations where we apply our synchronizing hybrid coupling rules to models of power grids previously used in the literature.

Stability enhancement and chatter suppression in continuous radial immersion milling

For continuous radial immersion milling operations, the dominant mode shape becomes difficult to determine when stiffness of the tool and workpiece are comparable, and this can pose a great challenge for ensuring machining processes stability. In this paper, we propose a rapid method to obtain time-varying modal parameters of the workpiece by combining experimental measurements with the receptance coupling method. Firstly, the contact parameters between the workpiece and vise were identified by a so-called dynamic coupling matrix. Then the mode shapes and the time-varying natural frequency of the workpiece were determined using the modal parameters of workpiece. Finally, the stability lobe diagrams (SLDs) were computed using the modal parameters and then were validated by undertaking immersion milling experiments. The experiments showed a more conservative and practical SLD for general workpiece under continuous radial immersion, where the workpiece mode had not always dominated the machining process. Based on the proposed method, we also explored two modifications in form of additional cylinder masses and passive support, to suppress chatter. Both modifications were effective in enhancing the minimum boundary of the conservative SLD, and the modification of passive support worked better. Although the modification of the workpiece could improve the stability boundary, it indirectly affected the dynamics of the milling tool through the interaction area between the workpiece and milling tool.

Investigation of time-varying natural frequencies of high-rise buildings under harsh excitations using a high-resolution combined scheme

High-rise buildings subjected to harsh excitations like typhoons or earthquakes usually present nonlinear features and exhibit time-varying behavior of structural modal properties. Under such circumstances, variation in structural natural frequencies can serve as a critical indicator for structural condition assessment. However, limited by noises contained in measurement records and time-frequency resolution of signal analysis, most instantaneous frequency identification methods are difficult to provide accurate estimation of time-varying natural frequencies of high-rise buildings. To address this issue, a combined scheme based on the variational mode decomposition method and adaptive superlets transform (VMD-ASLT) for time-varying natural frequency identification is presented in this paper. Through numerical simulation studies and field measurements of dynamic responses of a 508 m high skyscraper, the noise robustness and accuracy of the combined scheme for time-varying structural natural frequency estimation are validated. Moreover, the combined scheme is further utilized to investigate the time-varying features of natural frequencies of the skyscraper under typhoon and earthquake excitations. This paper aims to provide an effective tool for time-varying structural natural frequency estimation and further reveal the variation of the dynamical behavior of high-rise buildings under harsh excitations.

Instantaneous modal identification under varying structural characteristics: A decentralized algorithm

One of the latest trends in structural health monitoring involves the use of wireless decentralized sensing systems, developed to reduce costs and speed up the whole monitoring process. The main purpose of this paper is to present a novel decentralized procedure for the instantaneous modal identification of time-varying structures, also suitable in the presence of environmental variations and non-stationary ambient excitation. In particular, a modal assurance criterion (MAC)-based clustered filter bank (CFB) is obtained, capable of decomposing structural responses into modal components for the evaluation of time-varying natural frequencies and modal shapes through a nonlinear energy operator. The proposed algorithm is relatively simple and usable with low-cost smart sensing systems, as it requires low computational effort and works with few data at a time. To prove the effectiveness of the presented method, a simulated near-real-time modal identification procedure has been performed on a full-scale bridge under progressive damage scenarios. The estimated modal parameters have then been used for damage diagnosis. The results reveal a good correspondence between identified modal parameters and reference values, showing also promising outcomes for both damage detection and localization.

Synchronization of Kuramoto Oscillators: A Regional Stability Framework

We develop a novel regional stability analysis framework based on the proposed region-parametrized Lyapunov function to study the synchronization of Kuramoto oscillators. A new synchronization definition is introduced and characterized by frequency boundedness and phase cohesiveness, the latter of which requires phase angles of any two connected nodes rather than any two arbitrary nodes to stay cohesive. This definition allows for time-varying natural frequencies and can lead to less conservative synchronization condition. Applying the analysis framework to Kuramoto oscillators, we derive two algebraic synchronization conditions that relate the underlying network topology and system parameters to the synchronization. Finally, we give estimations of the region of attraction explicitly in terms of phase angles as well as the energy function. They require no calculation for critical equilibrium points compared to traditional methods for power systems. The numerical example shows that two synchronization conditions can complement each other for predicting the synchronization.

Analysis of Dynamic Characteristics of a Propeller Blade Subjected to Large Material Removal in Milling

A propeller blade, as a typical example of low-rigidity components, is prone to chatter and deformation in machining process, especially when large material removal is applied. In order to foresee the problems and then optimize the process, identification of the dynamic behavior of the workpiece is of great importance. This paper studies the dynamic characteristics of the workpiece in the machining process from plate to propeller blade using Finite Element Method. The results show that the time-varying natural frequencies of the workpiece decrease gradually at the beginning steps of the process due to the influence of material removal, and increases afterwards influenced by the geometry of the blade.

Development of a sweeping Helmholtz resonator for noise control

Helmholtz resonators (HRs) are widely used to reduce narrow frequency band noise. In this paper, by using microphone and loudspeaker in HR as sensor and actuator, a sweeping HR with time-varying natural frequency, which can eliminate the complexity of changing the physical dimension of HR during operation, is developed. The natural frequency of the HR is continuously swept by using a time-varying Proportional-Integral (PI) controller. The main advantage of the proposed sweeping HR is without requiring of the accuracy value of the targeted control frequency. Finally, the experimental results are presented to verify the control performance of the proposed sweeping HR. Noise reduction of 6 dB in the 120–170 Hz band was obtained when one sweeping HR was installed in a rigid duct.

Making good use of structural health monitoring systems of long-span cable-supported bridges

Many long-span cable-supported bridges have emerged in recent years, but are exposed to harsh environment conditions. The installation of long-term structural health monitoring (SHM) systems to the bridges has become a trend to monitor their loading conditions, assess their performance, detect their damage, and guide their maintenance with the utmost goals of ensuring their functionality, safety and sustainability. Nevertheless, it is not very clear how to make good use of SHM systems toward these goals. This paper takes the Tsing Ma suspension bridge in Hong Kong as an example and recapitulates the relevant works done by the author and his colleagues and students in the past 20 years to manifest how the SHM system installed in the bridge has been utilized since 1997. The SHM system installed in the bridge is briefly introduced first. How to use the SHM system for investigating highway loading, railway loading, wind characteristics, and temperature effects is then presented. Identification of time-varying natural frequencies and modal damping ratio of the bridge under strong winds using the data recorded by the SHM system is also demonstrated. Toward the performance assessment and damage detection of the bridge, SHM system-based computer simulation and damage assessment are targeted and some typical examples are given. The establishment of SHM system-based bridge rating system for bridge maintenance is also briefly introduced.

Active fault-tolerant linear parameter varying control for the pitch actuator of wind turbines

This paper proposes a fault-tolerant control method using the virtual actuator for the problem of the pitch actuator failure. The simplified second-order transfer function of the pitch actuator is transformed into the identification equation using the Euler transformation. For the purpose of fault estimation, a least-squares batch identification algorithm is adopted to estimate the time-varying natural frequency and damping ratio. Then, according to the convex decomposition theory, the nonlinear model of wind turbines is converted to a linear parameter variation model. The fault-tolerant control structure of the virtual actuator is obtained by applying the state feedback law. In the light of the polyhedral approximation theory, an infinite number of linear matrix inequalities can be transformed into a finite number of linear matrix inequalities. The feedback controller is obtained after solving finite linear matrix inequalities. Finally, the simulation results show that the fault-tolerant control method with the fault estimation is capable of handling the pitch actuator failure and maintaining a constant power output.

Fault Estimation and Fault-Tolerant Control of Wind Turbines Using the SDW-LSI Algorithm

The dynamic response of the pitch angle slows down when the pitch actuator of wind turbines fails, and the fault leads to fluctuations in the generator speed and in the output power. According to identification and analytical theories, a fault-tolerant control combined with fault estimation is proposed to solve this problem. The simplified two-order transform function of the pitch actuator is transformed into the identification equation by means of the Euler transformation method. Next, the time-varying natural frequency and the damping ratio of pitch actuators are regarded as gradual change and abrupt change parameters; these two parameters are estimated using the proposed sliding data window least squares-based iterative (SDW-LSI) identification algorithm. The sliding data window length is adjusted when changes in the system parameters are detected. Then, according to analytical theory, a compensation equation is derived in the pitch actuator, and the estimated values are fed back to the compensation module to adjust the relations before and after fault occurrences in the pitch actuator to eliminate the effects caused by the pitch actuator failure. Finally, the feasibility of the SDW-LSI algorithm is validated by choosing the fault of high air content in the hydraulic oil.

Vibration-based damage identification of reinforced concrete member using optical sensor array data

To detect and locate the structural damage from direct measurements can be done only when the sensors are very closely located to the damage initiating point, which is generally impossible to predict, particularly for the reinforced concrete structures. With the availability of high-resolution distributed sensing, using optical tracker on light targets, the damage location as well as the level of damage can be identified. The objective of this article is to conduct structural system identification of a reinforced concrete frame by using the proposed structural integrity index (identify the element curvature and null-space damage index) and the estimation of finite element strain. Finally, a discussion on the identified time-varying system natural frequency and stiffness/strength degradation of the reinforced concrete structure from global measurement in relation to the calculated structural integrity index using optical sensing array data and element strain on the identification of damage location and damage severity are presented.

Structural damage assessment using output-only measurement: Localization and quantification

In this article, a systematic way of structural damage assessment algorithm, including identification of damage location and damage quantification, is proposed using output-only measurement. First, the null-space-based and subspace-based damage detection methods are used to confirm the damage severity of a structure. Then, the stochastic subspace identification technique is adopted to identify the time-varying system natural frequencies from the global response measurement. Finally, the novelty index, defined as the Euclidean norm of the time–frequency Hilbert amplitude spectrum of measurement between the intact and the damaged structures, is applied to locate the damage. To quantify the damage, the complete system realization is obtained from the identified modal properties through stochastic subspace identification method. From which, the inter-story stiffness reduction ratio can be identified using the normalized stiffness matrix. For case of limited measurement, the multi-setup operational modal analysis is applied to construct the complete system matrix. Verification of the proposed damage assessment algorithm using response data from a series of shaking table test of a six-story steel structure with the cut in column member to simulate the damage is demonstrated.

Instantaneous frequency identification of time-varying structures by continuous wavelet transform

A method based on the wavelet ridges of continuous wavelet transform is proposed for the instantaneous frequency identification of time-varying structures. To eliminate noise effect, a penalty function is imposed first, and then the dynamic optimization technique is implemented for wavelet ridge extraction. The instantaneous frequencies are then identified from the extracted wavelet ridges. To validate the proposed method, a numerical example of a two degree-of-freedom spring–mass–dashpot system with time-varying stiffness is studied. The numerical results indicated that the proposed method is efficient in extracting wavelet ridges and tracking the instantaneous frequencies of the time-varying system even the numerical responses are contaminated by 10% Gauss white noise. An experiment on the cable with varying tension force is set up in the laboratory. The time-varying natural frequency is achieved by applying linear and sinusoidal varying tension forces respectively. The instantaneous cable frequencies are then identified by the proposed method. The experiment results further verified that the proposed method can effectively identify the instantaneous frequencies of time-varying structures with a high accuracy.

The Prediction of Nonlinear Responses and Active Stiffness Control of Moving Slender Continua Subjected to Dynamic Loadings in a Vertical Host Structure

Slender continua such as long ropes, cables and belts are used as tension and payload-carrying members in various engineering applications. They are deployed in terrestrial mine/underground equipment and high-rise building installations through to tethered offshore tension members, tethered space satellite systems and rotating momentum exchange tethers in Earth’s orbit. The slender continua are inherently non-linear and this leads to large non-linear responses with passages through resonances taking place when the time-varying natural frequencies of the system approach the frequency of the inertial load resulting from the dynamic loadings. In this paper the lateral nonlinear dynamic behaviour of long slender continua moving at speed in a tall host structures is analyzed. A mathematical model comprising nonstationary nonlinear ordinary differential equations is used to describe the dynamic behaviour of the system equipped with a multi-modal active stiffness controller. The active control is implemented by an axial motion of the support which results in substantial reduction of the response

Recursive Hilbert-Huang Transform Method for Time-Varying Property Identification of Linear Shear-Type Buildings under Base Excitations

This paper presents a recursive Hilbert-Huang transform method for the time-varying property identification of shear-type buildings under base excitations. To overcome nonorthogonality and modal perturbation issues, all significant intrinsic mode functions of each signal and their Hilbert transforms were summed to track any variation of structural parameters of a multistory building over time. Given floor masses, both the stiffness and damping coefficients of the building were identified one by one from the top to bottom story. The overall accuracy of the identified parameters was measured by an index of accuracy based on the weighted root-mean-squared evaluation proposed in this study. One- and two-story shear buildings with abruptly, gradually, and periodically varying parameters were used as examples. The numerical results indicated that the proposed method is efficient, robust, and accurate in tracking variations of the properties of multistory buildings. Finally, the proposed method was applied into the identification of the time-varying natural frequency of a real-world high-voltage switch structure due to the friction mechanism used in the switch. The range of the identified frequency by the proposed method was in good agreement with that attained by the conventional least-squares method.

Structural damage diagnosis based on on-line recursive stochastic subspace identification

This paper presents a recursive stochastic subspace identification (RSSI) technique foron-line and almost real-time structural damage diagnosis using output-only measurements.Through RSSI the time-varying natural frequencies of a system can be identified. Toreduce the computation time in conducting LQ decomposition in RSSI, the Givensrotation as well as the matrix operation appending a new data set are derived. Therelationship between the size of the Hankel matrix and the data length in each shiftingmoving window is examined so as to extract the time-varying features of the systemwithout loss of generality and to establish on-line and almost real-time systemidentification. The result from the RSSI technique can also be applied to structuraldamage diagnosis. Off-line data-driven stochastic subspace identification was usedfirst to establish the system matrix from the measurements of an undamaged(reference) case. Then the RSSI technique incorporating a Kalman estimator isused to extract the dynamic characteristics of the system through continuousmonitoring data. The predicted residual error is defined as a damage feature andthrough the outlier statistics provides an indicator of damage. Verification ofthe proposed identification algorithm by using the bridge scouring test data andwhite noise response data of a reinforced concrete frame structure is conducted.

Generalising the Kuramoto model for the study of neuronal synchronisation in the brain

In this article, we have generalised the Kuramoto model to allow one to model neuronal synchronisation more appropriately. The generalised version allows for different connective arrangements, time-varying natural frequencies and time-varying coupling strengths to be realised within the framework of the original Kuramoto model. By incorporating the above mentioned features into the original Kuramoto model one can allow for the adaptive nature of neurons in the brain to be accommodated. Extensive tests using the generalised Kuramoto model were performed on a N = 4 coupled oscillator network. Examination of how different connective arrangements, time-varying natural frequencies and time-varying coupling strengths affected synchronisation separately and in combination are reported. The effects on synchronisation for large N are also reported.

Application of the Empirical Mode Decomposition-Hilbert Spectrum Method to Identify Near-Fault Ground-Motion Characteristics and Structural Responses

In this article, the empirical mode decomposition method combined with the Hilbert spectrum method (EMD + HHT) is used to analyze the free-field ground motion and to estimate the global structural property of building and bridge structure through the measurement of seismic response data. The EMD + HHT method provides a powerful tool for signal processing to identify nonlinear and nonstationary data. Based on the decomposed ground-motion signal, the absolute input energy of each decomposed wave was studied (the fling step [pulselike wave] can be separated from the recorded near-fault ground motion). Through application of the EMD + HHT method to building and bridge seismic response data, the time-varying system natural frequency and damping ratio can also be estimated. Damage identification from seismic response data of buildings and bridges, particularly from the Chi-Chi earthquake data, is also described. Manuscript received 31 July 2000.

A New Wave Technique for Free Vibration of a String With Time-Varying Length

We introduce a new technique to analyze free vibration of a string with time-varying length by dealing with traveling waves. When the string length is varied, the natural frequencies and vibration energy are not constant. Thus, free response is not represented by discrete standing waves but by traveling waves, and a given phase of oscillation travels along the string. String tension and nonzero instantaneous transverse velocity at the moving boundary results in energy variation. When the string undergoes retraction, free vibration energy increases exponentially with time, causing dynamic instability. The new wave technique gives the time-varying natural frequency and the exact amount of energy transferred into the vibrating string at the moving boundary.

Dynamic stability analysis of a closed-loop flexible link mechanism

This paper presents an efficient and accurate stability analysis method for a closed-loop flexible mechanism. Based on single link modes, the modal properties of a flexible mechanism are derived from the second order perturbation method. Since the low mode shapes of the flexible mechanism become time-invariant, the equations of motion can be decoupled using these modes, regardless of the curve veering. Therefore the stability of the flexible mechanism can be analysed efficiently for each mode. Also the relationships between the instability conditions and the time-varying natural frequency are derived from in detail investigation on the monodromy matrix. In this proposed stability analysis method, unstable regions can be found out efficiently for each mode through doing the stability analysis only at a few speeds satisfying Ω = ω dash i/m or Ω = ω dash /(m + 1 2 ) within the operating range of interest. Also the ranges of unstable regions are determined from the derived relations without doing the secondary stability analysis in the neighborhood of Ω = ω dash i/m or Ω = ω dash i/(m + 1 2 ) . Numerical results of a flexible four-bar mechanism are compared with those from several existing methods to verify the numerical efficiency and accuracy of the proposed method.