Complex Exponential Method Research Articles

Noise elimination algorithm for modal analysis

Modal analysis is an ongoing interdisciplinary physical issue. Modal parameters estimation is applied to determine the dynamic characteristics of structures under vibration excitation. Modal analysis is more challenging for the measured vibration response signals are contaminated with noise. This study develops a mathematical algorithm of structured low rank approximation combined with the complex exponential method to estimate the modal parameters. Physical experiments using a steel cantilever beam with ten accelerometers mounted, excited by an impulse load, demonstrate that this method can significantly eliminate noise from measured signals and accurately identify the modal frequencies and damping ratios. This study provides a fundamental mechanism of noise elimination using structured low rank approximation in physical fields.

Dynamic Data Driven Approach for Modeling Human Error

Abstract Mitigating human errors is a priority in the designs of complex systems, especially through the use of body area networks. This paper describes early developments of a dynamic data driven platform to predict operator error and trigger appropriate intervention before the error happens. Using a two-stage process, data was collected using several sensors (e.g., electroencephalography, pupil dilation measures, and skin conductance) during an established protocol - the Stroop test. The experimental design began with a relaxation period, 40 questions (congruent, then incongruent) without a timer, a rest period followed by another two rounds of questions, but under increased time pressure. Measures such as workload and engagement showed responses consistent with what is expected for Stroop tests. Dynamic system analysis methods were then used to analyze the raw data using principal components analysis and the least squares complex exponential method. The results show that the algorithms have the potential to capture mental states in a mathematical fashion, thus enabling the possibility of prediction.

Operational modal analysis applied to the concert harp

Operational modal analysis (OMA) methods are useful to extract modal parameters of operating systems. These methods seem to be particularly interesting to investigate the modal basis of string instruments during operation to avoid certain disadvantages due to conventional methods. However, the excitation in the case of string instruments is not optimal for OMA due to the presence of damped harmonic components and low noise in the disturbance signal. Therefore, the present study investigates the least-square complex exponential (LSCE) and the modified least-square complex exponential methods in the case of a string instrument to identify modal parameters of the instrument when it is played. The efficiency of the approach is experimentally demonstrated on a concert harp excited by some of its strings and the two methods are compared to a conventional modal analysis. The results show that OMA allows us to identify modes particularly present in the instrument׳s response with a good estimation especially if they are close to the excitation frequency with the modified LSCE method.

Resonant frequency and Q factor extraction from temporal responses of ultra‐high Q optical resonators

Resonant frequency extraction from time signal simulations of optical resonators is often required to resolve closely spaced resonances in addition to estimating high Q factors. Traditional Fourier transform-based fitting methods thus require very long time signals, limiting their usage. Complex exponential fitting-based methods such as matrix pencil, modified Prony and harmonic inversion provide better accuracy, but each has its own advantages as well as disadvantages. In this study, it is shown that the matrix pencil method is limited by the number of time samples, but provides accurate results, whereas the harmonic inversion method provides less accurate results with high efficiency. The difference formulation of the modified Prony method implemented with multiple precision, while providing the best accuracy, is the least efficient approach and requires careful adjustment of its parameters to obtain a solution.

A Combined Numerical and Modal Analysis on Vertical Vibration Response of Railway Vehicle

In this paper the vertical vibration response of a 9 degrees-of-freedom (DOF) 4-axle freight wagon, modeled as a multi-body system is investigated. The Lagrange's equation is used to obtain the equations of motion, and the corresponding system matrices are then assembled. A combined modal analysis and numerical integration of the convolution integral is adopted, which is achieved by programming a MATLAB script. Modal analysis is used to uncouple the differential equations and thereafter, the convolution integrals are numerically integrated using piecewise constants as interpolating functions. The Complex-Exponential Method (CEM) is then used to extract damping ratio, mode shapes and the system's natural frequencies from test data, this information is then used to compute the numerical solution. The developed models are then validated with measured data.

New Operational Modal Analysis Method of Spindle System Based on Multiple Pulse Excitation

Modal parameters of the spindle system is an important basis for the prediction of processing stability and parameters optimization. Aiming at the difficulty in the implementation of effective incentive for the spindle system, a new operational modal analysis(OMA) method based on multiple pulse excitation is brought forward, pulse excitations are respectively applied on the tool, toolholder and spindle, response and cross-correlation functions of vibration signals are achieved and modal parameters are identified through the poly-reference least square complex exponential(pLSCE) method. False modes derived from the recognition process is removed to improve the accuracy of modal parameters identification by the modal assurance criterion method. Comparative analysis shows that the maximum relative error of the natural frequency and damping ratio is 4.57% and 11.02% respectively and the OMA results are in good agreement with the hammer modal test results. Results indicate the modal parameters of spindle system can be accurately identified by the cross-correlation functions of response signals under multiple pulse excitation, the work provide a new method for OMA of spindle system.

New Analysis Methodology for Dynamic Soil Characterization Using Free-Decay Response in Resonant-Column Testing

AbstractThe resonant-column test is widely used for dynamic characterization of soils under different confinement and shear-strain conditions. The free-decay response of a soil specimen in resonant-column testing shows a nonlinear behavior when the strain levels exceed a threshold shear strain. However, the dynamic parameters are commonly determined assuming a linear single-degree-of-freedom (SDOF) model. This paper presents a new analysis methodology based on the complex exponential method (CEM) for the nonlinear dynamic characterization of soil specimens using the free-decay response in torsional fixed-free resonant-column testing. This analysis methodology represents a solution to the chronic problem of evaluating the dynamic properties of soils while avoiding the negative effects of imposing many loading cycles at strain levels greater than the threshold shear strain, which, in turn, change the original dynamic properties of soil specimens. The effectiveness of the proposed analysis methodology is dem...

Modal Parameters Identification of Civil Engineering Structures Based on the Random Decrement Technique

Modal identification technique is an effective measure for building materials health diagnosis, structural optimization design and safety assessment in structural engineering field. The time-domain method can only use the response signals to identify the modal parameters under ambient excitation, which became a wide concern topic in recent years. According to the points above, the theories of random decrement technique, complex exponential method and time-series method are presented. The random decrement technique is combined with the other two methods to become joint algorithms. A numerical simulation model is constructed to verify the feasibility and validity of the two joint algorithms.

Modal Parameter Identification of Civil Engineering Structures under Seismic Excitations

Modal parameter identification of civil engineering structures under seismic excitations has important implications for health diagnosis, plastic analysis and optimization design of structure. A numerical simulation model of frame construction was carried out. Apply two types of seismic waves on the structure. The seismic excitations are Kobe wave and Shanghai wave which are both generated by actual earthquake records. According to the acceleration response of the layers, the first three order modal parameters can be identified by using complex exponential method. Compared the results with theoretical values, and analyzed the accuracy, the method was considered to have an effective application.

Modal Parameters Identification with Particle Swarm Optimization

The paper presents method of the modal parameters identification based on the Particle Swarm Optimization (PSO) algorithm. The basic PSO algorithm is modified in order to achieve fast convergence and low estimation error of identified parameters values. The procedure of identification as well as algorithm modifications are presented and some simple examples for the SISO systems are provided. Results are compared with the results obtained for Least Square Complex Exponential (LSCE) method.

Structural Modal Parameter Identification Based on Natural Excitation Technique

Natural excitation technique has found an increasingly wide utilization in civil engineering field. Modal parameter identification in time domain method can identify the structural parameters in the use of impulse response data as input data. The theory of NExT method is presented. By constructing a numerical simulation example under white-noise excitation, and calculating the data by NExT method, the modal parameters can be identified according to complex exponential method and time series-method in time domain. The results and analysis indicate the validity of the method and provide a reference for engineering practice.

Simplified evaluation of embankment dam health due to ground vibration using dam health index (DHI) approach

In order to execute dam safety planning, it is necessary to develop a method to monitor dam health, which considers and simulates the actual physical failure processes of an embankment dam. The objective of this study is to monitor the behaviour of the earthen dam during the impact of ground force through experimental modal analysis. The model of an earthen dam was constructed on a steel plate, which could be easily moved by input force. Accelerometers were installed on the model in many positions to measure respondent acceleration. The post-processing data were processed to show signs such as natural frequency and mode shape using the least-square complex exponential method. Natural frequency shifts were tracked throughout the testing period and the effects of the varying water levels were identified. During vibration, the effect of liquefaction observed in tests was found to be the first factor to deteriorate on the upstream side of the embankment model. The measurement position of the accelerometer was found to be very important for the health monitoring of the embankment dam. The proposed dam health index is the comparison of acceleration at the crest and the upstream side in both time and frequency domains which can identify damage to the embankment dam.

Identification of the technical state of suspension elements in railway systems

The running safety and passenger comfort levels in a vehicle are tightly related to the technical state of the suspension elements. The technical state of the suspension depends of the service life time as its components become old and wear out. In this paper, a study on the dynamic behaviour of a railway vehicle is established in relation to the damping elements in one of its suspension stages. An experimental measurement model is developed, obtaining a set of useful signals for the identification of the dynamic parameters of the vehicle and developing a test through the application of the operational modal analysis technique, using least-squares complex exponential method as a basis to validate the numerical model of the multi-body system. Then, the study focuses on developing numerical simulations for the identification of the technical state of the dampers by the registration of dynamic variables under commercial service conditions and on estimating the state of the suspension elements.

Operational modal analysis of a 2.5 MW wind turbine using optical measurement techniques and strain gauges

ABSTRACTThis work presents the results of in‐field tests performed on a 2.5 MW, 80 m diameter wind turbine. During the two test campaigns, dynamic response of the structure was monitored by using three different measurement systems, namely conventional strain gauges, photogrammetry and laser interferometry, whereas the turbine was both at parked condition and rotating. The recorded data were analysed by using an operational modal analysis algorithm based on the least square complex exponential method and several turbine parameters (eigenfrequencies and damping ratios) were extracted. The obtained system parameters were then qualitatively compared with the results presented in a study from literature, which includes both aeroelastic simulations and in‐field measurements performed on a similar size and capacity wind turbine. Copyright © 2012 John Wiley & Sons, Ltd.

The Comparison Investigation of OMA Methods on Time Domain

Operational modal analysis (OMA) is an effective method to identify structural modal parameters from response signal under operational condition. Aiming at the evaluation of different time domain OMA methods in structural modal parameters identification, both numerical simulation and experimental investigation of cantilever beam have been applied to different methods, such as Sparse Time Domain (STD) method, Least Square Complex Exponential (LSCE) method and Eigensystem Realization Algorithm (ERA), etc. The comparison results indicated that ERA is the best one, LSCE method follows and STD method is worst.

Ultrasonic transducers characterisation for evaluation of stiff geomaterials

The pulse velocity test (PVT) is an ASTM standard for the dynamic characterisation of geomaterials such as stiff clays, cemented sands, rooks and concrete. The PVT is based on the first arrival of the compressional wave. The analysis of full waveforms in ultrasonic testing is important in evaluating the variation with frequency of the dynamic properties of materials (phase velocity and material damping). Reliable full waveforms are also required to calibrate numerical simulations for the interpretation of ultrasonic wave propagation in viscoelastic materials. However, the analysis of full waveforms is rarely performed in practice because of the difficulties involved in the characterisation of ultrasonic transducers and their coupling with the medium. This paper presents a new methodology for measurement of the frequency response and impulse response functions of ultrasonic transducers. The proposed methodology uses the complex exponential method to extract dynamic properties from impulse response functions. Ultrasonic tests and numerical simulations are conducted on a calibration aluminium bar and a cemented sand specimen to demonstrate the applicability of the new methodology. The results show that this methodology can be successfully used for dynamic characterisation of ultrasonic transducers for evaluation of the wave velocity and damping ratio of stiff geomaterials.

Second law analysis of porous thermoacoustic stack systems

Abstract The objective of this paper is to analyze the irreversibility of the porous thermoacoustic stacks in terms of entropy generation. Thermoacoustic stacks are modeled in this paper as porous channels having wall with finite thickness. The flow field in the porous channel is described by the Darcy momentum equation. The thermal field inside the porous stack is modeled by volume averaged energy equation with local thermal equilibrium assumption. While the thermal field inside the solid wall is modeled by the heat conduction equation. The entire problem is treated as a conjugate heat transfer problem. The governing momentum equation inside the porous stack and the energy equations inside both porous stack and solid wall are simplified and linearized using a first order perturbation expansion in the low Mach number limit. The linearized governing differential equations are solved using the complex exponential method. Velocity and temperature results thus obtained are applied for subsequent entropy generation analysis. Entropy generation rate is used as a measure of irreversibilities associated with viscous and heat transfer effects in the porous stack region. For the specific thermoacoustic situation considered in this paper, a time-averaged entropy generation rate followed by local and global entropy generation rates are calculated and graphically presented. The entropy generation distribution in the stack thus enables the designers to find and modify the parameters producing high energy losses characterized by large entropy production rates. A limited experimental work is performed to measure the temperature difference generated across the stack ends. A fair qualitative agreement between the experimental and analytical results is obtained.

Application of joint time-frequency distribution for estimation of time-varying modal damping ratio

The logarithmic decrement method has been long used to estimate damping ratios in systems with only one modal component such as linear single degree of freedom (SDOF) mechanical systems. This paper presents an application of a methodology that uses joint time-frequency distribution (JTFD) as input, instead of the raw signal, to systems with several vibration modes. A most important feature of the present approach is that it can be applied to a system with time-varying damping ratio. Initially the precision and robustness of the method is determined using a synthetic model with multiple harmonic components, one of them displaying a time-varying damping ratio, subsequently the results obtained from experiments with a reduced model are presented. A comparison is made between the results obtained with this methodology and those using the classical technique of Least Squares Complex Exponential Method (LSCE) in order to highlight the advantages of the former, such as, good precision, robustness and excellent performance in extreme cases, e.g., when very low frequency components and time varying damping ratio are present.

ModalCAD—Interactive Dynamic Characteristic Identification Software for Experimental and Operational Modal Analysis of Engineering Structures

Abstract In this paper the development of interactive and comparative dynamic characteristic identification software titled as the ModalCAD is described. The software is developed for vibration monitoring of civil engineering structures and constructed by using MATLAB, which is a mathematical tool developed by The Mathworks. The modal analysis of structures consists of four distinct steps: Data collection, digital signal processing, determination of the modal parameters (eigenfrequencies, damping ratios, mode shapes, and modal scaling factors) with modal data presentation/validation and model updating. The ModalCAD software is a powerful tool that deals with modal parameter identification and validation procedure. The ModalCAD offers extensive functionalities for the visualization and processing of the measurement data, the identification of system models, and the determination and visualization of the structure’s modal parameters. The program disposes of a graphical user interface, which what makes it very intuitive and easy to handle. The most common modal parameter estimation techniques have been used in the ModalCAD. The Operating Vectors method, Complex Exponential method, and Polyreference Time Domain method are implemented in a user-friendly way. By pushing buttons the user is guided through the whole process of input-output and output-only modal analysis: Preprocessing the data, system identification, extracting modal parameters, animating mode shapes, and evaluating model validation tools. The possibilities of the program are demonstrated with a three dimensional frame model. It can be said that the ModalCAD software can be used as a scientific tool in future structural health monitoring studies of researchers.

Traditional and operational modal testing of masonry vaults

This paper discusses the practical and technical differences between the usual form of experimental modal analysis (EMA) and operational modal analysis (OMA), as applied to Gothic-style masonry vaulted structures. In situ vibration measurements were collected from the masonry fan vaults of the National Cathedral in Washington, DC, USA. Instrumented impact hammer excitation was used during the experimental traditional modal analysis (TMA) tests, while excitation by peal bells, carillon bells, organ, an orchestra and chorus, and ambient noise were exploited for OMA. The acoustic inputs of the first four excitation types were measured using a microphone and were found to approximate a uniform acoustic excitation across the frequency bandwidth of interest during the carillon and the orchestra and chorus excitations. For both TMA and OMA, system identification was completed by the least-squares complex exponential method. The natural frequencies were found to be consistent for all excitation sources and modal test techniques. Certain natural frequencies found by TMA, however, were omitted from the sequence of frequencies as determined in the OMA. This paper illustrates that OMA is a suitable alternative to global vibration analysis of a masonry building, especially when there are concerns about the use of a hammer or shaker for this purpose.