Least Square Complex Exponential Research Articles

Dynamic parameter identification of cold-formed storage rack systems using shaking table test

In this paper, 1:3 scale shaking table tests were performed on three cold-formed steel rack systems with three levels of different heights at the structural laboratory, Yildiz Technical University, to evaluate the factors that affect the dynamic characteristics of the rack systems that are exposed to different excitation frequencies representing the ground motion. The experiments were conducted using a small shaking table designed for this purpose. The dynamic characteristics of the racks were predicted with the help of the signal processing toolbox in MATLAB using the test output data. The results demonstrated that as the mass of the rack structure increases, the rack system vibration frequency caused by external excitation decreases. Also, the damping ratio of the rack systems increases with an increase in the rack height due to the increase in stiffness, and then it starts decreasing because the structure's stiffness begins to decrease with long-term vibration. The modal analysis results demonstrated that the peak-picking (PP) method outperformed the least-squares complex exponential (LSCE) and least-squares rational function estimation (LSRF) approaches in damping estimation. However, each approach achieved nearly identical results for the response frequency in the same mode.

An Investigation of the Vibration Modes of an External Gear Pump through Experiments and Numerical Modeling

This paper presents an experimental and numerical modal analysis for an external gear pump considering its mounting on a test rig in a laboratory setting. Most of the previous studies on experimental modal analysis (EMA) of hydraulic pumps focused on the modal frequencies to allow model validation. However, the mode shapes of pump bodies have not extensively been discussed. Furthermore, the nature of the pump components assembly and mounting poses some modeling challenges, such as the uncertain material properties of each component, the behavior of the bolted joints, and some critical modeling boundary conditions related to pump mounting. In this regard, the experimentally obtained vibration modes of a reference pump using the least-square complex exponential (LSCE) method are analyzed with an emphasis on the characteristics of the mode shapes. Then, simple modeling strategies are proposed and validated by performing the analysis from the component level to the full assembly. As a result, the mode shapes are categorized depending on the type of motions that the modes exhibit. It is observed that the pump casing does not show any substantial deformation but is close to the rigid body motion. Moreover, without considerably increasing model complexities, the proposed numerical approach provides reasonable accuracy with average errors in modal frequencies of 6%, as well as good agreement in terms of mode shapes. The vibration reduction strategy is briefly discussed based on the measured mode shapes, and the proposed modeling approaches can be useful to study external gear pumps with minimal model complexities yet allowing reasonable result accuracy.

Variation of reliability-based seismic analysis of an electrical cabinet in different NPP location for Korean Peninsula

The area of this study will cover the location-wise seismic response variation of an electrical cabinet in nuclear power point (NPP) based on classical reliability analysis. The location-based seismic ground motion (GM) selection is carried out with the help of probabilistic seismic hazard analysis using PSHRisk-tool, where the variation of reliability analysis can be understood from the relation between the reliability index and intensity measure. Two different approaches such as the first-order second moment method (FOSM) and Monte Carlo Simulation (MCS) are helped to evaluate and compare the reliability assessment of the cabinet. The cabinet is modeled with material uncertainty utilizing Steel01 as the material model and the fiber section modeling approach is considered to characterize the section's nonlinear reaction behavior. To verify the modal frequency, this study compares the FEM result with recorded data using Least-Squares Complex Exponential (LSCE) method from the impact hammer test. In spite of a few investigations, the main novelty of this study is to introduce the reader to check and compare the seismic reliability assessment variation in different seismic locations and for different earthquake levels. Alongside, the betterment can be found by comparing the result between two considered reliability estimation methods.

The Recorded Seismic Response of the Santa Maria Di Collemaggio Basilica to Low-intensity Earthquakes

ABSTRACT The seismic response of masonry monumental structures is a debated matter. In this paper, the authors compare the dynamic response of the Santa Maria di Collemaggio basilica under low-intensity earthquakes to the dynamic response under operational conditions. A permanent number of accelerometers records the dynamics of the Santa Maria di Collemaggio basilica under both operational and seismic excitation. It is questioned whether the earthquake intensity and the ambient parameters affect the modal parameters. The Least-Squares Complex Exponential (LSCE) method leads to the FRF function estimation. The stable frequencies identify the linear modal parameters which are likely to reproduce the seismic response. The authors endeavour to discuss whether the detected variations of the modal parameters are due to possible structural or material non-linearities. A time-frequency analysis confirms the results of the linear identification method. Further, the estimate of the dynamic amplification factors gives a glance over the global response by evidencing the possible existence of a macro-element response pattern.

Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet

This paper investigates the modal analysis of wind instruments as seen from the input of their air column. Beside the treatment of analytical models, a particular emphasis is given to the analysis of measured input impedances. This requires special care because the measurements cover only a limited frequency band and are affected by some unknown errors. This paper describes how the Prony analysis and the Least Squares Complex Exponential (LSCE) classical techniques can be used in this context and how the main pitfalls can be avoided in their application. A physically acceptable method of reconstruction of the low frequency band is proposed. A technique using fictitious points in the high frequency range is described in order to ensure the passivity of the resonator in the whole frequency band. The principles of a real-time synthesis of clarinet sounds based on the modal representation of the resonator is given as an application, with a method to efficiently handle the modal representation during the transition between fingerings.

Modal analysis in relation to the casing of an electric power steering system

The article presents the results of modal analysis (experimental and numerical using Finite Element Method - FEM) with reference to the power steering worm drive gear housing. The experimental analysis was performed by the Least Squares Complex Exponential (LSCE) method using a modal hammer equipped with a force sensor which allowed the measurement and recording of the excitation. Numerical analysis was based on the Finite Element Method in PLM Siemens NX 10. Based on results from the experimental modal analysis the FEM numerical model was tuned. The resulting consistency of results led to the conclusion the correctness of the model FEM. The adapted numerical model was used for further analysis with respect to modified power steering worm drive gear housing designs. The obtained results allowed to estimate how the change of the material and adjusting the geometrical form to the strength conditions will affect the frequency and form of the vibration of the modified worm drive gear housing.

Experimental modal analysis of electrical submersible pumps

The dynamic behaviour of an electrical submersible pump (ESP) under operational conditions installed in a test well is investigated by identification of its natural frequency and damping parameters. The study is conducted using an experimental modal analysis technique, the Least Square Complex Exponential (LSCE) method. The excitation was generated at one single point, because of the boundary conditions, by an impact hammer (i.e., single-input, multiple-output, or SIMO, analysis was performed), and the response signals were acquired by accelerometers fixed over the pump housing, thereby characterizing output-only processes. To evaluate the complex exponential function to fit the autoregressive function used to model the impact response function (IRF), auxiliary criteria, the averaged normalised power spectrum density (ANPSD) were used. Results have shown that the ESPs would have natural frequencies within the operational frequency range, from 30 to 62Hz, leading to the operation in resonance conditions.

Chatter stability prediction for CNC machine tool in operating condition through operational modal analysis

The stability of high-speed machining operations is crucial in machining process and presents a key issue for insuring better surface quality, increasing productivity and protecting both machines and safe workpiece. Stability prediction in milling is based on experimental modal analysis by the estimation of frequency response functions using a tap test. One limitation of accurately estimating the stability using such approach is the change in process and the dynamic characteristics of the machine tool under operation. This paper proposes a signal processing procedure applied to vibrations in machining process in order to obtain spindle’s modal variations in operation. The novelty of the proposed approach consists in removing “virtual modes”, caused by harmonic excitations, from the system response before performing operational modal analysis. Thus, the proposed procedure combines two existing techniques that are the Cepstral Editing Procedure and the Least Square Complex Exponential. The importance of the developed methodology is in adjusting the chatter stability criterion for material removal on a dynamic basis. The main work is given as follows: first of all, the Cepstral Editing Procedure (CEP) algorithm is applied on the acceleration signals for removing deterministic vibrations caused by harmonic excitations. The residue signal is the system response to white noise excitation. The frequency response functions (FRF) are then calculated from these signals at different cutting conditions. The outcome is compared to the result of impact test on the spindle under static condition. Similarities in the form of FRFs obtained in static and operational conditions validate the proposed approach while variations of modal properties under different cutting conditions are successfully captured. Secondly, the Least Square Complex Exponential (LSCE) method in operational modal analysis is invoked to find the natural frequencies and damping ratios of the system at different spindle speeds and cutting depths. Then, the dynamic chatter stability lobes diagrams (SLD) are established which account for spindle’s speed-dependent modal variations. A significant change in the stability border is observed which is interesting in machining fields. It will be shown that some depths of cut that are stable with static stability lobes become unstable with dynamic stability lobes and vice versa.

Dynamic Performance Analysis of the Towers of a Long-Span Bridge Based on GPS Monitoring Technique

The present study investigates the parameter identification and the dynamic performance of a long-span bridge tower based on the output of a global positioning system (GPS) health monitoring system. The random decrement (RD) algorithm is used to estimate the tower displacement impulse response. Three methods are applied to extract the dynamic performance including least squares complex exponential (LSCE) method, Hilbert envelope method (HEM), and eigensystem realization algorithm (ERA). Results reveal that the HEM and LSCE method are more suitable to extract fundamental frequency and modal and damping ratios of the tower. Furthermore, the dynamic properties and statistical time series analysis of the GPS measurements illustrate that the traffic loads have a high significant impact on the semistatic and dynamic performances.

A Method for Identification of Machine-tool Dynamics under Machining

Dynamic properties of machine-tool structures are likely to change under machining conditions. Thus, the dynamic parameters obtained by traditional experimental modal analysis in the static state may not characterize accurately the dynamics of the machine tool structure in operation. This paper proposes a new method of so-called AEMA (Active Excitation Modal Analysis) to identify the dynamic modal parameters of a machine tool structure during machining. A random cutting excitation technique realized by cutting a specially designed workpiece is proposed to provide strong and evenly distributed excitation within the frequency range of interest. The surface of the workpiece has a long narrow random zigzag width, which randomizes the resulting cutting forces. The LSCE (Least Square Complex Exponential) method is employed to estimate the modal parameters from just the measured responses. Then an algorithm based on two novel tools, the harmonic frequency fence and the spectrum abruptness ratio, is presented to eliminate the harmonic modes attributed to AC power and rotation frequency. The abruptness ratio is used to detect the basic frequency, and then the fence filters out the harmonic modes caused by peaks at integer multiples of the basic frequency through narrow frequency fence slots followed by a damping ratio limit. Finally, the proposed AEMA method is experimentally validated and shows satisfactory results.

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.

Vega In-Flight Modal Identification with the Operational Modal Analysis Technique

Operational modal analysis is an interesting procedure that allows identification of the modal characteristic parameters of structures excited randomly by environmental loads. In this paper, an existing operational modal technique, the natural excitation technique is studied and implemented to obtain the modal parameters of the Vega launcher excited by in-flight loads during its maiden flight. The modal parameters of the Vega launcher, obtained with the operational modal technique, are compared with those from a finite element model designed for the same flight event. Because the dynamic system is not stationary due to propellant mass loss, modal identification is only possible using a series of linearized models over short periods of time. In this work, the extraction of modal parameters is performed in the time window that shows the highest excitation of mode shapes. The time domain modal analysis method, Least-Squares Complex Exponential, is used to extract the modal parameters from the correlation functions generated by the natural excitation technique. Results show good agreement with the corresponding ones obtained from the finite element model; this demonstrates that the natural excitation technique can be successfully employed for the extraction of modal parameters of launch vehicles during the flight phase.

Modal Parameter Estimation for Underdamped Linear Dynamic Systems

Modal parameter estimation is the estimation of frequency, damping ratio, and modal coefficients from experimental data. Modal analysis techniques are a common method used to determine these properties. The Least-Squares Complex Exponential (LSCE) and the Eigensystem Realization Algorithm (ERA) are one of the popular methods of modal analysis techniques. This paper presents an experimental verification of the LSCE and ERA methods. The investigation focuses on the estimation of natural frequencies, damping ratio and modal coefficients. To investigate this, artificial analytical data were processed in MATLAB environment to estimate the modal parameters. The identified vibration parameters from the LSCE and ERA were compared with the values based on classical dynamic theory, and the natural frequency and damping ratios percent of error were calculated.

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.

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.

Uncertainty in Operational Modal Analysis of Hydraulic Turbine Components

Operational modal analysis (OMA) allows modal parameters, such as natural frequencies and damping, to be estimated solely from data collected during operation. However, a main shortcoming of these methods resides in the evaluation of the accuracy of the results. This paper will explore the uncertainty and possible variations in the estimates of modal parameters for different operating conditions. Two algorithms based on the Least Square Complex Exponential (LSCE) method will be used to estimate the modal parameters. The uncertainties will be calculated using a Monte-Carlo approach with the hypothesis of constant modal parameters at a given operating condition. In collaboration with Andritz-Hydro Ltd, data collected on two different stay vanes from an Andritz-Hydro Ltd Francis turbine will be used. This paper will present an overview of the procedure and the results obtained.

Generalized Eigenvalue Decomposition in Time Domain Modal Parameter Identification

This paper is intended to point out the relationship among current time domain modal analysis methods by employing generalized eigenvalue decomposition. Ibrahim time domain (ITD), least-squares complex exponential (LSCE) and eigensystem realization algorithm (ERA) methods are reviewed and chosen to do the comparison. Reformulation to their original forms shows these three methods can all be attributed to a generalized eigenvalue problem with different matrix pairs. With this general format, we can see that single-input multioutput (SIMO) methods can easily be extended to multi-input multioutput (MIMO) cases by taking advantage of a generalized Hankel matrix or a generalized Toeplitz matrix.

Application of Modal Analysis to Cylinder Structure Based on Random Vibration Test

This paper presents the application of modal analysis and parameter identification using data of random vibration test to a cylinder structure. It is deduced that the impulse response function can be substituted by the cross-correlation function computed directly from the response-only data based on the white noise excitation or broadband input. So the modal parameter identification can be done by the least squares complex exponential (LSCE) method. And the modal parameters are obtained from the random vibration test data by the complex exponential method. Compared with the results of traditional modal test, the results of random vibration test are proved to be correct, and also the feasibility of this idea is proved well.

A UNIFIED MATRIX POLYNOMIAL APPROACH TO MODAL IDENTIFICATION

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue–eigenvector problem as well.