Extract Modal Parameters Research Articles

An investigation into NVC characteristics of vehicle behaviour using modal analysis

NVC characterizations of vehicle behavior is one essential part of the development targets in automotive industries. Therefore understanding dynamic behavior of each structural part of the vehicle is a major requirement in improving the NVC characteristics of a vehicle. The main focus of this research is to investigate structural dynamic behavior of a passenger car using modal analysis part by part technique and apply this method to derive the interior noise sources. In the first part of this work computational modal analysis part by part tests were carried out to identify the dynamic parameters of the passenger car. Finite elements models of the different parts of the car are constructed using VPG 3.2 software. Ls-Dyna pre and post processing was used to identify and analyze the dynamic behavior of each car components panels. These tests had successfully produced natural frequencies and their associated mode shapes of such panels like trunk, hood, roof and door panels. In the second part of this research, experimental modal analysis part by part is performed on the selected car panels to extract modal parameters namely frequencies and mode shapes. The study establishes the step-by-step procedures to carry out experimental modal analysis on the car structures, using single input excitation and multi-output responses (SIMO) technique. To ensure the validity of the results obtained by the previous method an inverse method was done by fixing the response and moving the excitation and the results found were absolutely the same. Finally, comparison between results obtained from both analyses showed good similarity in both frequencies and mode shapes. Conclusion drawn from this part of study was that modal analysis part-by-part can be strongly used to establish the dynamic characteristics of the whole car. Furthermore, the developed method is also can be used to show the relationship between structural vibration of the car panels and the passengers’ noise comfort inside the cabin.

Application of adaptable functional series vector time-dependent autoregressive model for extraction of real modal parameters for identification of time-varying systems

Abstract This paper presents a method for extraction of real modal parameters for identification of time-varying systems using adaptable functional series vector time-dependent autoregressive (AFS-VTAR) model. In the practical application of AFS-VTAR model, both real modal parameters and computational ones may mix together in the identified results. In order to extract the real ones from computational ones, a new method based on the eigen-decomposition of the state matrix constructed in AFS-VTAR is proposed. The efficiency of the proposed method is successfully demonstrated first through numerical simulations applied to a time-varying 3-degree-of-freedom system and then experimentally by applying it to a flexible robot in motion.

An adaptive filtering-based solution for the Bayesian modal identification formulation

The online identification of the dynamic properties of large structures is an integral part of structural health monitoring. The success of any vibration-based condition monitoring system requires a computationally efficient identification procedure with the potential to be used online. Computational efficiency and automation are the two fundamental requirements of an effective identification procedure. In this study, we propose a solution of a Bayesian-based formulation for the online extraction of structural modal parameters using output-only data. The proposed algorithm uses a Bayesian maximum a posteriori (MAP) estimation; the objective function is defined as a posterior probabilistic density estimation of the dynamic parameters obtained from observations. The conditional probability distribution function (PDF) is computed using a Bayesian approach to minimum mean-square estimation. To reduce the computational costs, we propose to employ an adaptive filtering technique where expansion and truncation of the conditional PDF are implemented to consider the measurement time series as finite-order Markov processes. The methodology is validated through analyses of two documented examples. Comparison with traditional identification methods clearly shows the superiority of the proposed algorithm. The findings demonstrate that the Bayesian-based methodology provides reliable modal parameter identification in dynamic systems, even for data with high noise content.

Modal parameter-based Damage Identification in Cylindrical Pipe using Dynamic Response

In the present study, a modal parameter-based technique has been presented to identify damage in steel cylindrical pipes under real measurement condition. For this purpose, an analytical formulation has been presented considering radial vibration of the pipe following Prescott’s equation and the relation of its damage with its dynamic properties has been established. The proposed approach and its efficacy have been numerically illustrated and localization as well as comparative quantification of severity of damage has been performed. The difference of modal parameters between the damaged and undamaged cross section of pipe successfully identifies the location of damage. In laboratory environment, specimens of pipes with various anomalies have been introduced to replicate various damage scenarios. Changes in frequency have been observed and tabulated. Ongoing experiments aim to observe similar outputs for different damage conditions. The accuracy of final methodology will rely on accurate extraction of modal parameters of the specimens.

Laboratory evaluation of a fully automatic modal identification algorithm using automatic hierarchical clustering approach

Earth has been a traditional building material to construct structures in many different continents. In particular, adobe buildings are widely diffused in South America, and in Peru where form part of the cultural identity of the nation. Nowadays, the knowledge of existing adobe buildings is far from a complete understanding of the constructive system and a structural health monitoring (SHM) can quantify and reduce uncertainties regarding their structural performance without causing damage to the buildings. In this process, the implementation of automatic tools for feature extraction of modal parameters is desirable. In particular, the automation is important because, during a long-term monitoring, a huge amount of data is recorded and the direct check of the data of the user is not possible. The present work is focused on the development of an automated procedure for managing the results obtained from the parametric identification method, in particular from the Data-Driven Stochastic Subspace Identification method, which requires an automatic interpretation of stabilization diagrams. The work presents a fully automated modal identification methodology based on the following steps: (i) digital signal pre-processing of the recorded data; (ii) modal parameter identification using models with varying dimensions; (iii) automatic analysis of the stabilization diagram with the application of soft and hard validation criteria and the use of hierarchical clustering approach to eliminate the spurious modes; and (iv) automatic choice of the most representative values of the estimated parameters of each clustered mode: natural frequency, damping and mode shape. The developed algorithm was firstly tested with an inverted steel pendulum to check the accuracy and sensitivity, and subsequently, an earthen wall built in PUCP Structure Laboratory was analysed to determine its dynamic behaviour. The developed algorithm shows high percentages of detected frequencies and high sensitivity to the environmental and structural changes.

Modal identification of Karun IV arch dam based on ambient vibration tests and seismic responses

This paper focuses on the operational modal analysis of the Karun IV dam, the highest concrete arch dam in Iran, based on the responses obtained from ambient vibration tests, which are carried out on the dam during 19 March 2014, and 3 March 2015 earthquake with an epicenter about 133 km northeast of the dam. The non-parametric FDD-Wavelet method is used for identification and extraction of modal parameters including natural frequencies, mode shapes and damping ratios. Nine and four natural frequencies are identified from ambient and seismic responses, respectively. Stabilization diagram and averaged coherence spectrum (ACS) are used to detect and eliminate spurious form true modes. Comparison of the results indicates that identification is performed properly and reliably.

Fully Automated Operational Modal Analysis using multi-stage clustering

The interest for robust automatic modal parameter extraction techniques has increased significantly over the last years, together with the rising demand for continuous health monitoring of critical infrastructure like bridges, buildings and wind turbine blades. In this study a novel, multi-stage clustering approach for Automated Operational Modal Analysis (AOMA) is introduced. In contrast to existing approaches, the procedure works without any user-provided thresholds, is applicable within large system order ranges, can be used with very small sensor numbers and does not place any limitations on the damping ratio or the complexity of the system under investigation. The approach works with any parametric system identification algorithm that uses the system order n as sole parameter. Here a data-driven Stochastic Subspace Identification (SSI) method is used. Measurements from a wind tunnel investigation with a composite cantilever equipped with Fiber Bragg Grating Sensors (FBGSs) and piezoelectric sensors are used to assess the performance of the algorithm with a highly damped structure and low signal to noise ratio conditions. The proposed method was able to identify all physical system modes in the investigated frequency range from over 1000 individual datasets using FBGSs under challenging signal to noise ratio conditions and under better signal conditions but from only two sensors.

Structural health monitoring: a tool for managing risks in sub-standard conditions

In the last decade the number of structural health monitoring (SHM) systems designed and implemented on historic structures increased exponentially. Monitoring perfectly meets principles and guidelines of the recently issued Italian and European seismic codes as it is considered a strategic activity in the knowledge process of historic buildings, in order to understand their structural behavior and have a deeper insight on their health conditions. Thanks to SHM it is possible to intervene on buildings with more confidence (and only when necessary), but also to prevent the execution of intrusive strengthening interventions, in full compliance with the minimum intervention principle, so important in the restoration field. The object of monitoring is to identify, locate and classify type and severity of damages induced by external actions or degradation phenomena and to assess their effects on the structural performance. In this way it is possible to take appropriate measures to reduce the danger of collapse and, when necessary, perform strengthening interventions to improve the structural and seismic capacity. Motivated by the above reasons, the paper provide a contribution to the application of integrated methodologies and techniques, based on SHM, for the assessment and protection of cultural heritage (CH) buildings and existing structures. Selected case studies, equipped with distributed sensors and acquisition systems, allowed the definition and successive validation of SHM as a knowledge-based assessment tool, implemented to: (1) avoid the execution of unnecessary interventions and assess structural vulnerabilities; (2) evaluate intervention needs, following an incremental approach during their execution; (3) control the damage states of buildings in a post-seismic scenario. Monitoring data, automatically processed through dedicated software for static monitoring and automated algorithms for modal parameters extraction, are then used for the assessment of the health conditions and the identification of active damaging processes based on numerical simulations and robust statistical models.

Understanding Power Spectrum Density Transmissibility

Power spectrum density transmissibility (PSDT) is a type of complex frequency domain function proposed recently. It describes the relation between cross-spectra of system outputs. Since PSDTs with same local-reference degree of freedom (DOF) combination but with different transferring output DOFs cross each other at the system’s poles under certain load condition, the functions have been used as the primary data in operational modal analysis (OMA) to extract modal parameters, and such technique is named as PSDT-based OMA (PSDTOMA). Because PSDT is a concept that appears recently, researches on which, especially, in-depth discussions aim at the essence and properties of PSDT are very rare. For appropriate application of PSDTOMA, it is necessary to perform further study on such problem obviously. In this paper, two paths to get PSDT, which, respectively, are referred to as PSDT estimator and PSDT syntheticism, are given firstly; some properties about PSDT are explored based on the PSDT syntheticism, and the relation between PSDT and single reference transmissibility function (STF) is analyzed. Finally, the above conclusions are verified with numerical values and experimental data.

DAMAGE DETECTION IN LARGE STRUCTURES USING MODES SHAPES AND ITS DERIVATIVES

Synopsis: Many techniques for structural damage detection using modal parameters have been developed over few years because the modal parameters are easily obtained from free, forced and ambient conditions. Many of the techniques have shown that mode shape curvature is efficient to localize damage in continuous system. Focusing on the damage detection/localization of typical Indian Railway bridges, in this paper, a numerical model of an existing steel truss Indian Railway Bridge (discrete system) was developed to check the validity of the mathematical model for continuous shear beam. Numerical model was based on the design drawings of the structure and Eigen value analysis was performed to extract modal parameters. Damage was simulated by modifying the member properties of particular truss members. Results demonstrate that change in fundamental mode shape due damage to a member is an excellent indicator of damage localization because it is discontinuous at damage location. Change in higher derivatives (slope and curvature) of the fundamental mode shape is found to have improved sensitivity in damage localization. These results are similar to those of the shear beams. However, the damage signature is different. Further studies are needed to understand such signatures for meaningful application of the method for existing structures.

Dynamic and fatigue performances of a large-scale space frame assembled using pultruded GFRP composites

This paper describes the dynamic and fatigue performances of a large-scale space frame assembled using pultruded glass fiber reinforced polymer (GFRP) composites, with reference to pedestrian bridge application. The experimental structure was assembled by circular hollow section (CHS) GFRP members with the assistance of a novel steel connection system. The results from free vibration tests were analyzed using peak-picking (PP) and stochastic subspace identification (SSI) methods to extract modal parameters, i.e. natural frequencies, damping ratios, and mode shapes. From both experimental and validated FE analysis results, the proposed space frame structure satisfied the standard requirements for pedestrian bridge application in terms of natural frequency. The torsion mode as the first order mode shape can be avoided when the contribution of a bridge deck is considered. Furthermore, the structure was examined with 2.1 million fatigue load cycles and then statically loaded up to failure. The failure load showed no decrease when compared with that of a space frame without fatigue. The structural stiffness and strain of critical compressive members measured at 0.3 million fatigue loading intervals showed no significant variations, indicating that the applied fatigue did not degrade structural components and connections.

Operational Modal Analysis of a wing excited by transonic flow

Operational Modal Analysis (OMA) is a promising candidate for flutter testing and Structural Health Monitoring (SHM) of aircraft wings that are passively excited by wind loads. However, no studies have been published where OMA is tested in transonic flows, which is the dominant condition for large civil aircraft and is characterized by complex and unique aerodynamic phenomena. We use data from the HIRENASD large-scale wind tunnel experiment to automatically extract modal parameters from an ambiently excited wing operated in the transonic regime using two OMA methods: Stochastic Subspace Identification (SSI) and Frequency Domain Decomposition (FDD). The system response is evaluated based on accelerometer measurements. The excitation is investigated from surface pressure measurements. The forcing function is shown to be non-white, non-stationary and contaminated by narrow-banded transonic disturbances. All these properties violate fundamental OMA assumptions about the forcing function. Despite this, all physical modes in the investigated frequency range were successfully identified, and in addition transonic pressure waves were identified as physical modes as well. The SSI method showed superior identification capabilities for the investigated case. The investigation shows that complex transonic flows can interfere with OMA. This can make existing approaches for modal tracking unsuitable for their application to aircraft wings operated in the transonic flight regime. Approaches to separate the true physical modes from the transonic disturbances are discussed.

An improved lower order method of modal parameter estimation for offshore structures using reconstructed signals

For modal parameter estimation of offshore structures, one has to deal with two challenges: 1) identify the interested frequencies, and 2) reduce the number of false modes. In this article, we propose an improved method of modal parameter estimation by reconstructing a new signal only with interested frequencies. The approach consists of three steps: 1) isolation and reconstruction of interested frequencies using FFT filtering, 2) smoothness of reconstructed signals, and 3) extraction of interested modal parameters in time domain. The theoretical improvement is that the frequency response function (FRF) of filtered signals is smoothed based on singular value decomposition technique. The elimination of false modes is realized by reconstructing a block data matrix of the eigensystem realization algorithm (ERA) using the filtered and smoothed signals. The advantage is that the efficiency of the identification process of modal parameters will be improved greatly without introducing any false modes. A five-DOF mass-spring system is chosen to illustrate the procedure and demonstrate the performance of the proposed scheme. Numerical results indicate that interested frequencies can be isolated successfully using FFT filtering, and unexpected peaks in auto spectral density can be removed effectively. In addition, interested modal parameters, such as frequencies and damping ratios, can be identified properly by reconstructing the Hankel matrix with a small dimension of ERA, even the original signal has measurement noises.

Multi-modal signal acquisition using a synchronized wireless body sensor network in geriatric patients.

Wearable home-monitoring devices acquiring various biosignals such as the electrocardiogram, photoplethysmogram, electromyogram, respirational activity and movements have become popular in many fields of research, medical diagnostics and commercial applications. Especially ambulatory settings introduce still unsolved challenges to the development of sensor hardware and smart signal processing approaches. This work gives a detailed insight into a novel wireless body sensor network and addresses critical aspects such as signal quality, synchronicity among multiple devices as well as the system's overall capabilities and limitations in cardiovascular monitoring. An early sign of typical cardiovascular diseases is often shown by disturbed autonomic regulations such as orthostatic intolerance. In that context, blood pressure measurements play an important role to observe abnormalities like hypo- or hypertensions. Non-invasive and unobtrusive blood pressure monitoring still poses a significant challenge, promoting alternative approaches including pulse wave velocity considerations. In the scope of this work, the presented hardware is applied to demonstrate the continuous extraction of multi modal parameters like pulse arrival time within a preliminary clinical study. A Schellong test to diagnose orthostatic hypotension which is typically based on blood pressure cuff measurements has been conducted, serving as an application that might significantly benefit from novel multi-modal measurement principles. It is further shown that the system's synchronicity is as precise as 30 μs and that the integrated analog preprocessing circuits and additional accelerometer data provide significant advantages in ambulatory measurement environments.

Research of complex modal parameters extraction of a multi-degree-of-freedom structure based on similarity search

We present a method for the extraction of modal parameters that could be useful for the parameter identification of complex structural dynamic modes of multi degree of freedom systems that may be subject to environmental load excitations. The approach is linear and in this sense it operates on the basis of the principles suggested by the so-called Rayleigh superposition method. This atoms which have the form of free vibration are constructed. The method combined with MP (Matching Putsuit) and GA (Genetic Algorithm). MP is borrowed to extract every most similar atom to the random decrement of the structure response to identify modal parameters. GA is used to speed up this process. The method is applied on the analysis of model experiments for an FPSO single point mooring system and results are compared against real monitoring data. It is shown that the method is capable of extracting successfully modal characteristics such as complex modal frequency, damping ratio and mode shapes.

Operational modal analysis approach based on multivariable transmissibility with different transferring outputs

In recent years, transmissibility functions have been used as alternatives to identify the modal parameters of structures under operating conditions. The scalar power spectrum density transmissibility (PSDT), which relates only two responses, was proposed to extract modal parameters by combining different PSDTs with different transferring outputs. In this sense, this paper proposes extending the scalar PSDT concept to multivariable PSDT by relating multiple responses instead of only two. This extension implies the definition of a transmissibility matrix, relating the cross-spectral density matrix among the responses at coordinates Z and U with the cross-spectral density matrix among the responses at coordinates Z and K. The coordinates in Z are known as the transferring outputs. By defining the same coordinates K and U, but with different transferring outputs Z, we prove that the multivariable PSDT converges to the same matrix when it approaches the system poles. This property is used to define only one matrix with different multivariable PSDTs with same coordinates K and U, but with different transferring outputs. The resulting matrix is singular at the system poles, meaning that by applying the inverse of the matrix, the modal parameters can be identified. Here, a numeric example of a beam model subjected to excitations and data from an operational vibration bridge test shows that the proposed method is capable of identifying modal parameters. Furthermore, the results demonstrate the possibility of estimating the same modal parameters by changing only the coordinates K and U, providing greater reliability during modal parameter identification.

Modal Parameter Analysis for Underdamped Mechanical Systems

There are many ways to model and to analyze discrete event systems. In general these systems lead to a non-linear characteristic equation description in linear algebra. This paper presents an analytical method for solving the characteristic equation of higher order, which arise when solving ordinary differential equations of motion of rigid body systems with 2 ≤ p° ≤ 10 degrees of freedom. The objective of this work was to express the characteristic equation in the form of product quadratic polynomial, from which the modal components could be found. To validate the model, the modal parameters extraction technique – Ibrahim Time Domain (ITD) – was used to extract modal parameters from artificial data developed in MATLAB environment. The extracted modal components were compared to those obtained from the analytical model.

周方向縮約法を用いた円筒シェル構造物のモード特性同定

For precision improvement of the noise prediction, the dynamic characteristics of structures need to be verified. This paper focuses on modal identification of the cylindrical shell structures. In such structures, vibration modes with complicated shapes exist densely. And structures made of composite material have high damping characteristics. Therefore, the experimental modal parameter extraction is somewhat difficult task. In this study, we investigate modal parameter identification method which is able to be applied to such structures. We propose circumference reduction method based on basis function, and non-linear least squares approach of curve-fitting. The circumference reduction method has an effect of reduction of modal density, so the difficulty of identification is improved. Using a simple cylindrical shell structure, the results of proposed method and FEM modal analysis are compared and evaluated. Furthermore, as an example of a real structure, the modal property of an automobile tire is identified. It is verified that the modal property of cylindrical shell structure can be identified effectively using proposed method.

NUMERICAL PARAMETRIC STUDY ON INTERVAL SHIFT VARIATION IN SIMO-SSTD TECHNIQUE FOR EXPERIMENTAL MODAL ANALYSIS (EMA)

SSTD (Single Station Time Domain) technique is one of the efficient methods used to extract modal parameters of a structure. Instead of extracting the parameters in frequency domain by utilising Fast Fourier Transform (FFT) as used by some other methods, this technique only relies on free decay responses to obtain the required parameters. In this paper, a parametric study on time shift interval on algorithm method is investigated. The accuracy assessment is made using simulated analytical data with known properties where percentage error between the results of simulated and this method can be calculated and compared.

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.