Parameter identification of linear structural dynamic systems

In this study, a frequency domain framework for estimating simultaneously the modal parameter and input load from the measured (modal) response of multi degree of freedom(MDOF) system is proposed. It is a technique to identify the modal and load model parameters, by theoretically developing a mathematical input model, and comparing it with the identified load from the assumed modal parameters. The proposed technique has inherent difference to the conventional modal identification in that it can effectively treat the shape of the load spectrum. In order to verify the estimation method proposed in this study, it was applied to a SDOF analytic model. From the simulation results, it was found that this technique has high reliability of modal parameter estimation and immunity to noise included in the response. It can be seen that it has robustness to the load model order and can stably estimate the model parameters. Furthermore, it is needed that this technique can be applied in various load conditions such as vortex induced load and buffeting load of full scale structure, later.

Modal parameter identification via ambient vibration is popular but faces challenges from uncertainties due to unknown inputs and low signal‐to‐noise ratio. Bayesian methods are gaining increasing attention for operational modal identification due to their ability to quantify uncertainties. However, improvements in computational efficiency are needed, particularly when addressing numerous modes and degrees of freedom. To address this challenge, this study proposes an innovative approach, termed the “Bayesian spectral decomposition” method (BSD), employing the decompose‐and‐conquer strategy. This novel method, operating within the frequency domain, identifies each mode individually by exploiting their inherent separated modal characteristics. For each mode, the response spectrum matrix undergoes an eigenvalue decomposition, yielding crucial eigenvalues (incorporating frequency and damping information) and eigenvectors (containing mode shape information). Subsequently, statistical properties of the eigenvalues and eigenvectors are utilized to establish likelihood functions for Bayesian parameter identification. By combining prior information, the posterior probability distribution functions of modal parameters are derived. The optimal solution is then obtained by resolving the maximum posterior probability distribution function problem. To further quantify the uncertainty of modal parameters, Gaussian distributions are employed to approximate the posterior probability distribution functions. The adoption of the decomposition approach circumvents the joint identification of all modal parameters, substantially reducing the parameter dimensions for optimization. Consequently, this strategy leads to decreased computational complexity and significantly improved computational stability. The effectiveness of the BSD is confirmed through simulated data generated from an 8‐story shear building as well as measured data collected from both an experimental shear frame and the Canton Tower. The results demonstrate that the proposed method achieves high accuracy in identifying modal parameters, greatly improves computational efficiency, and effectively quantifies the uncertainties in modal parameters.

This research focuses on the time-domain identification of modal parameters using impact response excitation from signals with a relatively small dynamic range and high noise contamination (e.g., from high-speed cameras). The information required to identify the modal parameters is limited and is contained mostly at the beginning of the signal. In order to perform an identification from such a response, the following challenges have to be overcome: a good frequency-domain separation (for close modes), a good localization in the time domain and an over-determination (to reduce uncertainty). To overcome these challenges this research introduces the Morlet-wave modal identification method as an extension of the Morlet-wave damping identification method, which has already proven capable of identifying the damping of short signals. Here, the method is extended to the modal parameters and an over-determination approach is proposed to reduce the uncertainty. The method identifies each mode shape separately from 10 to a maximum of 400 oscillations and at damping levels from 0.02% to 2% with a strong presence of noise in the signal. The method is tested on an experimental example and the results are compared to the classical modal identification methodology.

The equations of motion of structures with elastic and viscoelastic materials in the time domain are derived. The development is consistent with finite element formulations and leads to systems of equations where the matrices are symmetric, real, and composed of constant coefficients. Four-parameter fractional derivative models are used to model the frequency dependence of the linear viscoelastic materials since experimental data can be fitted successfully over wide frequency ranges. The resulting equations of motion are known as the elastic-viscoelastic equations of motion. Numerical procedures for solving the elastic-viscoelastic equations of motion in the time domain are developed. The closed-form, steady state solution of a single degree of freedom system is obtained in the frequency domain and is used to validate the results obtained by using the numerical procedures. The dynamic response of a multi-degree of freedom structure is obtained by using the numerical procedures.

Monitoring Structural Health Using a Probabilistic Measure

The presented research is focused on a derivation of a mathematical model of a passenger wagon based on a dynamical model in a plane with three degrees of freedom. Vertical oscillation of a passenger wagon is calculated in two different software, namely Matlab and Simpack. It is considered that three degrees of freedom are defined as following: a vertical deflection of a front bogie frame, a vertical deflection of a rear bogie frame (in a running direction) and a vertical deflection of a wagon body. The Lagrange’s equations of the second kind method is used for a derivation of the equations of motion, i.e. for a derivation of a mathematical model of wagon oscillation. Subsequently, the derived equations of motion are solved in the Matlab software as well as in the Simpack software. Both software apply calculation in a time domain. Evaluation of the results is focused on an investigation of ride comfort for passengers. This ride comfort is expressed by the NMV index calculated in five points on a wagon body floor. These calculations come from the formulation defined in the corresponding standard. The results of the NMV indices are presented in the bar graphs based on the numerical values of the NMV indices.

This paper presents a dynamic variable structure system and its controller design conditions. The dynamic variable structure system, which is a class of hybrid dynamic systems, consists of plural subsystems which are switched by switching conditions. A key feature of the dynamic variable structure system is that each subsystem can have different degrees of freedom. In this paper, we employ switching fuzzy models to represent the nonlinear subsystem's dynamics, switching conditions and conservation laws with respect to states, momentum and/or energy of the system. We derive controller design conditions for dynamic variable structure systems.

A global multiple-input multiple-output modal parameter scheme is employed with the frequency response function (FRF) matrix, to accurately estimate modal parameters of the closely coupled modes of a flexible disk-flexible shaft system from simulated data. The Lagrangian approach is combined with the assumed mode method to derive the governing equations of motion, where the uncoupled disk and shaft modes are employed as the assumed functions. The corresponding state space equations are obtained, which were integrated to provide response at points of interest (output, or response degrees of freedom) due to excitation at desired points (input, or excitation degrees of freedom). Random noise is added to the obtained time signal to simulate actual vibration measurements. The excitation and response time signals are used to generate the corresponding FRF matrix, used in the modal parameter estimation scheme. The extracted modal parameters are found to be in excellent agreement with theoretical results.

Accurate and timely identification of modal parameters of long-span bridges is important for bridge health monitoring and wind tunnel tests. Wavelet analysis is one of the most advantageous methods for identification because of its good localization characteristics in both time and frequency domain. In recent years, the wavelet method has been applied more frequently in parameter identification of linear and nonlinear systems. In this article, based on wavelet ridges and wavelet skeleton, the improved modal parameter identification method was studied. To find the appropriate time-frequency resolution, an optimal wavelet basis design principle based on minimum Shannon entropy was proposed. Aiming at endpoint effect in wavelet transform, a prediction continuation method based on support vector machine (SVM) was proposed, which can effectively suppress the endpoint effect of the extended samples. In view of the fact that the ridges of metric matrices obtained by the traditional crazy climber algorithm cannot fully reflect the distribution of ridges of modulus value matrices of wavelet coefficients, an improved high-precision crazy climber algorithm was put forward to accurately identify the position of the ridge of wavelet coefficients. Finally, taking a long-span cable-stayed bridge and a long-span suspension bridge as the engineering background, improved continuous wavelet transform (CWT) was applied to modal parameter identification of bridge under ambient excitation. The modal parameters such as modal frequency, damping ratio, and mode shape were obtained. Compared with the calculation value of the numerical simulation of long-span cable-stayed bridge and wind tunnel test of long-span suspension bridge, the reliability of CWT for modal parameter identification of long-span bridges under ambient excitation was verified.

If a system and its observation are both represented in state space with linear equations, the system noise and the measurement noise are white, Gaussian, and mutually uncorrelated, and the system and measurement noise statistics are known exactly; then, a Kalman filter (KF) [1] with the same order as the system provides optimal state estimates in a way that is simple and fast and uses little memory. Because such estimators are of interest for designers, numerous linear and nonlinear problems have been solved using the KF, and many articles about KF applications appear every year. However, the KF is an infinite impulse response (IIR) filter [2]. Therefore, the KF performance may be poor if operational conditions are far from ideal [3]. Researchers working in the field of statistical signal processing and control are aware of the numerous issues facing the use of the KF in practice: insufficient robustness against mismodeling [4] and temporary uncertainties [2], the strong effect of the initial values [1], and high vulnerability to errors in the noise statistics [5]-[7].

The technique for identification (determination of the parameters) of the model of high-pressure discharge lamp by comparing the simulated and experimental data was developed. Searching for the model parameters is divided into two main stages: 1) determining the degree of influence of each parameter change on the model output; 2) directly searching for the minimum functional divergence. Divergence evaluation is carried out by determining the value of the functional - the sum of the squares of divergences during the studied time period. When searching for minimum divergence, a corresponding set of model parameters is determined. The technique for determining the parameters of the mathematical model of high-pressure discharge lamp was designed to determine such parameters of the model, which allow to describe it with the necessary precision. Trial computational experiment showed the performance of the model parameter determination program, developed using the technique. It was found that the models that are based on the current-voltage characteristics of lamps are promising. The need to determine the model parameters is caused by the requirement for the accuracy of the research, and the availability of regular deviations in characteris­tics of lamps of the same type from different manufacturers, batches and even between units in batches from that of manufacturers and general. Ensuring the model accuracy is also important in developing and creating complex control systems that can be realized with microprocessor control, where the model is used for calculating the control object behavior and selecting control signals.

The onset of a typical bacterial growth curve shows a period of very slow increase in population counts. This is a period of physiological adaptation to new environmental conditions. While in mathematical biology much progress was made in recent years to describe physiologically structured populations, these models typically have too many degrees of freedom to easily allow a model identification against experimental data. Therefore, and for all practical purposes, microbiologists have proposed simpler models of physiological adaptation in the past, usually in connection with standard growth curves. In this paper we compare the performance of four such lag-time models, each of which described by a scalar differential equation, when combined with a model of a siderophore producing bacterial population under iron limitation. In each case this yields a system of five nonlinear ordinary differential equations that we compare against experimental data, by solving the associated vector optimization problem. Our main finding is that a big step in accuracy is made already by including a simple lag-time model that only introduces one additional degree of freedom in the parameter identification problem (the initial state of health of the population), and that this can be reliably improved if a further degree of freedom, describing the dynamics of the physiological recovery process, is included. The vector optimization problem is solved by scalarizing it with a linear functional and solving the resulting scalar optimization problem. The growth parameters that are identified in this procedure are found to be robust with respect to the scalarization coefficient.

Operational modal analysis is a procedure that allows the extraction of modal parameters of a structure in its operating environment. It is based on the idealized premise that input to the structure is white noise. In some cases, when free decay responses are corrupted by unmeasured random disturbances, the response data can be processed into cross-correlation functions that approximate free decay responses. Modal parameters can be computed from these functions by time domain identification methods such as the Eigenvalue Realization Algorithm (ERA). The extracted modal parameters have the same characteristics as impulse response functions of the original system. Operational modal analysis is performed on Ares I-X in-flight data. Since the dynamic system is not stationary due to propellant mass loss, modal identification is only possible by analyzing the system as a series of linearized models over short periods of time via a sliding time-window of short time intervals. A time-domain zooming technique was also employed to enhance the modal parameter extraction. Results of this study demonstrate that free-decay time domain modal identification methods can be successfully employed for in-flight launch vehicle modal extraction.

A MATHEMATICAL MODEL FOR WIND TURBINE BLADES

Parameter identification with the pseudo-two-dimensional (p2D) model has been an important research topic in battery engineering because some of the physicochemical parameters used in the model can be measured, while some can only be estimated or calculated based on the measurement data. Various methods, either in the time domain or frequency domain, have been proposed to identify the parameters of the p2D model. While the methods in each domain bring their advantages and disadvantages, a comprehensive comparison regarding parameter identifiability and accuracy is still missing. In this present work, some selected physicochemical parameters of the p2D model are identified in four different cases and with different methods, either only in the time domain or with a combined model. Which parameters are identified in the frequency domain is decided by a comprehensive analysis of the analytical expression for the DRT spectrum. Finally, the parameter identifiability results are analyzed and the validation results with two highly dynamic load profiles are shown and compared. The results indicate that the model with ohmic resistance and the combined method achieves the best performance and the average voltage error is at the level of 12 mV.