Online identification of a two-mass system in frequency domain using a Kalman filter

Some of the most widely recognized online parameter estimation techniques used in different servomechanism are the extended Kalman filter (EKF) and recursive least squares (RLS) methods. Without loss of generality, these methods are based on a prior knowledge of the model structure of the system to be identified, and thus, they can be regarded as parametric identification methods. This paper proposes an on-line non-parametric frequency response identification routine that is based on a fixed-coefficient Kalman filter, which is configured to perform like a Fourier transform. The approach exploits the knowledge of the excitation signal by updating the Kalman filter gains with the known time-varying frequency of chirp signal. The experimental results demonstrate the effectiveness of the proposed online identification method to estimate a non-parametric model of the closed loop controlled servomechanism in a selected band of frequencies

Characterization of Dynamic Structures Using Parametric and Non-parametric System Identification Methods

The effects of soil-foundation-structure (SFS) interaction and extreme loading on structural behaviors are important issues in structural dynamics. System identification is an important technique to characterize linear and nonlinear dynamic structures. The identification methods are usually classified into the parametric and non-parametric approaches based on how to model dynamic systems. The objective of this study is to characterize the dynamic behaviors of two realistic civil engineering structures in SFS configuration and subjected to impact loading by comparing different parametric and non-parametric identification results. First, SFS building models were studied to investigate the effects of the foundation types on the structural behaviors under seismic excitation. Three foundation types were tested including the fixed, pile and box foundations on a hydraulic shake table, and the dynamic responses of the SFS systems were measured with the instrumented sensing devices. Parametric modal analysis methods, including NExT-ERA, DSSI, and SSI, were studied as linear identification methods whose governing equations were modeled based on linear equations of motion. NExT-ERA, DSSI, and SSI were used to analyze earthquake-induced damage effects on the global behavior of the superstructures for different foundation types. MRFM was also studied to characterize the nonlinear behavior of the superstructure during the seismic events. MRFM is a nonlinear non-parametric identification method which has advantages to characterized local nonlinear behaviors using the interstory stiffness and damping phase diagrams. The major findings from the SFS study are: *The investigated modal analysis methods identified the linearized version of the model behavior. The change of global structural behavior induced by the seismic damage could be quantified through the modal parameter identification. The foundation types also affected the identification results due to different SFS interactions. The identification accuracy was reduced as the nonlinear effects due to damage increased. *MRFM could characterize the nonlinear behavior of the interstory restoring forces. The localized damage could be quantified by measuring dissipated energy of each floor. The most severe damage in the superstructure was observed with the fixed foundation. Second, the responses of a full-scale suspension bridge in a ship-bridge collision accident were analyzed to characterize the dynamic properties of the bridge. Three parametric and non-parametric identification methods, NExT-ERA, PCA and ICA were used to process the bridge response data to evaluate the performance of mode decomposition of these methods for traffic, no-traffic, and collision loading conditions. The PCA and ICA identification results were compared with those of NExT-ERA method for different excitation, response types, system damping and sensor spatial resolution. The major findings from the ship-bridge collision study include: *PCA was able to characterize the mode shapes and modal coordinates for velocity and displacement responses. The results using the acceleration were less accurate. The inter-channel correlation and sensor spatial resolution had significant effects on the mode decomposition accuracy. *ICA showed the lowest performance in this mode decomposition study. It was observed that the excitation type and system characteristics significantly affected the ICA accuracy

The Harmonic Analysis of Kernel Functions

Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian process with zero mean and with a certain kernel (i.e. covariance) function. Choosing the kernel is one of the most challenging and important issues. In the present paper we introduce the harmonic analysis of this non-stationary process, and argue that this is an important tool which helps in designing such kernel. Furthermore, this analysis suggests also an effective way to approximate the kernel, which allows to reduce the computational burden of the identification procedure

The cost efficiency of German banks: a comparison of SFA and DEA

We investigate the consistency of efficiency scores derived with two competing frontier methods in the financial economics literature: Stochastic Frontier and Data Envelopment Analysis. We sample 34,192 observations for all German universal banks and analyze whether efficiency measures yield consistent results according to five criteria between 1993 and 2004: levels, rankings, identification of extreme performers, stability over time and correlation to standard accounting-based measures of performance. We find that non-parametric methods are particularly sensitive to measurement error and outliers. Furthermore, our results show that accounting for systematic differences among commercial, cooperative and savings banks is important to avoid misinterpretation about the status of efficiency of the total banking sector. Finally, despite ongoing fundamental changes in Europe?s largest banking system, efficiency rank stability is very high in the short run. However, we also find that annually estimated efficiency scores are markedly less stable over a period of twelve years, in particular for parametric methods. Thus, the implicit assumption of serial independence of bank production in most methods has an important influence on obtained efficiency rankings. --Cost Efficiency,Banks,Stochastic Frontier Approach,Data Envelopment Analysis

Evaluation of non-parametric identification techniques in second order models plus dead time

In this paper, a set of non-parametric identification techniques are used in order to obtain second order models plus dead time for an underdamped system. Initially, non-parametric techniques were used to identify the system from the temperature data of a coal-heated oven. In this case, the identification techniques proposed by Stark, Jahanmiri-Fallahi and Ogata were used, which require obtaining two or three points of the step response for the system under study. In addition, the Matlab PID Tuner app was used to identify the underdamped system and compare the results with the other methods. The results show that the PID Tuner and the method proposed by Ogata are the ones that best represent the dynamics of the underdamped system, taking into account the values for the integral absolute error (IAE) and the correlation coefficient. With the Stark method an IAE of 181.56 was obtained, while with the PID Tuner the best performance was achieved with an IAE of 21.59. In terms of the results obtained with the cross correlation, the best performance was achieved with the PID tuner and the Stark method. Copyright © 2020 Institute of Advanced Engineering and Science. All rights reserved

Analytical And Experimental Study Of Monitoring For Chain-like Nonlinear Dynamic Systems

Inverse analysis of nonlinear dynamic systems is an important area of research in the eld of structural health monitoring for civil engineering structures. Structural damage usually involves localized nonlinear behaviors of dynamic systems that evolve into different classes of nonlinearity as well as change system parameter values. Numerous parametric modal analysis techniques (e.g., eigensystem realization algorithm and subspace identification method) have been developed for system identification of multi-degree-of-freedom dynamic systems. However, those methods are usually limited to linear systems and known for poor sensitivity to localized damage. On the other hand, non-parametric identification methods (e.g., artificial neural networks) are advantageous to identify time-varying nonlinear systems due to unpredictable damage. However, physical interpretation of non-parametric identification results is not as straightforward as those of the parametric methods. In this study, the Multidegree-ofFreedom Restoring Force Method (MRFM) is employed as a semi-parametric nonlinear identi- fication method to take the advantages of both the parametric and non-parametric identification methods. The MRFM is validated using two realistic experimental nonlinear dynamic tests: (i) largescale shake table tests using building models with different foundation types, and (ii) impact test using wind blades. The large-scale shake table test was conducted at Tongji University using 1:10 scale 12-story reinforced concrete building models tested on three different foundations, including pile, box and fixed foundation. The nonlinear dynamic signatures of the building models collected from the shake table tests were processed using MRFM (i) to investigate the effects of foundation types on nonlinear behavior of the superstructure and (ii) to detect localized damage during the shake table tests. Secondly, the MRFM was applied to investigate the applicability of this method to wind turbine blades. Results are promising, showing a high level of nonlinearity of the system and how the MRFM can be applied to wind-turbine blades. Fuiii ture studies were planned for the comparison of physical characteristic of this blade with blades created made of other material

Comparing Semi-Parametric Model Learning Algorithms for Dynamic Model Estimation in Robotics

Physical modeling of robotic system behavior is the foundation for controlling many robotic mechanisms to a satisfactory degree. Mechanisms are also typically designed in a way that good model accuracy can be achieved with relatively simple models and model identification strategies. If the modeling accuracy using physically based models is not enough or too complex, model-free methods based on machine learning techniques can help. Of particular interest to us was therefore the question to what degree semi-parametric modeling techniques, meaning combinations of physical models with machine learning, increase the modeling accuracy of inverse dynamics models which are typically used in robot control. To this end, we evaluated semi-parametric Gaussian process regression and a novel model-based neural network architecture, and compared their modeling accuracy to a series of naive semi-parametric, parametric-only and non-parametric-only regression methods. The comparison has been carried out on three test scenarios, one involving a real test-bed and two involving simulated scenarios, with the most complex scenario targeting the modeling a simulated robot's inverse dynamics model. We found that in all but one case, semi-parametric Gaussian process regression yields the most accurate models, also with little tuning required for the training procedure

Non-linear system identification in structural dynamics: advances in characterisation of non-linearities and non-linear modal analysis

Many new methods for theoretical modelling, numerical analysis and experimental testing have been developed in non-linear dynamics in recent years. Although the computational power has greatly improved our ability to predict non-linear behaviour, non-linear system identification, a central topic of this thesis, still plays a key role in obtaining and quantifying structural models from experimental data. The first part of the thesis is motivated by the industrial needs for fast and reliable detection and characterisation of structural non-linearities. For this purpose a method based on the Hilbert transform in the frequency domain is proposed. The method detects and characterises structural non-linearities from a single frequency response function and does not require a priori knowledge of the system. The second part of the thesis is driven by current research trends and advances in non-linear modal analysis and adaptive time series processing using the Hilbert-Huang transform. Firstly, the alternatives of the Hilbert transform, which is commonly used in structural dynamics for the estimation of the instantaneous frequency and amplitude despite suffering from a number of numerical issues, are compared to assess their potential for non-linear system identification. Then, a possible relation between the Hilbert-Huang transform and complex non-linear modes of mechanical systems is investigated. Based on this relation, an approach to experimental non-linear modal analysis is proposed. Since this approach integrates the Hilbert-Huang transform and non-linear modes, it allows not only to detect and characterise structural non-linearities in a non-parametric manner, but also to quantify the parameters of a selected model using extracted non-linear modes. Lastly, a new method for the identification of systems with asymmetric non-linear restoring forces is proposed. The application of all proposed methods is demonstrated on simulated and experimental data.Open Acces

Structural health monitoring and damage detection using an intelligent parameter varying (IPV) technique

Most structural health monitoring and damage detection strategies utilize dynamic response information to identify the existence, location, and magnitude of damage. Traditional model-based techniques seek to identify parametric changes in a linear dynamic model, while non-model-based techniques focus on changes in the temporal and frequency characteristics of the system response. Because restoring forces in base-excited structures can exhibit highly non-linear characteristics, non-linear model-based approaches may be better suited for reliable health monitoring and damage detection. This paper presents the application of a novel intelligent parameter varying (IPV) modeling and system identification technique, developed by the authors, to detect damage in base-excited structures. This IPV technique overcomes specific limitations of traditional model-based and non-model-based approaches, as demonstrated through comparative simulations with wavelet analysis methods. These simulations confirm the effectiveness of the IPV technique, and show that performance is not compromised by the introduction of realistic structural non-linearities and ground excitation characteristics