Identification of Stochastic Wiener Systems using Indirect Inference

We study identification of stochastic Wiener dynamic systems using so-called indirect inference. The main idea is to first fit an auxiliary model to the observed data and then in a second step, often by simulation, fit a more structured model to the estimated auxiliary model. This two-step procedure can be used when the direct maximum-likelihood estimate is difficult or intractable to compute. One such example is the identification of stochastic Wiener systems, i.e.,~linear dynamic systems with process noise where the output is measured using a non-linear sensor with additive measurement noise. It is in principle possible to evaluate the log-likelihood cost function using numerical integration, but the corresponding optimization problem can be quite intricate. This motivates studying consistent, but sub-optimal, identification methods for stochastic Wiener systems. We will consider indirect inference using the best linear approximation as an auxiliary model. We show that the key to obtain a reliable estimate is to use uncertainty weighting when fitting the stochastic Wiener model to the auxiliary model estimate. The main technical contribution of this paper is the corresponding asymptotic variance analysis. A numerical evaluation is presented based on a first-order finite impulse response system with a cubic non-linearity, for which certain illustrative analytic properties are derived.Comment: The 17th IFAC Symposium on System Identification, SYSID 2015, Beijing, China, October 19-21, 201

On second-order cone positive systems

Internal positivity offers a computationally cheap certificate for external (input-output) positivity of a linear time-invariant system. However, the drawback with this certificate lies in its realization dependency. Firstly, computing such a realization requires to find a polyhedral cone with a potentially high number of extremal generators that lifts the dimension of the state-space representation, significantly. Secondly, not all externally positive systems posses an internally positive realization. Thirdly, in many typical applications such as controller design, system identification and model order reduction, internal positivity is not preserved. To overcome these drawbacks, we present a tractable sufficient certificate of external positivity based on second-order cones. This certificate does not require any special state-space realization: if it succeeds with a possibly non-minimal realization, then it will do so with any minimal realization. While there exist systems where this certificate is also necessary, we also demonstrate how to construct systems, where both second-order and polyhedral cones as well as other certificates fail. Nonetheless, in contrast to other realization independent certificates, the present one appears to be favourable in terms of applicability and conservatism. Three applications are representatively discussed to underline its potential. We show how the certificate can be used to find externally positive approximations of nearly externally positive systems and demonstrated that this may help to reduce system identification errors. The same algorithm is used then to design state-feedback controllers that provide closed-loop external positivity, a common approach to avoid over- and undershooting of the step response. Lastly, we present modifications to generalized balanced truncation such that external positivity is preserved where our certificate applies

Seismic Evaluation of a Large Network of Bridges by Simplified Automated Procedures and Consequent System Identifications by Dynamic Tests

This work presents the seismic evaluation of a large network of infrastructures located in the Veneto Region in the North-East of Italy. A large bridge database was subject to investigation, and simplified automated seismic valuation methods were developed in order to estimate the behavior of different types of structures located in seismic zones. In particular, analyses of infrastructures insistent in seismic zones, including surveys, investigations, seismic evaluation and seismic hazard assessment of the infrastructure in reference to parametric study of the structural vulnerability have been carried out. After estimating the safety factor of each structure based on the most vulnerable structural element, the key infrastructures on which execute system identification and simulate the response through numerical models were distinguished. In fact, the second step of this study is the structural identification of highly damaged bridges where a straightforward procedure has been applied. Static and modal parameters have been estimated for masonry arch bridges, concrete arch and continuous bridges, reticular and box girder steel bridges. The structural identification was used not only for calibration purposes but also for short and long term structural health monitoring (SHM) and damage detection. The SHM systems revealed good efficiency by maintaining the analyzed bridges open to traffic and constantly controlled

Nonlinear Model Updating in Structural Dynamics

Identification of nonlinear structural dynamics has received a significant attention during last decades. Yet, there are many aspects of the identification methods of nonlinear structural models to be improved. The main objective of this study is to introduce novel identification approaches for nonlinear structures. The first step in identifying nonlinear structural elements is to detect their exact location. Hence, the first section of this study focuses on the localization of nonlinear elements in structural dynamics utilizing base excitation measured data. To this end, a localization approach is used to find the location of nonlinear electromagnetic restoring force applied to the tip of a cantilever beam.Inferring the exact location of nonlinear elements, identification methods are utilized to identify and characterize the mathematical model of nonlinear structures. However, various sources of noise and error may affect the accuracy of the identified model. Therefore, in the second part of the thesis, the effect of various sources of inaccuracy on the results of nonlinear model identification is investigated. It is shown that measurement noise, expansion error, modelling error, and neglecting the effect of higher harmonics may lead to an erroneously identified model.An optimization-based framework for the identification of nonlinear systems is proposed in this work in order to avoid the bottlenecks mentioned above. The introduced method is applied to a test rig composed of a base-excited cantilever beam subjected to an electromagnetic force at the tip. According to the nonlinear response of the system, four different functions are assumed as candidate models for the unknown nonlinear electromagnetic force. The measured response is compared with the reconstructed response using various models and the most appropriate mathematical model is selected.Utilizing optimization-based identification method to characterize complex mathematical models with large number of unknown parameters would be computationally expensive. Therefore, this study introduces a harmonic-balance-based parameter estimation method for the identification of nonlinear structures in the presence of multi-harmonic response and force. For this purpose, a method with two different approaches are introduced: Analytical Harmonic-Balance-based (AHB) approach and the Alternating Frequency/Time approach using Harmonic Balance (AFTHB). The method is applied to five simulated examples of nonlinear systems to highlight different features of the method. The method can be applied to all forms of both smooth and non-smooth nonlinear functions. The computational cost is relatively low since a dictionary of candidate basis functions is avoided. The results illustrate that neglecting higher harmonics, particularly in systems with multi-harmonic response and force, may lead to an inaccurate identified model. The AFTHB approach benefits from including significant harmonics of the response and force. Applying this method leads to accurate algebraic equations for each harmonic, including the effect of higher harmonics without truncated error. In the last part of this study, the AFTHB method is applied to two experimental case studies and identifies the nonlinear mathematical model of the structures. The first case is composed of a cantilever beam with a nonlinear electromagnetic restoring force applied to the tip which is excited by a multi-harmonic external force. In the second experimental case study, a configuration of linear springs applies a geometric nonlinear restoring force to the tip of a cantilever beam resulting in internal resonance in the dynamics of the system. The good performance of the AFTHB approach in estimating the unknown parameters of the structure is illustrated by the results of identification

Experimental modal analysis using ambient and earthquake vibrations : theory, software and applications

This thesis addresses the problem of identifying the modal properties of structures using vibration measurements. Modal identification methodologies are proposed based on vibration measurements induced by artificial, ambient or earthquake loads applied on the structure. A modal model of the structure is identified using a weighted least-squares approach and measured time histories at selected locations of a structure. For artificially induced and ambient vibration measurements, the identification is performed in the frequency domain using respectively frequency response functions and cross power spectral densities. For earthquake induced vibrations, the identification is performed in both time and frequency domains. The modal identification methods presented in this work treat generalized non-classically damped modal models. The identification of the modal parameter (modal frequencies, modal damping ratios, modeshape components and modal participation factors) is accomplished by introducing a computationally very efficient three step approach as follows. In the first step, stabilization diagrams are constructed containing frequency and damping information. The modeshape components and participation factors are estimated in a second least-squares step, based on the user selection of the stabilized poles. The first two steps involve non-iterative procedures and result in solving linear algebraic systems of equations. Finally, in order to improve the estimation of the modal characteristics, especially for the challenging case of closely spaced and overlapping modes, a third step is introduced to solve a fully nonlinear optimization problem using available iterative gradient-based optimization algorithms. In this thesis, theoretical developments as well as software implementation issues are presented. The methodologies and software developed are applied for the identification of the modal characteristics of a small laboratory structure for the case of artificial induced vibration measurements, as well as the identification of the modal characteristics of three bridges, the under construction R/C bridge of Egnatia Odos located at Metsovo (Greece), and two other representative R/C bridges of Egnatia Odos located at Polymylos and Kavala (Greece) for the cases of ambient and earthquake induced vibration measurements. Results provide qualitative and quantitative information on the dynamic behaviour of the systems and their components under different types of excitations. All modal identification methodologies presented in this work are implemented in user-friendly software, termed Modal Identification Tool (MITooL). The software which includes graphical user interface allows the full exploration and analysis of signals that are measured on a structure when it is excited by artificial, ambient or earthquake loads. A user manual is also presented which gives details for the operations and prospects of the MITooL software. Step-by-step examples of modal identification are presented to demonstrate the applicability of the software

Control Relevant System Identification Using Orthonormal Basis Filter Models

Models are extensively used in advanced process control system design and implementations. Nearly all optimal control design techniques including the widely used model predictive control techniques rely on the use of model of the system to be controlled. There are several linear model structures that are commonly used in control relevant problems in process industries. Some of these model structures are: Auto Regressive with Exogenous Input (ARX), Auto Regressive Moving Average with Exogenous Input (ARMAX), Finite Impulse Response (FIR), Output Error (OE) and Box Jenkins (BJ) models. The selection of the appropriate model structure, among other factors, depend on the consistency of the model parameters, the number of parameters required to describe a system with acceptable accuracy and the computational load in estimating the model parameters. ARX and ARMAX models suffer from inconsistency problem in most open-loop identification problems. Finite Impulse Response (FIR) models require large number of parameters to describe linear systems with acceptable accuracy. BJ, OE and ARMAX models involve nonlinear optimization in estimating their parameters. In addition, all of the above conventional linear models, except FIR, require the time delay of the system to be separately estimated and included in the estimation of the parameters. Orthonormal Basis Filter (OBF) models have several advantages over the other conventional linear models. They are consistent in parameters for most open-loop identification problems. They are parsimonious in parameters if the dominant pole(s) of the system are used in their development. The model parameters are easily estimated using the linear least square method. Moreover, the time delay estimation can be easily integrated in the model development. However, there are several problems that are not yet addressed. Some of the outstanding problems are: (i) Developing parsimonious OBF models when the dominant poles of the system are not known (ii) Obtaining a better estimate of time delay for second or higher order systems (iii) Including an explicit noise model in the framework of OBF model structures and determine the parameters and multi-step ahead predictions (iv) Closed-loop identification problems in this new OBF plus noise model frame work This study presents novel schemes that address the above problems. The first problem is addressed by formulating an iterative scheme where one or two of the dominant pole(s) of the system are estimated and used to develop parsimonious OBF models. A unified scheme is formulated where an OBF-deterministic model and an explicit AR or ARMA stochastic (noise) models are developed to address the second problem. The closed-loop identification problem is addressed by developing schemes based on the direct and indirect approaches using OBF based structures. For all the proposed OBF prediction model structures, the method for estimating the model parameters and multi-step ahead prediction are developed. All the proposed schemes are demonstrated with the help of simulation and real plant case studies. The accuracy of the developed OBF-based models is verified using appropriate validation procedures and residual analysis

Mapping prior information onto LMI eigenvalue-regions for discrete-time subspace identification

In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding LMI regions. In this paper, first we argue on what kind of practical information can be extracted from historical data or step-response experiments to possibly improve the dynamical properties of the corresponding model and, also, on how to mitigate the effect of the uncertainty on such information. For instance, prior knowledge regarding the overshoot, the period between damped oscillations and settling time may be useful to constraint the possible locations of the eigenvalues of the discrete-time model. Then, we show how to map the prior information onto LMI regions and, when the obtaining regions are non-convex, to obtain convex approximations.Comment: Under revie

Advanced methods for loss-of-flow accident precursors identification in a superconducting magnet cryogenic cooling circuit

In nuclear fusion systems, such as ITER, Superconducting Magnets (SMs) will be employed to magnetically confine the plasma. A Superconducting Magnet Cryogenic Cooling Circuit (SMCCC) must keep the SMs at cryogenic temperature to preserve their superconductive properties. Thus, a Loss-Of-Flow Accident (LOFA) in the SMCCC is to be avoided. In this work, a three-step methodology for the prompt identification of LOFA precursors (i.e., those component failures leading to a LOFA) is developed. First, accident scenarios are randomly generated by Monte Carlo sampling of the SMCCC components failures and the corresponding transient system response is simulated by a deterministic thermal-hydraulic code. In this phase, fast-running Proper Orthogonal Decomposition (POD)based Kriging metamodels, adaptively trained to mimic the behavior of the detailed long-running code, are employed to reduce the associated computational burden. Second, the scenarios generated are grouped by a Spectral Clustering (SC) embedding the Fuzzy C-Means (FCM), in order to characterize the principal patterns of system evolution towards abnormal conditions (e.g., a LOFA). Third, an On-line Supervised Spectral Clustering (OSSC) approach is developed to assign signals measured during plant operation to one of the prototypical clusters identified, which may reveal the corresponding LOFA precursors (in terms of combinations of failed SMCCC components). The devised method is applied to the simplified model of a cryogenic cooling circuit of a single module of the ITER Central Solenoid. Results show that the approach developed timely identifies 95% of LOFA events and approximately 80% of the corresponding precursors

Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle

To restore functional use of paralyzed muscles by automatically controlled stimulation, an accurate quantitative model of the stimulated muscles is desirable. The most commonly used model for isometric muscle has had a Hammerstein structure, in which a linear dynamic block is preceded by a static nonlinear function, To investigate the accuracy of the Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with surface electrodes, were used to identify a Hammerstein model but also four local models which describe the responses to small signals at different mean levels of activation. Comparison of the local models with the Linearized Hammerstein model showed that the Hammerstein model concealed a fivefold variation in the speed of response. Also, the small-signal gain of the Hammerstein model was in error by factors up to three. We conclude that, despite the past widespread use of the Hammerstein model, it is not an accurate representation of isometric muscle. On the other hand, local models, which are more accurate predictors, can be identified from the responses to short PRBS sequences. The utility of local models for controller design is discussed

Identification of Nonlinear Normal Modes of Engineering Structures under Broadband Forcing

The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step processes acquired input and output data to derive an experimental state-space model of the structure. The second step converts this state-space model into a model in modal space from which NNMs are computed using shooting and pseudo-arclength continuation. The method is demonstrated using noisy synthetic data simulated on a cantilever beam with a hardening-softening nonlinearity at its free end.Comment: Journal pape