Identification Of Structural Models Research Articles

Bayesian two-stage structural identification with equivalent formulation and EM algorithm

For structural model identification using a Bayesian two-stage approach, modal properties (e.g., natural frequencies) are first extracted from measured data in Stage I and then used for determining structural properties (e.g., stiffness) in Stage II. With sufficient data that allow the problem to be globally identifiable, the computational problem often reduces to optimizing a ‘measure-of-fit’ function to yield the ‘most probable value’ (MPV) that informs the ‘best estimate’, and determining the Hessian of the function to yield the posterior covariance matrix that informs the remaining uncertainty. Recent developments deal with the presence of model error, and the increasing complexity calls for proper computational strategy. In this spirit, assuming Gaussian model error, this work develops a hypothetical yet mathematically equivalent formulation for the two-stage problem, which facilitates development of effective algorithms for MPV using Expectation-Maximization techniques. By treating hypothetically the MPV of modal properties in Stage I as ‘data’ and model error as latent variables, the Q-function in the M−step can be expressed as a sum of two terms that can be optimized with respect to structural parameters and model error parameters. The optimization of structural parameters reduces to that of a Stage II problem without model error, for which existing algorithms can be applied. Analytical expressions are also derived for computing the posterior covariance matrix. The proposed methodology is investigated with synthetic data for model errors associated with sensor misalignment and model simplification, lab data for the effect of number of modes and measured degrees of freedom (DoFs), and field data for reality tests.

A solution to the global identification problem in DSGE models

We develop an analytical framework to study global identification in structural models with forward-looking expectations. Our identification condition combines the similarity transformation linking the observationally equivalent state space systems with the constraints imposed on them by the model parameters. The key step of solving the identification problem then reduces to finding all roots of a system of polynomial equations. We show how it can be done using the concept of a Gröbner basis and recently developed algorithms to compute it analytically. In contrast to frameworks relying on numerical search, our approach can prove whether a model is identified or not at a given parameter point, explicitly delivering the complete set of observationally equivalent parameter vectors. We present the solution to the global identification problem for several popular dynamic stochastic general equilibrium (DSGE) models.

Fracturing of Solids as a Thermodynamic Process

Instead of a number of different approaches or a formal description of experimental data, a unified approach is proposed to consider failure and deformation as thermodynamic processes. Mathematical modeling of the processes is carried out using rheological models of the material. Parametric identification of structural models is carried out using minimal necessary experiments. Based on results of these experiments, the scope of applicability conditions for this material and test modes necessary for parametric identification of models are selected. One fracture criterion is used that formally corresponds to the achievement of a threshold concentration of micro-damage in any volume of the material. Calculations of durability under conditions of varying temperature and variable loads are based on the relationship of plastic flow and failure processes distributed over the volume of the material. They are performed numerically over time steps depending on the ratio of the rate of change of temperature and stresses.

STRUCTURAL EQUATION MODELING (SEM) ANALYSIS OF MOTIVATION, TRAINING AND DEVELOPMENT, AND ORGANIZATIONAL CULTURE ON WORK DISCIPLINE AND EMPLOYEE PERFORMANCE AT PEKANBARU WATER REGIONAL COMPANY

In accordance with the topic chosen by the author, the purpose of this study is to find out the relationship between motivation, training and development, and organizational culture on work discipline and employee performance in PDAM Pekanbaru, Riau. In this case, we use motivation, training and development, and organizational culture as independent variables and work discipline and employee performance as the dependent variable. Through the data obtained in this study, we can study, analyze and evaluate each variable and its relationship to employees in PDAM Pekanbaru in order to optimize the human resources they have. This research is expected to provide benefits for related parties. The method used in this research is Structural Equation Modeling (SEM) Analysis. Steps being taken in this method include developing theoretical models, developing flowcharts, converting flowcharts into structural equations and measurement models, selecting the type of input matrix and estimating proposed models, evaluating structural model identification, evaluating hypothesis testing compatibility, and interpreting and modifying models. Each methodology has advantages and disadvantages.

Acrostic in Byzantine Hymnography and Slavonic Spiritual Poetry in Byzantine Hymnography

The purpose of the work is to investigate the functioning of the acrostiс verse in various contexts of the spiritual culture of the European space. This ancient form is used in Old Testament poetry, Byzantine hymnography, Ukrainian sacred monody and spiritual song. The methodological basis is the application of systemic and complex approaches, which ensured the establishment of valuable social and cultural functional elements within the historical development of mankind. The use of comparative method of research contributed to the identification of structural models that ensured the integrity and systematicity of the evolution of culture on the example of form-forming structures. In this context, we also use the heuristic method of research, which contributes to the modeling of structural connections within cultural and artistic forms. The use of the specified research methods contributed to obtaining own theoretical results. The scientific novelty of the study is determined by the originality of the theoretical principle of comparing the form of the acrostic in different genres over time intervals. Conclusions. The ways of arranging poetic texts, which laid the foundations of Byzantine hymnography, are a complex system formed on the basis of ancient metrical and melodic constructions. The acrostic became the evidence of the adaptation of such experience of ancient forms of poetry – as a source of a number of important form-creating processes. The long-term use of the acrostic is evidence of the use of liturgical experience in the context of synthesising the “technological developments” of ancient cultures and singling out among them the most functional, in particular, the acrostic.
 Key words: acrostiс, Byzantine hymnography, sacred monody, baroque poetry, Bohohlasnyk, spiritual song.

Irregular identification of structural models with nonparametric unobserved heterogeneity

One of the most important empirical findings in microeconometrics is the pervasiveness of heterogeneity in economic behavior (cf. Heckman, 2001). This paper shows that cumulative distribution functions and quantiles of the nonparametric unobserved heterogeneity have an infinite efficiency bound in many structural economic models of interest. The paper presents general and precise conditions to prove such results. The usefulness of the theory is demonstrated with several relevant examples in economics, including, among others, the proportion of individuals with severe long term unemployment duration, Average Marginal Effects (AME) in a correlated random coefficient model without monotonicity, and the distribution and quantiles of random coefficients in linear, binary and the popular semiparametric Mixed Logit model.

Structural Model Identification Using a Modified Electromagnetism-Like Mechanism Algorithm.

A modified electromagnetism-like mechanism (EM) algorithm is proposed to identify structural model parameters using modal data. EM is a heuristic algorithm, which utilizes an attraction–repulsion mechanism to move the sample points towards the optimal solution. In order to improve the performance of original algorithm, a new local search strategy, new charge and force calculation formulas, new particle movement and updating rules are proposed. The test results of benchmark functions show that the modified EM algorithm has better accuracy and faster convergence rate than the original EM algorithm and the particle swarm optimization (PSO) algorithm. In order to investigate the applicability of this approach in parameter identification of structural models, one numerical truss model and one experimental shear-building model are presented as illustrative examples. The identification results show that this approach can achieve remarkable parameter identification even in the case of large noise contamination and few measurements. The modified EM algorithm can also be used to solve other optimization problems.

Output‐only model updating of adjacent buildings from sparse seismic response records and identification of their common excitation

Output-only identification of civil structures is a challenging yet in escapable task, as input excitations are unmeasurable in many real-world situations. This paper presents a new output-only technique to jointly identify the model parameters of adjacent buildings from their recorded seismic responses. Classic output-only identification techniques are based on various limiting assumptions about the unknown input signal (e.g., whiteness), which are often violated for earthquakes. While other advanced output-only (e.g., blind) identification techniques have recently been developed, their applications can be limited due to their computational costs and sensor density requirements. The proposed method assumes that two adjacent buildings experience the same foundation input motion during an earthquake. Both systems are then identified by investigating the uncommon portions of their measured responses through a cross-relation (CR) method. To relax the CR method's nominally restrictive identifiability criteria, mechanics-based finite element (FE) models of the two buildings are utilized and updated, instead of direct identification of their impulse response functions (IRFs). An unscented Kalman filter (UKF) is employed for model updating, which also quantifies the estimation uncertainties. Having identified the buildings, their common input excitation is recovered through a stable deconvolution approach. The overall method is verified through a synthetic example, and identifiability conditions are investigated. While the proposed method is limited to linear-elastic ranges of response, it is capable of handling limited measurements (e.g., single biaxial accelerometer for each building); therefore, it offers an ideal solution for identification of structural models of sparsely instrumented buildings along with their foundation input motions at regional scales.

Mathematical Modeling of Failure and Deformation Processes in Metal Alloys and Composites

Based on experimental examples, the strength characteristics of metal alloys and composites under tensile and compressive loads are considered to demonstrate both their similarity and difference. Under tensile loads, their behavior is essentially the same. Under compressive loads, the composite shows different properties, but similar to the behavior of a metal alloy under tension. When tensioned and compressed, it fractured as a material with a different structure. When a metal alloy is cyclically compressed, the damage accumulation process is attenuated, which reduces the alloy longevity during subsequent tension. The analysis of experimental data for various types of loading from the standpoint of the kinetic concept of fracture is carried out. Instead of a number of incompatible approaches or a formal description of experimental data, that based on the theory of reaction rates is used. Mathematical modeling of processes is carried out using rheological models of the material. Structural models of the material, called physical media, reflect the thermodynamic processes of flow, failure, and changes in the structure of the material. Parametric identification of structural models is carried out on the basis of the minimum necessary basic experiment: loading of specimens with different speeds at several temperature values and by the amplitude dependence of inelasticity. Based on results of these experiments, the scope of applicability conditions for this material and test modes necessary for parametric identification of models are selected. One fracture criterion is used, which formally corresponds to the achievement of a threshold concentration of micro-damage in any volume of the material, leading to macro-fracture. The application of mathematical models for calculating the longevity of materials depending on the temperature and force loading conditions and the nature of their changes is shown. Calculations of longevity under constant, monotonously increasing and variable loads under conditions of constant or changing temperatures are based on the relationship of plastic flow and failure processes distributed over the volume of the material. They are performed numerically by time steps depending on the ratio of the rate of change of temperature and stresses.

The role of geometry on stability of large domes: Roman Pantheon as cultural emblem and constructive reference

This paper focuses on large domes’ building techniques and use of geometric rules in the design and construction of religious structures. A quick excursus on the cultural heritage in Italy and abroad highlights how domes have been used almost exclusively in sacred architecture, rather than in civic buildings, for most of history. Born of the need to cover large spaces without facing with the encumbrance of vertical elements, the domed cover, ideal for places of worship crowded by hundreds of faithful, has assumed, over the centuries, a symbolic meaning to every religion. In fact, identifying the shape of a large dome in the urban landscape immediately means to recognize the sacredness of that place. The ancient Romans who believed in the gods, Christians, Hindus and Muslims, all used this very peculiar architectural element in churches or mosques to express a kind of spiritual symbolism and, as mentioned, the fact that the shape of the dome arises from a functional reason, it has over time got pushed aside. Furthermore, the circle is a geometric form that possesses a great symbolic force, generated by the idea that, having no beginning and no end, reflected perfection, the eternal, and also the heavens. In this perspective, drawing a circle both in the horizontal and vertical section, the ultimate paradigm for all monumental domes was the Roman Pantheon which, with its centrally placed "oculus" or “eye of heaven” proved to be a model for all other domes after it, retaining its position as the most ancient and well preserved dome in the world. Therefore, this article concentrates on the study of the Pantheon as an emblem and reference model for all monumental domes. By analyzing the “meaning” of its architectural design and its structural and geometric characteristics, the research dissects a comparison between similar large domes, similar to each other, such as that of St. Francesco di Paola in Naples and the Mosta Dome in Malta. The comprehension of these valuable architectural artifacts lies between the search for their original geometry and the identification of structural models through which their shape was defined, namely the geometric and proportional rules of the past.

Fundamental two-stage formulation for Bayesian system identification, Part I: General theory

Structural system identification is concerned with the determination of structural model parameters (e.g., stiffness, mass) based on measured response data collected from the subject structure. For linear structures, one popular strategy is to adopt a ‘two-stage’ approach. That is, modal identification (e.g., frequency, mode shape) is performed in Stage I, whose information is used for inferring the structural parameters in Stage II. Different variants of Bayesian two-stage formulations have been proposed in the past. A prediction error model is commonly introduced to build a link between Stages I and II, treating the most probable values of the natural frequencies and mode shapes identified in Stage I as ‘data’ for Stage II. This type of formulation, which casts a prediction error model through descriptive statistics, involves heuristics that distort the fundamental nature of the Bayesian approach, although it has appeared to be inevitable. In this paper, a fundamental theory is developed for the Bayesian two-stage problem. The posterior distribution of structural parameters is derived rigorously in terms of the information available in the problem, namely the prior distribution of structural parameters, the posterior distribution of modal parameters in Stage I and the distribution of modal parameters conditional on the structural parameters that connects Stages I and II. The theory reveals a fundamental principle that ensures no double-counting of prior information in the two-stage identification process. Mathematical statements are also derived that provide insights into the role of the structural modeling error. Beyond the original structural model identification problem that motivated the work, the developed theory can be applied in more general settings. In the companion paper, examples with synthetic and real experimental data are provided to illustrate the proposed theory.

Identification of Structural Model for Chaotic Systems

This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the basis of the attractors which can be identified and the mere sight of models. It is known that the knowledge of the symmetry group allows you to specify the form of a minimal system. Forming a group transformation can be found in the reconstructed attractor. The affine system as the basic model is selected. Type of a nonlinear system is the subject of calculations. A theoretical analysis is performed and proof of the possibility of constructing models in the central invariant manifold reduced. This developed algorithm for determining the observed symmetry in the attractor. The results of identification used in real systems are an application.

Identification of structural models using a modified Artificial Bee Colony algorithm

A modified version of the Artificial Bee Colony (ABC) algorithm is presented to identify structural systems. ABC is a heuristic algorithm with simple structure, ease of implementation and robustness. A nonlinear factor for convergence control is introduced in the algorithm to enhance the balance of global and local searches. To investigate the applicability of this proposed technique to system identification, three examples are studied under different conditions regarding data availability, noise pollution level, priori knowledge of parameters, etc. Simulation results show the proposed technique produces excellent parameter estimation, even with few measurements and high noise corruptions.

Building New Plants or Entering by Acquisition? Firm Heterogeneity, Identification and Entry Barriers

In many industries firms can enter into new markets either by building a new plant (greenfield entry) or by acquiring an existing incumbent facility. The structural empirical literature on entry has usually ignored acquisitions as an option for entrants. Understanding what drives this decision has relevant implications for the identification of structural models of entry. The existence of firm heterogeneity plays an important role in this identification. I present an example of this result by estimating a model of entry for the U.S. cement industry using data from the U.S. Census. In this industry, the comparative advantage (e.g., TFP or size) of new entrants versus incumbents, as well as regulatory entry barriers, are important factors in determining the means of expansion. The biases that arise when assuming that entry by acquisition is not an available option for entrants can be as high as 134.8% for greenfield sunk entry costs. Finally, I use the estimates of the model to show the effects of the Reagan-Bush administration's permissive merger policy. I find that a less permissive policy would decrease the number of acquired plants by 90%, greenfield entry would increase by 21%, consumer surplus would decrease by 14.7% and cement production would increase by 18.2%.

Econometric Analysis of Structural Systems with Permanent and Transitory Shocks

This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the influential work of Blanchard and Quah (1989), and shows that structural equations with known permanent shocks can not contain error correction terms, thereby freeing up the latter to be used as instruments in estimating their parameters. The approach is illustrated by a re-examination of the identification schemes used by Wickens and Motto (2001), Shapiro and Watson (1988), King, Plosser, Stock, Watson (1991), Gali (1992, 1999) and Fisher (2006).

Econometric analysis of structural systems with permanent and transitory shocks

This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the influential work of Blanchard and Quah [1989. The dynamic effects of aggregate demand and supply disturbances. The American Economic Review 79, 655–673] , and shows that structural equations with known permanent shocks cannot contain error correction terms, thereby freeing up the latter to be used as instruments in estimating their parameters. The approach is illustrated by a re-examination of the identification schemes used by Wickens and Motto [2001. Estimating shocks and impulse response functions. Journal of Applied Econometrics 16, 371–387], Shapiro and Watson [1988. Sources of business cycle fluctuations. NBER Macroeconomics Annual 3, 111–148], King et al. [1991. Stochastic trends and economic fluctuations. American Economic Review 81, 819–840] , Gali [1992. How well does the ISLM model fit postwar US data? Quarterly Journal of Economics 107, 709–735; 1999. Technology, employment, and the business cycle: Do technology shocks explain aggregate fluctuations? American Economic Review 89, 249–271] and Fisher [2006. The dynamic effects of neutral and investment-specific technology shocks. Journal of Political Economy 114, 413–451].

On Econometric Analysis of Structural Systems with Permanent and Transitory Shocks and Exogenous Variables

This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the influential work of Blanchard and Quah (1989), and shows that structural equations for which there are known permanent shocks must have no error correction terms present in them, thereby freeing up the latter to be used as instruments in estimating their parameters. The proposed approach is illustrated by a re-examination of the identification scheme used in a monetary model by Wickens and Motta (2001), and in a well known paper by Gali (1992) which deals with the construction of an IS-LM model with supply-side effects. We show that the latter imposes more short-run restrictions than are needed because of a failure to fully utilize the cointegration information.

Input/output versus output-only data processing for structural identification—Application to in-flight data analysis

The problem of structural model identification under both known and unknown input excitations, is addressed. In-flight data analysis is an important instance of that problem. Input/output and output-only eigenstructure identification methods are described and compared, within two classes of methods: subspace-based and prediction error. In particular, different types of relevant projections for handling the known and unknown inputs are discussed. The relevance of the methods is emphasized through numerical results obtained on real flight test data sets.

Multi-objective framework for structural model identification

Structural identification based on measured dynamic data is formulated in a multi-objective context that allows the simultaneous minimization of the various objectives related to the fit between measured and model predicted data. Thus, the need for using arbitrary weighting factors for weighting the relative importance of each objective is eliminated. For conflicting objectives there is no longer one solution but rather a whole set of acceptable compromise solutions, known as Pareto solutions, which are optimal in the sense that they cannot be improved in any objective without causing degradation in at least one other objective. The strength Pareto evolutionary algorithm is used to estimate the set of Pareto optimal structural models and the corresponding Pareto front. The multi-objective structural identification framework is presented for linear models and measured data consisting of modal frequencies and modeshapes. The applicability of the framework to non-linear model identification is also addressed. The framework is illustrated by identifying the Pareto optimal models for a scaled laboratory building structure using experimentally obtained modal data. A large variability in the Pareto optimal structural models is observed. It is demonstrated that the structural reliability predictions computed from the identified Pareto optimal models may vary considerably. The proposed methodology can be used to explore the variability in such predictions and provide updated structural safety assessments, taking into consideration all Pareto structural models that are consistent with the measured data. Copyright © 2005 John Wiley & Sons, Ltd.

STOCHASTIC SUBSPACE-BASED STRUCTURAL IDENTIFICATION AND DAMAGE DETECTION —APPLICATION TO THE STEEL-QUAKE BENCHMARK

Numerical results from the application of new stochastic subspace-based structural identification and damage detection methods to the steel-quake structure are discussed. Particular emphasis is put on structural model identification, for which we display some modeshapes.