Observability in linear systems of equations and inequalities: Applications

Castillo, Enrique; Conejo, Antonio J.; Pruneda, Rosa Eva; Solares, Cristina

doi:10.1016/j.cor.2005.05.035

Cited by 51 publications

(39 citation statements)

References 4 publications

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“…Observability techniques for electric energy systems can be classified as topological [1][2][3][4], which generally involve combinatorial computational complexity, algebraic [5][6][7][8][9][10][11][12][13][14], and hybrid [15][16][17].…”

Section: Literature Reviewmentioning

confidence: 99%

An efficient algebraic approach to observability analysis in state estimation

Pruneda

Solares

Conejo

et al. 2010

Electric Power Systems Research

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Section: Literature Reviewmentioning

confidence: 99%

An efficient algebraic approach to observability analysis in state estimation

Pruneda

Solares

Conejo

et al. 2010

Electric Power Systems Research

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“…[26] When the observability of unknown variables is determined, the values of those observable variables are determined by the particular solution z p of Equation 4. It is to highlight that in SSI by OM, if any deflection, force, or structural parameter is observed, this information might help to observe new parameters in the adjacent beam elements through a recursive process.…”

Section: Structural System Identification By Observability Methodsmentioning

confidence: 99%

“…[29] An algebraic technique to analyze the observability of the solution of a linear system is checking the null space of the coefficient matrix. [26] This technique can be applied to the identification of parameters in physical and engineering problems in which the final systems are in the form of monomial ratio equations. [30] The application of OM has to be tailor-made due to the different characteristics of problems in different fields.…”

Section: Introductionmentioning

confidence: 99%

“…[19] Observability Method (OM) is a mathematical tool dealing with the observability, that is, the existence and the uniqueness of the solution of a system of equations (or a subset of it). [26] It has been applied to many engineering fields, for example, water distribution systems, [27] power systems, [28] traffic networks. [29] An algebraic technique to analyze the observability of the solution of a linear system is checking the null space of the coefficient matrix.…”

Section: Introductionmentioning

confidence: 99%

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Static structural system identification for beam-like structures using compatibility conditions

Lei

Coderque

2017

Struct Control Health Monit

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SummaryDue to the inevitable noise existing in the measured responses, structural system identification is often a challenging task in terms of the accuracy of the estimations. Structural system identification by the observability method, which is characterized by the analysis of null spaces, is a powerful tool to determine the observability of structural parameters. However, it did not cope well with measurement errors so far. In this paper, for the first time, functional relations among displacements, denoted by the term compatibility conditions, in beam-like structures are derived by the observability method. Then, compatibility conditions are imposed in an optimization procedure to minimize the discrepancy between the measured response and the compatible one. The compatible response obtained by the optimization is used to obtain the final estimations of the parameters. In a simply supported bridge example, the proposed method is thoroughly evaluated regarding the number of measurements, error levels, and load cases. In an example of a continuous bridge, different load cases are used to estimate the bending stiffnesses of different zones. The accuracy and the efficacy of the proposed method are verified by the numerical results.

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“…3) What is the subset of variables that become observable given another subset of variables? Castillo et al (2007) provided a general method to solve the observability problem in the case of systems of linear equations or inequalities. However, since many problems in engineering are non-linear, this method cannot be directly used in many practical cases.…”

Section: Observabilitymentioning

confidence: 99%

New Tool to Help Decision Making in Civil Engineering

Castillo

Galant

Nogal

et al. 2015

Journal of Civil Engineering and Management

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Abstract. Structural collapses have indirectly produced important progress in science. The last lesson learnt from structural collapses reveals the important role of polyrational systems of equations in the Civil Engineering field, as all problems in Physics and Engineering involving scale variables lead to systems of these equations. Since no efficient methods are known to solve this type of equations, a powerful and efficient method to multivariate polyrational equations using observability techniques is presented in this paper. It is pointed out that this method can be applied to solve different Civil Engineering problems. The information obtained by this tool can be used to assist decision making and risk management processes during maintenance and service life. As an example of its use, a structural damage detection problem is solved.

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Observability in linear systems of equations and inequalities: Applications

Cited by 51 publications

References 4 publications

An efficient algebraic approach to observability analysis in state estimation

An efficient algebraic approach to observability analysis in state estimation

Static structural system identification for beam-like structures using compatibility conditions

New Tool to Help Decision Making in Civil Engineering

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