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Optimal sensor placement is used to establish the optimal sensor quantity and layout. In this study, the minimum quantity and locations of measurement sensors were assumed to satisfy the constraint conditions of the optimal sensor placement. A set of strain data in a truss structure was expanded to another set of displacements corresponding to the entire degrees of freedom from the relationship between the strain and displacement. It indicates to reduce the number of sensors because the strain depends on the displacements in a finite element model. The damaged truss element was traced using the expanded data that satisfied the prescribed constraints. The proposed optimal sensor placement method has a merit to explicitly determine the optimal sensor locations without any numerical scheme and statistical methods. The method was applied to the damage detection of a single-damaged truss structure. It was shown that the optimal sensor placement method depended on the sensor layout irrespective of the same quantity of sensors. In addition, a numerical example was used to compare sensitivities to damage detection based on the sensor placement and the existence of external noise contained in the measurement data. [ABSTRACT FROM AUTHOR]

Abstract: Physical parameters to be estimated based on measured data from dynamic or static tests of systems do not coincide with analytical parameters due to measurement noise, model inadequacies, and structural damages. Measured data can be regarded as constraints to explain the behavior of the dynamic or static systems. The existence of constraints requires the additional forces to satisfy the measured data. The variation in the responses by constraints is expressed by the changes of physical parameters. Minimizing a square function of the difference between the analytical and corrected parameter matrices, this study derives the analytical equations to describe the constrained static and dynamic responses and the corrected forms of physical parameter matrices. It is shown that the derived equations coincide with the equations provided by Udwadia and Kalaba for dynamic systems and by Eun et al. for static systems. The validity of the proposed method is illustrated in applications. [Copyright &y& Elsevier]

Abstract: The physical parameters obtained from modal tests do not satisfy the dynamic constraints of eigenvalue function and orthogonality requirements due to modeling and measurement errors. The purpose of this study is to present the analytical equations on the updated stiffness and mass matrices in the satisfaction of such dynamic constraints. Minimizing the cost functions of the difference between analytical and desired physical parameter matrices, the corrected parameter matrices are straightforwardly derived by utilizing the Moore–Penrose inverse without using any multipliers. The cost functions given by a few researchers are utilized. From the comparison of the existing analytical results and the proposed equations, the validity of the proposed methods is evaluated in an application. [Copyright &y& Elsevier]

Sensor measurements of civil structures provide basic information on their performance. However, it is impossible to install sensors at every location owing to the limited number of sensors available. Therefore, in this study, we propose an optimal sensor placement (OSP) algorithm while reducing the system order by using the constraint condition between the master and slave modes from the target modes. The existing OSP methods are modified in this study, and an OSP approach using a constrained dynamic equation is presented. The validity and comparison of the proposed methods are illustrated by utilizing a numerical example that predicts the OSPs of the truss structure. It is observed that the proposed methods lead to different sensor layouts depending on the algorithm criteria. Thus, it can be concluded that the OSP algorithm meets the measurement requirements for various methods, such as structural damage detection, system identification, and vibration control. [ABSTRACT FROM AUTHOR]

Structural reanalysis aims to determine the variations in the displacement of a structure due to the addition or deletion of elements without solving the full degrees of freedom. The iterations change the design parameters at each step and utilize the factorization of the stiffness matrix of the initial design. This study develops a new reanalysis method to determine the additional forces that act on the initial structure and the displacements of the modified structure. It utilizes the compatibility conditions at the interfaces between the initial structure and the added or deleted members as static constraints, and applies the generalized inverse method to describe the static behavior of the constrained structure. The structural elements that are added may be statically stable substructures or floating members that possess rigid-body freedom. Examples are included to show the effectiveness of the proposed method. Une réanalyse structurale vise à déterminer les variations du mouvement d’une structure en raison de l’ajout ou du retrait de membrures sans résoudre tous les degrés de liberté. Les itérations changent les critères de conception à chaque étape et utilisent la factorisation de la matrice de rigidité de la conception initiale. Cette étude a développé une méthode de réanalyse pour déterminer les forces additionnelles qui agissent sur la structure initiale et les mouvements de la structure modifiée. Elle utilise les conditions de compatibilité aux interfaces entre la structure initiale et les membrures ajoutées ou retirées comme contraintes statiques et elle applique la méthode inverse généralisée pour décrire le comportement statique de la structure sous contraintes. Les éléments structuraux ajoutés peuvent être des sous-structures statiquement stables ou des membrures flottantes possédant le degré de liberté des corps rigides. Des exemples sont présentés afin de montrer l’efficacité de la méthode proposée. [ABSTRACT FROM AUTHOR]