## Engineering and Mathematical Sciences

#### Presentation Title

ARMA Models for Detection of Earthquake-Induced Damage in Instrumented Buildings

#### Abstract

System identification is the process of developing or improving a mathematical representation of a physical system using experimental data. The main advantage of system identification is the improvement of the analytical model of a structure. When performing system identification experiments, it is important to have appropriate input(s) and output(s). The identification task is to identify a model which properly find a map between input and output.

Techniques to identify a model from input and output data typically contain two steps: First, a family of candidate models is chosen and the particular member in this family is determined which satisfactorily describes the observed data. The determination is based on some error criterion such as minimizing the measurement residuals due to the input and output noises. Second, the determined model is transformed to the desired form for further use such as modal parameter identification or controller designs.

Assessing the state of health of structural systems after extreme loadings such as ground motions is a way to determine whether the structure is safe to use or not. A strategy that has great potential for post-earthquake safety assessment is the use of measurements obtained from sensors. Although this idea is immediately appealing, there are many difficulties in transferring the concept to an approach that can operate robustly in the conditions encountered in practice. Some facts worth noting from the outset are:

• Structures are only partially instrumented; a typical situation is to have instrumentation at the base, the roof, and perhaps one or two intermediate floors.
• Full characterization of the input is difficult. The lack of a full characterization of the input derives from several sources. One that can be easily resolved is lack of sufficient sensors to estimate rocking. A much more difficult one, however, is the fact that the forces that come from interaction of the structure with the soil along basement walls contribute to the input and cannot be readily measured.
• Measurements are noisy.
• Damage is a generic term used to describe a perception on the state of a system but is not a directly measurable quantity.

This procedure described has been applied to several buildings of CESMD database and the results are in agreement with the empirical observations from the field in all cases. A data-driven approach for post-earthquake posting of buildings has been done based on the analysis of residuals obtained as differences between measured responses and reference signals computed using a set of observers.

The advantage of implementing this method is that the health state of the structure could be evaluated without needing a model of it. So, the behavior of the structure could be captured just with instrumenting the building, which can be optimized such that with a minimum number of sensors, the response of structure can be predicted for future events.

Eric Hernandez

#### Student College

College of Engineering and Mathematical Sciences

#### Program/Major

Civil Engineering

#### Primary Research Category

Engineering & Physical Sciences

#### Share

COinS

ARMA Models for Detection of Earthquake-Induced Damage in Instrumented Buildings

System identification is the process of developing or improving a mathematical representation of a physical system using experimental data. The main advantage of system identification is the improvement of the analytical model of a structure. When performing system identification experiments, it is important to have appropriate input(s) and output(s). The identification task is to identify a model which properly find a map between input and output.

Techniques to identify a model from input and output data typically contain two steps: First, a family of candidate models is chosen and the particular member in this family is determined which satisfactorily describes the observed data. The determination is based on some error criterion such as minimizing the measurement residuals due to the input and output noises. Second, the determined model is transformed to the desired form for further use such as modal parameter identification or controller designs.

Assessing the state of health of structural systems after extreme loadings such as ground motions is a way to determine whether the structure is safe to use or not. A strategy that has great potential for post-earthquake safety assessment is the use of measurements obtained from sensors. Although this idea is immediately appealing, there are many difficulties in transferring the concept to an approach that can operate robustly in the conditions encountered in practice. Some facts worth noting from the outset are:

• Structures are only partially instrumented; a typical situation is to have instrumentation at the base, the roof, and perhaps one or two intermediate floors.
• Full characterization of the input is difficult. The lack of a full characterization of the input derives from several sources. One that can be easily resolved is lack of sufficient sensors to estimate rocking. A much more difficult one, however, is the fact that the forces that come from interaction of the structure with the soil along basement walls contribute to the input and cannot be readily measured.
• Measurements are noisy.
• Damage is a generic term used to describe a perception on the state of a system but is not a directly measurable quantity.

This procedure described has been applied to several buildings of CESMD database and the results are in agreement with the empirical observations from the field in all cases. A data-driven approach for post-earthquake posting of buildings has been done based on the analysis of residuals obtained as differences between measured responses and reference signals computed using a set of observers.

The advantage of implementing this method is that the health state of the structure could be evaluated without needing a model of it. So, the behavior of the structure could be captured just with instrumenting the building, which can be optimized such that with a minimum number of sensors, the response of structure can be predicted for future events.