^{1}

^{1}

^{2}

^{1}

^{2}

Edited by: Nikos D. Lagaros, National Technical University of Athens, Greece

Reviewed by: Stavros Chatzieleftheriou, National Technical University of Athens, Greece; Peng Pan, Tsinghua University, China

Specialty section: This article was submitted to Earthquake Engineering, a section of the journal Frontiers in Built Environment

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

A method of physical parameter system identification (SI) is proposed here for three-dimensional (3D) building structures with in-plane rigid floors in which the stiffness and damping coefficients of each structural frame in the 3D building structure are identified from the measured floor horizontal accelerations. A batch processing least-squares estimation method for many discrete time domain measured data is proposed for the direct identification of the stiffness and damping coefficients of each structural frame. Although previous researches on the SI of 3D building structures are limited to a class of structures with regular eccentricity, this article removes this limitation. Advantageous features of the proposed identification method are that it is unnecessary to specify the stiffness eccentricities (location of the center of stiffness) before identification, and the identification of all stiffness and damping parameters can be performed simultaneously. The reliability and accuracy of the proposed method are demonstrated by numerical simulations.

A new physical parameter system identification (SI) theory is proposed in this article for three-dimensional (3D) building structures with in-plane rigid floors in which the stiffness and damping coefficients of each structural frame in the 3D building structure are identified from the measured floor horizontal accelerations. Research on physical parameter SI of 3D building structures with eccentricity is very limited (for example, Omrani et al.,

Recently, the business continuity plan (BCP) has been discussed academically and practically with great interest in the construction and operating management of various built environments. Unexpected hazards experienced during the last few decades made BCP a key subject, and many significant attempts on BCP have been made. It is recognized worldwide that the structural health monitoring plays a key role in BCP.

The structural health monitoring has a long history in many engineering fields, such as civil, mechanical, and aerospace engineering (Boller et al.,

In the field of physical parameter SI, Nakamura and Yasui (

To develop a hybrid method of the modal parameter SI and physical parameter SI, some researchers proposed a reliable SI method in which the physical parameters are identified from the preidentified modal parameters (Hjelmstad et al.,

As another effective approach, the SI method using Kalman filter or extended Kalman filter was developed many years ago (Hoshiya and Saito,

A method of physical parameter SI is proposed here for 3D building structures with in-plane rigid floors. A batch processing least-squares estimation method for many discrete time domain measured data is proposed for the direct identification of the stiffness and damping coefficients of each structural frame in the 3D building structure. The reliability and accuracy of the proposed method are demonstrated by numerical simulations.

Consider an

This building model is subjected to the horizontal ground acceleration

Let

A more detailed explanation can be found in Figures

Let

The vectors

The mass matrix

The mass _{i}_{ri}

On the other hand, the stiffness matrix

In Eq.

Finally, the damping matrix

In this section, a new formulation of direct SI is presented. An advantageous feature of the proposed identification method is that it is unnecessary to specify the stiffness eccentricities (location of center of stiffness) before identification.

Assume that

By transforming the equations of motion into the equations in terms of unknown parameters, i.e., stiffness and damping coefficients, the following relations are derived.

As for

The errors in Eq.

The sum of the squares of the errors _{1} to _{2} can be expressed by

The differential of

The least-squares estimation method incorporating the batch processing (Takewaki and Nakamura,

It is important to note that the identification of all stiffness and damping parameters can be performed simultaneously.

To verify the validity and accuracy of the proposed method, a three-story model and a five-story model as shown in Figures

Number of stories | Coordinates of center of mass |
Number of stories | Coordinates of center of mass |
||||
---|---|---|---|---|---|---|---|

3 story | 5 story | ||||||

G4 = (7,10.5) | G5 = (7,10.5) | ||||||

Lx = 10 | Ly = 15 | 16,500 | Lx = 10 | Ly = 15 | 16,500 |

Figure

To investigate the effect of the input direction of ground motions on the identification accuracy, ϕ = 0, π/5 were used in addition to ϕ = π/4. It has been confirmed that the sufficient accuracy is maintained regardless of the input motion direction. As for the effect of the location of data window used for identification on the identification accuracy, no remarkable effect has been observed except during the short duration at the beginning. Furthermore, it has been found that the duration longer than 2 s is sufficient.

To investigate the effect of noise on the accuracy of identification (Koyama et al.,

Figure

Since the present theory has flexibility and generality (treatment of each vertical frame as independent stiffness and damping element), it can be extended to 3D building structures with in-plane flexible floors by specifying the in-plane flexibility of floors. There are four degrees of freedom in each story (four horizontal degrees of freedom). The four degrees of freedom in each story are related by introducing the in-plane shear stiffness of flexible floors. Because the batch processing least-squares estimation method explained in Section “

A method of physical parameter SI has been proposed for 3D building structures in which the stiffness and damping coefficients of each structural frame in the building structure are identified from the measured floor horizontal accelerations. The following conclusions have been derived.

A batch processing least-squares estimation method for many discrete measured data has been proposed for the direct identification of the stiffness and damping coefficients of each story. A model with in-plane rigid floors has been used as the model for the physical parameter SI. Advantageous features of the proposed identification method are that it is unnecessary to specify the stiffness eccentricities (location of center of stiffness) before identification, and the identification of all stiffness and damping parameters can be performed simultaneously.

Numerical simulations have been conducted for three-story and five-story 3D building structures with different mass and stiffness eccentricities. It has been demonstrated that, irrespective of the condition of mass and stiffness eccentricities, the proposed method is reliable and accurate in noise-free models. On the other hand, the identification accuracy degrades gradually as the noise level increases. However, a certain accuracy level can be maintained by limiting the level of noise.

KS formulated the problem, conducted the computation, and wrote the paper. SY supervised the research, helped the computation, and wrote the paper. IT supervised the research and wrote the paper.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer SC and the handling editor declared their shared affiliation, and the handling editor states that the process nevertheless met the standards of a fair and objective review.

Part of the present work is supported by the Grant-in-Aid for Scientific Research (KAKENHI) of Japan Society for the Promotion of Science (No. 15H04079) and Sumitomo Rubber Industries, Co. This support is greatly appreciated.