Introduction

Since ancient times, earthquakes have significantly impacted people’s livelihoods. For example, the 2010 Haiti earthquake1, 2011 Tohoku earthquake and tsunami2, and 2016 Kumamoto earthquake3. As a result, preparation for earthquakes is becoming increasingly important. A key issue is the diagnosis of damage caused by earthquakes4. This is particularly important for detached wooden houses in Japan5. Therefore, research on structural health monitoring of detached wooden houses is gaining momentum6.

Structural health monitoring can be broadly divided into two types: characteristics and responses. Characteristic monitoring is used to evaluate the characteristics of a building, including its vibrational properties, stiffness, and damping. It can assess the structural integrity of a building based on changes before, during, and after an earthquake7,8,9. For example, it has been reported that when an earthquake damages structural parts, the stiffness and natural frequency of the building decrease7,8. However, natural frequencies are affected by other factors such as aging, temperature, and humidity10. Therefore, using natural frequencies to assess building damage is difficult. In contrast, response monitoring evaluates a building’s response to external forces such as earthquakes and wind. It is based on acceleration, interstory drift, and other building responses and can directly evaluate the damage caused by earthquakes.

As a response monitoring method for high-rise buildings, the interstory drift angles of each layer are measured by attaching an accelerometer to each floor11. The interstory drift angle is obtained by dividing the interstory drift between building by the height between the layers. It can assess the damage to a building by comparing it with a threshold value established by preliminary structural analysis. However, the requirement for a preliminary structural analysis is impractical for adapting to individual houses already built. In addition, it has been reported that large displacements of buildings cause large errors when this method is used12. To overcome these problems, methods that use restoring force characteristics for structural health monitoring have attracted attention in recent years13,14. The restoring force refers to the force that causes a building to return to its original shape when it is deformed, for example, by shaking, as in an earthquake. When the deformation of the building is relatively small, that is, when the deformation is within the elastic range, the building recovers completely. In contrast, when large displacements cause damage to the building, that is, the deformation is within the inelastic range, permanent deformation remains and the restoring force becomes smaller. Therefore, the extent of damage can be determined by measuring the characteristics of the restoring force against an earthquake and checking whether the displacements are within the elastic or inelastic range.

The restoring force characteristics can be obtained from the response acceleration and interstory drift. To achieve this, a method using multiple accelerometers has been proposed13,14. In this method, accelerometers are attached to the first and second floors. The response acceleration corresponded to the accelerations of the second floor, and the interstory drift was calculated by integrating the difference between the two accelerations. However, this conventional technology requires a highly accurate time synchronization of the accelerometers attached to each layer. This requires a complex and expensive system that is difficult to adapt to individual houses. Furthermore, the interstory drift is calculated by integrating the acceleration twice, which results in integration errors, and there are still measurement restrictions14; therefore, additional methods are required to measure the interstory drift of individual houses accurately.

To measure interstory drift, displacement memory sensors15, laser displacement transducers16, GNSS (Global Navigation Satellite System) displacement transducers17, optical position sensors18, and camera-based methods19,20,21,22,23 have been proposed. However, displacement memory sensors, laser displacement transducers, and GNSS displacement transducers must be installed and synchronized with multiple sensors, which is still problematic for individual houses. Optical position sensors require installation of an LED light source on the ceiling. For camera-based methods, displacement measurement methods have been researched for structural monitoring, such as railway bridge24,25,26, building19,20,21,22,23, and various other structures27, have been researched for structural monitoring. The studies on buildings, in particular, have applied methods to measure interstory drift and successfully demonstrated them. However, these camera-based methods cannot obtain the restoring force characteristics because the response acceleration cannot be measured using only a camera.

In this study, we propose a new and simple measurement method to obtain restoring force characteristics using a camera and an accelerometer. The interstory drift is measured using a camera. The response acceleration, which could not be measured by the camera alone, was calculated by adding the ground acceleration measured by the accelerometer to the interstory acceleration measured by the camera. Furthermore, these instruments can be used to obtain the restoring-force characteristics of a house when a single-mass system is assumed. The proposed method can directly measure displacement using a camera, eliminating the need to integrate acceleration and avoiding integration errors. It can also eliminate synchronization difficulties because the camera and accelerometer are wired, connected to each other, and run on the same clock. Furthermore, the proposed device can calculate the response acceleration, which is difficult to calculate in the conventional form. In this study, the concept of the proposed method is verified using a small-scale model, and the effect of camera sampling rate on the proposed method is evaluated. In addition, a compact prototype device consisting of a camera and accelerometer is fabricated, and the restoring force characteristics of a full-scale two-by-four wood-framed building is demonstrated using the fabricated device.

Proposed method

The proposed method is illustrated in Fig. 1. This method aims to obtain a skeleton curve, which is a restoring force characteristic, using a camera and an accelerometer. Figure 1 (a) shows an overview of the measurement setup. A camera and accelerometer are installed on the first floor. The accelerometer measures the ground acceleration and is used to calculate the response acceleration. The camera measures the interstory drift directly and is used to calculate the response acceleration. The proposed method considers a detached house as a single-degree-of-freedom (SDOF) model according to previous studies28,29,30. The section comprising the second floor and above is considered the mass, and the first floor is considered the ground. Therefore, the displacement of the mass in the SDOF model corresponds to the interstory drift between the first and second floors. In general, the equation of motion for a single-mass system is expressed as follows:

m\ddot{X}+Q=-m{a}_{0}.
(1)

where \:Q denotes the restoring force of the building, \:X denotes the interstory drift between the first and second floors, \:\ddot{X} denotes twice the derivative of \:X, \:{a}_{0} denotes the ground acceleration, and \:m denotes the building mass. Therefore, the response acceleration corresponding to the restoring force can be expressed as