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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/.)

We propose a novel sensor system for monitoring the structural health of a building. The system optically measures the relative-story displacement during earthquakes for detecting any deformations of building elements. The sensor unit is composed of three position sensitive detectors (PSDs) and lenses capable of measuring the relative-story displacement precisely, even if the PSD unit was inclined in response to the seismic vibration. For verification, laboratory tests were carried out using an

Recently, relative-story displacement measurements have attracted much attention because of their capability of directly monitoring building damage [

A possible solution is to measure the local inclination angle and the torsion angle as well as the relative-story displacement. Such a measurement has already been realized in the image stabilizer of a digital camera by which the captured image is automatically stabilized against unstable handling using an embedded gyro sensor [

In this paper, we propose a novel sensor system composed of three pairs of position sensitive detectors (PSDs) and light emitting diode (LED) arrays. The three LED arrays are fixed on the ceiling whereas the three PSDs are installed in one place on the floor so that each PSD captures the motion of the corresponding LED array. First, we show that, using this sensor system, the relative-story displacement, the local inclination angle, and the torsion angle can be measured independently. Because the LED light propagates otropically, the inclination angle of the LED,

_{0}, 0, 0) and (0, _{0}, 0), respectively.

The position of three LED light sources fixed on the ceiling is located at (0, 0, _{0}, 0, _{0}, _{x}, _{y}) is the lateral displacement of the LED1, and (_{x}, _{y}) is the inclination angle of the PSD unit1 [_{2}, _{2}) focused on the PSD2 is expressed as:

We assume that in _{x}, _{y} and the torsion angle _{2}, _{2}) and (_{3}, _{3}) in response to the torsional motion of the upper layer is depicted in _{1}, _{1}, _{2}, _{2}, _{3}, _{3}) are included. Namely, for solving these simultaneous equations, the _{x}, _{y}, _{y}, _{x}) can be determined without _{2} as follows:

_{1}, _{2}, _{3}) and (_{1}, _{3}) can be calculated independently. Namely, (_{1}, _{2}, _{3}) can be calculated using (_{x}, _{y}, _{1}, _{3}) can be calculated using (_{y}, _{x}). We note that the relative-story displacement _{x} depends not on the torsion angle _{y}. This indicates that, for measuring the relative-story displacement, we must focus on the inclination angle _{y} rather than the torsion angle

_{x} and the inclination angle _{y}. Two pairs of LED arrays and PSD units were set up laterally at a distance of 3.5 m. To simply verify the methodology, we utilized two PSD units and solved the problem concerning two-degrees of freedom. In the three-pair-combined PSD unit system, the PSD unit2 and the PSD unit3 are arranged symmetrically, indicating that the verification is sufficient by concerning the two-degrees of freedom. As shown in

In the static experiment, the shaking table was fixed and the PSD units were displaced using the _{y}-direction were measured using the PSD unit1 and the PSD unit2. In this experiment, the values (_{x}, _{y}) measured by the laser distance meter and the autocollimator were used as the reference.

In the dynamic response experiment, the _{y} and the displacement _{x} were simultaneously measured in real time using the PSD unit1 and the PSD unit2 when the shaking table and the

_{1} and _{2} are the output voltages from PSD1 and PSD2, respectively, in the unit of volt, _{x} is the lateral displacement of the _{y} is the inclination angle of the

Note that (_{1}, _{2}) is in the units of millimeters, but (_{1}, _{2}) involves the rotational component in addition to the displacement. The matrix for transforming (_{1}, _{2}) into (_{x}, _{y}) can be determined as the inverse of the transformation matrix in

We investigated the resolution, which was the most important performance of the combined PSD unit system. The resolution is given by the following equations [

By using the matrix ^{−1}, the resolution of the combined PSD unit system can be calculated as follows:
_{1} is the resolution in the displacement measurement, _{2} is that in the inclination angle measurement, and _{1} and _{2} are the resolution of the PSDs. We assume that _{1} = _{2} = 0.6 μm in accordance with the data sheet from the vendor [

As shown in _{0}, and the focal length of the lens _{0} (=120 mm) and focal length

_{y} and the displacement _{x} were simultaneously measured in real time using the PSD unit1 and the PSD unit2 when the shaking table and the

A novel sensor system to measure both the relative-story displacement and the local inclination angle was developed using three pairs of PSD units. We established the theory for calculating the relative-story displacement and the local inclination angle from the output voltage of the PSD units and verified the theory by both static experiment and dynamic experiments. The accuracy of the LDS system was experimentally evaluated to be approximately 150 μm in the relative displacement measurement and 100 μrad in the inclination angle measurement. It is clear that the proposed sensor system can measure the relative-story displacement even if the PSD unit is inclined due to the seismic vibration. This indicates that the proposed sensor system can be installed in any point of an actual building. Moreover, because the calculation of the relative-story displacement and the inclination angle is a comparatively easy task, we can realize real-time multipoint measurements. In short, this system is useful for identifying the damage-sensitive elements and evaluating the seismic capacity of the building.

This research was supported by “Ambient SoC Global COE Program of Waseda University”, Grants-in-Aid for Young Scientists (B) of KAKENHI (21710172), and Grants-in-Aid for Scientific Research (B) of KAKENHI (21360271) of the Ministry of Education, Culture, Sports, Science and Technology, Japan.

Schematic diagram of the relative-story displacement sensor.

Cross-section view of the relative-story displacement sensor.

Displacement of the light spot which comes from the LED and is focused on the PSD surface by the lens in response to the torsional motion of the upper layer. The schematic shows the _{0}·_{0}·

Experimental setup for measuring the relative-story displacement and the inclination angle using two PSD units.

Output voltages from the PSD units according to _{x} and _{y} in the static experiments.

The results of the dynamic experiments using the shaking table and the _{x}; and _{y}.