MEMS Vibrational Power Generator for Bridge Slab and Pier Health Monitoring

Micro energy harvesters (MEH) based on microelectromechanical systems (MEMS) are rapidly developing, providing a green and virtually infinite energy source. The electrostatic vibratory power generator outputs electric power when it vibrates, motivating us to apply it to vibrating civil infrastructures excited by ambient and daily traffic loadings. In this study, an innovative monitoring system utilizing MEH devices was proposed for detecting slab damage and pier scours for bridge structures. Its performance was numerically investigated with finite element models, where the damage in slabs was modeled with a reduced Young’s modulus and scours with fixed boundaries of inclined depth. It was shown that the powers generated at each MEH varied as the target structure’s modal frequency shifted and amplitude changed by damage or scour. A power generation index was proposed to identify slab damage and a reference-free method was introduced to detect uneven pier scours. Utilizing an electrostatic vibration-based MEH (MEMS vibrational power generator), this pioneering study showed that MEMS vibrational power generators can work as sensors for an infrastructure structural health monitoring system.


Development of Sensors with MEMS Technologies
It is expected that various sensing devices would be installed in infrastructure and a lot of services utilizing big data would be created and socially provided by the Internet [13][14][15]. In a "Trillion sensors society", which is aimed for by the TSensors (Trillion Sensors) project [16,17], it is clearly indicated that our society and life are greatly changed in all fields, such as medical health care, agriculture, environment, and infrastructure, and the whole society is connected to the network by many sensor terminals.
In infrastructure monitoring, developments in sensor device and IoT technology are indispensable. At the same time, it is considered that a self-powered (battery-free) device is necessary to build the sensor network and deliver reliable and long-term performance for civil infrastructures in their service life with environmental conditions. Energy harvesters are categorized into three types depending on the operational principles: electromagnetic transduction [18,19], electrostatic transduction [18,20], and piezoelectric transduction [18,21]. Several studies have been conducted on characterizing the environment-and bridge structural type-dependent vibrations and on quantifying the powers harvested from those vibrations using comb-shaped silicon electrets (see Figure 1) [22].
In the electret electrostatic microelectromechanical systems (MEMS) energy harvester, as shown in Figure 2, the electret is a vibrating mass supported by a spring and forms a variable capacitance when it is facing a fixed electrode through an air gap. It is possible to output the current with power generation based on the frequency response synchronized with the movement of the electrode (oscillation). The structure can be designed to efficiently obtain the generation amount only in a certain frequency band [22]. As a small wireless device of coin size for the purpose of frequency detection of environmental vibration, it can be easily mounted without any space and wiring problems. Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 13 Figure 1. A schematic model of the vibration energy harvester [22]. A vibration-based micro energy harvester (MEH) device is proposed to monitor the health of RC concrete slabs and pier scours in this study. MEH devices are introduced with microelectromechanical systems (MEMS) technology. They harvest micro energy from its environmental energy source such as light, wind, heat, and electromagnetic field vibration and convert it into electric energy. If they can be integrated into (or embedded in) infrastructure monitoring sensors, they can supply the sensors' power and, to a certain extent, make the sensors self-sustaining, needing no cable connection to the electricity power grid.
In terms of power-generating capacity, light-, vibration-, and wind-sourced MEH devices perform comparatively better than the other choices, such as heat-and electromagnetic-sourced MEH. Among the three types of MEH (light-, vibration-, and wind-based), a vibration-based MEH device is the only one that can function in lightless, windless, dark, or night conditions and inside the box girders. Therefore, a vibration-based MEH is proposed for bridge structural health monitoring. The vibration-based MEH device used herein (see Figure 3) was identical to those proposed in previous studies [22], which is an inexpensive coin-sized device that can generate over 100 µW RMS (root mean square) of output electric power under 0.03 GRMS accelerations.

MEMS Vibrational Power Generator
As described above, the vibration power generation device (MEMS vibrational power generator) has a fixed and a movable comb electrode. Presuming that the same impedance as the internal  A vibration-based micro energy harvester (MEH) device is proposed to monitor the health of RC concrete slabs and pier scours in this study. MEH devices are introduced with microelectromechanical systems (MEMS) technology. They harvest micro energy from its environmental energy source such as light, wind, heat, and electromagnetic field vibration and convert it into electric energy. If they can be integrated into (or embedded in) infrastructure monitoring sensors, they can supply the sensors' power and, to a certain extent, make the sensors self-sustaining, needing no cable connection to the electricity power grid.
In terms of power-generating capacity, light-, vibration-, and wind-sourced MEH devices perform comparatively better than the other choices, such as heat-and electromagnetic-sourced MEH. Among the three types of MEH (light-, vibration-, and wind-based), a vibration-based MEH device is the only one that can function in lightless, windless, dark, or night conditions and inside the box girders. Therefore, a vibration-based MEH is proposed for bridge structural health monitoring. The vibration-based MEH device used herein (see Figure 3) was identical to those proposed in previous studies [22], which is an inexpensive coin-sized device that can generate over 100 µW RMS (root mean square) of output electric power under 0.03 GRMS accelerations.

MEMS Vibrational Power Generator
As described above, the vibration power generation device (MEMS vibrational power generator) has a fixed and a movable comb electrode. Presuming that the same impedance as the internal A vibration-based micro energy harvester (MEH) device is proposed to monitor the health of RC concrete slabs and pier scours in this study. MEH devices are introduced with microelectromechanical systems (MEMS) technology. They harvest micro energy from its environmental energy source such as light, wind, heat, and electromagnetic field vibration and convert it into electric energy. If they can be integrated into (or embedded in) infrastructure monitoring sensors, they can supply the sensors' power and, to a certain extent, make the sensors self-sustaining, needing no cable connection to the electricity power grid.
In terms of power-generating capacity, light-, vibration-, and wind-sourced MEH devices perform comparatively better than the other choices, such as heat-and electromagnetic-sourced MEH. Among the three types of MEH (light-, vibration-, and wind-based), a vibration-based MEH device is the only one that can function in lightless, windless, dark, or night conditions and inside the box girders. Therefore, a vibration-based MEH is proposed for bridge structural health monitoring. The vibration-based MEH device used herein (see Figure 3) was identical to those proposed in previous studies [22], which is an inexpensive coin-sized device that can generate over 100 µW RMS (root mean square) of output electric power under 0.03 G RMS accelerations.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 13  A vibration-based micro energy harvester (MEH) device is proposed to monitor the health of RC concrete slabs and pier scours in this study. MEH devices are introduced with microelectromechanical systems (MEMS) technology. They harvest micro energy from its environmental energy source such as light, wind, heat, and electromagnetic field vibration and convert it into electric energy. If they can be integrated into (or embedded in) infrastructure monitoring sensors, they can supply the sensors' power and, to a certain extent, make the sensors self-sustaining, needing no cable connection to the electricity power grid.
In terms of power-generating capacity, light-, vibration-, and wind-sourced MEH devices perform comparatively better than the other choices, such as heat-and electromagnetic-sourced MEH. Among the three types of MEH (light-, vibration-, and wind-based), a vibration-based MEH device is the only one that can function in lightless, windless, dark, or night conditions and inside the box girders. Therefore, a vibration-based MEH is proposed for bridge structural health monitoring. The vibration-based MEH device used herein (see Figure 3) was identical to those proposed in previous studies [22], which is an inexpensive coin-sized device that can generate over 100 µW RMS (root mean square) of output electric power under 0.03 GRMS accelerations.

MEMS Vibrational Power Generator
As described above, the vibration power generation device (MEMS vibrational power generator) has a fixed and a movable comb electrode. Presuming that the same impedance as the internal

MEMS Vibrational Power Generator
As described above, the vibration power generation device (MEMS vibrational power generator) has a fixed and a movable comb electrode. Presuming that the same impedance as the internal Appl. Sci. 2020, 10, 8258 4 of 13 impedance of the vibration power generator is connected to the device, the expected RMS output power can be calculated from Equations (1) and (2), where the conversion efficiency from the linear equivalent circuit of the electrostatic actuator is considered [22].
The effective value is the root mean square (RMS) of all instantaneous values within a certain interval, which means the power contained in the vibration waveform. Since all values other than the acceleration are determined by the structure of the MEMS vibrational power generator, the power generation depends only on the magnitude of the effective acceleration value. Knowing that acceleration is proportional to vibration amplitude and frequency squared, it is expected that the generated energy would increase as amplitude and frequency increase.
The force factor A is expressed by Equation (3) and the relationship between the force factor and the current I (short circuit current) is expressed by Equation (4).
where n is number of comb electrodes,  Table 1 shows the design parameters of the MEMS vibrational power generator which is investigated in this study.

Objective
This study focuses on bridge structural health monitoring by installing on slabs and piers the vibration-based power generation devices, which can generate power by converting environmental vibrations into electric energy by electrostatic induction and can detect slab damage and pier scours by the change in the generated energy. An energy generation index to detect slab damage and a reference-free method to detect uneven pier scour are proposed. To illustrate and verify them, numerical slab models and pier models are constructed, and their modal frequencies and mode shapes are obtained by eigenvalue analyses. Damage-induced change in modal frequency and mode shapes are investigated, in which the analytical details are given in Section 2. The energy generated from the vibrations of the numerical models are calculated and the proposed methods are introduced, with their verification in Section 3. Finally, several concluding remarks are provided in the last section.

Outline of Eigen-Modal Analysis
It is known that the dominant vibration frequency of a structure generally decreases when the stiffness of bridge components is reduced with a sort of material and structural deterioration. In this study, a vibration analysis was conducted on slab and pier models with several damage scenarios to reveal the frequency change and modal amplitude change caused by damage. For the slab model, it consisted of six uniform panels, whose material properties were tuned down to model damage. For the pier model, it consisted of four identical panels and the riverbed level was tuned down to model scouring.
This numerical vibration analysis was conducted using finite element analysis software suite ABAQUS 6.14. After the finite element models' construction, eigenvalue analysis was conducted to obtain the modal properties for each model. Based on the vibration analysis results, generated power is calculated according to the MEH device structure. The eigenvalue problem for a finite element model is involved in solving the eigenequation shown in Equation (5).
where K is the global stiffness matrix (sparse positive definite matrix of size n × n), M is the global mass matrix (sparse positive-definite matrix of size n × n), λ is the eigenvalue, x is the eigenvector, and n is the number of degrees of freedom. In ABAQUS, the Lanczos inverse power method is used to solve the eigenvalue problem, especially in a case where lower vibration modes are of more concern. Figure 4 shows the slab model in this study, which consists of six concrete panels and two steel footing girders of I shape. Simplifying the model, there is no reinforcement simulated in geometrical information. They were all modelled with solid elements, in which the panels as well as the panels and girders are rigidly connected. To investigate the damage (deterioration)-induced modal property change, four cases in Figure 5 were considered and this study only investigated single panel damage: one intact case (labelled as Case 0) and three damage cases (Case 1, 2, and 3). Case 0 served as the reference, whose material properties for concrete and steel bars were set as those given by the design drawings, while Cases 1, 2, and 3 had their first (P1), second (P2), and third panel (P3) damaged, respectively, whose concrete material properties were tuned down (see Table 2). Steel bars were considered intact all the time. As mentioned previously, eigenvalue analysis was conducted for the four cases to obtain their modal frequencies and modal shapes.

Slab Model with Concrete Material Deterioration
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13

Outline of Eigen-Modal Analysis
It is known that the dominant vibration frequency of a structure generally decreases when the stiffness of bridge components is reduced with a sort of material and structural deterioration. In this study, a vibration analysis was conducted on slab and pier models with several damage scenarios to reveal the frequency change and modal amplitude change caused by damage. For the slab model, it consisted of six uniform panels, whose material properties were tuned down to model damage. For the pier model, it consisted of four identical panels and the riverbed level was tuned down to model scouring.
This numerical vibration analysis was conducted using finite element analysis software suite ABAQUS 6.14. After the finite element models' construction, eigenvalue analysis was conducted to obtain the modal properties for each model. Based on the vibration analysis results, generated power is calculated according to the MEH device structure. The eigenvalue problem for a finite element model is involved in solving the eigenequation shown in Equation (5).
where K is the global stiffness matrix (sparse positive definite matrix of size n × n), M is the global mass matrix (sparse positive-definite matrix of size n × n), λ is the eigenvalue, x is the eigenvector, and n is the number of degrees of freedom. In ABAQUS, the Lanczos inverse power method is used to solve the eigenvalue problem, especially in a case where lower vibration modes are of more concern. Figure 4 shows the slab model in this study, which consists of six concrete panels and two steel footing girders of I shape. Simplifying the model, there is no reinforcement simulated in geometrical information. They were all modelled with solid elements, in which the panels as well as the panels and girders are rigidly connected. To investigate the damage (deterioration)-induced modal property change, four cases in Figure 5 were considered and this study only investigated single panel damage: one intact case (labelled as Case 0) and three damage cases (Case 1, 2, and 3). Case 0 served as the reference, whose material properties for concrete and steel bars were set as those given by the design drawings, while Cases 1, 2, and 3 had their first (P1), second (P2), and third panel (P3) damaged, respectively, whose concrete material properties were tuned down (see Table 2). Steel bars were considered intact all the time. As mentioned previously, eigenvalue analysis was conducted for the four cases to obtain their modal frequencies and modal shapes.   Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13

Outline of Eigen-Modal Analysis
It is known that the dominant vibration frequency of a structure generally decreases when the stiffness of bridge components is reduced with a sort of material and structural deterioration. In this study, a vibration analysis was conducted on slab and pier models with several damage scenarios to reveal the frequency change and modal amplitude change caused by damage. For the slab model, it consisted of six uniform panels, whose material properties were tuned down to model damage. For the pier model, it consisted of four identical panels and the riverbed level was tuned down to model scouring.
This numerical vibration analysis was conducted using finite element analysis software suite ABAQUS 6.14. After the finite element models' construction, eigenvalue analysis was conducted to obtain the modal properties for each model. Based on the vibration analysis results, generated power is calculated according to the MEH device structure. The eigenvalue problem for a finite element model is involved in solving the eigenequation shown in Equation (5).
where K is the global stiffness matrix (sparse positive definite matrix of size n × n), M is the global mass matrix (sparse positive-definite matrix of size n × n), λ is the eigenvalue, x is the eigenvector, and n is the number of degrees of freedom. In ABAQUS, the Lanczos inverse power method is used to solve the eigenvalue problem, especially in a case where lower vibration modes are of more concern. Figure 4 shows the slab model in this study, which consists of six concrete panels and two steel footing girders of I shape. Simplifying the model, there is no reinforcement simulated in geometrical information. They were all modelled with solid elements, in which the panels as well as the panels and girders are rigidly connected. To investigate the damage (deterioration)-induced modal property change, four cases in Figure 5 were considered and this study only investigated single panel damage: one intact case (labelled as Case 0) and three damage cases (Case 1, 2, and 3). Case 0 served as the reference, whose material properties for concrete and steel bars were set as those given by the design drawings, while Cases 1, 2, and 3 had their first (P1), second (P2), and third panel (P3) damaged, respectively, whose concrete material properties were tuned down (see Table 2). Steel bars were considered intact all the time. As mentioned previously, eigenvalue analysis was conducted for the four cases to obtain their modal frequencies and modal shapes.

Pier Model with Scour
The pier's dimensions and the FE model are shown in Figure 6. The observation points are marked by red points No. 1, 2, and 3, where the powers generated by the MEMS vibrational power generator were to be calculated. The concrete material properties are as follows: elastic modulus 30 GPa, Poisson's ratio 0.2, and density 2400 kg/m 3 . The x-axis pointed toward the river flow direction (perpendicular to bridge longitudinal), the y-axis toward the bridge longitudinal, and the z axis toward bridge transverse.

Pier Model with Scour
The pier's dimensions and the FE model are shown in Figure 6. The observation points are marked by red points No. 1, 2, and 3, where the powers generated by the MEMS vibrational power generator were to be calculated. The concrete material properties are as follows: elastic modulus 30 GPa, Poisson's ratio 0.2, and density 2400 kg/m 3 . The x-axis pointed toward the river flow direction (perpendicular to bridge longitudinal), the y-axis toward the bridge longitudinal, and the z axis toward bridge transverse.
Two cases were considered: one free from and the other one subject to scouring. As shown in Figure 7, the scouring-free pier model had a uniform riverbed of height 3000 mm and the scouring pier model had an inclined riverbed linearly varying from 500 mm at P1 (upstream side) to 3000 mm at P4 (downstream side). The riverbeds were modelled by fixed boundary conditions for simplicity.

Slab Model
For all slab cases (Case 0, 1, 2, and 3), eigenvalue analysis was conducted to obtain their modal frequencies and mode shapes. Table 3 shows the first two bending modal frequencies (Modes 1 and 3) and the first torsion mode (Mode 2). As expected, the three modal frequencies in Case 1, 2, and 3 were all smaller than those in Case 0; when damage occurred somewhere in the slab (Case 1, 2, and 3), the modal frequency dropped.
However, it is difficult to localize the damage in the slab merely from the frequency change. Comparing the three modal frequencies from Case 1, 2, and 3, no clues are found to localize the damage. This is because modal frequencies do not provide any spatial information. To localize Two cases were considered: one free from and the other one subject to scouring. As shown in Figure 7, the scouring-free pier model had a uniform riverbed of height 3000 mm and the scouring pier model had an inclined riverbed linearly varying from 500 mm at P1 (upstream side) to 3000 mm at P4 (downstream side). The riverbeds were modelled by fixed boundary conditions for simplicity.

Pier Model with Scour
The pier's dimensions and the FE model are shown in Figure 6. The observation points are marked by red points No. 1, 2, and 3, where the powers generated by the MEMS vibrational power generator were to be calculated. The concrete material properties are as follows: elastic modulus 30 GPa, Poisson's ratio 0.2, and density 2400 kg/m 3 . The x-axis pointed toward the river flow direction (perpendicular to bridge longitudinal), the y-axis toward the bridge longitudinal, and the z axis toward bridge transverse.
Two cases were considered: one free from and the other one subject to scouring. As shown in Figure 7, the scouring-free pier model had a uniform riverbed of height 3000 mm and the scouring pier model had an inclined riverbed linearly varying from 500 mm at P1 (upstream side) to 3000 mm at P4 (downstream side). The riverbeds were modelled by fixed boundary conditions for simplicity.

Slab Model
For all slab cases (Case 0, 1, 2, and 3), eigenvalue analysis was conducted to obtain their modal frequencies and mode shapes. Table 3 shows the first two bending modal frequencies (Modes 1 and 3) and the first torsion mode (Mode 2). As expected, the three modal frequencies in Case 1, 2, and 3 were all smaller than those in Case 0; when damage occurred somewhere in the slab (Case 1, 2, and 3), the modal frequency dropped.
However, it is difficult to localize the damage in the slab merely from the frequency change. Comparing the three modal frequencies from Case 1, 2, and 3, no clues are found to localize the damage. This is because modal frequencies do not provide any spatial information. To localize

Slab Model
For all slab cases (Case 0, 1, 2, and 3), eigenvalue analysis was conducted to obtain their modal frequencies and mode shapes. Table 3 shows the first two bending modal frequencies (Modes 1 and 3) and the first torsion mode (Mode 2). As expected, the three modal frequencies in Case 1, 2, and 3 were all smaller than those in Case 0; when damage occurred somewhere in the slab (Case 1, 2, and 3), the modal frequency dropped. However, it is difficult to localize the damage in the slab merely from the frequency change. Comparing the three modal frequencies from Case 1, 2, and 3, no clues are found to localize the damage. This is because modal frequencies do not provide any spatial information. To localize damage while focusing on mode shapes (e.g., see Figure 8 for Case 0), it is proposed to install the MEH devices on multiple panels to catch the relative change in energies harvested from different locations. The proposal is further discussed in Section 3.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 13 damage while focusing on mode shapes (e.g., see Figure 8 for Case 0), it is proposed to install the MEH devices on multiple panels to catch the relative change in energies harvested from different locations. The proposal is further discussed in Section 3.

Pier Model
Similarly, for the two cases (scouring-free and scouring pier models), eigenvalue analysis was conducted to obtain their modal frequencies and mode shapes. Knowing that the pier is a cantileverlike structure, the change in its bottom boundary due to scour conditions would similarly change its vibration properties. Therefore, the FEM model is simplified by omitting the superstructure with little loss of generality on the alteration of vibration behavior. Future and further work would be required to adequately model the boundary condition for the top of the pier with regard to mass and stiffness of the bridge deck. Table 4 gives the modal frequencies of the first three modes. All three modal frequencies in the scouring case were about 30% smaller than those in the scouring-free case; as expected, the modal frequencies dropped as scouring occurred.  Figure 9 shows the first three mode shapes for both the scouring-free and scouring cases, and Figure 10 shows the relative amplitude for the three observation points and the two cases. It is observed that the 1st mode is a longitudinal bending mode, and when scouring occurred, the relative amplitude in y-direction increased at Point No. 1 but decreased at Point No. 3. The 2nd mode is a torsional mode, and when scouring occurred, the relative amplitude in y-direction increased at Point No. 1 and decreased at Point No. 3. The 3rd mode is a lateral bending mode, and when scouring occurred, the relative amplitude changed little. In addition, the above three modes presented small z-direction amplitude as they are all bending modes, so the vibration in the z-direction is hardly useful in scouring detection.

Pier Model
Similarly, for the two cases (scouring-free and scouring pier models), eigenvalue analysis was conducted to obtain their modal frequencies and mode shapes. Knowing that the pier is a cantilever-like structure, the change in its bottom boundary due to scour conditions would similarly change its vibration properties. Therefore, the FEM model is simplified by omitting the superstructure with little loss of generality on the alteration of vibration behavior. Future and further work would be required to adequately model the boundary condition for the top of the pier with regard to mass and stiffness of the bridge deck. Table 4 gives the modal frequencies of the first three modes. All three modal frequencies in the scouring case were about 30% smaller than those in the scouring-free case; as expected, the modal frequencies dropped as scouring occurred.  Figure 9 shows the first three mode shapes for both the scouring-free and scouring cases, and Figure 10 shows the relative amplitude for the three observation points and the two cases. It is observed that the 1st mode is a longitudinal bending mode, and when scouring occurred, the relative amplitude in y-direction increased at Point No. 1 but decreased at Point No. 3. The 2nd mode is a torsional mode, and when scouring occurred, the relative amplitude in y-direction increased at Point No. 1 and decreased at Point No. 3. The 3rd mode is a lateral bending mode, and when scouring occurred, the relative amplitude changed little. In addition, the above three modes presented small z-direction amplitude as they are all bending modes, so the vibration in the z-direction is hardly useful in scouring detection.

Numerical Results on Power Generation
It is assumed in the numerical analysis of this study that the MEH devices are installed on the target slabs at the observation points No. 1 to 6, as shown earlier in Figure 3. Since the proposed MEH devices can be tuned very sensitively to a certain narrow frequency band of interest, it would be reasonable to assume that the devices harvested the energies from slab vibrations of a single mode. From the eigenvalue analysis (Section 2.4), each pier model's modal frequencies and mode shapes have been provided. For the following numerical analysis, the slabs are assumed to harmonically vibrate with the modal frequency and mode shape of a specified mode, and the harvested powers are

Numerical Results on Power Generation
It is assumed in the numerical analysis of this study that the MEH devices are installed on the target slabs at the observation points No. 1 to 6, as shown earlier in Figure 3. Since the proposed MEH devices can be tuned very sensitively to a certain narrow frequency band of interest, it would be reasonable to assume that the devices harvested the energies from slab vibrations of a single mode. From the eigenvalue analysis (Section 2.4), each pier model's modal frequencies and mode shapes have been provided. For the following numerical analysis, the slabs are assumed to harmonically vibrate with the modal frequency and mode shape of a specified mode, and the harvested powers are

Numerical Results on Power Generation
It is assumed in the numerical analysis of this study that the MEH devices are installed on the target slabs at the observation points No. 1 to 6, as shown earlier in Figure 3. Since the proposed MEH devices can be tuned very sensitively to a certain narrow frequency band of interest, it would be reasonable to assume that the devices harvested the energies from slab vibrations of a single mode. From the eigenvalue analysis (Section 2.4), each pier model's modal frequencies and mode shapes have been provided. For the following numerical analysis, the slabs are assumed to harmonically vibrate with the modal frequency and mode shape of a specified mode, and the harvested powers are calculated using the equations given in Section 1.4 and taking the harmonic vibrations at the observation points of interest as input. The computation on conversion from FEM results to generated energy from the vibrational MEMS device, using Equations (1)-(4), is followed by expressing sinusoidal vibrational waveform as the relationship between displacement and time in accordance to relative vibration amplitude and frequency provided from FEM analysis at each node of interest. Figure 11 shows the output power generated by the MEH for Cases 0 to 3. In all the subfigures, blue bars represent power generation in Case 0 (intact), where the slab is in a healthy condition, while red bars represent those in deteriorated cases, i.e., Cases 1, 2, or 3. Gray bars show the difference of power generation amount between intact and deteriorated cases. The results indicate that generally, natural frequency decreases when the concrete structure deteriorates, thus the power generation amount also decreases since the main factor for power generation amount is the target structure's natural frequency. However, at several points, power generation amount increases, even when natural frequency decreases with the damage in RC structure.

Detecting Slab Deterioration Using Vibration-Based MEH
It is observed in Figure 11 that the generated power increases at the deteriorated panels and decreases at the other five panels for nearly all of the cases in three modes of vibration. However, the generated power at the observation points depends on material and structural conditions; hence, it is almost impossible to detect the most deteriorated panel by a direct comparison between the generated powers on different panels. In the case that all panels are intact, their generated powers shall keep in a ratio as presented for Case 0 in Figure 11. Herein, a power generation index I j (j = 1 to 6) is proposed as follows for the j-th test panel to normalize this location-dependent factor, so as to fairly evaluate the health state of panels at any location.
for j = 1, 2, 3, 4, 5, 6 where P i is the power generated from Panel i in the intact case (Case 0) and P j the power generated from Panel j in the test case (could be intact or damaged). Generally, all modes could be taken to calculate e j and to identify damage. Herein, the 3rd mode was selected for its larger power being generated and its outcome is illustrated in Figure 12.
It is observed in Figure 11 that the generated power increases at the deteriorated panels and decreases at the other five panels for nearly all of the cases in three modes of vibration. However, the generated power at the observation points depends on material and structural conditions; hence, it is almost impossible to detect the most deteriorated panel by a direct comparison between the generated powers on different panels. In the case that all panels are intact, their generated powers shall keep in a ratio as presented for Case 0 in Figure 11. Herein, a power generation index Ij (j = 1 to 6) is proposed as follows for the j-th test panel to normalize this location-dependent factor, so as to fairly evaluate the health state of panels at any location.
for j = 1, 2, 3, 4, 5, 6 (6) where Pi is the power generated from Panel i in the intact case (Case 0) and Pj the power generated from Panel j in the test case (could be intact or damaged). Generally, all modes could be taken to calculate ej and to identify damage. Herein, the 3rd mode was selected for its larger power being generated and its outcome is illustrated in Figure 12.  Table 5 shows the power generation indices and the modified power generation for Cases 1, 2, and 3, where Panels #1, #2, and #3 are deteriorated, respectively. The results display that all deteriorated panels are pointed out with larger modified power generation, qualifying our proposed index.

MEH Power Generation in Pier Models
The power generated by the MEH at the observation points No. 1, 2, and 3 (see Figure 6) can be calculated with Equations (1)-(4), as well for both the scouring-free and scouring pier models. Figure  13 shows the generated power for the two models and the first three modes. Note that the power is presented in a relative manner with respect to the maximum power in the same model and the same mode. As expected, the 1st mode generates the most power in the y-direction at all three observation points as it is a longitudinal bending mode; the 2nd mode generates in the y-direction at observation  Table 5 shows the power generation indices and the modified power generation for Cases 1, 2, and 3, where Panels #1, #2, and #3 are deteriorated, respectively. The results display that all deteriorated panels are pointed out with larger modified power generation, qualifying our proposed index.

MEH Power Generation in Pier Models
The power generated by the MEH at the observation points No. 1, 2, and 3 (see Figure 6) can be calculated with Equations (1)-(4), as well for both the scouring-free and scouring pier models. Figure 13 shows the generated power for the two models and the first three modes. Note that the power is presented in a relative manner with respect to the maximum power in the same model and the same mode. As expected, the 1st mode generates the most power in the y-direction at all three observation points as it is a longitudinal bending mode; the 2nd mode generates in the y-direction at observation points No. 1 and 3 as it is a torsion mode; the 3rd mode generates in the x-direction at all three observation points as it is a lateral bending mode. Little power is generated in the z-direction (vertical direction) for all modes.
points No. 1 and 3 as it is a torsion mode; the 3rd mode generates in the x-direction at all three observation points as it is a lateral bending mode. Little power is generated in the z-direction (vertical direction) for all modes.  Figure 13 also implies that detecting the pier scour is possible if the power generated by the MEH devices are monitored in the x-and y-directions. Especially monitoring that at point No. 2, an obvious change in generated power could be observed when scour occurred.

Detecting Pier Scour by Vibration-Based MEH
Practically, as it is nearly impossible to obtain data from the perfectly scouring-free state, a scouring detection method that requires no reference state data (reference-free method) is of great importance. In Figure 13b, it is observed that when uneven scouring occurred, an unequal power was generated at the three observation points in the y-direction. Although the generated energy is small for the 3rd mode, this observation is also true as supported by a closer look in Figure 14 (subject to normalization with respect to the maximum out of the three observation points). When no uneven scouring occurred (the riverbed is flat), the power generated by the MEH at the three observations is almost equal.   Figure 13 also implies that detecting the pier scour is possible if the power generated by the MEH devices are monitored in the x-and y-directions. Especially monitoring that at point No. 2, an obvious change in generated power could be observed when scour occurred.

Detecting Pier Scour by Vibration-Based MEH
Practically, as it is nearly impossible to obtain data from the perfectly scouring-free state, a scouring detection method that requires no reference state data (reference-free method) is of great importance. In Figure 13b, it is observed that when uneven scouring occurred, an unequal power was generated at the three observation points in the y-direction. Although the generated energy is small for the 3rd mode, this observation is also true as supported by a closer look in Figure 14 (subject to normalization with respect to the maximum out of the three observation points). When no uneven scouring occurred (the riverbed is flat), the power generated by the MEH at the three observations is almost equal.
points No. 1 and 3 as it is a torsion mode; the 3rd mode generates in the x-direction at all three observation points as it is a lateral bending mode. Little power is generated in the z-direction (vertical direction) for all modes.  Figure 13 also implies that detecting the pier scour is possible if the power generated by the MEH devices are monitored in the x-and y-directions. Especially monitoring that at point No. 2, an obvious change in generated power could be observed when scour occurred.

Detecting Pier Scour by Vibration-Based MEH
Practically, as it is nearly impossible to obtain data from the perfectly scouring-free state, a scouring detection method that requires no reference state data (reference-free method) is of great importance. In Figure 13b, it is observed that when uneven scouring occurred, an unequal power was generated at the three observation points in the y-direction. Although the generated energy is small for the 3rd mode, this observation is also true as supported by a closer look in Figure 14 (subject to normalization with respect to the maximum out of the three observation points). When no uneven scouring occurred (the riverbed is flat), the power generated by the MEH at the three observations is almost equal.  Based on the observations above, a reference-free method could be proposed for detecting uneven pier scour using MEMS vibrational power generator devices as follows. (1) To install MEMS vibrational power generator devices at multiple observation points of equal height at the pier cap. The observation points are suggested to be one at the upstream side, one at the downstream side, and one in the middle; the selection of other observation points is not fully investigated yet and could be an open question. (2) To monitor the power generated by the MEMS vibrational power generator devices in the longitudinal direction. If the powers generated at the observation points are unequal, it would be detected as uneven pier scour. In considering measurement noises, a certain threshold could be introduced to quantify the unequal powers, which is 5% in this study. The above proposal is limited to detecting uneven pier scours per the assumptions and modeling in this study. Further investigations could be conducted on detecting even pier scour and more complicated scouring states.

Conclusions
This study aimed to use a MEMS vibrational power generator to detect a bridge's slab damage and pier scour. Eigenvalue analysis of a bridge slab and pier using FEM models, in which slab damage was modelled by a reduced Young's modulus and pier scour was modelled by fixed boundaries of an inclined depth. In the eigenvalue analysis, the change in modal frequency and mode shape caused by the slab damage and pier scour consolidated the proposal of this present study.
Utilizing a electrostatic vibration-based MEMS-MEH, the change in natural frequency and amplitude could be monitored by the change in the generated power. A power generation index to detect the deteriorated panel in a slab was proposed and its applicability was verified with the numerical models. As for detecting uneven pier scour, a reference-free method was proposed with a MEMS vibrational power generator installed at multiple points of equal height at the cap and monitoring unequal generated powers. When an unequal power generation distribution is found, it may indicate the uneven pier scour.
The slab and pier models studied herein were simplified and the vibrations used to calculate the MEH generated energy were simply harmonic. The conclusions drawn above could apply only to the bridge types and damage patterns similar to those in this study. More complicated bridge types, models, and vibration patterns would help in generalizing the proposed methods.