Long-Term Structural Health Monitoring of Kashima Lighthouse

Abstract

The Kashima Lighthouse, one of the lighthouses that suffered damage in the 2011 Great East Japan Earthquake, required a careful investigation to estimate its long-term behavior and seismic vulnerability. This study, therefore, undertook a meticulous process of the dynamic testing, dynamic identification, and long-term structural health monitoring of the Kashima Lighthouse. The results of dynamic tests reveal that the fundamental frequencies of the Kashima Lighthouse are estimated to be around 2.60 Hz and 2.63 Hz in the east–west and north–south directions, respectively. The natural modes and damping factors are identified using an SSIM (Stochastic Subspace Identification Method). This paper also discusses the result of long-term structural health monitoring, where machine learning techniques were applied for data processing, highlighting the rigor and thoroughness of this research.

1. Introduction

The construction of Western-style lighthouses in Japan began in 1869, following the signing of the “Edo Treaty” in 1866. Before that, Japanese beacons carried out the functions of lighthouses. However, they hardly functioned because regular, routine maintenance was not conducted on these beacons. As a result, Japan’s coastal waters were called “the dark sea”. The “Edo Treaty” allowed Japan to build lighthouses that enabled ships from Western countries to safely navigate the seas near Japan. Following the construction of the Kannon Saki Lighthouse in 1868, approximately 120 lighthouses were built during 44 years of the Meiji period. Sixty-six of these lighthouses existed in 2001, providing light to keep the seas safe [1].

The Japanese Coast Guard (JCG) is in charge of lighthouse maintenance. The JCG’s policy is to use lighthouses as beacons while improving their structural safety and considering their historical and cultural value. Thus, to provide planned maintenance, they assembled a “Lighthouse Examination Committee”, which comprises well-informed persons, in 1985. They established a “Lighthouse Facility Preservation Committee” in 1991.

East Japan’s lighthouses suffered extensive damage from the 2011 Great East Japan Earthquake. In the past, dismantling and rebuilding lighthouses that suffered from earthquake disasters were carried out to prevent the risk of collapse (Figure 1). Rebuilding using the same structural style was unrealizable in the Building Standard Law of Japan [2] when the masonry lighthouses of the Meiji period were dismantled by earthquake disasters. Therefore, earthquake resistance must be improved to preserve Meiji lighthouses as the “Heritage of Industrial Modernization”.

For ships to navigate safely and efficiently, it is always necessary to check their position, avoid dangerous obstacles, and take a safe course. Navigation signs are essential indicators for this purpose. Even today, when GPS and GNSSs (Global Navigation Satellite Systems) have been developed, lighthouses, as one of the navigation signs, still play an indispensable role. There are over 3000 navigation signs in Japan, surrounded by the sea. Therefore, the maintenance of lighthouses has become a serious issue in Japan.

Few studies on lighthouses have been conducted; some have clarified fundamental vibration characteristics through vibration experiments [3,4,5], some have developed and proposed equations for estimating natural periods through vibration experiments [6,7], and some have evaluated seismic performance [8,9,10].

Vibration characteristics must be precisely estimated when evaluating a structure’s earthquake resistance. However, as mentioned earlier, there are a few examples of lighthouse vibration tests. Fortunately, we recently had the opportunity to examine the Kashima Lighthouse (built with reinforced concrete). The fundamental frequencies, damping factor, and natural modes were identified from the results of ambient vibration tests. Long-term monitoring is discussed in this paper [11,12].

The structural assessment of lighthouses, chimneys [13,14,15], and bell towers [16,17,18] is complex, despite their simple cantilever-like behavior, because of the high stresses acting at the base [16]. Moreover, general issues characterizing the preservation of historical structures exist, such as the aging of materials, the presence of cracks and other damage or degradation phenomena, successions of interventions and structural modifications, and uncertainties about material properties. Historical structures are sensitive to thermal variation effects and dynamic actions, such as wind and earthquakes [17]. Bell towers are frequently connected to adjacent churches as well. Long-term structural health monitoring is valuable when Automated Operational Modal Analysis (OMA) [19] or a machine learning approach [20] is used to conduct damage assessment automatically. In non-stationary cases, such as during earthquakes, refined linear chirplet transform for time–frequency analysis is useful [21].

The first lighthouse was completed and first lit in 1869, during the early Meiji era. This was part of a broader effort to modernize Japan’s coastal infrastructure as the country opened its doors to international trade. This lighthouse was one of the first built using Western-style technology and design, reflecting Japan’s efforts to adopt modern techniques. The lighthouse not only served an important functional purpose in ensuring safe navigation but also symbolized Japan’s modernization during the Meiji period. It represents the adoption of Western technology and the nation’s transition to a more industrialized state. The lighthouse is a significant cultural heritage site, offering insight into Japan’s historical development and maritime history. Its beauty and historical importance also make it a popular spot for lighthouse enthusiasts and tourists alike. The Kashima Lighthouse is one of them and was built in Kashima-shi, Ibaraki, Japan 1971, as shown in Figure 2. The height of the lighthouse from the ground to the floor level is 27.05 m, the outer diameter at the bottom is 4.80 m, the inner diameter at the base is 4.0 m, and the diameter changes gradually from the lower part to the upper part (outer diameter change rate: −46.1 mm/m; inner diameter change rate: −30.7 mm/m). The wall thickness is 0.40 m at the ground level and 0.20 m at the upper end. The inner landing and the inner wall are made of reinforced concrete (RC), and the stairs are made of steel. The foundation is a direct foundation. A building is attached to the west side of the lighthouse, but it is structurally separated from the lighthouse by an expansion joint.

Continuous long-term monitoring aims to control the conservation state of the structure by estimating its primary dynamic characteristics. This operation requires the definition of an initial reference, “Status 0”, concerning any variations that can be detected, especially those due to the deterioration of materials and damage induced by operating actions in general and by seismic events in particular.

The reference condition is defined through in-depth dynamic experimentation and structural identification, which is also functional for designing the continuous monitoring system.

2. Experimental Vibration Test

Continuous monitoring requires data acquisition even under the normal operating conditions of the structure, and therefore, it is essential to detect vibrations under environmental conditions.

In 2014, Hidaka et al. confirmed that ambient vibration tests were helpful in identifying the vibration characteristics of lighthouses by comparing the results with those obtained from forced excitation tests conducted using a vibration generator [3,4]. Therefore, in this section, a series of ambient vibration tests were carried out, and dynamic identification was executed.

2.1. Vibration Characteristics of Ground

2.1.1. Ambient Vibration Test of Ground Motion

In the first stage of dynamic testing, ambient vibrations were measured on the ground to obtain data on the dynamic structural properties of the Kashima Lighthouse. An electrodynamic velocity sensor (S’s product, Zevenhuizen, The Netherlands, measurement frequency: 0.2–42 Hz) was used to conduct an ambient vibration test at the bottom of the lighthouse. Considering the surrounding facilities’ influence, the sensor was positioned away at a distance greater than the lighthouse’s frame height (Figure 3). The sampling frequency was 100 Hz. The ambient vibration test of ground motion was conducted on 15 December 2014.

2.1.2. Result of Ambient Vibration Test of Ground Motion

Ambient vibration is composed of waves with various periods. The function of breaking down the measured data into a wave for every period is called the Fourier spectrum. It is widely known that the spectrum ratio of the horizontal motion to the vertical movement of the ground (the H/V spectral ratio) shows the amplification factor and predominant frequency of the earth’s surface layer. Therefore, ambient vibration tests can easily estimate the amplification characteristics of earthquake motion [22].

In this case, we divided the measured data into several sets, comprising 16,384 points in each dataset. Assuming that each dataset is independent, the result obtained by averaging (ensemble average) all the datasets was regarded as the ground’s H/V spectral ratio. In addition, we used a Hanning window to revise the measured data. The data for one hour were targeted for analysis, and an overlap of 50% was used to increase data quantity.

Figure 4 shows the H/V spectral ratio representing the vibration characteristics of the ground of the Kashima Lighthouse. The predominant frequency of the land was 8.42 Hz, as shown in Figure 4. Based on this result, the class of this soil was estimated as first-class (the predominant period: ≤0.2 s) in “Aids to navigation structure design standard”.

2.2. Vibration Characteristics of Structure

2.2.1. Ambient Vibration Test of Structure

In the second phase of dynamic testing, to identify the fundamental vibration characteristics of the Kashima Lighthouse, such as natural frequencies, mode shapes, and damping factors, the ambient vibration test of the lighthouse was carried out using 32 uniaxial acceleration sensors at eleven points (S1–S11: low-noise sensors were used specifically to measure ambient vibration at ground level. S’s product, measurement range: ±2942 gal; frequency response: DC—400 Hz; resolution: ≤0.000049 m/s²). Sensors S1–S10 were used with three axes, and sensor S11 was used with two axes (Y and Z directions).

Figure 5 shows the measuring points of each sensor. The axis of each sensor was realigned to the following directions: the direction orthogonal to the opening was set as the X direction, the direction parallel to the door as the Y direction, and the vertical direction as the Z direction. The sampling frequency was 200 Hz. The ambient vibration test of the Kashima Lighthouse was conducted on 15 December 2014.

2.2.2. Basic Analysis Method

The data measured with each sensor in the lighthouse were divided into several windows with 32,768 points each, and Fourier spectra were calculated using the ensemble average. In addition, we used a Hanning window to revise the measured data. The data for 60 min were targeted for analysis, and an overlap of 50% was used to increase data quantity. The data were measured when the lens of the lighthouse stopped turning.

In general, the vibration of a building results from the combined influence of its superstructure, foundation, and influence ground. When the vibration system of a building includes the peripheral ground, it is called a “total vibration system”. A vibration system in which only the vibration of the ground (influence ground) affects the vibration of the building is called a “ground interlocking system”. The ground vibration has horizontal and vertical (foundation rotational) motions. The vibration system of a building removing this horizontal motion is called a “sway fixed system”. Its superstructure and foundation rotational motion are only considered in such a system. A vibration system influenced only by its superstructure is called a “foundation fixed system”. Figure 6 shows these vibration systems for a building.

The natural period usually becomes shorter in the following order: total vibration system, ground interlocking system, sway fixed system, and foundation fixed system.

In this paper, the vibration characteristics provided by the Fourier spectrum are the vibration characteristics of the total vibration system. In addition, the ratio of the Fourier spectrum of each floor level to the Fourier spectrum of 1st floor level (1 FL) is called the transfer function, and the properties of vibration provided by the transfer function are the vibration characteristics of the sway fixed system.

2.2.3. Results of Basic Analysis

Figure 7 shows the Fourier spectra obtained from sensors S2, S6, and S10. To clarify the torsional vibration of the lighthouse, the relative accelerations between accelerometers S1 and S2 (light chamber) and S9 and S10 (1 FL) in the X direction were calculated. The Fourier spectrum of the relative acceleration is shown in Figure 8. The natural frequency in the torsional mode is estimated to be 20.68 Hz. As for the vertical direction, the transfer function in the vertical movement of S2 (light chamber) concerning S10 (1 FL) is shown in Figure 9. The natural frequency of the stretching vibration mode is estimated to be 24.90 Hz.

Table 1. Natural frequencies identified by ambient vibration tests.

	Natural Frequencies (Hz)			Remarks
	1st	2nd	3rd
X direction	2.62	11.72	29.42
Y direction	2.61	12.47	29.42
Z direction	16.67	24.90	-	1st: rigid body mode 2nd: stretch mode
Torsional	20.68	-	-

shows the representative natural frequencies estimated from Figure 7, Figure 8 and Figure 9. Due to the small aperture and staircase, the primary mode has a higher frequency in the X direction than in the Y direction. However, the natural frequencies estimated here vary with seasonal changes (temperature). It can be seen that the fundamental natural frequencies in each direction are lower in summer and higher in winter, including daily variations.

The first-order damping factor at S2 (light chamber) was evaluated using the random decrement (RD) technique. In the RD method, the waveform is divided into small samples of 10 s, and the maximum value of the obtained random response waveform becomes the initial value. The small samples are superimposed while being shifted one peak at a time. The random component disappears, and only the free vibration component remains. An envelope connecting maximum values for about 10 s from the second cycle of the free vibration waveform is fitted using a least-square approximation with exponential function exp(−h₁ω₀t). Then, the damping factor h₁ is estimated.

Here, ω₀ is the first-order natural angular frequency (rad/s), and t is the elapsed time (s). To estimate the first-order damping ratio, a bandwidth of 1.0 Hz with a central frequency of 2.62 Hz in the X direction and 2.61 Hz in the Y direction was applied to the response waveform, and then 9000 small samples were superimposed. The resulting RD waveform is shown in Figure 10. The first mode damping ratios were estimated to be 1.01% and 0.99% in the X and Y directions, respectively.

Ambient vibration examinations were performed at sampling frequencies of 100 Hz and 200 Hz, with 100 Hz considered sufficient. Also, the window is related to frequency resolution; we used 16,384 and 32,768, but a minimum of 8192 is acceptable.

2.2.4. SSIM Analysis

The identification analysis required the preliminary treatment of the signals to remove any spurious components due to noise and non-structural responses. In particular, the spectral analysis highlighted the presence of frequency components lower than 40 Hz (Figure 7). Therefore, we proceeded by sampling the signals again with a reduced sampling frequency and a 48 Hz low-pass filter. Then, a Stochastic Subspace Identification Method (SSIM) was used to extract the structure’s natural frequencies, mode shapes, and damping parameters from these measurements [23]. The SSIM is a technique used in system identification, particularly in the context of dynamic systems. It is employed to estimate the state-space model of a system based on input–output data. The method is “stochastic” because it relies on the statistical properties of the data rather than on deterministic models. The advantage of the SSIM is that it does not require prior knowledge of the system’s order or structure, making it a flexible and efficient tool for system identification from experimental data.

The analysis was carried out in three steps: first, the signals detected in the horizontal and vertical directions were analyzed in the frequency range from 0.5 to 10 Hz; second, the same components were analyzed in the range from 9 to 20 Hz; and third, the same components were analyzed in the range from 19 to 40 Hz.

The selection of vibration frequencies and their corresponding mode shapes was based on the recurrent forms, with equivalent viscous damping less than 12% and a level of affinity higher than 90%, evaluated using the “Modal Assurance Criterion” (MAC), as shown in Equation (1):

$$MA{C}_{i,j}={\displaystyle \frac{{\left|{\Psi }_i^T{\Psi }_j\right|}^2}{\left|{\Psi }_i^T{\Psi }_i\right|\left|{\Psi }_j^T{\Psi }_j\right|}}$$

(1)

where Ψ_i and Ψ_j are the i-th and j-th mode shapes.

The MAC is a numerical measure used to assess the similarity between two mode shapes (either from experiments or simulations) in vibration analysis. A MAC value close to 1 indicates that the two mode shapes are very similar, while a value close to 0 suggests they are quite different.

2.2.5. Results of SSIM Analysis

The fundamental frequencies and damping factors identified by the SSIM are shown in

Table 2. Natural frequencies and damping factors identified by ambient vibration tests (SSIM).

	1st Mode		2nd Mode		3rd Mode		Remarks
	Frequency	Damping	Frequency	Damping	Frequency	Damping
X direction	2.65 Hz	0.34%	13.14 Hz	7.60%	29.95 Hz	1.72%
Y direction	2.67 Hz	0.50%	13.06 Hz	6.05%	-	-
Z direction	15.18 Hz	11.24%	27.79 Hz	6.25%	-	-	1st: rigid body mode 2nd: stretch mode
Torsional	29.95 Hz	1.72%	-	-	-	-

, and

Table 3. Mode shapes identified by SSIM.

Direction	1st	2nd	3rd
X
Y
Z
Torsion

shows the corresponding mode shapes.

3. Long-Term Structural Health Monitoring

Based on the dynamic identification of ambient vibration tests, the setup adopted for long-term structural health monitoring, depicted in Figure 11, consists of 12 accelerometers of the same type used in the ambient vibration test. The sensors are placed in six positions along the height of the lighthouse (five in the X direction, five in the Y direction, and two in the Z direction). Vibration data were continuously acquired for about three years.

At the Kashima Lighthouse, the crack width, inclination angle, and temperature at the position reported in Figure 12 from 18 March 2015 to 17 May 2018 were observed as static characteristics. Acceleration was observed as a dynamic characteristic.

Eleven earthquakes with a measured seismic intensity of 3.0 (seismic intensity class 3 by the Japan Meteorological Agency) at the Strong-motion Seismograph Networks K-NET (at the position of IBR018) were analyzed. Figure 12a,b show the relationship between the fundamental natural frequency, the fundamental damping factor, and the acceleration of the lantern (Accelerometer 1) immediately before and during the earthquake, respectively. In addition, the acceleration immediately before the earthquake was taken as the RMS (root mean square) value for one hour, and the acceleration during the earthquake was taken as the maximum value of the absolute acceleration. The fundamental natural frequency was estimated from the Fourier spectrum obtained with the frame size matching the duration of the earthquake. The RD method estimated the fundamental damping factor at the ambient vibration [6]. In addition, the fundamental damping factor during the earthquake was estimated by curve-fitting the transfer function of the lantern (Accelerometer 1) for 1 FL (Accelerometer 6) with the transfer function of a one-degree-of-freedom system [6].

The fundamental natural frequency has amplitude dependence. It decreases as acceleration increases and decreases by 1% to 15% during an earthquake compared to its value immediately before the earthquake. Additionally, the fundamental damping factor does not have an explicit amplitude dependency but varies from 0.2% to 2.0%. The fundamental damping factor of the existing lighthouse obtained from ambient vibration tests and free vibration tests ranges from 1% to 4%, so the fundamental damping factor during the earthquake ranges from 2% to 5% [24]. However, according to Figure 12b, there is no tendency for the fundamental damping factor to increase as the vibration amplitude increases.

This paper describes only the observed inclination angle and the fundamental natural frequency in detail. Data were deleted to exclude periods containing earthquakes and strong winds when the RMS value of the acceleration measured by Accelerometer 6 installed in 1 FL was more significant than the average value plus the standard deviation over the observation period.

Figure 13 shows the plotted observation data of the tilt angle on the XY plane, and Figure 14 shows the time series data.

Figure 13 and Figure 14 depict the observed inclination angle and the fundamental natural frequency in the X and Y directions, respectively. It is revealed that the inclination angles tended to shift toward the south and east sides in summer and toward the north and west sides in winter, including diurnal vibration. Moreover, the structure gradually inclined to the north and west sides throughout the observation period. In winter, the sun’s altitude is low, so the sunshine time to the south side wall is long. It is considered that the south side wall surface has a higher temperature than the north side wall surface; the south side expands and tilts to the north side. In addition, it was found that the inclination angle gradually shifted to the west side throughout the observation period. Since the crack width (Displacement meters 1 to 3) on the south surface of the tower was not developed, the subsidence of the foundation ground can be considered as one of the factors. Still, it is necessary to clarify this through follow-up observations.

Figure 15 shows the fundamental natural frequency observation data in the X and Y directions. The fundamental natural frequency was low in summer and high in winter, including day variation in each direction. The influence of solar radiation, amplitude dependence, the occurrence of temperature stress, etc., can be considered as factors of this change. Still, it was not clarified, and continuous observation is necessary. Also, the timing of earthquakes with a measured seismic intensity of at least 3.0 (seismic intensity class 3–4 by the Japan Meteorological Agency) is indicated by triangles in Figure 15 (▴).

Although the earthquake caused a temporary decrease in the fundamental natural frequency, no damage was observed for two reasons. The first is that the fundamental natural frequency gradually recovered from several weeks to one year, and the second is that the inclination angle and the crack width did not change abruptly.

The three years of monitoring were conducted continuously without any problems. As crack width, inclination angle, and temperature were observed as static characteristics and acceleration was observed as a dynamic characteristic, it was impossible to perform a synchronized analysis of seismic acceleration, crack width, and inclination. Therefore, after the reinforcement work, all data were measured at 100 Hz.

For long-term monitoring, the system aims to provide information on the structure’s capacity to continue playing its designed role.

In the last few years, advances in data collection and storage systems and computational capabilities have made it possible to perform long-term monitoring, i.e., to obtain a structure’s continuous response, such as natural frequencies, mode shapes, and damping. This monitoring system generally tracks the condition of a structure and answers questions about its load-bearing capacity, safety, and serviceability after a particular event or due to the aging of materials and components.

For example, in earthquake-prone areas, evaluating structural integrity based on test data acquired by monitoring systems is of paramount importance in post-event activities.

Prior investigations regarding the dynamic behavior and surveillance of lighthouses include a study by O’Shea et al. [25]. A method of integrating sensors to enhance the visualization of structural health monitoring through BIM was developed.

Sensor networks, which are continuously acquired over a long period, generate large amounts of data and require appropriate algorithms to extract valuable and reliable knowledge from data. In this context, methods rooted in the fields of machine learning and data mining have proven to be very effective. For example, Worden and Manson highlighted that some of the machine learning methods, neural networks, and support vector machines have high performance in identifying damage as a deviation from the expected normal response [26].

A network of twelve accelerometers and three thermocouples installed at Ghirlandina Tower (Modena, Italy) has been continuously acquiring data since August 2012, and the method of automatically identifying the vibration modes of the structure has proven successful [20]. By applying machine learning techniques, it was possible to track changes over time in the six modes of the tower, highlighting seasonal variations in modal characteristics.

3.1. Machine Learning [20]

The starting point in time is assumed to be a normal condition. The procedure is designed in four main phases:

• Step 1: Model selection and validation.
• Step 2: System identification.
• Step 3: Clustering and mode classification.
• Step 4: Long-term monitoring.

3.1.1. Model Selection and Validation

The first step is to define an Autoregressive Model (AR), which assumes a linear relationship among the signals at one instant t and the same signals at p previous instants. In the case of a single channel, this relationship is represented by Equation (2):

$$y_t=w_0+w_1{y}_{t-1}+\cdots +w_p{y}_{t-p}$$

(2)

Writing the same equation at N different moments t_j, we obtain the simultaneous linear equations shown in Equation (3):

$$\left\{\begin{array}{c}{y}_{t_1}=w_0+w_1{y}_{t_1-1}+\cdots +w_p{y}_{t_1-p}\\ y_{t_2}=w_0+w_1{y}_{t_2-1}+\cdots +w_p{y}_{t_2-p}\\ \dots \\ y_{t_N}=w_0+w_1{y}_{t_N-1}+\cdots +w_p{y}_{t_N-p}\end{array}\right.$$

(3)

In matrix notation, this becomes $\left\{y\right\}=\left[Y\right]\left\{w\right\}$.

The following simultaneous equations can be written for all the measured signals at instant t:

$$\left[\begin{array}{c}\left\{y_{t_1}\right\}\\ \left\{y_{t_1}\right\}\\ ⋮\\ \left\{y_{t_N}\right\}\end{array}\right]=\left[\begin{array}{cccc}1& \left\{y_{t_1-1}\right\}& \dots & \left\{y_{t_1-p}\right\}\\ 1& \left\{y_{t_2-1}\right\}& \dots & \left\{y_{t_2-p}\right\}\\ ⋮& ⋮& \ddots & ⋮\\ 1& \left\{y_{t_N-1}\right\}& ⋮& \left\{y_{t_N-p}\right\}\end{array}\right]\left[\begin{array}{cccc}{W}_{1,0}& W_{2,0}& \dots & W_{n_{\mathit{ch}},0}\\ \{W_1^{\left(1\right)}{\}}^T& \{W_2^{\left(1\right)}{\}}^T& \dots & \{W_{n_{\mathit{ch}}}^{\left(1\right)}{\}}^T\\ ⋮& ⋮& \ddots & ⋮\\ \{W_1^{\left(p\right)}{\}}^T& \{W_2^{\left(p\right)}{\}}^T& ⋮& \{W_{n_{\mathit{ch}}}^{\left(p\right)}{\}}^T\end{array}\right]\Rightarrow \left[Y_{\mathit{current}}\right]\left[Y_{\mathit{past}}\right]\left[W\right]$$

(4)

The length of the signals and the order of the AR model are automatically selected based on the function of mean fitting, evaluated by the coefficient of determination for each channel $\left(R_j^2\right)$ between the signals and the analytical ones.

3.1.2. System Identification

The data generated by the monitoring system can be regarded as a continuous sequence of data blocks, each consisting of n_ch signals composed of N + p samples, where the order p and the length in N samples are the result of the model selection and validation phase.

A linear system of equations such as (4) can be defined for each data block, and the corresponding matrix [W] can be estimated. This results in a succession of matrices [W]¹, [W]²,… [W]ⁱ,… [W]^p.

The coefficients of the matrix [W] can be reformulated so that the eigenmodes of the structure can be estimated. To this aim, Equation (4) can be redefined as follows:

$$\left\{y_t\right\}=\left\{w_0\right\}+\left[W^{\left(1\right)}\right]\left\{y_{t-1}\right\}+\left[W^{\left(2\right)}\right]\left\{y_{t-2}\right\}+\dots +\left[W^{\left(p\right)}\right]\left\{y_{t-p}\right\}$$

(5)

$$\left\{z_t\right\}=\left\{z_0\right\}+\left[A\right]\left\{z_{t-1}\right\}$$

(6)

where $\left\{z_t\right\}={\left\{{\left\{y_t\right\}}^T {\left\{y_{t-1}\right\}}^T {\left\{y_{t-2}\right\}}^T\dots . {\left\{y_{t-p+2}\right\}}^T {\left\{y_{t-p+1}\right\}}^T \right\}}^T$.

The eigenmodes of the matrix [A] are characterized by the natural frequencies f_i, damping factors ξ_i, and the mode shapes {Φ_i} of the time series representation (for i = 1, 2,…n_chp).

3.1.3. Clustering

This process phase aims to select the identified vibration modes to be monitored over time.

Before clustering, a preliminary selection can be made in which simple engineering criteria are applied to define the vibration modes. Referring to the civil and mechanical applications of structural health monitoring, the following requirements are assumed for the modes to be tracked over time:

• The deformation shape must be accurate or near-real;
• The modal damping ξ must be less than a threshold value ξ_lim;
• If the acquired signals are pre-processed with a band pass filter with f₁ and f₂ as cut-off frequencies, each natural frequency f_i must be in the range of (f₁, f₂).

Based on the natural frequencies, damping value, and mode shapes, vibration modes identified over a limited period are clustered. For each cluster, it is determined whether it needs to be considered and whether it is worth monitoring.

Several clustering algorithms are available in the data mining literature; in this application, DBSCAN was chosen mainly because the number of clusters is not predefined, and the shape is arbitrary.

At the end of the clustering phase, each one of the M × n_chp modes is either included in one of the N_c identified clusters or remains unclassified.

3.1.4. Long-Term Monitoring

Once the clustering phase is completed, the monitoring of the identified structural parameters can be activated.

The clusters identified in the previous phase can be interpreted as structural vibration modes or input excitation modes.

Each time a new signal block is acquired, the following steps are performed:

• The matrix of linear coefficients [W] is estimated to solve a linear regression problem (Equation (4));
• The matrix [A] is built based on the coefficients of [W] (Equation (6)), and its n_chp modes are evaluated;
• Each eigenmode is classified as belonging to one of the N_c clusters or left unclassified.

The assignment to a specific class uses the support vector machine method, one of the most successful classification methods in statistical learning theory.

Tracking one mode over time can be used to detect abrupt changes, e.g., after a structure has sustained severe damage or drift due to aging.

3.2. Automatic Monitoring of Kashima Lighthouse

The first phase was applied to two weeks of signals selected as a baseline.

The modes were then calculated based on the three-month data collected on the Kashima (from 19 March 2015 to 3 July 2015) Lighthouse by the long-term SHM system described in Section 3.1.2 (Step 2). A baseline of two-week modes was successively clustered by the DBSCAN methodology and classified by engineering judgment (Step 3). Finally, in Step 4, all the modal parameters were classified.

The automatic monitoring was then activated.

Figure 16 shows, as an example, the results of the continuous monitoring of frequency, damping, and mode shape for the first bending mode in the X–Z plane, the second bending mode in the same plane, and the torsional one.

Figure 16 shows the time evolutions of the modal frequencies and damping of the first and second bending modes and the torsional mode (

Table 4. Natural frequencies and damping factors identified by long-term monitoring.

	1st Mode		2nd Mode
	Frequency	Damping	Frequency	Damping
X direction	2.61 Hz	0.7%	13.61 Hz	6.4%
Torsional	21.03 Hz	2.3%	-	-

). The automatic monitoring procedure failed to correctly classify the vertical modes because only two sensors were used in the Z direction at the base and the top of the lighthouse. This caused the modes to be excluded when filtered in the MAC-based classification.

Although the timeline is short, it is worth noting that a slight variation can be observed in the first flexural modes and in the torsional ones between May and June 2015. Based on the author’s experience, a hypothesis is that the variation could be ascribed to the effects of the lighthouse’s interaction with the adjacent short construction in correspondence with the seasonal increase in air temperature. The confirmation of this hypothesis is required to follow the evolution of the monitored parameter, at least for an annual cycle.

4. Concluding Remarks

Based on measured data, this paper studied the vibration characteristics of the existing lighthouse, which plays an essential role in navigation and national wealth. The conclusions obtained in this study are as follows:

Based on the strong motion observation results of the Kashima Lighthouse for about three years, we can quantitatively show the rate of decrease in fundamental natural frequency during earthquakes against ambient vibrations. The fundamental damping factor had no amplitude dependence.

Furthermore, we can qualitatively and quantitatively show the tendency of the daily fluctuation in static and dynamic properties.

The method of automatically identifying vibration modes implements a concrete approach to long-term continuous structural health monitoring. The process belongs to the data-driven framework, based on machine learning and data mining algorithms, and it is developed in four steps: model selection and validation, system identification, clustering, and monitoring. The results prove the method’s ability to automatically identify the relevant structural modes with a very limited classification error, detect novelties in the dynamic response, and detect symptoms of probable damage caused in real-time. They also highlight some long-term trends due to the environmental deterioration of materials. This machine learning approach was used to automatically conduct the damage assessment of the Ghirlandina Tower in Modena, Italy, and was indeed successful in detecting changes in natural frequencies due to tower tilt [20].

The results of this study provide evidence of fundamental characteristics that should be clarified when establishing preservation methods to keep the existing lighthouse on site. In the future, due to the development of the results of this research, this method can be considered as a tool for determining the order of priority in promoting seismic resistance efficiently; it is possible to propose a procedure for selecting existing lighthouses with a low possibility of earthquake resistance [7]. For this purpose, a future subject of study is identifying an evaluation method that can easily predict the shaking of an existing lighthouse at the time of the earthquake, examine the influence of material deterioration on shaking, and prove the stress of the whole member.