Improving Active Preview Control System of Structures Using Online Prediction of Seismic Waves

Tsuji, Tokuo; Nakamura, Hideharu

doi:10.1061/(ASCE)EM.1943-7889.0000979

Open access

Technical Papers

Jul 14, 2015

Improving Active Preview Control System of Structures Using Online Prediction of Seismic Waves

Authors: Tokuo Tsuji [email protected] and Hideharu Nakamura [email protected]Author Affiliations

Publication: Journal of Engineering Mechanics

Volume 142, Issue 2

https://doi.org/10.1061/(ASCE)EM.1943-7889.0000979

PDF

Abstract

This paper presents a study on the applicability of the preview control method for improving the performance of active seismic control systems. The active preview control method is examined as described for its ability to improve vibration suppression as follows: (1) the relation between the number of preview steps and the degree of improvement in control performance is clarified by analysis using predicted earthquake waves, and (2) to evaluate the applicability to an actual structure, predicted surface seismic waves are calculated by an autoregressive model from observed KiK-net data on 100–200-m-deep underground seismic waves and the applicability of the method is confirmed.

Introduction

Active control techniques are designed to calculate the controlling force by minimizing the evaluation function, which is comprised of the quadratic form of the quantity of states and the controlling forces (Kobori 1993; Yoshikawa and Imura 1994; Ikeda 2004; Seto 1998; Phillips et al. 2012). While passive controls for absorbing vibration energy provide stable performance and costs relatively less, active control has a large effect using external energy but it is needed to take care of malfunctions that cause vibration. Though active control techniques are in practical use as described in Spencer Jr. and Nagarajaiah (2003) and Thenozhi and Yu (2013), future advancements in sensors, computers, and actuators will likely lead to new control techniques for nonlinear models including bridges and building structures.

The authors proposed an active control method (Nakamura et al. 2010) using hyper vision technology (Ishii et al. 2004), which can measure displacements of structures at intervals of

1 / 100 - 1 / 1, 000 s

. The effectiveness of the method was confirmed by conducting a series of shaking table tests (Nakamura et al. 2010). This paper examines the adoption of a preview control method (Sheridan 1966; Hayase and Ichikawa 1969; Tomizuka and Rosenthal 1979; Katayama et al. 1985) that uses projected data on future external forces in an effort to improve active control performance. The improvement of vibration control performance in a multi-degree-of-freedom system is quantitatively clarified by numerical analyses, and it is confirmed that the surface seismic wave can be predicted by using ground and underground recordings of seismic waves. Similar studies (Tateishi and Nishioka 2001; Marzbanrad et al. 2004) for civil engineering structures do not address the practical application of predicting seismic waves. This study is an extension of a previous paper (Nakamura et al. 2010), and is intended to add the preview control function to the previously proposed active control system. This study is intended to clarify the following:

1.

The equations are determined to derive the preview controlling force and clarify the relation between the number of preview steps and the degree of improvement in vibration control performance;

2.

The feasibility of calculating a predicted seismic wave for preview control is confirmed by using seismic wave data recorded by a seismograph set up several hundred meters below the ground surface; and

3.

The feasibility of the preview control system is examined by predicting seismic waves that have errors caused by factors such as ground conditions.

Concerning point (1), a new formula is provided for calculating the controlling force by adding an optimum preview controlling force term to the formula using values observed by multipoint displacement measurement, which was described in Nakamura et al. (2010). Experiments and analyses are described for confirming the improvements in control performance accomplished by the addition of such an active preview control system.

Concerning point (2), whenever an earthquake occurs in Japan, the Earthquake Early Warning System provides advance warning of estimated seismic intensities and the time when the principal motion is expected to arrive. This system has been in operation around the country since 2007 (Megro and Fujinawa 2007; Fujita et al. 2011). These estimations are based on the prompt analyses using wave-form data observed by seismographs near the epicenter. This concept can be applied to a similar system that can anticipate seismic waves prior to their actual arrival time. One possible application, which is discussed in this paper, is to establish an active preview control system using data on predicted seismic wave behavior that has been formulated by applying an autoregressive model (Hannan 1970) in high speed computations on seismic wave data transmitted from a seismograph set up several hundred meters below the target structure. It is considered possible to predict seismic motion approximately 0.05–0.3 s prior to its occurrence at the ground surface by performing ground vibration analyses at extremely high-speeds. In previous computer methods (Lysmer and Kuhlemeyer 1969; Schnabel et al. 1972; Lysmer and Waas 1972; Lysmer et al. 1975), seismological models are used for analyzing the seismic response of soil structures and soil-structure interactions, resulting in the programs SHAKE, QUAD−4, FLUSH, and SASSI. These methods are not designed to predict future ground waves online. It is demonstrated how a predicted seismic wave at the ground surface can be calculated by using the underground observation data provided by the strong-motion seismograph network (National Research Institute for Earth Science and Disaster Prevention 1996), and the possibility of application to actual structures is examined.

Concerning point (3), the robustness of the active control system is examined when using predicted seismic wave data obtained by the one-dimensional wave propagation theory and it is compared to the case when using actual wave data observed at the ground surface. The ability of the control system to accommodate errors inherent in predicting seismic wave data is confirmed.

The proposed active preview control method is described in “Proposed Active Preview Control Method” section. The method for calculating a predicted seismic wave by analyzing KiK-net data is described in “Predicted Seismic Waves Using Autoregressive Model” section. In “Analysis of Preview Control Quality” section, it is described how predicted seismic waves can be applied to an active preview control system and how this can contribute to the robustness of the control system. The relation between the number of preview steps and the improvement of control performance is analytically examined.

Proposed Active Preview Control Method

Recurrence Relations Applied to Active Control

The authors have proposed the active control procedure (Nakamura et al. 2010; Shiojiri and Nakamura 1976) as described subsequently based in part on the following factors. First, when necessary, analytical evaluation that includes the material nonlinearity effect is considered for plasticity to Level-2 seismic motion as specified by Japan Road Association (2002). Two, the method is made possible by the development of a high-speed camera device that measures multipoint displacements and acceleration at the base of a structure. The control procedure is a single-step time-integration scheme based on the general solution of simultaneous ordinary differential equations. Therefore, flexible correspondence is possible when calculating the following recurrence relation matrices beforehand corresponding to various elastic-plastic states. The equations of motion of

n

-degree-of-freedom are given by Eq. (1) in matrix form

[M] {\ddot{U}} + [C] {\dot{U}} + [K] {U} = {P}

(1)

where

M

,

C

,

K

= mass, damping, and stiffness matrices;

\ddot{U}

,

\dot{U}

,

U

= acceleration, velocity, and displacement vectors; and

P (t)

,

t

= external force vector and time, respectively. Eq. (1) is transformed into Eq. (2)

\dot{Y} = A Y + Q

(2)

where

Y = {\begin{matrix} \dot{U} \\ U \end{matrix}}

A = [\begin{matrix} - M^{- 1} C & - M^{- 1} K \\ I & 0 \end{matrix}]

Q = {\begin{matrix} M^{- 1} & P \\ 0 \end{matrix}}

Eq. (3) is the general solution of Eq. (2), from which the recurrence relation of Eq. (4) is obtained:

Y (t) = e^{A t} Y (0) + e^{A t} \int_{0}^{t} e^{- A s} Q (s) d s

(3)

Y (t + Δ t) = e^{A Δ t} Y (t) + e^{A Δ t} \int_{t}^{t + Δ t} e^{- A s} Q (s) d s

(4)

If rational approximation is adopted for exponential function,

e^{A Δ t}

becomes the next expression

e^{A Δ t} = \frac{I + A \frac{Δ t}{2} + A^{2} \frac{1}{2!} {(\frac{Δ t}{2})}^{2} + A^{3} \frac{1}{3!} {(\frac{Δ t}{2})}^{3} + \dots}{I - A \frac{Δ t}{2} + A^{2} \frac{1}{2!} {(\frac{Δ t}{2})}^{2} - A^{3} \frac{1}{3!} {(\frac{Δ t}{2})}^{3} + \dots}

(5)

There are many exponential function approximations available; however, it is clear that the selection of an approximation method of exponential functions is important for obtaining numerical stability. As a result of an investigation comprehensively considering the calculation efficiency, accuracy, and numerical stability, it was confirmed to be the best to consider up to second order terms of

Δ t

of denominator and numerator around the rational approximation of Eq. (6).

If

Q (s)

is constant during time increment

Δ t

, Eq. (6) is derived from Eq. (4).

{\begin{matrix} {\dot{U}}_{t + Δ t} \\ U_{t + Δ t} \end{matrix}} = [\begin{matrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{matrix}] {\begin{matrix} {\dot{U}}_{t} \\ U_{t} \end{matrix}} + [\begin{matrix} H_{11} \\ H_{21} \end{matrix}] {P_{t}}

(6)

where

{\dot{U}}_{t + Δ t}

,

U_{t + Δ t}

= velocity and displacement vectors at time

t + Δ t

; and

{\dot{U}}_{t}

,

U_{t}

,

P_{t}

= velocity; displacement, and seismic force vectors at time

t

. Coefficient matrices of the recurrence relations [Eq. (6)] are

[\begin{matrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{matrix}] = e^{A Δ t}

(7)

[\begin{matrix} H_{11} \\ H_{21} \end{matrix}] = \int_{0}^{Δ t} e^{A (Δ t - s)} [\begin{matrix} I \\ 0 \end{matrix}] d s M^{- 1} = [\begin{matrix} B_{11}^{'} \\ B_{21}^{'} \end{matrix}] M^{- 1}

(8)

where

E_{11}

,

E_{12}

,

E_{21}

and

E_{22} ∶ n \times n

matrices, and

B^{'} = [\begin{matrix} B_{11}^{'} & B_{12}^{'} \\ B_{21}^{'} & B_{22}^{'} \end{matrix}] = \int_{0}^{Δ t} e^{A s} d s = A^{- 1} (e^{A Δ t} - I)

By adding a controlling force to the right-hand side of Eq. (6), though it depends on the mechanical characteristics of the control system, it can be said that Eq. (9) is appropriate, since the controlling forces are not necessarily changed ideally as in a step function

{\begin{matrix} {\dot{U}}_{t + Δ t} \\ U_{t + Δ t} \end{matrix}} = [\begin{matrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{matrix}] {\begin{matrix} {\dot{U}}_{t} \\ U_{t} \end{matrix}} + [\begin{matrix} H_{11} \\ H_{21} \end{matrix}] {P_{t}} + [\begin{matrix} G_{11} & G_{12} \\ G_{21} & G_{22} \end{matrix}] {\begin{matrix} F_{t + Δ t} \\ F_{t} \end{matrix}}

(9)

where

F_{t + Δ t}

,

F_{t}

= controlling force vectors at time

t + Δ t

,

t

. The coefficient matrix of the right side third term is as follows:

[\begin{matrix} G_{11} & G_{12} \\ G_{21} & G_{22} \end{matrix}] = \int_{0}^{Δ t} e^{A (Δ t - s)} [\begin{matrix} \frac{s}{Δ t} I & \frac{Δ t - s}{Δ t} I \\ 0 & 0 \end{matrix}] d s [\begin{matrix} M^{- 1} & 0 \\ 0 & M^{- 1} \end{matrix}] = [\begin{matrix} B_{11}^{'} - \frac{1}{Δ t} B_{11}^{''} & \frac{1}{Δ t} B_{11}^{''} \\ B_{21}^{'} - \frac{1}{Δ t} B_{21}^{''} & \frac{1}{Δ t} B_{21}^{''} \end{matrix}] [\begin{matrix} M^{- 1} & 0 \\ 0 & M^{- 1} \end{matrix}]

(10)

where

B^{''} = [\begin{matrix} B_{11}^{''} & B_{12}^{''} \\ B_{21}^{''} & B_{22}^{''} \end{matrix}] = \int_{0}^{Δ t} s e^{A s} d s = A^{- 1} {Δ t e^{A Δ t} - A^{- 1} (e^{A Δ t} - I)

The control period of this system should be less than the main period of earthquakes and the natural period of structures. Most earthquakes have a small response spectrum less than 0.1 s. The natural period of most structures is larger than 0.1 s. Therefore, the control period and

Δ t

are set as 0.01 or 0.005 s. The sensing devices and the actuators in this research work in 200 Hz.

Using eigenvector

{U_{i}}

, the displacement vector

{U}

of the whole structure of

n

-degrees-of-freedom can be expressed as Eq. (11) (Chopra 1995):

U = z_{1} {U_{1}} + z_{2} {U_{2}} + \dots + z_{n} {U_{n}}

(11)

Though there is no limitation in the number of observed displacements, if the two main eigenvectors

{U_{1}}

and

{U_{2}}

are assumed to contribute to the vibration, and corresponding mode amplitudes to be

z_{1} (t)

and

z_{2} (t)

,

U

is approximated by Eq. (12) as follows:

U \approx [\begin{matrix} U_{1} & U_{2} \end{matrix}] {\begin{matrix} z_{1} \\ z_{2} \end{matrix}}

(12)

If the observed displacements are assumed to be

u_{a}

and

u_{b}

, they are shown as the next expression as follows:

\begin{matrix} U \\ \begin{matrix} {\begin{matrix} ⋮ \\ u_{a} \\ u_{b} \\ ⋮ \end{matrix}} \end{matrix} \end{matrix} = \begin{matrix} \begin{matrix} U_{1} & U_{2} \end{matrix} & Z \\ \begin{matrix} [\begin{matrix} ⋮ & ⋮ \\ u_{1 a} & u_{2 a} \\ u_{1 b} & u_{2 b} \\ ⋮ & ⋮ \end{matrix}] \end{matrix} & \begin{matrix} {\begin{matrix} z_{1} \\ z_{2} \end{matrix}} \end{matrix} \end{matrix}

(13)

Taking out only the necessary parts of Eqs. (13) and (14) is obtained

U \approx [\begin{matrix} U_{1} & U_{2} \end{matrix}] {[\begin{matrix} u_{1 a} & u_{2 a} \\ u_{1 b} & u_{2 b} \end{matrix}]}^{- 1} {\begin{matrix} u_{a} \\ u_{b} \end{matrix}}

(14)

Though it is clear that the displacement of the whole structure can be provided from the limited observed displacements by Eq. (14), it is evident that the selection of appropriate eigenmodes is very important. The number of control points and directions are also limited, as well as the number of measurement points. Excessive controlling forces not only demand excessive power from the control system, but also excite the higher-order vibration modes and cause unstable vibrations; therefore, the parameter

α

is introduced as the controlling force adjustment. Eq. (9) can be transformed into to the next expression:

U_{t + Δ t} = E_{21} {\dot{U}}_{t} + E_{22} U_{t} + H_{21} P_{t} + G_{21} F_{t + Δ t} + G_{22} F_{t}

(15)

B

is defined as

B = E_{21} {\dot{U}}_{t} + E_{22} U_{t} + H_{21} P_{t} + G_{22} F_{t}

(16)

Eq. (17) is obtained from Eq. (15)

U_{t + Δ t} - B = G_{21} F_{t + Δ t}

(17)

where

B

= displacement vector

U_{t + Δ t}

at the next step without controlling forces. The controlling forces are the components of the controlling force vector

F_{t + Δ t}

. If the controlling forces are

f_{1}

and

f_{2}

, Eq. (17) can be written as follows:

\begin{matrix} U_{t + Δ t} \\ \begin{matrix} {\begin{matrix} ⋮ \\ u_{t + Δ t, a} \\ ⋮ \\ u_{t + Δ t, b} \\ ⋮ \end{matrix}} \end{matrix} \end{matrix} - \begin{matrix} B \\ \begin{matrix} {\begin{matrix} ⋮ \\ b_{a} \\ ⋮ \\ b_{b} \\ ⋮ \end{matrix}} \end{matrix} \end{matrix} = \begin{matrix} G_{21} & F_{t + Δ t} \\ [\begin{matrix} ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ ⋮ & g_{1} & ⋮ & g_{2} & ⋮ \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ ⋮ & g_{3} & ⋮ & g_{4} & ⋮ \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \end{matrix}] & \begin{matrix} {\begin{matrix} ⋮ \\ f_{1} \\ ⋮ \\ f_{2} \\ ⋮ \end{matrix}} \end{matrix} \end{matrix}

(18)

where

α (0 < α \leq 1)

is the coefficient to determine the ratio of displacement with the controlling force in time step

t + Δ t

to displacement without the controlling force. The necessary parts of Eqs. (18) and (19) are obtained

{\begin{matrix} f_{1} \\ f_{2} \end{matrix}} = (1 - α) {[\begin{matrix} g_{1} & g_{2} \\ g_{3} & g_{4} \end{matrix}]}^{- 1} {{\begin{matrix} u_{t, a} \\ u_{t, b} \end{matrix}} - {\begin{matrix} b_{a} \\ b_{b} \end{matrix}}}

(19)

The calculated forces work for reducing the velocity. The term

(1 - α)

works as a damping factor. The value of the best

α

cannot be set uniformly since it differs depending on the structural shape and the capacity of the controlling system. Remarkable control effects are found under the high-amplification condition even when

α

is approximately 0.9. Since the seismic forces that are used in this paper are strong, 0.98 is used as

α

for numerical analyses, and a sufficient control effect is confirmed. This parameter

α

is essential and corresponds to the control gain in other control theories.

Active Control Using the Preview Control Method

Preview control can be used for optimizing the displacement and the controlling force when seismic waves are predicted in advance. Two approaches can be used for this application. One approach uses the single quadric evaluation function for composing a preview servo system and the other approach adds the preview evaluation to the existing feedback control system. The second approach is employed in this paper. The preview control force is assumed to be constant during

Δ t

and to be changed by step. Then the equation can be expressed as

{\begin{cases} Δ {\dot{U}}_{(k + 1) Δ t} \\ Δ U_{(k + 1) Δ t} \end{cases}} = [\begin{matrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{matrix}] {\begin{cases} Δ {\dot{U}}_{k Δ t} \\ Δ U_{k Δ t} \end{cases}} + [\begin{matrix} B_{11}^{'} \\ B_{21}^{'} \end{matrix}] M^{- 1} {Δ P_{k Δ t}} + [\begin{matrix} H_{11} \\ H_{21} \end{matrix}] {Δ F_{k Δ t}}

(20)

Then this equation is arranged as

Δ Y_{(k + 1) Δ t} = e^{A Δ t} Δ Y_{k Δ t} + \bar{H} Δ {\bar{S}}_{k Δ t} + \bar{G} Δ {\bar{F}}_{k Δ t}

(21)

where

{\bar{S}}_{k Δ t}

= seismic wave;

{\bar{F}}_{k Δ t} = {[\begin{matrix} {\bar{f}}_{1}, \end{matrix} {\bar{f}}_{2}]}^{T}

= control force;

\bar{H}

= partial components of

{[\begin{matrix} B_{11}^{' T} & B_{22}^{' T} \end{matrix}]}^{T}

corresponding to the direction of the seismic wave; and

\bar{G}

= partial components of

{[\begin{matrix} H_{11}^{T} & H_{21}^{T} \end{matrix}]}^{T}

corresponding to

{\bar{f}}_{1}

and

{\bar{f}}_{2}

.

The target displacement is always zero for controlling structures. The seismic wave factor is the previous value.

M_{d}

step future is assumed to be previewed. The quadratic form function is evaluated as

J = \sum_{k = - M_{d} + 1}^{\infty} [Δ Y_{k Δ t}^{T} \bar{Q} Δ Y_{k Δ t} + Δ {\bar{F}}_{k Δ t}^{T} \bar{R} Δ {\bar{F}}_{k Δ t}]

(22)

where

\bar{Q}

and

\bar{R}

= weighting matrices for state quantity and controlling force. In this equation;

k = - M_{d} + 1

= current step, and the control force is derived for minimizing the summation from the current step to future. The control force is defined as

Δ {\bar{F}}_{k Δ t} = {\bar{F}}_{0} Δ Y_{k Δ t} + \sum_{j = 1}^{M_{d}} {\bar{F}}_{d} (j) Δ {\bar{S}}_{(k + j) Δ t}

(23)

Feedback parameters

{\bar{F}}_{0}

and preview feed-forward parameters

{\bar{F}}_{d} (j)

are calculated as

{\bar{F}}_{0} = - {[\bar{R} + {\bar{G}}^{T} \bar{P} \bar{G}]}^{- 1} {\bar{G}}^{T} \bar{P} e^{A Δ t}

(24)

{\bar{F}}_{d} (j) = - {[\bar{R} + {\bar{G}}^{T} \bar{P} \bar{G}]}^{- 1} {\bar{G}}^{T} {(ξ^{T})}^{j} \bar{P} \bar{H} (j \geq 0)

(25)

where

ξ = e^{A Δ t} + \bar{G} {\bar{F}}_{0}

; and

\bar{P}

= positive definite matrix for minimizing the evaluation function as the solution of Riccati’s equation. The control force of the optimization preview servo system is calculated as

Δ {\bar{F}}_{k Δ t} = \sum_{j = 1}^{M_{d}} {\bar{F}}_{d} (j) Δ {\bar{S}}_{(k + j) Δ t}

(26)

The preview force is calculated using the calculated coefficient

{\bar{F}}_{d}

and discrete preview seismic wave

Δ P_{k Δ t}

. The control force is calculated as the summation of the preview force and the force calculated in Eq. (19). The brief structure of the system is shown in Fig. 1. The weight matrices

\bar{Q}

and

\bar{R}

in Eq. (22) for normalizing the preview control force are defined as

\bar{Q} = [\begin{matrix} M & 0 \\ 0 & K \end{matrix}]

(27)

\bar{R} = [\begin{matrix} 0.01 & 0 \\ 0 & 0.01 \end{matrix}]

(28)

\bar{Q}

should be optimized for the controlling object.

\bar{Q}

, defined as Eq. (27), denotes the summation of the kinetic energy and the elastic energy, which is then minimized. The weight matrix of controlling force

\bar{R}

is

r \times r

and a positive definite matrix where

r

is the number of the control device. When the diagonal elements of

\bar{R}

become smaller, the response displacement becomes smaller, but the controlling force becomes larger. Since the control device is limited in its ability to output control force, the optimal value must be found. The value is defined as 0.01 by trial and error.

Predicted Seismic Waves Using Autoregressive Model

If an epicenter is far to a certain degree, a body wave is propagated almost vertically in the vicinity of the ground surface as in Snell’s law (Japan Society of Civil Engineers 2001). The seismic wave at the ground surface is calculated using an autoregressive model based on the one-dimensional wave propagation theory and observed waves recorded by seismographs set up several hundred meters below the ground surface. The calculated values are designated as the predicted seismic wave. The seismic wave at the ground surface is predicted in advance by analyzing underground seismic motion data 0.05–0.3 s before the actual wave reaches the ground surface. The autoregressive model predicts the current variable, which depends linearly on its previous values. The proposed method also uses the previous underground seismic wave as follows:

{{\bar{S}}_{k Δ t}} = \sum_{i = 1}^{p} Φ_{i} {\begin{matrix} {\bar{S}}_{(k - i) Δ t} \\ {\hat{S}}_{(k - i) Δ t} \end{matrix}}

(29)

where

{\bar{S}}_{k Δ t}

,

{\hat{S}}_{k Δ t}

and

Φ_{i}

= a ground wave, an underground wave, and the parameter of an AR model, respectively. The parameters

Φ_{i}

are determined using the Yule-Walker equations.

{\bar{S}}_{(k + 1) Δ t}

is calculated by Eq. (29) with the predicted

{\bar{S}}_{k Δ t}

,

{\hat{S}}_{k Δ t} = 0

,

{\bar{S}}_{(k - i) Δ t} (1 \leq i \leq p - 1)

, and

{\hat{S}}_{(k - i) Δ t} (1 \leq i \leq p - 1)

. This procedure is repeated and

{\bar{S}}_{(k + i) Δ t} (0 \leq i \leq M_{d} - 1)

is calculated.

Φ_{i}

is determined in advance and is not updated during the calculation for preview control. At every step of preview control, the observed ground and underground waves in the past are inputted and future waves are predicted. The calculation time at each control step is less than 0.1 ms, where

M_{d} = 200

and is significantly smaller than the control period. The predicted wave is calculated online at every control period.

Analysis of Preview Control Quality

The two-layer framed structure as shown in Fig. 2 is used for simulation. The floor is made of duralumin plates (

1000 \times 550 \times 10 mm

) and the column is comprised of a strip of steel plating with a rectangular cross-section (

800 \times 32 \times 9 mm

) like a leaf spring. Therefore, the stiffness in the shaking direction is low compared with that in the orthogonal direction. The main vibrations occur in the shaking direction and the vertical direction. The natural vibration modes and periods up to the fifth were calculated by eigenvalue analysis. Since the third and higher-order modes have low sensitivity, the first and second modes were used for the simulation. The first and second natural periods of this structure are 0.359 and 0.125 s, and participation factors are 0.25 and

- 0.07

, respectively. The natural periods are adjusted for simulating steel construction with 10–20 m height. The detail on this structure is shown in Table 1 and vibration modes are shown in Fig. 3. The damping constant is acquired experimentally and set as 1% both for the first mode and the second mode of Rayleigh damping.

Fig. 2. Structure model on the shaking table

Table 1. Parameters of the Structure

Degree of modes	Natural period (s)	Participation factor
1	0.359	0.249
2	0.125	$- 0.0703$
3	0.0484	$0.416 \times 10^{- 12}$
4	0.0420	$- 0.139 \times 10^{- 12}$
5	0.0181	$- 0.163 \times 10^{- 6}$

Fig. 3. Analysis result of the natural vibration mode: (a) first mode; (b) second mode; (c) third mode; (d) fourth mode; (e) fifth mode

In previous research (Nakamura et al. 2010), a high-speed optical device (Ishii et al. 2004) was used for measuring the deformation of the structure. The displacement of the structure directly is used for the control system.

Predicted Seismic Wave Calculation Using KiK-Net Data

The effectiveness of active preview control and the number of preview steps required should be confirmed. In addition, it is necessary to confirm the possibility of calculating predicted seismic waves and the robustness of the control system against expected errors when applied to an actual structure.

KiK-net is a strong-motion seismograph network that consists of pairs of seismographs installed on the ground surface and several hundred meters below ground, deployed at approximately 700 locations nationwide by the National Research Institute for Earth Science and Disaster Prevention. The following KiK-net data in Table 2 at the site (Table 3) is used to confirm the feasibility of the proposed method of obtaining predicted seismic waves.

Table 2. Earthquake Information

Name	Chuetsu-oki	Chuetsu
Occurrence time	July 16/2007-10:13	October 23/2004-17:56
Magnitude	6.6	6.8
Epicenter	37.56 N, 138.61 E	37.29 N, 138.87 E
Depth	17 km	13 km

Table 3. Site of Measurement

Site	Kawanishi, Niigata-ken
Site code	NIGH11
Latitude, longitude	37.1728 N, 138.7440 E
Altitude	$+ 165 m$
Depth	205 m

Fig. 4 shows the locations of actual epicenters in relation to the observation point. The two epicenters are approximately 45 and 18 km from the observation point. According to the borehole log shown in (National Research Institute for Earth Science and Disaster Prevention 2001), the

S

-wave velocity is about

550 m / s

on average, and arrival time from the underground observation point to the surface is about 0.38 s. This is sufficient time to observe, transmit, and process seismographic observation data using current technology for predicting seismic waves. For testing the effectiveness of the one-dimensional wave propagation theory, SHAKE is used for estimating ground waves using underground waves during the Chuetsu-oki Earthquake (2007). As shown in Fig. 5, the ground wave is estimated based on the one-dimensional wave propagation theory. Autoregressive (AR) parameters are calculated using the seismic waves (January 4, 2001) which has more than

2 m / s^{2}

(200 gal.). Fig. 6(a) shows a comparison of the observed wave at the ground surface and the wave that is predicted 0.2 s before for the ground surface at observation point NIGH11 during the Chuetsu-oki Earthquake (2007). Principal motion during the initial 16 s is extracted from the original KiK-net data. Fig. 7(a) shows a comparison of the observed wave at ground surface and the wave which is predicted 0.2 s before for the ground surface by analyses at observation point NIGH11 during the Chuetsu Earthquake (2004). The analysis, by comparing predicted waves and observed waves at the ground surface, confirms to some degree that prediction of seismic waves at the ground surface is possible. Predicted seismic waves are calculated step-by-step by using observed waves until that time. Predicted waves at ground surface after 7, 8, 9 s are shown in Figs. 6(b–d) and 7(b–d). The error gradually grows with the passage of time, since the analysis by AR method uses only information until that time. Considering the data shown in Figs. 6(b–d) and 7(b–d), the predicted data is limited to approximately 0.3–0.4 s, corresponding to the time it takes the

S

-wave to travel from the underground observation point to the ground surface. Since the ability to accurately predict waves decreases as the duration of prediction time is increased, predicted values are of little importance in active preview control. Therefore, it is important to improve prediction accuracy in the near future.

Fig. 4. Location of the NIGH11 Site, and the epicenters of Chuetsu-oki and Chuetsu earthquakes

Fig. 5. Comparison between calculated wave by *SHAKE* at ground surface and observed waves at NIGH11 Site during the Chuetsu-oki earthquake (2007)

Fig. 6. Comparison between predicted wave at ground surface and observed waves at NIGH11 Site during the Chuetsu-oki earthquake (2007): (a) comparison between observed waves at ground surface and predicted wave at ground surface analyzed 0.2 s before; (b) predicted wave at surface after 7 s; (c) predicted wave at surface after 8 s; (d) predicted wave at surface after 9 s

Fig. 7. Comparison between predicted wave at ground surface and observed waves at NIGH11 Site during the Chuetsu earthquake (2004): (a) comparison between observed waves at ground surface and predicted wave at ground surface analyzed 0.2 s before; (b) predicted wave at surface after 7 s; (c) predicted wave at surface after 8 s; (d) predicted wave at surface after 9 s

Active Preview Control Simulation Using Predicted Seismic Waves

The amount of response displacement is reduced when using preview control in the simulation of the Chuetsu and Chuetsu-oki earthquakes, as shown in Figs. 8 and 9. The waveform of the control forces is shown in Figs. 10 and 11. The relation between the number of preview steps and the amount of displacement is shown in Tables 4 and 6. The reduction rates are about 70 and 90% with 20 preview steps (0.1 s). The number of preview steps

M_{d}

in Eq. (26) is changed and tested with the Chuetsu and Chuetsu-oki waves. The relation between the maximum response rate, maximum control force, and preview steps is shown in Tables 4–7. The time of the maximum displacement and control force are also shown in these tables. The presence of a reduction effect for the predicted seismic wave is confirmed, even though the effect is less than for the observed wave. The rate of reduction increases as the number of preview steps increases. The preview period of 0.5 s shows good effect. Table 8 shows the maximum displacement and the rate of reduction for preview control. The preview control dramatically increases the rate of reduction. The control force with preview control has generally the same as that with feedback control without preview. The control force increases earlier than the control without preview for preparing a seismic wave in the future. With the Chuetsu wave, the maximum control force with preview control is larger than that without preview. However the reduction rate in maximum response displacement is larger than the growth rate in maximum control force, and even if the control force without preview is strengthened to the same value as the preview control, the reduction rate does not increase as much as with the preview control. This confirms that preview control effectively reduces the displacement against rapid seismic waves. The accuracy of preview control depends on the accuracy of the predicted ground wave. As shown in the previous section, a wave on the ground surface 0.4 s in advance can be predicted using data for actual waves observed at 200 m below the ground. The results by comparing data for seismic waves at two different earthquake epicenters are confirmed. Therefore, it is confirmed that the preview method can feasibly be applied to actual structures. Seismic waves at different locations may not be predicted using the multireflection theory for the analysis of horizontally layered ground. In order to improve accuracy, multiple seismographs should be set at varying depths. The propagation characteristics will be clear and the accuracy for the future less than 0.1 s is certainly improved. In the future, other locations will be verified and the prediction method will be improved.

Fig. 8. Response displacement comparison of Chuetsu-oki wave

Fig. 9. Response displacement comparison of Chuetsu wave

Fig. 10. Control force comparison of Chuetsu-oki wave

Fig. 11. Control force comparison of Chuetsu wave

Table 4. Displacement and Control Force Rate on Preview Steps (Chuetsu-Oki Wave/Predicted Wave at Ground) Time Increment

Δ t = 0.005 (s)

Preview steps	Displacement (cm)	Control force (N)	Displacement ratio (%)	Force ratio (%)	Displacement time (s)	Force time (s)
0	0.693	1.28	100.0	100.0	11.090	9.220
2	0.656	1.30	94.7	101.6	11.090	9.215
20	0.515	1.37	74.4	106.9	11.100	9.205
50	0.417	1.22^a	60.2	95.4	11.060	11.020
80	0.410^a	1.27	59.2	98.7	12.530	11.020

a

The minimum value in each column.

Table 5. Displacement and Control Force Rate on Preview Steps (Chuetsu-Oki Wave/Observed Wave at ground) Time Increment

Δ t = 0.005 (s)

Preview steps	Displacement (cm)	Control force (N)	Displacement ratio (%)	Force ratio (%)	Displacement time (s)	Force time (s)
0	0.693	1.28	100.0	100.0	11.090	9.220
2	0.652	1.26	94.1	98.4	11.090	9.215
20	0.484	1.13	69.9	88.3	11.105	9.215
50	0.399	1.06	57.6	82.4	11.085	9.180
80	0.374^a	0.93^a	54.0	72.1	11.085	9.175

a

The minimum value in each column.

Table 6. Displacement and Control Force Rate on Preview Steps (Chuetsu Wave/Predicted Wave at Ground) Time Increment

Δ t = 0.005 (s)

Preview steps	Displacement (cm)	Control force (N)	Displacement ratio (%)	Force ratio (%)	Displacement time (s)	Force time (s)
0	3.67	5.91	100.0	100.0	6.245	6.355
2	3.53	6.10	96.1	103.2	6.245	6.160
20	3.27	6.78	89.2	114.8	6.245	6.150
50	3.22	6.38^a	87.8	108.0	6.245	6.165
80	3.19^a	6.39	86.8	108.1	6.245	6.160

a

The minimum value in each column.

Table 7. Displacement and Control Force Rate on Preview Steps (Chuetsu Wave/Observed Wave at Ground) Time Increment

Δ t = 0.005 (s)

Preview steps	Displacement (cm)	Control force (N)	Displacement ratio (%)	Force ratio (%)	Displacement time (s)	Force time (s)
0	3.67	5.91	100.0	100.0	6.245	6.355
2	3.45	6.02	94.1	101.9	6.245	6.155
20	2.61	6.64	71.2	112.3	6.260	6.140
50	1.86	5.50	50.7	93.0	6.245	6.130
80	1.60^a	5.42^a	43.7	91.8	6.240	6.145

a

The minimum value in each column.

Table 8. Result of Preview Control

Name	Chuetsu-oki		Chuetsu
Measurement	Displacement (cm)	Reduction ratio (%)	Displacement (cm)	Reduction ratio (%)
Uncontrolled	0.976	—	9.68	—
Preview	0.410	58.0	3.19	67.0
Feedback	0.693	29.0	3.67	62.1

Note: Predicted wave at ground.

Conclusion

A preview control method is proposed for improving the efficiency of active control systems. The results are as follows:

1.

The preview control method is introduced and described for application to active seismic control systems or structures and the effectiveness of the system is confirmed by simulation tests. Since the controlling force is generated preemptively, the displacement is reduced against sudden seismic force. The simulation shows that even a preview of 0.4 s is enough to control the structure response.

2.

Ground waves and the underground waves that were measured simultaneously by KiK-net are used. It is confirmed that the ground surface wave can be predicted using ground waves and underground waves recorded at a depth of 200 m. The results of simulation tests using AR method show that the ground waves can be predicted within the period of time required for the

S

-wave to reach the ground surface. Even though the locations of the epicenters are different, the same calculations are effective in the prediction of the wave.

3.

The simulation of the preview control method using the predicted seismic wave shows that the maximum displacement can be reduced, thereby confirming that the predicted wave is effective for reducing the displacement. The simulation tests shows that the future wave at the ground surface can be predicted using an underground seismograph. In addition, the preview control method and its predicted wave can be used for actual structures.

Acknowledgments

The authors would like to express their gratitude to Professor Idaku Ishii (Hiroshima University) for his helpful suggestions about hyper-vision technology, and the authors would also like to express their gratitude to Associate Professor Tatsuo Kan-no (Hiroshima University) for providing them with the materials related to the earthquake response analysis of horizontally layered sites. The authors also wish to express their thanks to Dr. Y. Shumuta (Central Research Institute of Electric Power Industry) for his valuable advice about application of the Earthquake Early Warning system. And their special thanks are due to the National Research Institute for Earth Science and Disaster Prevention for permission to use the KiK-net data.

References

Chopra, A. K. (1995). Dynamics of structures, Vol. 3, Prentice Hall, Upper Saddle River, NJ.

Google Scholar

Fujita, S., Minagawa, K., Tanaka, G., and Shimosaka, H. (2011). “Intelligent seismic isolation system using air bearings and earthquake early warning.” Soil Dyn. Earthquake Eng., 31(2), 223–230.

Crossref

Google Scholar

Hannan, E. J. (1970). Multiple time series, Wiley, New York.

Crossref

Google Scholar

Hayase, M., and Ichikawa, K. (1969). “Optimal servosystem utilizing future value of desired function.” Trans. SICE, 5(1), 86–94.

Crossref

Google Scholar

Ikeda, Y. (2004). “Active and semi-active control of buildings in Japan.” J. Jpn. Assoc. Earthquake Eng., 4(3), 278–282.

Crossref

Google Scholar

Ishii, I., Kato, K., Kurozumi, S., Nagai, H., Numata, A., and Tajima, K. (2004). “Development of a mega-pixel and milli-second vision system using intelligent pixel selection.” 1st IEEE Technical Exhibition Based Conf. on Robotics and Automation (TExCRA 2004), IEEE, 9–10.

Google Scholar

Japan Road Association. (2002). “Specifications for highway bridges, part V seismic design.” Maruzen, Tokyo, Japan.

Google Scholar

Japan Society of Civil Engineers. (2001). “Introduction to Earthquake engineering: The professional engineers.” Maruzen, Tokyo, Japan.

Google Scholar

Katayama, T., Ohki, T., Inoue, T., and Kato, T. (1985). “Design of an optimal controller for a discrete-time system subject to previewable demand.” Int. J. Control, 41(3), 677–699.

Crossref

Google Scholar

Kobori, T. (1993). Vibration control structure-theory and practice, Kajima Institute, Tokyo, Japan.

Google Scholar

Lysmer, J., and Kuhlemeyer, R. L. (1969). “Finite dynamic model for infinite media.” J. Eng. Mech. Div., 95(4), 859–877.

Crossref

Google Scholar

Lysmer, J., Udaka, T., Tsai, C., and Seed, H. B. (1975). “FLUSH—A computer program for approximate 3-d analysis of soil-structure interaction problems.”, Univ. of California, Berkley, CA.

Google Scholar

Lysmer, J., and Waas, G. (1972). “Shear waves in plane infinite structures.” J. Eng. Mech. Div., 98(1), 85–105.

Google Scholar

Marzbanrad, J., Ahmadi, G., and Jha, R. (2004). “Optimal preview active control of structures during earthquakes.” Eng. Struct., 26(10), 1463–1471.

Crossref

Google Scholar

Megro, K., and Fujinawa, Y. (2007). Early earthquake warning, Tokyo-horei, Tokyo, Japan.

Google Scholar

Nakamura, H., Tsuji, T., Ishii, I., Satake, R., Nakayama, T., and Motoyama, J. (2010). “Studies on active control of structures using hyper vision technology.” Struct. Eng. Earthquake Eng., 27(1), 14–27.

Crossref

Google Scholar

National Research Institute for Earth Science and Disaster Prevention. (1996). “Digital strong-motion seismograph network kik-net.” 〈http://www.kyoshin.bosai.go.jp/〉 (Jul. 2, 2015).

Google Scholar

National Research Institute for Earth Science and Disaster Prevention. (2001). “Soil and rock condition, site: Kawanishi, Niigata-ken, Site Code: NIGH11.” 〈http://www.kyoshin.bosai.go.jp/cgi-bin/kyoshin/db/siteimage.cgi?1+NIGH11+kik+def〉 (Jul. 2, 2015).

Google Scholar

Phillips, B. M., and Spencer, B. F., Jr. (2012). “Model-based multiactuator control for real-time hybrid simulation.” J. Eng. Mech., 219–228.

Google Scholar

Schnabel, P., Lysmer, J., and Seed, H. (1972). “SHAKE—A computer program for earthquake response analysis of horizontally layered sites.”, Univ. of California, Berkley, CA.

Google Scholar

Seto, K. (1998). Vibration control of structures, Corona, Tokyo, Japan.

Google Scholar

SHAKE, QUAD−4, FLUSH, and SASSI [Computer software]. Berkeley, CA, University of California, Berkeley.

Google Scholar

Sheridan, T. B. (1966). “Three models of preview control.” IEEE Trans. Hum. Factors Electron., HFE-7(2), 91–102.

Crossref

Google Scholar

Shiojiri, H., and Nakamura, H. (1976). “On a method for dynamic response computation for structural analysis.” Proc. Jpn. Soc. Civ. Eng., 1976(246), 21–33.

Crossref

Google Scholar

Spencer, B., Jr., and Nagarajaiah, S. (2003). “State of the art of structural control.” J. Struct. Eng., 845–856.

Crossref

Google Scholar

Tateishi, A., and Nishioka, T. (2001). “Control of structural response against earthquakes by using information on predicted external force.” 7th Dynamics and Design Conf., Japan Society of Mechanical Engineers, 372–375.

Google Scholar

Thenozhi, S., and Yu, W. (2013). “Advances in modeling and vibration control of building structures.” Annu. Rev. Control, 37(2), 346–364.

Crossref

Google Scholar

Tomizuka, M., and Rosenthal, D. E. (1979). “On the optimal digital state vector feedback controller with integral and preview actions.” J. Dyn. Syst. Meas. Control, 101(2), 172–178.

Crossref

Google Scholar

Yoshikawa, T., and Imura, J. (1994). Modern control theory, Shoko-do, Tokyo, Japan.

Google Scholar

Information & Authors

Information

Published In

Journal of Engineering Mechanics

Volume 142 • Issue 2 • February 2016

Copyright

This work is made available under the terms of the Creative Commons Attribution 4.0 International license, http://creativecommons.org/licenses/by/4.0/.

History

Received: Jul 25, 2014

Accepted: May 28, 2015

Published ahead of print: Jul 14, 2015

Published online: Jul 15, 2015

Discussion open until: Dec 15, 2015

Published in print: Feb 1, 2016

Authors

Affiliations

Tokuo Tsuji [email protected]

Assistant Professor, Graduate School and Faculty of Information Science and Electrical Engineering, Kyushu Univ., 744 Moto-oka, Nishi-ku, Fukuoka-shi, Fukuoka 819-0395, Japan (corresponding author). E-mail: [email protected]

View all articles by this author

Hideharu Nakamura [email protected]

Adviser, Tokyo Electric Power Services Co. Ltd., 1-7-12 Shinonome, Koto-ku, Tokyo 135-0062, Japan; Professor Emeritus, Engineering, Hiroshima Univ., 1-4-1 Kagamiyama, Higashi-Hiroshima-shi, Hiroshima 739-8527, Japan. E-mail: [email protected]

View all articles by this author

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Improving Active Preview Control System of Structures Using Online Prediction of Seismic Waves

Abstract

Introduction

Proposed Active Preview Control Method

Recurrence Relations Applied to Active Control

Active Control Using the Preview Control Method

Predicted Seismic Waves Using Autoregressive Model

Analysis of Preview Control Quality

Predicted Seismic Wave Calculation Using KiK-Net Data

Active Preview Control Simulation Using Predicted Seismic Waves

Conclusion

Acknowledgments

References

Information & Authors

Information

Published In

Copyright

History

Authors

Affiliations

Metrics & Citations

Metrics

Citations

Download citation

View Options

Media

Figures

Other

Tables

PREVIOUS ARTICLE

NEXT ARTICLE

Verify Phone

Congrats!

Abstract

Introduction

Proposed Active Preview Control Method

Recurrence Relations Applied to Active Control

Active Control Using the Preview Control Method

Predicted Seismic Waves Using Autoregressive Model

Analysis of Preview Control Quality

Predicted Seismic Wave Calculation Using KiK-Net Data

Active Preview Control Simulation Using Predicted Seismic Waves

Conclusion

Acknowledgments

References

Information

Published In

Copyright

History

Authors

Affiliations

Metrics

Citations

Download citation

Figures

Other

Share

Copy the content Link

Share with email

Share

Request Username

Create a new account

Change Password

Password Changed Successfully

Verify Phone

Congrats!