Structural vibration control systems

Abstract

To improve vibration control performance.SOLUTION: A vibration control system of a structure is represented by a mass model comprising: a support end; a first mass point aligned with the support end in a predetermined direction; a first spring element connecting the support end and the first mass point, the first spring element generating elastic reaction force that acts along an orthogonal direction orthogonal to the predetermined direction; a second mass point that can be displaced relative to the first mass point in the orthogonal direction; and an exciter that is connected to the first mass point, and excites the second mass point in the orthogonal direction. In the vibration control system, a control rule for controlling exciting force of the exciter is determined using reinforcement learning.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a vibration control system for a structure. [Background technology]

[0002] Active Mass Damper (AMD), which damps vibrations by actively moving a mass, is known as a method for reducing vibrations in structures, such as horizontal vibrations of buildings and vertical vibrations of floors, caused by various disturbances (see, for example, Patent Document 1). In AMD, control is generally performed according to control laws based on control engineering. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 1-275867 Summary of the Invention [Problem to be solved by the invention]

[0004] Control laws based on control engineering require control theory, making it difficult to maximize the capabilities of AMD (i.e., to move the mass optimally).

[0005] The present invention has been made in view of the above problems, and an object of the present invention is to improve vibration damping performance. [Means for solving the problem]

[0006] The main invention for achieving the above object is a vibration control system for a structure represented by a mass point model having: a support end; a first mass point aligned with the support end in a predetermined direction; a first spring element connecting the support end and the first mass point, the first spring element generating an elastic reaction force acting along an orthogonal direction orthogonal to the predetermined direction; a second mass point displaceable in the orthogonal direction relative to the first mass point; and a vibrator connected to the first mass point and vibrating the second mass point in the orthogonal direction, wherein a control law for controlling the excitation force of the vibrator is determined using reinforcement learning, the second mass point is a mass of a mass damper that suppresses vibration of the first mass point, and a reward in the reinforcement learning is determined based on a conserved quantity of the first mass point, The reward in the reinforcement learning is a competitive type expressed by the following equation (16): It is characterized by: JPEG0007806777000001.jpg47170 [Effects of the Invention]

[0007] According to the present invention, it is possible to improve vibration damping performance. [Brief explanation of the drawings]

[0008] [Figure 1] Fig. 1A is a diagram showing the configuration of a vibration control system for a structure according to a first embodiment, Fig. 1B is a diagram showing a model of Fig. 1A, and Fig. 1C is an equivalent diagram of Fig. 1B. [Figure 2] 4 is a block diagram showing the configuration of a control portion of the actuator 40. FIG. [Figure 3] FIG. 10 is a flow diagram of constructing an AMD control system in a comparative example. [Figure 4] FIG. 2 is a flow diagram of constructing an AMD control system in this embodiment. [Figure 5] Fig. 5A is a diagram showing the configuration of a vibration control system for a structure according to the second embodiment, and Fig. 5B is a diagram showing a model of Fig. 5A. [Figure 6] Fig. 6A is a diagram showing the configuration of a vibration control system for a structure according to the third embodiment, and Fig. 6B is a diagram showing a model of Fig. 6A. [Figure 7] FIG. 10 is a diagram showing a modified example of the third embodiment. [Figure 8] FIG. 10 is a diagram showing another modified example of the third embodiment. [Figure 9] Fig. 9A shows the configuration of a vibration control system for a structure according to the fourth embodiment, and Fig. 9B is a diagram modeling Fig. 9A. [Figure 10] FIG. 10 is a diagram showing a modified example of the fourth embodiment. [Figure 11] FIG. 10 is a diagram showing another modified example of the fourth embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0009] At least the following matters will become clear from the description of this specification and the accompanying drawings.

[0010] A vibration control system for a structure is revealed that is represented by a mass point model having a support end, a first mass point aligned with the support end in a predetermined direction, a first spring element connecting the support end and the first mass point, the first spring element generating an elastic reaction force acting along an orthogonal direction perpendicular to the predetermined direction, a second mass point that is displaceable relative to the first mass point in the orthogonal direction, and a vibrator connected to the first mass point and vibrating the second mass point in the orthogonal direction, wherein a control law for controlling the vibration force of the vibrator is determined using reinforcement learning. Such a structural vibration control system can realize a control law that is superior to control laws based on control theory (such as optimal control), which can enhance the ability of vibration control (AMD) by exciting the second mass point with a vibrator, thereby improving vibration control performance.

[0011] In such a vibration control system for a structure, it is desirable that a reward in the reinforcement learning is determined based on a conserved quantity of the first mass point. Such a vibration control system for a structure can provide an excellent control law.

[0012] In such a vibration control system for a structure, it is desirable that the conserved quantity be of a counter type. Such a vibration control system for a structure can provide an excellent control law.

[0013] In such a vibration control system for a structure, it is desirable that the conserved quantity is energy. Such a structural vibration control system can provide a more excellent control law.

[0014] In such a vibration control system for a structure, it is desirable that the energy includes at least kinetic energy. Such a vibration control system for a structure can improve vibration control performance.

[0015] In such a vibration control system for a structure, it is desirable that the energy further includes potential energy of a spring system. Such a vibration control system for a structure can further improve vibration control performance.

[0016] The vibration control system for such a structure may further include a second spring element that is provided in parallel with the vibrator and whose spring direction is the orthogonal direction. According to such a vibration control system for a structure, it is possible to improve vibration control performance even when the second spring element is provided.

[0017] In a vibration control system for such a structure, the specified direction may be a vertical direction, the orthogonal direction may be a horizontal direction, and a rolling support may be provided on the first mass point to support the second mass point so that the second mass point can roll in the horizontal direction. According to such a vibration control system for a structure, the horizontal vibration of the first mass point can be controlled by vibrating (rolling) the second mass point in the horizontal direction on the first mass point.

[0018] In a vibration control system for such a structure, the specified direction may be a vertical direction, the orthogonal direction may be a horizontal direction, and the second spring element may be a laminated rubber that supports the second mass point on top of the first mass point. According to such a vibration control system for a structure, horizontal vibration of the first mass point can be controlled by horizontally vibrating the second mass point supported on the first mass point by laminated rubber.

[0019] In such a vibration control system for a structure, the predetermined direction may be a horizontal direction, and the orthogonal direction may be a vertical direction. Such a vibration control system for a structure can control vertical vibrations of a bridge, for example.

[0020] ===First Embodiment=== <<About the vibration control system configuration>> Fig. 1A is a diagram showing the configuration of a vibration control system for a structure according to a first embodiment, Fig. 1B is a model of Fig. 1A, and Fig. 1C is an equivalent diagram of Fig. 1B. Fig. 2 is a block diagram showing the configuration of a control portion of actuator 40.

[0021] As shown in Fig. 1A, the structure to be damped in the first embodiment is a bridge 10 that is fixed at both longitudinal ends (support ends 12) and spans the horizontal direction. A mass 20 is provided in the center of the longitudinal direction of this bridge 10 via a spring 30 and an actuator 40. Also, as shown in Fig. 2, a group of sensors 60 (e.g., an acceleration sensor that detects acceleration, a displacement sensor that detects displacement (relative displacement, etc.)) that detects the states of the bridge 10 and mass 20, and a controller 70 that calculates state quantities and controls the excitation of the actuator 40 based on the output of each sensor in the group of sensors 60 are provided.

[0022] When Figure 1A is modeled as a mass point model, it becomes a two-mass point model as shown in Figure 1B, and when it is further simplified it becomes as shown in Figure 1C. In Figures 1B and 1C, the bridge 10 and the mass 20 are each shown as a mass point. Of these, the mass point representing the bridge 10 corresponds to the first mass point, and the mass point representing the mass 20 corresponds to the second mass point.

[0023] 1B and 1C, the bridge 10 is aligned horizontally with the support end 12. The spring element 14 (corresponding to the first spring element) shown in the mass model in FIGS. 1B and 1C corresponds to the rigidity of the bridge 10. The spring element 14 connects the support end 12 and the bridge 10 (first mass point), and generates an elastic reaction force that acts in a direction (here, the vertical direction) perpendicular to the direction (here, the horizontal direction) in which the bridge 10 and the support end 12 are aligned.

[0024] The mass 20 is a weight (mass body) for AMD control, and is provided on the bridge 10 (aligned vertically with the bridge 10) via a spring 30. This allows the mass 20 to be displaced relative to the bridge 10 in the vertical direction.

[0025] The spring 30 (corresponding to the second spring element) is disposed between the bridge 10 and the mass 20 (disposed in parallel with the actuator 40) so that the spring direction is in the vertical direction, and supports the mass 20.

[0026] The actuator 40 (vibrator) is connected to the bridge 10 and vibrates the mass 20 in the vertical direction under the control of the controller 70.

[0027] By adjusting (controlling) the excitation force (control force) of this actuator 40, it is possible to suppress the vertical shaking (up and down vibration) of the bridge 10 caused by people walking on the bridge 10.

[0028] As shown in FIG. 1C, the vibration control system for a structure according to this embodiment is a two-mass system model, and its behavior can be simulated by solving the state equation of the following formula (1) by numerical analysis. JPEG0007806777000002.jpg6170

[0029] The terms of formula (1) are shown in formulas (2) to (5) below. JPEG0007806777000003.jpg90170where, JPEG0007806777000004.jpg163170

[0030] <<AMD Control (Comparative Example)>> Figure 3 is a flowchart of constructing an AMD control system in the comparative example. Here, optimal control, which is known as an example of active control, is used.

[0031] First, the settings of each parameter are performed (S001). Here, for the purpose of making the [displacement, velocity] and the absolute value of the control force of [Mass 20, Bridge 10] as small as possible at each step, the evaluation function J is defined as the sum of the squares of the [displacement, velocity] and the control force of [Mass 20, Bridge 10] weighted as shown in the following formula (6). JPEG0007806777000005.jpg8170

[0032] In formula (6), x(t) is the above formula (4), u(t) is the control force, and ε is the weight applied to the control force. Also, Q is the weight applied to x(t), and JPEG is 20170. [[ID=ID=19]]

[0033] JPEG0007806777000007.jpg28170

[0034] JPEG0007806777000008.jpg39170

[0035] Next, the feedback gain of the control law is calculated (S002). When theoretically obtaining the feedback gain of x(t) that minimizes the evaluation function J, the control force u(t) is represented by the following formula (9). JPEG0007806777000009.jpg8170 Here, P is the solution of the Riccati equation represented by the following formula (10). JPEG0007806777000010.jpg8170

[0036] JPEG0007806777000011.jpg27170The control law can be obtained by solving this equation.

[0037] Next, the effectiveness of the obtained control law is confirmed by a simulation in which walking excitation force is input (S003).

[0038] If the control law check result is bad (No in S004), the process returns to step S001 and the parameters are reset. On the other hand, if the control law check result is good (Yes in S004), implementation is performed (S005). That is, based on x(t) acquired and calculated in real time from each sensor (acceleration sensor, displacement sensor, etc.) of the sensor group 60, a control force u(t) is calculated and applied to the actuator 40.

[0039] Note that in this example, optimal control (which is also synonymous with optimal feedback control, LQ control, LQR control, and optimal regulator control) has been explained, but other known control methods (control laws) for active control include LQG control, bilinear optimal control, instantaneous optimal control, suboptimal control, suboptimal merging control, pole placement control, skyhook control, H∞ control, PID control, sliding mode control, On / Off control, EF (Energy Function) control, fuzzy control, predictive control, hysteresis control, direct output feedback control, direct velocity feedback control (DVFB control), disturbance cancellation control, μ synthesis control, and gain-scheduled control.

[0040] However, there was a possibility that the control using the control rules as described above could not maximize the capabilities of AMD. Specifically, in the above optimal control, since the control force represented by the linear combination of state variables is assumed, it is necessary to design with a safety factor for various constraints, which may result in an inefficient control rule. In addition, the designer had to adjust the parameters by trial and error through multiple simulations so as to satisfy various constraints that differ for each property. Therefore, a large part depended on the designer's experience, and an optimal solution was not necessarily obtained, and the design required time and effort. Also, since it was necessary to obtain a theoretical solution, the degree of freedom of the evaluation function was low, and it was difficult to optimize for a specific disturbance. Moreover, it was difficult to apply a linear theory to a structure having a non-linear restoring force, such as a concrete structure.

[0041] Therefore, in this embodiment, by using artificial intelligence (hereinafter referred to as AI) for AMD control, the vibration control performance is improved. Note that machine learning by AI is classified into three types: supervised learning, unsupervised learning, and reinforcement learning. In this embodiment, reinforcement learning is used among them.

[0042] <<AMD Control (This Embodiment)>> FIG. 4 is a flowchart of constructing an AMD control system in this embodiment. In this embodiment, reinforcement learning by AI is used as described above. Reinforcement learning is a method of learning actions that maximize value through trial and error even without teacher data. Also, as algorithms for reinforcement learning, Q-Learning and DQN (Deep Q-Learning) are used.

[0043] <Parameter Setting> First, each parameter (state s t , reward R t , action a t ) is set (S101).

[0044] 〔Action a t 〕 Action a tis the control force output to the actuator 40 at time t. The number of discretizations and the maximum control force are set for the control force of the actuator 40. In this embodiment, the maximum control force is set to 100 (N) and divided into 5 as follows. a t ={-100,-50,0,50,100} (12)

[0045] [State s t 〕 Status t is the state quantity of bridge 10 and mass 20 at time t, and what is the input and action a t It is desirable to give a reward to an action that reduces the state quantity, but in the case of vibration caused by a spring, it is necessary to distinguish whether the reduction in the state quantity is due to natural reduction caused by vibration or reduction caused by control of the actuator 40. In particular, in the case of a competitive reward setting (described later) as in this embodiment, if the vibration frequencies of both are different, the influence of the vibration becomes significant due to the phase difference in the responses of both.

[0046] To clarify this, we consider the conserved quantity S(t) defined by the following equation (13) as a state quantity that is independent of the phase during response, while eliminating the influence of vibration as much as possible. JPEG0007806777000012.jpg58170

[0047] JPEG0007806777000013.jpg28170

[0048] JPEG0007806777000014.jpg47170

[0049] [Reward r t 〕 JPEG0007806777000015.jpg38170

[0050] JPEG0007806777000016.jpg6170 If the reward set in this embodiment is expanded, a battle type expressed by the following equation (16) can be achieved. JPEG0007806777000017.jpg47170

[0051] The opponent can be no mass, passive control (with or without damping), existing active control, or your own active control (self-matching), and can be calculated as S(t) after a prior response analysis, or it can be a function F(t) of time t that is set appropriately (including 0 and constants). · If the learning target is semi-active, the opponent can be semi-active or the opponent mentioned above. · The standard is ε=δ, but by making the value of ε smaller than δ, you can set up stronger opponents. If you target a strong opponent from the beginning, the learning will not converge. It is better to gradually make the opponent stronger.

[0052] Also, other instant rewards SR t The following are examples (the words in brackets ( ) are optional combinations): ·S(t) is a linear combination of the (average, sum, maximum) of the (absolute value, raw value, reciprocal, absolute value of the reciprocal) of the (displacement, velocity, acceleration) of [bridge 10, mass 20] for the most recent n time steps. The reward is the difference, double difference, derivative, double derivative, reciprocal of S(t) (in this case, there is no opponent). ·You can also include the term square 20 in S(t). You can give a negative reward at each step until convergence. - Negative rewards may be given if clearance is exceeded. - Clipping of rewards is permitted.

[0053] JPEG0007806777000018.jpg6170 - At regular intervals (including just at the end), rewards are given according to special indices that represent the magnitude of shaking over time. These indices include habitability evaluation rank, measured seismic intensity, and values ​​obtained by simulating the indoor environment and racks using Unity, etc., to evaluate the damage situation and cargo falling conditions. JPEG0007806777000019.jpg17170

[0054] <Learning execution> Next, learning is performed (S102). As described above, reinforcement learning is performed in this embodiment. Reinforcement learning is a framework for an agent placed in a certain environment to acquire optimal behavioral rules through interaction with the environment. Here, a simulation of a mass point model with learning waves as input is repeated multiple times, and learning is performed as follows: JPEG0007806777000020.jpg38170

[0055] [Q-Learning] Q-learning is a representative reinforcement learning method that uses an action value function (Q function) to obtain an optimal policy. The Q function defines the expected cumulative reward that will be obtained in the future when a certain action is continuously selected in a certain state, in a table format, for all combinations of states and actions. By repeatedly updating the Q function according to the following formula, an optimal policy that maximizes the cumulative reward is obtained. JPEG0007806777000021.jpg7170Here, α is the learning rate (0<α<1), a coefficient that adjusts the update speed of the Q function, and γ is the discount rate (0<γ<1), a coefficient that determines how much to discount and consider future Q values ​​(reward).

[0056] JPEG0007806777000022.jpg16170

[0057] [DQN] JPEG0007806777000023.jpg82170

[0058] <Confirmation of control law> JPEG0007806777000024.jpg60170

[0059] Then, the result is judged to be good or bad (S104). If the result is bad (NO in S104), the process returns to step S101 and the parameters are set again.

[0060] If the result is good (YES in S104), implementation is performed (S105). That is, the s obtained and calculated in real time from each sensor (acceleration sensor, displacement sensor, etc.) of the sensor group 60 is t Based on this, the control force u(t) calculated by equation (19) or equation (20) is applied to the actuator 40.

[0061] According to this embodiment (AI control), a higher vibration suppression effect was obtained compared to the comparative example (optimal control) in the verification of the simulation in step S103 and the implementation (experiment) in step S105. In particular, a higher vibration suppression effect was obtained when DQN was used as the reinforcement learning algorithm.

[0062] JPEG0007806777000025.jpg38170, etc. (this is referred to as condition 3). When this condition 3 is compared with the above-mentioned conditions 1 and 2, it has been confirmed that vibrations can be appropriately damped in the order of condition 2 (mechanical energy + damping term), condition 1 (mechanical energy), and condition 3. In this way, by determining the reward in reinforcement learning based on the mechanical energy of the bridge 10, an excellent control law can be obtained, thereby improving vibration damping performance.

[0063] As described above, in this embodiment, the control law for performing AMD control (the control law for controlling the excitation force of the actuator 40) is acquired through reinforcement learning using AI. This makes it possible to maximize the capabilities of AMD and improve vibration control performance.

[0064] Furthermore, with AI control, various constraints such as maximum control force and clearance can be defined in the form of states and rewards, and nonlinear control using neural networks is possible, making it possible to obtain control rules that maximize the control effect within various constraints.

[0065] Furthermore, if the state and reward setting methods and various hyperparameters are determined in advance, trial and error for each property can be reduced, resulting in stable control laws and reducing the time and effort required for design.

[0066] Furthermore, because the optimal control law is updated sequentially through repeated simulations (there is no need to obtain a theoretical solution), it is possible to design control laws with a high degree of freedom. For example, in a competitive reward system, it is possible to further improve the control effect by using an excellent control as an opponent, or to customize the control effect while taking into account the constraints of the device. It is also possible to optimize control for free vibrations by using an impulse as the disturbance, or to optimize control for disturbances that are thought to be likely to occur in structures, for example. This allows for the acquisition of control laws with better vibration suppression effects than the comparative example (optimal control) or control laws that are more specialized for specific environments.

[0067] === Second Embodiment === Fig. 5A is a diagram showing the configuration of a vibration control system for a structure according to the second embodiment, and Fig. 5B is a diagram showing a model of Fig. 5A.

[0068] 5A, the structure to be damped in the second embodiment is a building 100, and a mass 200 is arranged at the top of the building 100 so that it can roll horizontally (rolling top AMD). As in the first embodiment, various sensors (not shown) are provided to detect the state of the building 100 and the mass 200, and a controller (not shown) is provided to control the actuator 400 based on the output of the sensors (the same applies to the third and fourth embodiments).

[0069] When Figure 5A is modeled as a mass point model, it becomes a two-mass point model as shown in Figure 5B. In Figure 5B, building 100 and mass 200 are each shown as mass points. Of these, the mass point representing building 100 corresponds to the first mass point, and the mass point representing mass 200 corresponds to the second mass point.

[0070] In the mass point model of Figure 5B, building 100 is aligned with support end 102 (here, the ground) in the vertical direction (corresponding to a predetermined direction). Also, spring element 104 in Figure 5B corresponds to the rigidity of building 100. Spring element 104 connects support end 102 and building 100 (first mass point), and generates an elastic reaction force that acts in a direction (here, the horizontal direction) perpendicular to the direction in which building 100 and support end 102 are aligned (here, the vertical direction).

[0071] Mass 200 is a weight (mass body) for AMD control, and is placed on top of building 100. In addition, rolling bearings 500 (rollers, etc.) that support mass 200 so that it can roll in the horizontal direction are provided on top of building 100 (between building 100 and mass 200). This allows mass 200 to be displaced horizontally relative to building 100.

[0072] The actuator 400 (vibrator) is connected to the building 100 and vibrates the mass 200 in the horizontal direction. By adjusting (controlling) the vibration force (control force) of this actuator 400, the lateral shaking (horizontal vibration) of the building 100 can be suppressed.

[0073] In the second embodiment, as in the first embodiment, the actuator 400 is controlled by an AI control law, thereby improving vibration damping performance.

[0074] Although a rolling type (rolling bearing) AMD was used here, this is not limited to this, and vibration can be similarly controlled using a sliding type (sliding bearing) AMD.

[0075] ===Third Embodiment=== Fig. 6A is a diagram showing the configuration of a vibration control system for a structure according to a third embodiment. Fig. 6B is a diagram showing a model of Fig. 6A. Note that the same components as those in the second embodiment (Figs. 5A and 5B) are designated by the same reference numerals, and their description will be omitted.

[0076] In the third embodiment, a laminated rubber 301 is provided between the building 100 and the mass 200. The laminated rubber 301 supports the mass 200 so that it can be displaced in the horizontal direction. Furthermore, if the mass 200 is displaced in the horizontal direction, the laminated rubber 301 restores it to its original position. As a result, as shown in FIG. 6B, a spring element 300, which represents the horizontal rigidity of the laminated rubber 301, is provided in parallel with the actuator 400 between the building 100 and the mass 200. This FIG. 6B is the same mass point model as FIG. 1C of the first embodiment (however, the direction is different), and therefore, in this case too, vibration control performance can be improved by controlling the actuator 400 using an AI control law.

[0077] <Modification> Fig. 7 is a diagram showing a modified example of the third embodiment. In Fig. 7, mass 200 is suspended from the top of building 100 by pendulum 302. This allows mass 200 to be displaced horizontally relative to building 100. The horizontal rigidity of pendulum 302 corresponds to spring element 300.

[0078] 8 is a diagram showing another modified example of the third embodiment. In this modified example, a platform 303 is provided on the top of the building 100. The top surface of the platform 303 is configured in a gently sloping bowl shape. A mass 200 supported for rolling by rolling bearings 500, and an actuator 400 are provided on the platform 303. This results in a structure that generates a restoring force (rigidity: spring element 300) that returns the mass 200 to the center when it is displaced in the horizontal direction.

[0079] When these modified examples (FIGS. 7 and 8) are modeled, the model becomes the same as that shown in FIG. 6B. Therefore, by controlling actuator 400 using a control law based on AI, it is possible to improve vibration damping performance.

[0080] ===Fourth Embodiment=== Fig. 9A is a diagram showing the configuration of a vibration control system for a structure according to the fourth embodiment. Fig. 9B is a diagram showing a model of Fig. 9A. Note that the same components as those in the third embodiment (Figs. 6A and 6B) are designated by the same reference numerals, and their description will be omitted.

[0081] In the fourth embodiment, a mass 150 is provided between the building 100 and the mass 200. The mass 150 is provided on the top of the building 100 via laminated rubber 161, and functions as a TMD (Tuned Mass Damper) that suppresses vibrations of the building 100 in tune with the swaying of the building 100.

[0082] Additionally, mass 200, supported by rolling bearings 500, and actuator 400 are provided on top of mass 150. Mass 200 is supported by rolling bearings 500 so as to be able to roll (displace horizontally) in the horizontal direction relative to mass 150, and actuator 400 is connected to mass 150 and vibrates mass 200 in the horizontal direction (AMD).

[0083] When FIG. 9A is modeled as a mass point model, the result is a three-mass point model shown in FIG. 9B. In FIG. 5B, building 100, mass 150, and mass 200 are each shown as a mass point. Even in this case where horizontal rigidity (spring element 160) of laminated rubber 161 is provided between mass 150 and building 100, building 100 and mass 150 move in unison, and can therefore be regarded as a single mass point (corresponding to a first mass point). Furthermore, spring element 104 and spring element 160 can be regarded as a single spring element (corresponding to a first spring element). Therefore, in this fourth embodiment, as in the previous embodiments, vibration control performance can be improved by controlling actuator 400 using an AI control law.

[0084] <Modification> 10 is a diagram showing a modified example of the fourth embodiment. In this example, a mass 150 is suspended from the top of a building 100 by a pendulum 162 (spring element 160). A mass 200 supported for rolling by a rolling bearing 500 and an actuator 400 are provided above the mass 150. The mass 200 is displaceable relative to the mass 150 in the horizontal direction, and the actuator 400 vibrates the mass 200 in the horizontal direction.

[0085] 11 is a diagram showing another modified example of the fourth embodiment. In this example, a cone-shaped base 163 (spring element 160) with a gently sloping upper surface is placed on the top of the building 100, and a mass 150 supported for rolling by rolling bearings 600 is placed on top of the base 163. Furthermore, a mass 200 supported by rolling bearings 500 and an actuator 400 are placed on top of the mass 150. The mass 200 is displaceable relative to the mass 150 in the horizontal direction, and the actuator 400 vibrates the mass 200 in the horizontal direction.

[0086] When these modified examples (FIGS. 10 and 11) are modeled, the model becomes the same as that shown in FIG. 9B. Therefore, by controlling actuator 400 using a control law based on AI, it is possible to improve vibration damping performance.

[0087] ===Other embodiments=== Although the embodiments of the present invention have been described above, the above embodiments are intended to facilitate understanding of the present invention and are not intended to limit the present invention. Furthermore, the present invention may be modified or improved without departing from the spirit thereof, and it goes without saying that the present invention includes equivalents thereof. For example, the following modifications are possible.

[0088] In the above-described embodiment, Q-learning and DQN (Deep Q-Learning) were used as reinforcement learning algorithms, but this is not limited thereto, and other reinforcement learning algorithms (e.g., Sarsa, Monte Carlo method, etc.) may also be used.

[0089] In the above-described embodiment, a bridge 10 or a building 100 is described as the structure (first mass point) for ease of understanding, but it goes without saying that the structure may be composed of pillars, beams, walls, floors, etc. [Explanation of symbols]

[0090] 10 bridge, 12 support end, 14 spring element (first spring element), 20 squares, 30 spring (second spring element), 40 actuator, 60 sensors, 70 controllers, 100 building, 102 support end, 104 spring element (first spring element), 150 masses, 160 spring elements, 161 Laminated rubber, 162 Pendulum, 163 Unit, 200 squares, 300 spring element (second spring element), 301 laminated rubber, 302 pendulum, 303 unit, 400 actuators, 500 rolling bearing, 600 rolling bearing,

Claims

[Claim 1] A support end; a first mass point aligned with the support end in a predetermined direction; a first spring element connecting the support end and the first mass point, the first spring element generating an elastic reaction force acting along a direction perpendicular to the predetermined direction; a second mass point that is displaceable relative to the first mass point in the orthogonal direction; a vibrator connected to the first mass point and configured to vibrate the second mass point in the orthogonal direction; A vibration control system for a structure represented by a mass point model having determining a control law for controlling the excitation force of the vibration exciter using reinforcement learning; the second mass point is a mass of a mass damper that suppresses vibration of the first mass point, determining a reward in the reinforcement learning based on a conserved quantity of the first mass point; The reward in the reinforcement learning is a competitive type expressed by the following equation (16): A vibration control system for a structure.

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