An intelligent semi-active control method for a base isolation structure

Abstract

The present invention discloses an intelligent semi-active control method for a base isolation structure, including a model-based reinforcement learning control algorithm for solving the controller using system parameters and a model-free reinforcement learning control algorithm for solving the controller using system input-output data. The control method designs the controller by a hybrid H2 / H ∞ control performance index. First, a mathematical model of the base isolation structure under uncertain excitations such as earthquakes, winds, and randomness is established; secondly, a hybrid H2 / H ∞ controller is designed by using a model-based reinforcement learning method and an off-policy model-free reinforcement learning method respectively; finally, the results of the two algorithms are compared to verify that both algorithms can ensure the seismic and shock absorption performance of the building structure. The present invention provides a simple, efficient, low-cost, and highly robust control algorithm for the seismic isolation and shock absorption design of building structures, improves the seismic and wind resistance capabilities of the structure, and ensures the structural safety.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent seismic isolation control of building structures and is applicable to the intelligent control of base-isolated structures; specifically, it relates to an intelligent semi-active control method for base-isolated structures. Background Art

[0002] With the rapid development of China's society and economy, the number of high-rise buildings such as residential buildings, hospitals, and office buildings has increased significantly. Ensuring the safety of buildings and indoor personnel is an urgent need for future urban construction in China. Due to the existence of uncertainties such as earthquakes, winds, and various types of random noise generated by nature in real life, scientifically constructing civil engineering structures is of great significance for improving their seismic and wind resistance capabilities and maintaining social stability. In recent years, new structural vibration control technologies represented by active / semi-active control technologies have introduced control methods such as robust control, optimal control, intelligent control, and adaptive control in modern control theory into the vibration control of engineering building structures, so as to realize the real-time regulation of control devices relying on the structure itself or external disturbance responses under the input of limited external energy, thereby suppressing the vibration response of building structures to the greatest extent. The semi-active control technology has excellent control effects and a wide range of adaptability, and is a structural control method with the highest cost performance and the most promising application prospects in civil engineering construction. The structural block diagram of the semi-active control technology is as Figure 2 shown. Its working principle is as follows: First, sensors are used to monitor the dynamic response of the building structure, then the measured information is transmitted to the controller end, and the magnitude of the force to be applied is given according to the set control algorithm. Finally, the signal of the controller is sent to the actuator, and after receiving the control signal, the actuator is driven by external energy to apply a force to the building structure.

[0003] Currently, most of the structural semi-active control methods are separate H2 control or separate H ∞ control. The former can ensure the optimal control performance of the building structure, but lacks robustness; while the latter can make the building structure more robust, but will sacrifice some control performance. Therefore, the present invention studies the hybrid H2 / H ∞ control method, which is an important robust control method and can ensure optimal control performance even under the influence of the worst-case external disturbance.

[0004] In addition, considering the influence of random noise on the system is also one of the key points of the present invention. Since random noise is inevitable in practical applications, the system affected by random noise is more general. At the same time, considering random noise and hybrid H2 / H ∞ control can better ensure the robustness of the system. However, due to the difficulty in obtaining an accurate system dynamics model in practical applications, the design of the controller will inevitably be affected. Summary of the Invention

[0005] In view of this, the object of the present invention is to propose an improved optimal semi-active control method, introducing stochastic hybrid H2 / H ∞ control and reinforcement learning algorithms into the design of semi-active controllers, optimizing the optimal controller, improving the robustness of the controller, and overcoming the defect that it is difficult to accurately model building structures. In addition, since the model considered in the present invention is sufficiently general, it has strong versatility and is applicable to various seismic isolation and vibration reduction control systems.

[0006] The present invention is implemented by the following scheme: An intelligent semi-active control method for a base-isolated structure, specifically including the following steps:

[0007] Step S1: Establish a motion equation for the base-isolated building structure system under seismic wave excitation, deduce its state space equation, and consider its influence by state and disturbance noises;

[0008] Step S2: Design an appropriate optimization objective function, and design a hybrid H2 / H controller using the ∞ formula and the Hamiltonian function, and the worst-case disturbance v * (t) and the optimal controller u * (t) can be solved by using system parameters;

[0009] Step S3: Design a reinforcement learning algorithm to transform the requirement for system parameters in Step S2 into using system states and input data;

[0010] Step S4: Collect data through seismic wave sensors, position sensors, and velocity sensors, conduct learning, and obtain the worst-case disturbance v * (t) and the optimal controller u * (t);

[0011] Step S5: Compare the worst-case disturbance v * (t) and the optimal controller u * (t) in Step S2 and Step S3. If the error is within a small range, it means that the model algorithm and the reinforcement learning algorithm are equally effective and can both ensure the seismic performance of the building structure.

[0012] Further, Step S2 specifically includes the following steps:

[0013] Step S11: Deduce the state space equation of the base-isolated structure:

[0014]

[0015] Where x(t), They are respectively the inter-story displacement and inter-story velocity of the $i$-th layer under control; $u(t)$ is the control input; $v(t)$ is the seismic wave input; in addition

[0016]

[0017] where $M$ b , $C$ b , $K$ b are respectively the mass, damping and stiffness matrices; $D$ b is the damper position matrix; $E$ b is the seismic wave excitation influence matrix.

[0018] Step S12: Further considering the influence of multiplicative and additive noises on the base-isolated structure, the dynamic model in S11 is modeled as the following stochastic system:

[0019]

[0020] where is the stochastic noise parameter matrix; $w_1$, $w_2$ are independent standard Brownian motions defined on the complete probability space .

[0021] Furthermore, step S2 specifically includes the following steps:

[0022] Step S21: Determine the optimization objective function according to the disturbance attenuation condition

[0023]

[0024] :

[0025]

[0026]

[0027] where $Q\geq0$, $R>0$ are symmetric matrices, $\gamma$ d >0 is the disturbance attenuation level,

[0028] Step S22: Determine the Hamiltonian function:

[0029]

[0030]

[0031] Step S23: Using the optimal first-order necessary condition, take the partial derivative of the Hamiltonian function to obtain the worst-case disturbance $v$ * (t)=L * $x(t)$ and the optimal controller $u$ * (t)=K *x(t)

[0032]

[0033]

[0034] Step S24: Obtain the random algebraic Riccati equation from Step S23:

[0035]

[0036]

[0037] Step S25: Alternately solve L i and K i by Algorithm 1 to obtain L * and K * , and then the worst-case perturbation v * * (t) and the optimal controller u * (t) can be obtained.

[0038]

[0039]

[0040] Furthermore, Step S3 specifically includes the following steps:

[0041] Step S31: The off-policy reinforcement learning algorithm only needs to collect the state and input data once to solve the controller, which greatly reduces the computational complexity compared with the general reinforcement learning algorithm and improves the algorithm efficiency. To propose the off-policy algorithm and not specify the external perturbation during the calculation, the state space model of the base-isolated structure needs to be rewritten as:

[0042]

[0043] Step S32: Calculate using the formula to obtain:

[0044]

[0045] Step S33: From Step S32, it can be obtained that:

[0046]

[0047]

[0048] where

[0049]

[0050]

[0051] H xu (P i ) = P i B = H ux (P i ) T ,

[0052] H xv (P i ) = P i C = H vx (P i ) T ,

[0053] H uv (P i ) = 0 = H vu (P i ) T ,

[0054] H uu (P i ) = 0,

[0055]

[0056]

[0057] and z = [x, u, v], svec is to straighten the matrix and remove duplicates; diag is a block diagonal matrix.

[0058] Step S34: Integrating from 0 to t in Step S33 f gives:

[0059]

[0060]

[0061] where

[0062]

[0063]

[0064]

[0065] Step S35: From Step S34, we get:

[0066]

[0067]

[0068] where Ψ is a constant matrix.

[0069] Furthermore, step S4 specifically includes the following steps:

[0070] Step S41: Collect data through seismic wave sensors, position sensors, and velocity sensors to form matrices and

[0071] Step S42: Define

[0072]

[0073] Apply the data collected in step S41 to Algorithm 2.

[0074]

[0075]

[0076] Step S43: By alternately solving L i and K i , obtain L * and J * , then the worst-case perturbation v * (t) and the optimal controller u * (t) can be obtained, and the system parameter matrix does not need to be known.

[0077] Furthermore, step S5 specifically includes the following steps:

[0078] Step S51: Use the norm comparison algorithm to compare L N+1 and K N+1 calculated by Algorithm 1 and Algorithm 2.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] 1. The present invention proposes an improved stochastic hybrid H2 / H ∞ semi-active controller design method, which solves the problem of insufficient robust performance of the LQR controller;

[0081] 2. The present invention proposes an improved reinforcement learning control algorithm, which avoids the problem of difficult to accurately model the building structure, improves the practicability of the algorithm, and the algorithm can directly use continuous state and input data for calculation without discretization;

[0082] 3. The present invention combines the improved stochastic hybrid H2 / H ∞ semi-active controller and the improved reinforcement learning control algorithm, which improves the robustness of the building structure vibration control;

[0083] 4. The improved semi-active control method proposed by the present invention can give full play to the seismic reduction effect of the base-isolated structure. Taking the seismic response of the entire floor as the optimization target of the stochastic hybrid H2 / H ∞ , it can effectively reduce the displacement response, inter-story displacement response and acceleration response of each floor of the structure at the same time, improving the safety of the structure and the comfort of the people therein;

[0084] 5. The design method of the semi-active controller described in the present invention is simple and feasible, and is easy to be widely promoted. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 is the overall structural block diagram of the present invention.

[0086] Figure 2 is the structural block diagram of the semi-active control technology.

[0087] Figure 3 is the convergence of L i and K i and the disturbance attenuation condition in Algorithm 2 of the present invention under the Kobe seismic wave.

[0088] Figure 4 is the displacement and velocity of the isolation layer of the present invention under the Kobe seismic wave.

[0089] Figure 5 is the control force of the isolation layer and the maximum inter-story displacement of the present invention under the Kobe seismic wave.

[0090] Figure 6 is the convergence of L i and K i and the disturbance attenuation condition in Algorithm 2 of the present invention under the EI_Centro seismic wave.

[0091] Figure 7 is the displacement and velocity of the isolation layer of the present invention under the EI_Centro seismic wave.

[0092] Figure 8 is the control force of the isolation layer and the maximum inter-story displacement of the present invention under the EI_Centro seismic wave. DETAILED DESCRIPTION OF THE INVENTION

[0093] The present invention will be further described below in conjunction with the drawings and embodiments.

[0094] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0095] It should be noted that the terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they specify the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0096] This embodiment provides an intelligent semi-active control method for a base isolation structure, which specifically includes the following steps:

[0097] Step S1: Establish a motion equation for the base isolation building structure system under seismic wave excitation, derive its state space equation, and consider its influence by state and disturbance noises;

[0098] Step S2: Design an appropriate optimization objective function, and use formulas and Hamiltonian functions to design a mixed H2 / H ∞ controller, and the worst-case disturbance and optimal controller can be solved by using system parameters;

[0099] Step S3: Design a reinforcement learning algorithm to transform the requirement for system parameters in Step S2 into using system states and input data;

[0100] Step S4: Collect data through seismic wave sensors, position sensors, and velocity sensors, conduct learning, and obtain a controller;

[0101] Step S5: Compare the worst-case disturbance v * (t) and the optimal controller u * (t) in Step S2 and Step S3. If their errors are within a small range, it means that the model algorithm and the reinforcement learning algorithm are equally effective and can both ensure the seismic performance of the building structure.

[0102] In this embodiment, Step S1 specifically includes the following steps:

[0103] Step S11: Derive the state space equation of the base isolation structure:

[0104]

[0105] where x(t), are respectively the inter-story displacement and inter-story velocity of the i-th floor under control; u(t) is the control input; v(t) is the seismic wave input; in addition

[0106]

[0107] where M b , C b , K b are the mass, damping, and stiffness matrices respectively; D b is the damper position matrix; E b is the seismic wave excitation influence matrix.

[0108] For an 8-story building structure

[0109] x = [x b , x1, x2,..., x8] T ,

[0110] M b = diag(m b , m1, m2,...m8),

[0111]

[0112]

[0113] E b = [1,1,1,1,1,1,1,1,1] T ,

[0114] D b = [1,0,0,0,0,0,0,0,0] T ,

[0115] where x b is the displacement of the isolation layer relative to the ground, and x1,..., x8 are the displacements of the i-th floor relative to the ground; m b = 4.5×10 5 kg is the mass of the isolation layer, m i = 3.456×10 5 kg for i = 1,2,...,8 are the masses of each floor of the superstructure; the stiffness of the isolation layer is k b = 1.085×10 4 kN / m, and the stiffness of each floor is k i = 3.4×10 5 , 3.2×10 5 , 2.85×10 5 , 2.69×10 5 , 2.43×10 5 , 2.07×10 5 , 1.69×10 5 , 1.37×10 5 kN / m, i = 1,2,...,8; the damping coefficient of the isolation layer is c b = 26.17 kNs / m, and the damping coefficient of each floor unit is ci = 490,467,410,386,349,298,243 and 196 kNs / m.

[0116] Step S12: Consider the influence of the state and disturbance noise on the base isolation structure:

[0117]

[0118] where is the random noise parameter matrix; w1, w2 are independent standard Brownian motions defined on the complete probability space defined on the complete probability space.

[0119] Select q1 = q2 = 1

[0120]

[0121] where

[0122]

[0123] In this embodiment, step S2 specifically includes the following steps:

[0124] Step S21: Determine the optimization objective function according to the disturbance attenuation condition

[0125]

[0126] Determine the optimization objective function:

[0127]

[0128]

[0129] where Q≥0, R>0 are symmetric matrices, γ d >0 is the disturbance attenuation level,

[0130] Select Q = I, R = 0.000003 and the disturbance attenuation level γ d = 10.

[0131] Step S22: Determine the Hamiltonian function:

[0132]

[0133]

[0134] Step S23: Use the optimal first-order necessary condition to take the partial derivative of the Hamiltonian function to obtain the worst-case disturbance v * (t) = L * x(t) and the optimal controller u* K(t) = K * x(t)

[0135]

[0136]

[0137] Step S24: Obtain the stochastic algebraic Riccati equation from Step S23:

[0138]

[0139]

[0140] Step S25: By alternately solving L i and K i , obtain L * and K * , then the worst-case disturbance v * (t) and the optimal controller u * (t) can be obtained.

[0141]

[0142]

[0143] In this embodiment, Step S3 specifically includes the following steps:

[0144] Step S31: To avoid specifying external disturbances during calculation, rewrite the state-space model of the base-isolated structure as:

[0145]

[0146] Step S32: Calculate According to the formula to obtain:

[0147]

[0148] Step S33: From Step S32, it can be obtained that:

[0149]

[0150]

[0151] where

[0152]

[0153]

[0154] H xu(P i ) = P i B = H ux (P i ) T ,

[0155] H xv (P i ) = P i C = H vx (P i ) T ,

[0156] H uv (P i ) = 0 = H vu (P i ) T ,

[0157] H uu (P i ) = 0,

[0158]

[0159]

[0160] and z = [x, u, v], svec is to straighten the matrix and remove duplicates; diag is a block diagonal matrix.

[0161] Step S34: Integrating from 0 to t in Step S33 f gives:

[0162]

[0163]

[0164] where

[0165]

[0166]

[0167]

[0168] Step S35: From Step S34, we get:

[0169]

[0170]

[0171] where Ψ is a constant matrix.

[0172] In this embodiment, step S4 specifically includes the following steps:

[0173] Step S41: Collect data through seismic wave sensors, position sensors, and velocity sensors to form a matrix and

[0174] Step S42: Define

[0175]

[0176] Apply the data collected in step S41 to Algorithm 2.

[0177]

[0178] Step S43: By alternately solving L i and K i , obtain L * and K * , and then the worst-case perturbation v * (t) and the optimal controller u * (t) can be obtained, and there is no need to know the system parameter matrix.

[0179] In this embodiment, step S5 specifically includes the following steps:

[0180] Step S51: Use the norm comparison algorithm to compare L N+1 calculated by Algorithm 1 and Algorithm 2 with K N+1 .

[0181] Figure 1 This is the flowchart of the present invention. Figure 3 (a) shows that the control gain of Algorithm 2 converges to the optimal control gain under the Kobe seismic wave, Figure 3 (b) shows that the control gain obtained by Algorithm 2 under the Kobe seismic wave can make the influence of the perturbation on the system less than the perturbation attenuation level γ d . Figure 4 (a) shows the displacements of the isolation layer caused by no control, LQR control, and hybrid H2 / H ∞ control respectively under the Kobe seismic wave, Figure 4 (b) shows the velocities of the isolation layer caused by no control, LQR control, and hybrid H2 / H ∞ control respectively under the Kobe seismic wave. Figure 5 (a) shows the control forces of LQR control and hybrid H2 / H ∞ control under the Kobe seismic wave, Figure 5 (b) shows no control, LQR control, and hybrid H2 / H ∞The maximum inter-story drift under control. It can be found that the hybrid H2 / H ∞ control effect is better than other control methods.

[0182] Figure 6 –8 are various experimental simulations under the EI_Centro seismic wave, which, together with various experimental simulations under the Kobe seismic wave, verify that the hybrid H2 / H ∞ control effect is better than other control methods.

[0183] In summary, the present invention combines frontier sciences such as stochastic theory, hybrid H2 / H ∞ semi-active controller and improved reinforcement learning control algorithm, and gives a design scheme for an intelligent semi-active control method for base-isolated structures. The invention can effectively improve the robustness of the vibration reduction control of building structures.

[0184] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the embodiments of the present invention. Therefore, the embodiments of the present invention will not be limited to these embodiments shown in the present invention, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An intelligent semi-active control method for a base isolation structure, characterized by the following steps: Step S1: Establish a dynamic equation for the base isolation structure under the excitation of uncertain factors such as earthquakes, winds, and randomness, and derive its state space equation, fully considering the influence of multiplicative noise and additive noise in the complex environment on the structure; Step S2: Select the optimization objective function, design a hybrid H2 / H controller using stochastic optimal control theory and game theory, and solve for the worst-case disturbance v(t) and the optimal controller u(t) using the system parameters; ∞ * (t) and the optimal controller u * (t);​ Step S3: Design an off-policy reinforcement learning control algorithm, and transform the requirements for system parameters in Step S2 into the use of system states and input data; this algorithm not only removes the requirement for accurate modeling of system parameters, but also reduces the influence of exploration noise introduced in the algorithm implementation on the control performance; Step S4: Collect data through seismic wave sensors, position sensors, and velocity sensors, perform learning, and obtain the disturbance v * (t) and the optimal controller u * (t); Step S5: Compare the worst-case perturbations v * (t) and the optimal controller u * (t). If their error is within a small range, both the model-based and model-free reinforcement learning control algorithms are equally effective and can ensure the seismic performance of the building structure; Step S1 is specifically as follows: Step S11: Derive the state space equation of the base isolation structure: wherein x(t), are respectively the inter-story displacement and inter-story velocity of the i-th floor; u(t) is the control input; v(t) is the external disturbance input such as seismic wave acceleration; in addition Among which M b , C b , K b are the mass, damping and stiffness matrices respectively; D b is the damper position matrix; E b is the excitation influence matrix of external uncertainties such as seismic waves; Step S12: Further consider the influence of multiplicative and additive noise on the base isolation structure, so the dynamic model in S11 is modeled as the following stochastic system: wherein is a random noise parameter matrix; w1 and w2 are independent standard Brownian motions defined on a complete probability space ; Step S2 is specifically as follows: Step S21: According to the disturbance attenuation condition Determine the optimization objective function: where \(Q\geq0\), \(R > 0\) are symmetric matrices, and \(\gamma\) d > 0 is the disturbance attenuation level. -u(τ) T Ru(τ), c2(X(τ), u(τ)) = X(τ) T QX(τ) + u(τ) T Ru(τ) Step S22: Determine the Hamiltonian function: Step S23: Using the optimal first-order necessary condition, take the partial derivative of the Hamiltonian function to obtain the worst-case perturbation v * (t) = L * x(t) and the optimal controller u * (t) = K * x(t), where Step S24: Obtain the stochastic algebraic Riccati equation from Step S23: Step S25: By alternately solving L i and K i , we obtain L * and K * , and then we can find the disturbance v * (t) and the optimal controller u * (t); Step S3 is specifically as follows: Step S31: In order not to specify external disturbances during calculation, rewrite the state space model of the base isolation structure as: Step S32: Calculate to obtain, according to the formula: Step S33: From Step S32, it can be obtained that: Where H xu (P i ) = P i B = H ux (P i ) T , H xv (P i ) = P i C = H vx (P i ) T , H uv (P i ) = 0 = H vu (P i ) T , H uu (P i ) = 0, And svec straightens the matrix and removes duplicate terms; diag is a block diagonal matrix; Step S34: Integrating step S33 from 0 to t f The integration yields: Where Step S35: From Step S34, it can be obtained that: Where Ψ is a constant matrix.

2. The intelligent semi-active control method for a base isolation structure according to claim 1, characterized by the following steps S4 is specifically as follows: Step S41: Collect data through a seismic wave sensor, a position sensor, and a velocity sensor to form a matrix and Step S42: Define Apply the data collected in Step S41 to the reinforcement learning algorithm; Step S43: By alternately solving L i and K i , we obtain L * and K * , and thus the worst-case perturbation and the optimal controller u * (t) can be obtained without the need to know the system parameter matrix.

3. The intelligent semi-active control method for a base isolation structure according to claim 1, characterized in that: Step S5 is specifically as follows: Step S51: Use the norm comparison algorithm to calculate L obtained from Algorithm 1 and Algorithm 2 N+1 and K N+1 .

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