CN115933392A - Intelligent semi-active control method for base isolation structure - Google Patents
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Abstract
The invention discloses an intelligent semi-active control method of a base isolation structure, which comprises a model-based reinforcement learning control algorithm for solving a controller by using system parameters and a model-free reinforcement learning control algorithm for solving the controller by using system input and output data. The control method is performed by mixing H 2 /H ∞ And controlling the performance index to design the controller. Firstly, establishing a mathematical model of a base isolation structure under uncertain excitation effects including earthquake, wind, randomness and the like; secondly, designing a mixture H by respectively adopting a model-based reinforcement learning method and a model-free reinforcement learning method of an off-strategy 2 /H ∞ A controller; and finally, comparing results of the two algorithms, and verifying that the two algorithms can guarantee the earthquake-resistant and shock-absorbing performance of the building structure. The invention provides a simple, efficient, low-cost and strong-robustness control algorithm for the shock insulation and shock absorption design of a building structure, improves the shock resistance and wind resistance of the structure, and ensures the safety of the structure.
Description
Technical Field
The invention belongs to the field of intelligent shock insulation control of building structures, and is suitable for intelligent control of a basic shock insulation structure; in particular to an intelligent semi-active control method of a basic shock isolation structure.
Background
With the rapid development of society and economy in China, high-rise buildings such as houses, hospitals and office buildings are greatly increased, and the guarantee of the safety of buildings and indoor personnel is an urgent need for city construction in the future in China. Because uncertain factors such as earthquake, wind and random noise generated by various natural world generally exist in real life, the scientific construction of civil engineering structures has great significance for improving the earthquake resistance and wind resistance and maintaining social stability. In recent years, a novel structural vibration control technology represented by an active/semi-active control technology introduces control methods such as robust control, optimal control, intelligent control, adaptive control and the like in a modern control theory into vibration control of an engineering building structure, so that a control device is regulated and controlled in real time by means of self structure or external interference response under the input of limited external energy, and the vibration response of the building structure is restrained to the maximum extent. The semi-active control technology has excellent control effect and wide application range, and is a structure control method with highest neutral cost ratio and the highest application prospect in civil engineering construction. A block diagram of the semi-active control technique is shown in fig. 2. The working principle is as follows: the method comprises the steps of monitoring the dynamic response of the building structure by using a sensor, transmitting measurement information to a controller, giving out the magnitude of force to be applied according to a set control algorithm, finally sending a signal of the controller to an actuator, and driving the actuator by an external energy source after receiving a control signal to apply acting force to the building structure.
Currently, most of the structural semi-active control methods are independent H 2 Control or H alone ∞ The former can ensure the optimal control performance of the building structure, but lacks robustness; the latter, however, makes the building structure more robust, at the expense of some control performance. Thus, the present invention investigated the combination of H 2 /H ∞ The control method, which is an important robust control method, can ensure that the optimal control performance can still be achieved under the influence of worst external disturbance.
In addition, it is considered that the system is influenced by random noise, and the method is also one of the important points of the invention. Because random noise inevitably exists in practical application, the system influenced by the random noise is more general, and the random noise and the mixture H are considered 2 /H ∞ The control can better ensure the robustness of the system. However, since it is difficult to obtain an accurate system dynamics model in practical applications, the design of the controller is inevitably affected.
Disclosure of Invention
In view of the above, the present invention is directed to an improved optimal semi-active control method for randomly mixing H 2 /H ∞ The control and reinforcement learning algorithm is introduced into the design of the semi-active controller, so that the optimal controller is optimized, the robustness of the controller is improved, and the defect that the building structure is difficult to accurately model is overcome. In addition, the model considered by the invention is generalized enough, so the method has strong universality and is suitable for various shock-isolating and shock-absorbing control systems.
The invention is realized by adopting the following scheme: an intelligent semi-active control method of a base isolation structure specifically comprises the following steps:
step S1: establishing a motion equation aiming at a basic shock insulation building structure system under the excitation of seismic waves, deducing a state space equation of the motion equation, and considering the influence of states and disturbance noise;
step S2: designing an appropriate optimization objective function, utilizing
Formula and Hamiltonian design mix H 2 /H ∞ A controller for solving the worst-case disturbance v by using the system parameters * (t) and optimal controller u * (t)；
And step S3: designing a reinforcement learning algorithm, and converting the requirements on the system parameters in the step S2 into a system using state and input data;
and step S4: data are collected through a seismic wave sensor, a position sensor and a speed sensor for learning, and disturbance v under the worst condition is obtained * (t) and optimal controller u * (t)；
Step S5: comparing the worst case disturbance v of step S2 and step S3 * (t) and an optimal controller u * And (t) if the error is in a small range, the anti-seismic performance of the building structure can be guaranteed based on the same effectiveness of the model algorithm and the reinforcement learning algorithm.
Further, step S2 specifically includes the following steps:
step S11: deducing a state space equation of the basic seismic isolation structure:
wherein
x(t)，/>
Respectively controlling the interlayer displacement and interlayer speed of the ith layer; u (t) is a control input; v (t) is seismic wave input; in addition, the inventive method is characterized in that
Wherein M is b ,C b ,K b Respectively mass, damping and rigidity matrixes; d b Is a damper position matrix; e b The seismic wave excitation influences the matrix.
Step S12: further considering that the base-isolated structure is affected by multiplicative and additive noise, then the dynamical model of S11 is modeled as a stochastic system as follows:
wherein
Is a random noise parameter matrix; w is a 1 、w 2 Is the complete probability space>
The independent standard brownian motion defined above.
Further, step S2 specifically includes the following steps:
step S21: according to disturbance attenuation conditions
Determining an optimization objective function:
wherein Q is not less than 0,R>0 is a symmetric matrix, γ d >0 is the level of attenuation of the disturbance,
step S22: determining a Hamiltonian:
step S23: utilizing the optimal first-order necessary condition to solve the partial derivative of the Hamiltonian to obtain the disturbance v under the worst condition * (t)＝L * x (t) and optimal controller u * (t)＝K * x(t)
Step S24: a random algebraic ricati equation is obtained by step S23:
step S25: alternative solution by Algorithm 1
L i And K i Get->
L * And K * That is to say that the worst-case disturbance v is obtained * (t) and optimal controller u * (t)。
Further, step S3 specifically includes the following steps:
step S31: the off-strategy reinforcement learning algorithm can realize the solving of the controller by only collecting the state and the input data once, greatly reduces the calculation complexity and improves the algorithm efficiency compared with the common reinforcement learning algorithm. In order to propose an off-strategy algorithm and not specify external disturbance in calculation, the state space model of the base isolation structure needs to be rewritten as:
step S32: computing
The formula yields:
step S33: from step S32, it can be found that:
wherein
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 z = [ x, u, v =],
svec is matrix straightening and repeated items are removed; diag is a block diagonal matrix.
Step S34: step S33 from 0 to t f The integration can result in:
wherein
Step S35: from step S34, it is possible to obtain:
where Ψ is a constant matrix.
Further, step S4 specifically includes the following steps:
step S41: by seismic sensors, position sensors, velocityThe sensors collect data, forming a matrix
And &>
Step S42: definition of
The data collected in step S41 is applied to algorithm 2.
Step S43: by alternately solving
L i And K i Get >>
L * And J * That is to say that the worst-case disturbance v is obtained * (t) and an optimal controller u * (t) and no knowledge of the system parameter matrix is required.
Further, step S5 specifically includes the following steps:
step S51: l calculated using norm comparison Algorithm 1 and Algorithm 2 N+1 And K N+1 。
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides an improved random mixing H 2 /H ∞ The design method of the semi-active controller solves the problem of insufficient robust performance of the LQR controller;
2. the invention provides an improved reinforcement learning control algorithm, which avoids the problem that a building structure is difficult to accurately model, improves the practicability of the algorithm, can directly use continuous states and input data for calculation, and does not need discretization;
3. the invention will improve the random mixing H 2 /H ∞ The semi-active controller is combined with an improved reinforcement learning control algorithm, so that the robustness of the vibration reduction control of the building structure is improved;
4. the improved semi-active control method provided by the invention can fully play the role of shock absorption of the base isolation structure. Random mixing H with earthquake response of full floor 2 /H ∞ The optimization target of the method can simultaneously and effectively reduce the displacement response, the interlayer displacement response and the acceleration response of each layer of the structure, and improve the safety of the structure and the comfort of people in the structure;
5. the design method of the semi-active controller is simple and feasible and is easy to widely popularize.
Drawings
Fig. 1 is a block diagram of the overall architecture of the present invention.
Fig. 2 is a block diagram of a semi-active control technology.
FIG. 3 shows the algorithm L of the present invention under Kobe seismic waves 2 i And K i Convergence and disturbance attenuation conditions.
FIG. 4 is the seismic isolation layer displacement and seismic isolation layer velocity under Kobe seismic waves of the present invention.
FIG. 5 is the seismic isolation layer control strength and maximum interlayer displacement under Kobe seismic waves of the present invention.
FIG. 6 shows L in algorithm 2 under EI _ Centro seismic waves according to the present invention i And K i Convergence and disturbance attenuation conditions.
FIG. 7 shows seismic isolation layer displacement and seismic isolation layer velocity under EI _ Centro seismic waves in accordance with the present invention.
FIG. 8 is the seismic isolation layer control strength and maximum interlayer displacement under EI _ Centro seismic waves of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure herein. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiment provides an intelligent semi-active control method of a base isolation structure, which specifically comprises the following steps:
step S1: establishing a motion equation aiming at a basic shock insulation building structure system under the excitation of seismic waves, deducing a state space equation of the motion equation, and considering the influence of states and disturbance noise;
step S2: designing an appropriate optimization objective function, utilizing
Formula and Hamiltonian design mix H 2 /H ∞ A controller that can solve for worst case disturbances and optimal controllers by using system parameters;
and step S3: designing a reinforcement learning algorithm, and converting the requirements on the system parameters in the step S2 into a system using state and input data;
and step S4: collecting data through a seismic wave sensor, a position sensor and a speed sensor, and learning to obtain a controller;
step S5: comparing the worst case disturbance v of step S2 and step S3 * (t) and optimal controller u * (t) if the error is smallWithin the range, the model algorithm and the reinforcement learning algorithm have the same effectiveness, and the anti-seismic performance of the building structure can be guaranteed.
In this embodiment, the step S1 specifically includes the following steps:
step S11: deducing a state space equation of the basic seismic isolation structure:
wherein
x(t)，/>
Respectively controlling the interlayer displacement and the interlayer speed of the ith layer; u (t) is a control input; v (t) is seismic wave input; in addition, the method can be used for producing a composite material
Wherein M is b ,C b ,K b Respectively are mass, damping and stiffness matrices; d b Is a damper position matrix; e b The seismic wave excitation influences the matrix.
For 8-storey building structures
x＝[x b ，x 1 ，x 2 ，...，x 8 ] T ，
M b ＝diag(m b ，m 1 ，m 2 ，...m 8 )，
E b ＝[1,1,1,1,1,1,1,1,1] T ,
D b ＝[1,0,0,0,0,0,0,0,0] T ,
Wherein x b Displacement of seismic isolation layers relative to the ground, x 1 ,...,x 8 Displacement of the ith layer relative to the ground; m is a unit of b ＝4.5×10 5 kg is the mass of the seismic isolation layer, m i ＝3.456×10 5 kg for i =1,2, 8 is the mass of each storey of the superstructure; stiffness of seismic isolation layer is k b ＝1.085×10 4 kN/m, stiffness per floor 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; damping coefficient of the seismic isolation layer is c b =26.17kNs/m, damping coefficient of each floor unit is c i =490,467,410,386,349,298,243 and 196kNs/m.
Step S12: considering the influence of the state and disturbance noise on the base isolation structure:
wherein
Is a random noise parameter matrix; w is a 1 、w 2 Is the complete probability space>
The independent standard brownian motion defined above.
Selecting q 1 ＝q 2 ＝1
Wherein
In this embodiment, the step S2 specifically includes the following steps:
step S21: according to disturbance attenuation conditions
Determining an optimization objective function:
wherein Q is not less than 0,R>0 is a symmetric matrix, γ d >0 is the level of attenuation of the disturbance,
selecting Q = I, R =0.000003 and disturbance attenuation level gamma d ＝10。
Step S22: determining a Hamiltonian:
step S23: utilizing the optimal first-order necessary condition to solve the partial derivative of the Hamiltonian to obtain the disturbance v under the worst condition * (t)＝L * x (t) and optimal controller u * (t)＝K * x(t)
Step S24: a random algebraic ricati equation is obtained by step S23:
step S25: by alternately solving
L i And K i Get->
L * And K * That is to say that the worst-case disturbance v is obtained * (t) and optimal controller u * (t)。
In this embodiment, the step S3 specifically includes the following steps:
step S31: in order to not specify external disturbance during calculation, the state space model of the base isolation structure is rewritten as follows:
step S32: computing
The formula yields:
step S33: from step S32, it can be found that:
wherein
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 z = [ x, u, v =],
svec is matrix straightening and repeated items are removed; diag is a block diagonal matrix.
Step S34: step S33 from 0 to t f The integration can result in:
wherein
Step S35: from step S34, it is possible to obtain:
where Ψ is a constant matrix.
In this embodiment, step S4 specifically includes the following steps:
step S41: data are collected by a seismic wave sensor, a position sensor and a speed sensor to form a matrix
And &>
Step S42: definition of
The data collected in step S41 is applied to algorithm 2.
Step S43: by alternatively solving
L i And K i Get->
L * And K * That is to say that the worst-case disturbance v is obtained * (t) and an optimal controller u * (t) and no knowledge of the system parameter matrix is required.
In this embodiment, step S5 specifically includes the following steps:
step S51: l calculated using norm comparison Algorithm 1 and Algorithm 2 N+1 And K N+1 。
FIG. 1 is a flow chart of the present invention. FIG. 3 (a) shows that the control gain of Kobe seismic algorithm 2 converges to the optimal control gain, and FIG. 3 (b) shows that the control gain obtained by Kobe seismic algorithm 2 can make the influence of disturbance on the system less than the disturbance attenuation level gamma d . FIG. 4 (a) shows the uncontrolled, LQR controlled and mixed H under Kobe seismic waves 2 /H ∞ Control ofRespectively resulting in displacement of seismic isolation layers, FIG. 4 (b) showing Kobe seismic wave uncontrolled, LQR controlled, and H mixed 2 /H ∞ The resulting velocity of the seismic isolation layers is controlled. FIG. 5 (a) shows LQR control and H mixing under Kobe seismic waves 2 /H ∞ The control force of control, FIG. 5 (b) is the uncontrolled, LQR controlled and mixed H under Kobe seismic waves 2 /H ∞ Controlled maximum interlayer displacement. It can be found that H is a mixture 2 /H ∞ The control effect is better than other control methods.
FIGS. 6-8 show various experimental simulations under EI _ Centro seismic waves, which together with various experimental simulations under Kobe seismic waves verify that H is mixed 2 /H ∞ The control effect is better than other control methods.
In summary, the invention combines stochastic theory, hybrid H 2 /H ∞ The design scheme of the intelligent semi-active control method of the basic shock isolation structure is provided by the advanced science of the semi-active controller, the improved reinforcement learning control algorithm and the like, and the robustness of the vibration reduction control of the building structure can be effectively improved.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the embodiments. Thus, the present embodiments are not intended to be limited to the embodiments shown herein but are to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (6)
1. An intelligent semi-active control method of a base isolation structure is characterized in that: the method comprises the following steps:
step S1: and establishing a dynamic equation aiming at the basic shock insulation structure excited by uncertain factors such as earthquake, wind, randomness and the like, and deducing a state space equation of the dynamic equation. The model fully considers the influence of multiplicative noise and additive noise in the complex environment on the structure;
step S2: selecting a proper optimization objective function, and designing a mixture H by using a random optimal control theory and a game theory 2 /H ∞ Controller for solving worst case disturbance v using system parameters * (t) and an optimal controller u * (t)；
And step S3: designing a reinforcement learning control algorithm of the off-strategy, and converting the requirements on the system parameters in the step S2 into a use system state and input data; the algorithm not only removes the requirement on accurate modeling of system parameters, but also reduces the influence of detection noise introduced in algorithm implementation on control performance.
And step S4: data are collected through a seismic wave sensor, a position sensor and a speed sensor and are learned, and disturbance v under the worst condition is obtained * (t) and optimal controller u * (t)；
Step S5: comparing the worst case disturbance v of step S2 and step S3 * (t) and an optimal controller u * (t), if the error is in a small range, the reinforcement learning control algorithm based on the model and the model-free algorithm have the same effectiveness, and the anti-seismic performance of the building structure can be guaranteed.
2. The intelligent semi-active control method of a base-isolated structure according to claim 1, wherein: the step S1 specifically comprises the following steps:
step S11: deducing a state space equation of the basic seismic isolation structure:
wherein
x(t)，/>
The interlayer displacement and the interlayer speed of the ith layer are respectively; u (t) is a control input; v (t) is seismic wave acceleration or the likeInputting external disturbance; in addition, the method can be used for producing a composite material
Wherein M is b ,C b ,K b Respectively are mass, damping and stiffness matrices; d b Is a damper position matrix; e b An excitation influence matrix of external uncertainties such as seismic waves.
Step S12: further considering that the base-isolated structure is affected by multiplicative and additive noise, then the dynamical model of S11 is modeled as a stochastic system as follows:
wherein A is j1 、C j2 Is a random noise parameter matrix; w is a 1 、w 2 To be defined in the complete probability space
And the standard brownian motion independent of each other.
3. The intelligent semi-active control method of a base-isolated structure according to claim 1, characterized in that: the step S2 specifically comprises the following steps:
step S21: according to disturbance attenuation conditions
Determining an optimization objective function:
wherein Q is not less than 0,R>0 is a symmetric matrix, γ d >0 is the level of attenuation of the disturbance,
step S22: determining a Hamiltonian:
step S23: utilizing the optimal first-order necessary condition to solve the partial derivative of the Hamiltonian to obtain the disturbance upsilon under the worst condition * (t)＝L * x (t) and optimal controller u * (t)＝K * x (t) in which
Step S24: a random algebraic ricati equation is obtained by step S23:
step S25: by alternately solving
L i And K i Get->
L * And K * That is, the worst-case disturbance v can be obtained * (t) and optimal controller u * (t)。
4. The intelligent semi-active control method of a base-isolated structure according to claim 1, characterized in that: the step S3 specifically comprises the following steps:
step S31: the off-strategy reinforcement learning algorithm can realize the solving of the controller by only collecting the state and the input data once, greatly reduces the calculation complexity and improves the algorithm efficiency compared with the common reinforcement learning algorithm. In order to propose an off-strategy algorithm and not specify external disturbance in calculation, the state space model of the base isolation structure needs to be rewritten as:
step S32: calculating out
The formula yields:
step S33: from step S32, it can be found that:
wherein
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 is matrix straightening and repeated items are removed; diag is a block diagonal matrix.
Step S34: step S33 from 0 to t f The integration can result in:
wherein
Step S35: from step S34, it is possible to obtain:
where Ψ is a constant matrix.
5. The intelligent semi-active control method of a base-isolated structure according to claim 1, wherein: the step S4 specifically comprises the following steps:
step S41: data are collected by a seismic wave sensor, a position sensor and a speed sensor to form a matrix
And
step S42: definition of
The data collected in step S41 is applied to a reinforcement learning algorithm.
Step S43: by alternately solving
L i And K i Get->
L * And K * That is to say that the worst-case disturbance v is obtained * (t) and an optimal controller u * (t) and no knowledge of the system parameter matrix is required.
6. The intelligent semi-active control method of a base-isolated structure according to claim 1, wherein: the step S5 specifically comprises the following steps:
step S51: l calculated using norm comparison Algorithm 1 and Algorithm 2 N+1 And K N+1 。
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