CN114117844B - Active damper control method and system of nonlinear structure - Google Patents
Active damper control method and system of nonlinear structure Download PDFInfo
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Abstract
The invention discloses a control method of an active damper with a nonlinear structure, which comprises the following steps: establishing a finite element model of a nonlinear structure; (2) building and training a seismic oscillation prediction model; (3) Establishing a mathematical model combining a nonlinear structure and the active damper, and establishing a damper behavior evaluation value function R (t, a) t+1 ) (ii) a (4) Obtaining R (t, a) according to the seismic motion at the future k moments obtained by the seismic motion prediction model t+1 ) Damper action a corresponding to maximum value at k moments in the future t+1 (ii) a (5) Collecting parameters of a nonlinear structure and seismic oscillation at the moment t; (6) Obtaining a real-time error rate function, based on a t+1 The product of the error rate function at this time t is multiplied by the damper adjustment, and step (4) is executed. The invention also discloses an active damper control system with the nonlinear structure. The invention considers the nonlinear behavior of the structure and improves the control accuracy and timeliness; by establishing a seismic oscillation prediction model, a large error caused by a slow effect of damper behavior on structural response is reduced.
Description
Technical Field
The present invention relates to a method and a system for controlling a damper, and more particularly, to a method and a system for controlling an active damper with a nonlinear structure.
Background
With the continuous development of the field of shock absorption control, the dampers for shock absorption are mainly classified into permanent dampers (the performance of which remains unchanged under an earthquake) and adjustable dampers (the performance of which can be adjusted according to the size of the earthquake, such as adjustable magnetorheological dampers and the like which have been proposed by scholars at present). The method of the adjustable damper is also divided into a passive method, a semi-active method and an active method, wherein the active method refers to that the self performance of the damper can be actively adjusted under the earthquake by designing a proper damper behavior determining system, so that the response of the structure under the earthquake is minimum. Due to the reasons of large uncertain factors, large difficulty in dynamics analysis and the like, the active damping method of the damper has started to be researched in recent years, and many problems need to be solved.
In active damper damping control, the conventional method is to consider the structure and the control state of the damper as linear. The control state of the damper is a linear state with a small error, but since the building structure itself is nonlinear, the error is large if the calculation and analysis are performed as assumed here. Assuming that the structure is linear means that when the response of the model structure is calculated, the response calculation of the structure is calculated by a linear formula, and is calculated by a non-linear formula. When the structure is subjected to a large earthquake, the structure enters a nonlinear state, so that the response of the structure can be underestimated if the stress and displacement calculation still adopts a linear calculation formula, and great misleading is brought to the design of the behavior of the damper.
There is currently no method for optimal (better) behavior determination of the damper behavior. If the conventional optimization scheme is directly applied to the damper behavior determination method, the following problems may occur: (1) there is no comprehensive evaluation index for damper behavior. The behavior determination of the damper should be established in the response of the structure. (2) There is no long-term evaluation mechanism for damper behavior. In the damper shock absorption control, the response of the structure at each moment can affect the response of the structure at the next moment to a certain extent, and the behavior of the damper can only affect the temporary response of the structure, but can affect the subsequent whole-course response of the structure all the time. (3) Too many behaviors and too large calculated values. If the behavior of the damper and the evaluation result of each behavior need to be calculated, the calculation amount is too large. (4) Since the response of the earthquake motion is transient, the change speed is fast, and the parameter adjustment of the damper is a relatively slow process, the value of the earthquake motion cannot be directly used as the value for seeking the optimal parameter of the damper at the moment.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a control method and a control system for an active damper with a nonlinear structure, and solves the problems that the existing damping control systems are all offline learning systems, and the damping control systems are all linear kinetic equations and do not consider the nonlinear response of the structure.
The technical scheme is as follows: the invention relates to a control method of an active damper with a nonlinear structure, which comprises the following steps:
(1) Establishing a finite element model of a nonlinear structure;
(2) Building and training a seismic oscillation prediction model;
(3) Establishing a mathematical model combining a nonlinear structure and the active damper, and establishing a damper behavior evaluation value function R (t, a) t+1 )；
(4) Obtaining earthquake motion at k time points in the future by the earthquake motion prediction model, and obtaining R (t, a) according to the earthquake motion at k time points in the future t+1 ) Damper action a corresponding to maximum value at k moments in the future t+1 ；
(5) Collecting parameters of a nonlinear structure and seismic oscillation at the moment t;
(6) Obtaining a real-time error rate function, based on a t+1 And (4) adjusting the damper by multiplying the error rate function at the current time t, and executing the step (4) at the next time t + 1.
Finite element model of the nonlinear structure
Wherein M is the mass of the nonlinear structure; c is Rayleigh damping of a nonlinear structure; k (t) is the tangential stiffness of the nonlinear structure at the moment t;
x (t) is the acceleration, speed and displacement of the nonlinear structure respectively;
is the ground motion acceleration.
The earthquake motion prediction model is a neural network model, and neurons of an input layer of the neural network model are earthquake motion E (t) at the time t, displacement x (t) of the structure and speed
Acceleration of a vehicle
Nerves of the output layerThe elements are seismic vibrations E (t + 1) -E (t + k) from t +1 to t + k respectively; training the neural network using historical seismic data.
The mathematical model of the combination of the nonlinear structure and the active damper is
Wherein, C z (t) providing additional damping to the nonlinear structure for the damper; k z (t) additional stiffness provided to the nonlinear structure by the damper, both magnitudes of which are given by the damper behavior merit function R (t, a) t+1 ) Optimal damper behavior a corresponding to optimal value t+1 And (4) determining.
The damper behavior evaluation value function is
R(t,a t+1 )＝r(t+1)+βr(t+2)+β 2 r(t+3)+···+β k-1 r(t+k)
Wherein the content of the first and second substances,
x max the maximum values of acceleration response, velocity response and displacement response of the nonlinear structure under the earthquake of all times are respectively; beta is a discount parameter; k represents the seismic oscillations at k future times that need to be considered when evaluating damper behavior.
Solving future k moments R (t, a) by dichotomy in step (4) t+1 ) Damper behavior a corresponding to the maximum value t+1 。
Arranging a sensor on the nonlinear structure in the step (5) to obtain the displacement x (t) and the speed of the nonlinear structure at the moment t
Acceleration of a vehicle
And seismic E (t).
Said real-time error rate function
And E' (t) is the actual earthquake motion at the time t, and E (t) is the earthquake motion predicted value of the earthquake motion prediction model at the time t-1 to the time t through the neural network.
The invention relates to an active damper control system with a nonlinear structure, which comprises a mathematical model module, a seismic motion prediction model module, a signal acquisition module, a real-time error rate function module and a damper control module;
the mathematical model module establishes a mathematical model combining a nonlinear structure and an active damper, wherein the nonlinear structure model is a finite element model; the vibration prediction model module is a neural network model and is used for predicting the seismic vibrations at k moments in the future; the signal acquisition module acquires parameters of a nonlinear structure and seismic oscillation at the moment t; the real-time error rate function module obtains a real-time error rate function; the damper control module obtains R (t, a) according to seismic oscillation at k moments in the future t+1 ) Damper action a corresponding to maximum value at k moments in the future t+1 According to a t+1 The product of this function of the error rate at the instant t adjusts the damper.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages:
(1) The combination of off-line pre-learning and on-line real-time interactive optimization fills the blank that the existing damping control systems are off-line learning systems and have no virtual-real combination.
(2) By modeling the structural fiber material, introducing the instantaneous tangential stiffness and instantaneous response of the structure, and considering the nonlinear behavior of the structure, the control effect is improved;
(3) The earthquake motion and the structural response measured actually are transmitted to the model in the virtual state in real time, so that real-time interaction and data updating are realized, the actual measurement result optimizes the prediction system and damper behavior selection in real time, and the accuracy and timeliness of the traditional method are improved;
(4) By establishing a seismic oscillation prediction model, the slow effect of damper behavior on structural response is reduced, larger errors caused by the factors in practice are reduced, and the control precision is improved;
(5) Further optimizing the behavior of the damper to the actual effect by establishing an error harmonic model;
(6) By binary optimization of the behavior evaluation value of the damper, the calculation workload is reduced, and the calculation efficiency of the method is improved.
Drawings
FIG. 1 is a flow chart of the method for controlling an active damper with a nonlinear structure according to the present invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
Consider the concrete frame structure that one deck was striden in this embodiment, its attenuator is adjustable viscous damper, and the one end of attenuator is located the side of one side and strides the post bottom, and the other end is located the top roof beam midpoint. The adjustable viscous damper realizes the adjustment of the damping and the rigidity of the whole structure by adjusting the damping of the adjustable viscous damper and the axial rigidity of the adjustable viscous damper.
The seismic step length t in this embodiment is 0.05s. t +1 represents the next longer time of the present time, i.e., the time of the present time is increased by 0.05s.
As can be seen from fig. 1, the method for controlling an active damper with a nonlinear structure according to the present invention includes the following steps:
establishing a finite element model of the layer-one-span nonlinear structure;
wherein M is the mass of the structure, K (t) is the rigidity of the structure, C (t) is the damping of the structure, and through finite element modeling and Rayleigh damping calculation formulas, the mass M =2000kg and the rigidity K (t = 0) =8.2 × 10 of the one-layer one-span structure can be calculated 6 N/m, rayleigh damping C (t = 0) =310 × 10 3 N · s/m; k (t) is the stiffness of the structure, and the value is the tangential stiffness of the structure at each moment t;
x (t) is the acceleration, velocity and displacement of the structure respectively;
is the ground motion acceleration. Of the initial time structure
The values of x (t) are all 0. When the structure enters a nonlinear state, the tangential stiffness K (t) and the real-time structural damping C (t) at each moment can be calculated in real time through a computer according to a mathematical model of time-course analysis under an earthquake. The basic natural vibration frequency and the basic natural vibration period of the structure are 63.76Hz and 0.09s respectively.
And (2) establishing and training a seismic oscillation prediction model.
The earthquake motion prediction model is a neural network model; the neural network is composed of three parts, namely an input layer consisting of 4 neurons, a hidden layer consisting of two 20 neurons and an output layer consisting of 4 neurons. The input layer neurons are seismic oscillation magnitude E (t), structural displacement x (t) and speed at t moment
Acceleration of a vehicle
And the neurons of the output layer respectively perform earthquake motion E (t + 1) -E (t + K) from t +1 to t + K. And training the neural network by using historical earthquake motion data in China and abroad until the parameters of the hidden layer of the neural network are trained to a better stable value. After the neural network is trained, the local vibration prediction model is built and used for later tests.
Step (3) establishing the combination of the layer-span nonlinear structure and the active damper according to the time-course dynamic model of the structure under the earthquakeA mathematical model is established, and a damper behavior evaluation value function R (t, a) is established t+1 ) The value of which refers to the behavior a of the damper evaluated at time t t+1 A larger value indicates a better behavior of the damper. The behavior a of the adjustable viscous damper is between 0 and 2000, when the value a is 0, the damper only has two ends connected with the structure and does not provide any damping and rigidity, and along with the increase of the value a, the larger the damper provides the damping and rigidity of the structure, the larger the rigidity and damping of the whole structure are. In this particular embodiment, the value of a is incremented from 0 to 2000 every 100, i.e. every time the next damper action a is calculated t+1 There are 20 cases.
The mathematical model of the combination of the nonlinear structure and the active damper is
Wherein, C z (t) additional damping to the structure for the damper, K z (t) additional stiffness to the structure is provided by the damper, both of which are measured by the damper behavior merit function R (t, a) t+1 ) Is determined by the optimal value of (a) of (b) t+1 And (4) determining.
The damper behavior evaluation value function of the present embodiment is established as follows:
R(t,a t+1 )＝r(t+1)+βr(t+2)+β 2 r(t+3)+β 3 r(t+4)
the evaluation function in this embodiment takes into account four steps, i.e. seismic oscillations of 4 moments in the future (i.e. 0.2 s) that need to be taken into account when evaluating the damper behaviour. Wherein
Wherein
x max Refers to the maximum value of the seismic historical response of the structure; beta is a discount parameter, which is 1.0 in the embodiment, and the embodiment does not consider the discount in the time of four step lengths in the futureNamely, the behavior evaluation values of the damper in the future 4 step times are considered as important as possible.
Step (4) seismic motion at k moments in the future is obtained through the seismic motion prediction model, and R (t, a) is obtained according to the seismic motion at k moments in the future t+1 ) Damper action a corresponding to maximum value at k moments in the future t+1 ；
Solving future k times R (t, a) by dichotomy t+1 ) Damper behavior a corresponding to the maximum value t+1 . Optimal damper behavior a for solving for 1 step in the future t+1 Wherein a is t+1 ∈[0,2000]Then solve a first t+1 An evaluation value of the damper at =0, and R (t, a) is calculated t+1 ＝0)＝r(t+1)+βr(t+2)+β 2 r(t+3)+β 3 r (t + 4) =0; solve a again t+1 Evaluation value R (t, a) of damper at time =1000 t+1 = 1000) =2.35 and a t+1 Evaluation value R (t, a) of damper at =2000 t+1 = 2000) =1.26. Because R (t, a) t+1 ＝1000)＞R(t,a t+1 ＝2000)＞R(t,a t+1 = 0), so a t+1 =2000 and a t+1 It must not be the maximum value when = 0. Then, continuously dividing the solution into equal parts of 0-1000 and 1000-2000, and solving the solution a t+1 Evaluation value R (t, a) of damper at time of =600 t+1 = 600) =3.56 and a t+1 Evaluation value R (t, a) of damper when =1400 t+1 = 1400) =1.82, so the maximum value can be considered to be within 0-1000. Continuously equally dividing 0-600 and 600-1000 to obtain 8230A by continuously solving the above solutions according to the above thought t+1 Value R (t, a) of =800 t+1 = 800) the value is maximum, i.e. the optimal behavior value of the damper considering seismic oscillation at 4 moments in the future can be identified as 800.
Step (5) obtaining physical quantity of the nonlinear structure; in the embodiment, the sensors are arranged on the layer-by-layer one-span structure, and the actual displacement x' (t) and the actual speed of the structure at the moment t are obtained
Actual acceleration
And fruitThe interstar seismic motion E' (t).
Step (6) calculating an error rate function at the moment according to the actual earthquake motion E' (t) at the moment and the earthquake motion E (t) predicted by the prediction system
And (5) multiplying the error rate function value calculated at the moment by the optimal damper behavior value solved in the step (4) to obtain the optimal behavior value which should be actually applied by the damper. For the present embodiment, the optimal behavior value actually applied by its damper is 800 × 1.16=928. At this moment, the damper should apply 928 action to the actual structure in the next long time, so that the damping effect is optimal.
The invention relates to an active damper control system with a nonlinear structure, which comprises a mathematical model module, a seismic motion prediction model module, a signal acquisition module, a real-time error rate function module and a damper control module; the mathematical model module establishes a mathematical model combining a nonlinear structure and an active damper, wherein the nonlinear structure model is a finite element model; the vibration prediction model module is a neural network model and is used for predicting the seismic vibrations at k moments in the future; the signal acquisition module acquires parameters of a nonlinear structure and seismic oscillation at the moment t; the real-time error rate function module obtains a real-time error rate function; the damper control module obtains R (t, a) according to seismic oscillation at k moments in the future t+1 ) Damper action a corresponding to maximum value at k moments in the future t+1 According to a t+1 The product of the error rate function at this time t adjusts the damper.
Claims (6)
1. A control method of an active damper with a nonlinear structure is characterized in that: the method comprises the following steps:
(1) Establishing a finite element model of a nonlinear structure;
(2) Building and training a seismic oscillation prediction model;
(3) Establishing a mathematical model combining a nonlinear structure and an active damper and establishingDamper behavior evaluation value function R (t, a) t+1 )；
(4) Obtaining earthquake motion at k times in the future by the earthquake motion prediction model, and obtaining R (t, a) according to the earthquake motion at k times in the future t+1 ) Damper action a corresponding to maximum value at k moments in the future t+1 ；
(5) Collecting parameters of a nonlinear structure and seismic oscillation at the moment t;
(6) Obtaining a real-time error rate function, based on a t+1 Adjusting the damper by multiplying the error rate function at the current moment t, and executing the step (4) at the next moment t + 1;
the finite element model of the nonlinear structure is as follows:
wherein M is the mass of the nonlinear structure; c is Rayleigh damping of a nonlinear structure; k (t) is the tangential stiffness of the nonlinear structure at the moment t;
x (t) is the acceleration, velocity and displacement of the nonlinear structure respectively;
is the ground motion acceleration;
the mathematical model of the combination of the nonlinear structure and the active damper is
Wherein, C z (t) providing additional damping to the nonlinear structure for the damper; k is z (t) additional stiffness provided to the nonlinear structure by the damper, both magnitudes of which are given by the damper behavior merit function R (t, a) t+1 ) Optimal damper behavior a corresponding to optimal value t+1 Determining;
dampingThe function of the evaluation value of the behavior of the device is R (t, a) t+1 )＝r(t+1)+βr(t+2)+β 2 r(t+3)+…+β k-1 r(t+k)
Wherein the content of the first and second substances,
respectively are the maximum values of acceleration response, velocity response and displacement response of the nonlinear structure under the earthquake of the past times; beta is a discount parameter; k represents the seismic oscillations at k future times that need to be considered when evaluating damper behavior.
2. The active damper control method of a nonlinear structure as recited in claim 1, wherein:
the earthquake motion prediction model is a neural network model, and neurons of an input layer of the neural network model are earthquake motion E (t) at the time t, displacement x (t) of the structure and speed
Acceleration of a vehicle
The neurons of the output layer are earthquake motion E (t + 1) -E (t + k) from t +1 to t + k respectively;
training the neural network using historical seismic oscillation data.
3. The active damper control method of a nonlinear structure as recited in claim 1, wherein: solving future k times R (t, a) by dichotomy in step (4) t+1 ) Damper behavior a corresponding to the maximum value t+1 。
4. The method of claim 1, wherein the active damper comprises: arranging sensors on the nonlinear structure in the step (5) to obtainDisplacement x (t), velocity of nonlinear structure at time t
Acceleration of a vehicle
And seismic E (t).
5. The method of claim 1, wherein the active damper comprises: said real-time error rate function
And E' (t) is the actual earthquake motion at the time t, and E (t) is the earthquake motion predicted value of the earthquake motion prediction model at the time t-1 to the time t through the neural network.
6. An active damper control system of a nonlinear structure, characterized by: the earthquake prediction system comprises a mathematical model module, an earthquake motion prediction model module, a signal acquisition module, a real-time error rate function module and a damper control module;
the mathematical model module establishes a mathematical model combining a nonlinear structure and an active damper, wherein the nonlinear structure model is a finite element model;
the vibration prediction model module is a neural network model and is used for predicting seismic vibrations at k moments in the future;
the signal acquisition module acquires parameters of a nonlinear structure and seismic oscillation at the moment t;
the real-time error rate function module obtains a real-time error rate function;
the damper control module obtains R (t, a) according to seismic oscillation at k moments in the future t+1 ) Damper action a corresponding to maximum value at k moments in the future t+1 According to a t+1 Adjusting the damper by multiplying the error rate function at the current time t;
the finite element model of the nonlinear structure is as follows:
wherein M is the mass of the nonlinear structure; c is Rayleigh damping of a nonlinear structure; k (t) is the tangential stiffness of the nonlinear structure at the moment t;
x (t) is the acceleration, velocity and displacement of the nonlinear structure respectively;
is the ground motion acceleration;
the mathematical model of the combination of the nonlinear structure and the active damper is
Wherein, C z (t) providing additional damping to the nonlinear structure for the damper; k z (t) additional stiffness provided to the nonlinear structure by the damper, both magnitudes of which are given by the damper behavior merit function R (t, a) t+1 ) Optimal damper behavior a corresponding to optimal value t+1 Determining;
the damper behavior evaluation value function is R (t, a) t+1 )＝r(t+1)+βr(t+2)+β 2 r(t+3)+…+β k-1 r(t+k)
Wherein the content of the first and second substances,
respectively are the maximum values of acceleration response, velocity response and displacement response of the nonlinear structure under the earthquake of the past times; beta is a discount parameter(ii) a k represents the seismic motion at k moments in the future that need to be considered when evaluating damper behavior.
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