CN103809458A - Magneto-rheological damping control method based on improved leapfrogging algorithm - Google Patents

Magneto-rheological damping control method based on improved leapfrogging algorithm Download PDF

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CN103809458A
CN103809458A CN201410076289.5A CN201410076289A CN103809458A CN 103809458 A CN103809458 A CN 103809458A CN 201410076289 A CN201410076289 A CN 201410076289A CN 103809458 A CN103809458 A CN 103809458A
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陈淑梅
林秀芳
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Fuzhou University
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Abstract

The invention discloses a magneto-rheological damping control method based on an improved leapfrogging algorithm. A fuzzy controller based on the magneto-rheological damping control method is used to establish a relation between a structural seismic response and input voltage of a magneto-rheological damper, wherein the structural seismic response is input of the fuzzy controller, and the input voltage of the magneto-rheological damper is output of the fuzzy controller. For solving the problem that difficulty is brought to design of the fuzzy controller due to the fact that parameter selection of the fuzzy controller depends on expert advice, the magneto-rheological damping control method uses the improved leapfrogging algorithm to adaptively optimize various parameters of the fuzzy controller, which comprise parameters of a membership function, fuzzy rules and input quantification factors, and therefore guarantees that the fuzzy controller after being optimized can provide superior voltage value for the magneto-rheological damper, and then enables the magneto-rheological damper to provide optimal damping force for constructions in an earthquake. The magneto-rheological damping control method based on the improved leapfrogging algorithm not only can improve effectiveness and stability of a control system, but also can guarantee shock absorption effects.

Description

A kind of based on the leapfrog magneto-rheologic damping control method of algorithm of improvement
Technical field
The present invention relates to a kind ofly belong to structural damping field based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, especially utilize MR damper to carry out the fuzzy control field of structural vibration, also relate to the intelligent design field of fuzzy controller.
Background technology
One of challenge that current structure slip-stick artist faces is how effectively to protect building free undermined, especially in the time that buildings is subjected to earthquake and high wind.Fact proved that because countless this infringement probably causes casualties and huge economic loss.MR damper is as a kind of semi-automatic control device, owing to having had the advantage such as high degree of adaptability of height reliability, low energy consumption demand and active control system of passive control system concurrently, receiving much concern in recent years.In addition, the advantage of MR damper be also embodied in manufacture and maintenance cost is relatively low, the large aspect such as damping force and wide dynamic range can be provided.Its damping property has all been verified in existing a large amount of experiments and theoretical research at present.But due to the non-linear feature of MR damper inherence, the control method that can give full play to its performance that design is applicable to becomes a great problem.
Due to fuzzy control theory can be effectively, stable, process the problems such as non-linear, uncertainty and heuristic knowledge easily, be subject to the favor of scientific research personnel and engineers.Although the existing method that MR damper is carried out to fuzzy control at present, itself depends on expertise fuzzy control method, and the parameter of fuzzy controller needs given in advance.Because it is also a very complicated job that design can be given full play to the fuzzy controller of MR damper performance, especially in the time that a high-rise need to be installed multiple damper, what now will design is a more complicated fuzzy controller with multi-input multi-output system.
At present, utilize evolution algorithm to be optimized and to become one of trend of design of Fuzzy Controller fuzzy controller.Forefathers have the precedent of the intelligent method Optimizing Fuzzy Controllers such as genetic algorithm utilized (for example, referring to Chinese patent 201210012197.1), particle cluster algorithm and genetic-ant colony algorithm (for example, referring to Chinese patent 201010193427.X).The algorithm that leapfrogs is proposed in 2002 by Eusuff and Lansey, and it has had the advantage of cultural gene algorithm and particle cluster algorithm concurrently, is a kind of up-to-date and evolution algorithm of being full of vitality.Up to now, leapfrog algorithm successfully for solving the problems such as water resource assignment network, Job-Shop and travelling salesman.Leapfroging algorithm because global search and Local Search carry out simultaneously, make search be difficult for being limited to local solution, is the good approach that solves the optimization problem of Fuzzy Controller Parameters.At present domestic not yet about utilizing the report of the algorithm optimization fuzzy controller that leapfrogs, the document of algorithm optimization fuzzy controller although existing one piece of utilization abroad leapfrogs, but this controller is for controlling ball-beam system, and only have the subordinate function of fuzzy controller and quantizing factor to be optimized, effect of optimization is more limited thus.
Summary of the invention
The present invention is to provide a kind of based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, realize distributing rationally of the each major parameter of fuzzy controller (comprising subordinate function, fuzzy rule and quantizing factor), thereby make the fuzzy controller after optimizing can give full play to the performance of MR damper, finally realize the object to the effective damping of buildings.
The invention is characterized in: a kind ofly it is characterized in that based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, comprise the following steps:
First apply the sharp power of seismic event to the buildings of MR damper is installed, produced floor response is input in fuzzy controller;
Then the selection of fuzzy controller decision variable is converted into and improves the applicable combinatorial optimization problem of algorithm that leapfrogs, and decision variable is encoded and produced at random the initial population of n individual composition, set up the multiple objective function of suitable control structure response simultaneously and determine the parameter setting that improves the algorithm that leapfrogs;
Then utilize the decision variable that improves the algorithm Stochastic search optimization fuzzy controller that leapfrogs, the fuzzy controller of optimizing is made response according to input, voltage is controlled in i.e. output, the input using this control voltage as MR damper, and damper can provide to buildings the damping force of response;
Buildings produces new structural response under damping force and seismic event act on simultaneously, and said process repeatedly, realizes the self-adaptation adjustment of Fuzzy Controller Parameters, until meet the condition of convergence of optimized algorithm, thus obtain optimum fuzzy controller.
Wherein, the method that adopts real-valued coding and non-real-valued coding to mix; Wherein, the jumping mode that the original algorithm that leapfrogs adopts is only applicable to real-valued coding, is applicable to non-real-valued coding and improve the new jumping mode of algorithm of leapfroging, and adopts random binary sequence to pass judgment on method, and it is specially:
X PW k + 1 ( j ) = X INF k ( j ) whenY ( j ) = 1 X PW k ( j ) whenY ( j ) = 0 ( j = 1,2 , · · · , pl )
Wherein X pWthat time mould is because representing that fragment of fuzzy rule in the worst frog in complex; X iNFrepresent for improvement of X pWthe fragment of the good frog; Y is the random binary sequence producing; X pW, X iNFwith Y length are all pl; In the method, X pWcoding or constant, or change over X iNFthe encoded radio of correspondence position.
The decision variable of this fuzzy controller has three classes, is respectively subordinate function, fuzzy rule and quantizing factor.
Improvement leapfrogs in algorithm and has also introduced inverted order mutation operation, mould because of in choose at random respectively several continuous programming codes in representing three sections of codings of three class decision variables and carry out inverted order.
Described fuzzy controller utilization improves the method design that leapfrog algorithm and fuzzy logic theory combine, and fuzzy controller is a multi-input multi-output system.
Advantage of the present invention:
1) compared with adopting the genetic algorithm of same-code mode, can more effectively search optimal value;
2) can effectively reduce the various responses (displacement response, acceleration responsive and relative storey displacement response etc.) of all floors, although relative storey displacement responds not in the object range of objective function optimization;
3) consider the factor that seismic event changes: in the time that seismic event excitation changes, under former seismic event incentive condition, optimize the still damping effectively of control system obtaining;
4) consider the deformation factor of buildings in earthquake: in the time that buildings, in seismic process, deformed damaged has occurred, before building deformation, optimize the control system obtaining and still can effectively carry out damping to the buildings after distortion;
5) utilize control method of the present invention, when increase the quantity of damper in buildings time (now the fuzzy controller of design is multi-input multi-output system), the effect of damping can be more obvious.
Accompanying drawing explanation
Fig. 1 is that the present invention is a kind of based on the leapfrog fuzzy intelligence control principle drawing of algorithm of improvement;
Fig. 2 is the schematic diagram that three floor models of MR damper have been installed in the present invention;
Fig. 3 is MR damper-building system that the present invention sets up in MATLAB/SIMULINK
Fuzzy control model figure;
Fig. 4 is the iteration comparison diagram that improves leapfrog algorithm and genetic algorithm in the present invention;
Fig. 5 is the present invention by the leapfrog input and output figure of subordinate function of the fuzzy controller that algorithm (when weight w=0.5) optimization obtains of improvement;
Fig. 6 is the displacement in controlled (solid line) and not controlled (dotted line) situation response comparison diagram in buildings in the present invention;
Fig. 7 is the absolute acceleration in controlled (solid line) and not controlled (dotted line) situation response comparison diagram in buildings in the present invention;
Fig. 8 be in the present invention in buildings in controlled (respectively at single damper and two damper in the situation that) and not controlled situation the peak value of response comparison diagram of each floor;
Fig. 9 is that the present invention considers that the rigidity of buildings increases the peak value of response comparison diagram of the each floor in the controlled and not controlled situation+20% time;
Figure 10 is that the present invention considers that seismic event accekeration increases the peak value of response comparison diagram of the each floor in the controlled and not controlled situation+50% time.
Embodiment
With reference to Fig. 1, the present invention relates to a kind ofly based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, comprise the following steps:
First apply the sharp power of seismic event to the buildings of MR damper is installed, produced floor response is input in fuzzy controller;
Then the selection of fuzzy controller decision variable is converted into and improves the applicable combinatorial optimization problem of algorithm that leapfrogs, and decision variable is encoded and produced at random the initial population of n individual composition, set up the multiple objective function of suitable control structure response simultaneously and determine the parameter setting that improves the algorithm that leapfrogs;
Then utilize the decision variable that improves the algorithm Stochastic search optimization fuzzy controller that leapfrogs, the fuzzy controller of optimizing is made response according to input, voltage is controlled in i.e. output, the input using this control voltage as MR damper, and damper can provide to buildings the damping force of response;
Buildings produces new structural response under damping force and seismic event act on simultaneously, and said process repeatedly, realizes the self-adaptation adjustment of Fuzzy Controller Parameters, until meet the condition of convergence of optimized algorithm, thus obtain optimum fuzzy controller.
The method that the algorithm that leapfrogs under this method adopts real-valued coding and non-real-valued coding to mix; Wherein, the jumping mode that the original algorithm that leapfrogs adopts is only applicable to real-valued coding, is applicable to non-real-valued coding and improve the new jumping mode of algorithm of leapfroging, and adopts random binary sequence to pass judgment on method, and it is specially:
X PW k + 1 ( j ) = X INF k ( j ) whenY ( j ) = 1 X PW k ( j ) whenY ( j ) = 0 ( j = 1,2 , · · · , pl )
Wherein X pWthat time mould is because representing that fragment of fuzzy rule in the worst frog in complex; X iNFrepresent for improvement of X pWthe fragment of the good frog; Y is the random binary sequence producing; X pW, X iNFwith Y length are all pl; In the method, X pWcoding or constant, or change over X iNFthe encoded radio of correspondence position.
The decision variable of above-mentioned fuzzy controller has three classes, is respectively subordinate function, fuzzy rule and quantizing factor.
Except the above, the improvement under this method leapfrogs in algorithm and has also introduced inverted order mutation operation, mould because of in choose at random respectively several continuous programming codes in representing three sections of codings of three class decision variables and carry out inverted order.
Above-mentioned fuzzy controller utilization improves the method design that leapfrog algorithm and fuzzy logic theory combine, and fuzzy controller is a multi-input multi-output system.
Fig. 1 is that the present invention is a kind of based on the leapfrog fuzzy intelligence control principle drawing of algorithm of improvement.As shown in Figure 1, using seismic response as input, fuzzy controller is by the required magnitude of voltage of output MR damper.The parameters of fuzzy controller is optimized adjustment by the improved algorithm that leapfrogs.MR damper can provide optimum damping damping force for buildings in obtaining the magnitude of voltage of optimizing.
Fig. 2 is the schematic diagram that three floor models of MR damper have been installed in the present invention, take three floor building models as example, first a MR damper is installed between ground and the ground floor of buildings, this system is applied to seismic event excitation, using the produce acceleration responsive of the highest two floors as the input of fuzzy controller, be output as the control voltage of MR damper.So the fuzzy controller in example is two single-input single-output system (SISO system)s.
The Optimal Parameters of fuzzy controller has three classes, is respectively subordinate function, fuzzy rule and quantizing factor.Make each input and output respectively have 5 subordinate functions, the linguistic variable of input is respectively NL (NegativeLarge), NS (NegativeSmall), Z (Zero), PS (PositiveSmall) and PL (PositiveLarge).The linguistic variable of output is respectively VS (VerySmall), S (Small), and M (Medium), L (Large) andVL (Very large), always has 15 subordinate functions.The present invention uses bell membership function:
μ = 1 1 + | x - c a | 2 b
Wherein a and b represent that respectively subordinate function is 0.5 o'clock width and the gradient in degree of membership, as the parameter to be optimized of subordinate function; Because fuzzy rule has identical initial conditions, only need encode to output signal, above-mentioned five linguistic variables are used respectively from 1 to 5 integer encode; In 35%~80% inverse of input quantizing factor the highest two-layer peak acceleration when not controlled, select.Therefore, coding is made up of 57 numbers altogether.Following table is coding structure, and 30 is parameter a and the b that represents 15 subordinate functions, and next 25 is 1 to 5 the integer (non-real-valued coding) that represents fuzzy rule, and latter two is quantizing factor.
a 1 a 2 a 15 b 1 b 2 b 15 g 1 g 2 r 1 r 2 r 25
In order to take into account the security of buildings and personnel's comfortableness wherein simultaneously, the objective function that improves the algorithm optimization that leapfrogs is defined as
Obj=wJ 1+(1-w)J 2 (2)
Wherein
J 1 = max | x i ( t ) | x unctrl
J 2 = max | x · · ai ( t ) | x · · a , unctrl
Wherein x i(t) and
Figure BDA0000472547300000063
respectively displacement and the absolute acceleration of i floor, x unctrlwith
Figure BDA0000472547300000064
respectively maximum displacement and the maximum absolute acceleration of buildings when not controlled.J 1and J 2to be respectively the minimized single-goal function of maximum displacement and maximum acceleration response.W is reflection J 1and J 2the weight of relative importance.
Described concrete steps are refined as:
1) be first definition and the setting that improves the algorithm that leapfrogs:
Step1: initialization improves the parameter (mould because of complex size n, mould because of the number of times of complex quantity m, variation probability, Local Search number of times k and global search etc.) of the algorithm that leapfrogs.
Step2: treating deals with problems carries out real-valued and non-real-valued hybrid coding, random initializtion kind X (0)=(x 1, x 2... x n).
Step3: according to objective function to each individual x in current population X (t) icalculate its fitness value F (x i).
Step4: whole population is resequenced and records globally optimal solution (frog) according to fitness value order from big to small.
Step5: population is divided into m mould because of complex.
Step6: utilize triangle probabilistic method from each mould because selecting several moulds because (or frog) composition time mould is because of complex complex.And write down time mould because of the frog of the worst in complex (being fitness value minimum) and the frog of best (being fitness value maximum).
Step7: the jumping mode and the above-mentioned random binary method jumping mode that fully utilize the original algorithm that leapfrogs are improved time mould because of the frog the worst in complex.
Step8: upgrade all moulds because of complex.
Step9: repeat the operation (all moulds are carried out to deep search because of complex) of Step6~Step8, until deep search number of times reaches k time.
Step10: all moulds are mixed into a new population again because of complex.
Step11: repeat the operation of Step3~Step10, until reach the condition of convergence.
Step12: determine optimum solution, thereby obtain optimum fuzzy controller.
2) then the derive equation of motion and the standard state space form derivation of MR damper-building system is as follows:
Suppose that buildings is the linear structure of a n degree of freedom, and l MR damper has been installed, be subject under lateral seismic wave excitation, its equation of motion is expressed as:
M x · · ( t ) + C x · ( t ) + Kx ( t ) = Γf ( t ) + MΛ x · · g ( t ) - - - ( 3 )
Wherein x (t)=[x 1(t), x 2(t) ..., x n(t)] t, x n(t) be the displacement on the relative ground of n layer; F (t)=[f 1(t), f 2(t) ..., f l(t)] t, f l(t) be l the control that MR damper is corresponding; Γ ∈ R n × lrepresent the position of l damper;
Figure BDA0000472547300000072
it is seismic acceleration; Λ is the vector relevant with the impact of ground motion; M, C, K is respectively mass matrix, damping matrix and the stiffness matrix of structure.Utilize state variable
Figure BDA0000472547300000073
formula (3) can be expressed as
z · ( t ) = Az ( t ) + B 1 f ( t ) + B 2 x · · g ( t ) - - - ( 4 )
Wherein
A = - M - 1 C - M - 1 K I 0 , B 1 = M - 1 Γ 0 , B 2 = Λ 0 .
In addition suppose,
Figure BDA0000472547300000076
the output vector of system, wherein
Figure BDA0000472547300000077
be absolute acceleration, output equation is defined as so
y(t)=Cz(t)+D 1f(t) (5)
Wherein
C = - M - 1 C - M - 1 K I 0 0 I D 1 = M - 1 Γ 0 0
Final formula (4) and formula (5) can become the form in standard state space:
z · ( t ) = Az ( t ) + Bu ( t ) - - - ( 6 )
Y (t)=Cz (t)+Du (t) (7) wherein, B=[B 1b 2], D=[D 10]. it is the output vector that combines damping force and seismic event acceleration.
In the case of this three floors building,
M = 98.3 0 0 0 98.3 0 0 0 98.3 kg
C = 175 - 50 0 - 50 100 - 50 0 - 50 50 Ns / m
K = 10 5 12 - 6.84 0 - 6.84 13.7 - 6.84 0 - 6.84 6.84 N / m
Due to n=3andl=1, obtain f (t)=f 1(t), Λ=[1 ,-1 ,-1] tand Γ=[1,0,0] t.
In addition, a 20s for seismic event 1940ElCentro horizontal direction is encouraged as ground, because buildings is a scaled down model, mounting structure similarity principle, accelerates 5 times of excitations as this model using seismic acceleration.
3) in MATLAB/SIMULINK, set up the fuzzy control model (as shown in Figure 3) of MR damper-building system.
4) finally according to step 1) the optimum fuzzy controller that obtains of method for step 3) model set up, can obtain optimum all floors various responses, control voltage and damping force.
Fig. 4 is the iteration comparison diagram that improves leapfrog algorithm and genetic algorithm in the present invention.Before the parameter of the optimum fuzzy controller of search, the leapfrog parameter of algorithm of improvement is set to: population scale N=200, and mould is because of complex size n=10, and mould is because of the quantity m=20 of complex, variation Probability p m=0.1, the number of times k=5 of local iteration, global search number of times is 120.To improve in order embodying the superior search performance of algorithm that leapfrogs, to use the genetic algorithm with same coding method to contrast with it.The parameter of genetic algorithm is set to: population scale is 200, and variation probability is 0.1, and iterations is 120.Rotating disk selection and two point intersect as the method for evolutional operation.As seen from Figure 4, improve the algorithm that leapfrogs and obtain less optimal value (0.2215) than genetic algorithm.
Fig. 5 is the present invention by the leapfrog input and output figure of subordinate function of the fuzzy controller that algorithm (when weight w=0.5) optimization obtains of improvement.The input quantizing factor in the second floor He San building of the fuzzy controller after optimization is respectively 1/510 and 1/950.
Fig. 6 is the displacement in controlled (solid line) and not controlled (dotted line) situation response comparison diagram in buildings in the present invention.Fig. 7 is the absolute acceleration in controlled (solid line) and not controlled (dotted line) situation response comparison diagram in buildings in the present invention.From these two figure, Intelligent Fuzzy Control strategy of the present invention can reduce displacement and acceleration responsive effectively.
Fig. 8 be in the present invention in buildings in controlled (respectively at single damper and two damper in the situation that) and not controlled situation the peak value of response comparison diagram of each floor.The situation of two dampers refers to: on the basis of above-mentioned Fig. 2 model, increase the MR damper between a Stall and second floor in buildings.Because will provide different control voltage for two MR damper, now the fuzzy controller of design is the system of a multiple-input and multiple-output, but still adopts control mode of the present invention.As seen from Figure 8, compare single damper, under two damper effects, the peak value of response of each floor has had significantly and has reduced.
Fig. 9 is that the present invention considers that the rigidity of buildings increases the peak value of response comparison diagram of the each floor in the controlled and not controlled situation+20% time.As seen from the figure, before building deformation, optimize the still response of Reducing distortion buildings effectively of fuzzy controller obtaining.
Figure 10 is that the present invention considers that seismic event accekeration increases the peak value of response comparison diagram of the each floor in the controlled and not controlled situation+50% time.As seen from the figure, in the time that seismic event response changes, the fuzzy controller that previously optimization had obtained still can reduce the response of buildings effectively.
Be more than preferred embodiment of the present invention, all changes of doing according to technical solution of the present invention, when the function producing does not exceed the scope of technical solution of the present invention, all belong to protection scope of the present invention.

Claims (5)

1. based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, it is characterized in that, comprise the following steps:
First apply the sharp power of seismic event to the buildings of MR damper is installed, produced floor response is input in fuzzy controller;
Then the selection of fuzzy controller decision variable is converted into and improves the applicable combinatorial optimization problem of algorithm that leapfrogs, and decision variable is encoded and produced at random the initial population of n individual composition, set up the multiple objective function of suitable control structure response simultaneously and determine the parameter setting that improves the algorithm that leapfrogs;
Then utilize the decision variable that improves the algorithm Stochastic search optimization fuzzy controller that leapfrogs, the fuzzy controller of optimizing is made response according to input, voltage is controlled in i.e. output, the input using this control voltage as MR damper, and damper can provide to buildings the damping force of response;
Buildings produces new structural response under damping force and seismic event act on simultaneously, and said process repeatedly, realizes the self-adaptation adjustment of Fuzzy Controller Parameters, until meet the condition of convergence of optimized algorithm, thus obtain optimum fuzzy controller.
2. as claimed in claim 1 a kind of based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, it is characterized in that: the method that adopts real-valued coding and non-real-valued coding to mix; Wherein, the jumping mode that the original algorithm that leapfrogs adopts is only applicable to real-valued coding, is applicable to non-real-valued coding and improve the new jumping mode of algorithm of leapfroging, and adopts random binary sequence to pass judgment on method, and it is specially:
X PW k + 1 ( j ) = X INF k ( j ) whenY ( j ) = 1 X PW k ( j ) whenY ( j ) = 0 ( j = 1,2 , · · · , pl )
Wherein X pWthat time mould is because representing that fragment of fuzzy rule in the worst frog in complex; X iNFrepresent for improvement of X pWthe fragment of the good frog; Y is the random binary sequence producing; X pW, X iNFwith Y length are all pl; In the method, X pWcoding or constant, or change over X iNFthe encoded radio of correspondence position.
3. as claimed in claim 1 a kind ofly it is characterized in that: the decision variable of this fuzzy controller has three classes based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, is respectively subordinate function, fuzzy rule and quantizing factor.
4. as claimed in claim 2 a kind of based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, it is characterized in that: improving leapfrogs in algorithm has also introduced inverted order mutation operation, mould because of in choose at random respectively several continuous programming codes in representing three sections of codings of three class decision variables and carry out inverted order.
5. as claimed in claim 4 a kind of based on the leapfrog magneto-rheologic damping control method of algorithm of improvement, it is characterized in that: described fuzzy controller utilization improves the method design that leapfrog algorithm and fuzzy logic theory combine, and fuzzy controller is a multi-input multi-output system.
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CN109800517B (en) * 2019-01-24 2022-05-13 闽江学院 Improved reverse modeling method for magnetorheological damper
CN110286586A (en) * 2019-05-09 2019-09-27 江苏大学 A kind of MR damper hybrid modeling method
CN111930012A (en) * 2020-07-24 2020-11-13 中北大学 Closed-loop control method of magnetorheological actuator
CN112987572A (en) * 2021-02-26 2021-06-18 河海大学 Priori knowledge-based particle swarm optimization method for adaptive ball bar system

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