CN105824783B - A kind of parameter identification method of the nonlinear dampling system for the mixing ant colony algorithm looked for food based on bacterium - Google Patents
A kind of parameter identification method of the nonlinear dampling system for the mixing ant colony algorithm looked for food based on bacterium Download PDFInfo
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Abstract
The invention belongs to the identification of the parameter of nonlinear dampling system, signal processing, swarm intelligence algorithm fields, and in particular to a kind of parameter identification method of the nonlinear dampling system for the mixing ant colony algorithm looked for food based on bacterium.The present invention includes installing displacement sensor, acceleration transducer for damper, sets excited frequency, loads sinusoidal excitation load；Data sampling rate is set, displacement and acceleration information are received by sensor and is filtered；Artificial bee colony algorithm parameter is initialized, field is generated using the chemotaxis of bacterium and solves, carry out local search etc..The present invention has implementation parameter few,, global convergence news speed simple with parameter setting, strong robustness, the characteristics of recognition result precision height etc., for the problem that the problems such as algorithmic procedure that least-squares estimation algorithm identifies nonlinear dampling system parameter is complex, and accuracy of identification is not high, more can adequately solve the parameter recognition speed and precision of nonlinear dampling system.
Description
Technical field:
The invention belongs to the identification of the parameter of nonlinear dampling system, signal processing, swarm intelligence algorithm fields, and in particular to one
The parameter identification method of the nonlinear dampling system for the mixing ant colony algorithm that kind is looked for food based on bacterium.
Background technique
For the parameter identification of nonlinear system, it is divided into the nonlinear system parameter identification and hard nonlinear system of known base
Parameter identification.The identification model of many nonlinear systems, such as Hammerstein model, Wiener mould are proposed both at home and abroad
Type and Hammerstein-Wiener model etc.；For corresponding nonlinear system model, and propose many parameter identification methods
Such as least-squares algorithm, stochastic gradient algorithm, iterative algorithm, maximum likelihood estimation algorithm, Newton's algorithm, particle swarm algorithm are come
The parameter of Identification of nonlinear systems.For the identification of the nonlinear system parameter of known base, parametric method was mostly used to combine
Linear system carries out the parameter identification of system, but parametric method was utilized to will lead to the increase of system parameter dimension to be identified
Cumbersome with the parameter setting of algorithm, slow so as to cause the complexity promotion bring convergence rate of algorithm, robust performance is not strong, and
The problems such as identification precision of influence system.
It and is a kind of novel bionical class evolution algorithm, including ant colony, population, artificial bee colony, people in swarm intelligence algorithm
The work shoal of fish and niche algorithm etc. are solving extensive traveling salesman problem, continuity optimization problem, constrained optimization problem, wirelessly
Sensor path is relatively wide by applying in optimization problem.Group can be made by carrying out targeted algorithm improvement for different application background
Intelligent algorithm is in global convergence speed, the different degrees of performance boost of acquisitions such as precision aspect of robust performance reconciliation.
For the present invention under the nonlinear system of known base, many least-squares estimation algorithms are generally existing due to identification
The problems such as convergence rate caused by dimension increases is slow, and identification precision is not high, and robustness is not strong and algorithm parameter setting is complicated, introduces
Based on the nonlinear dampling system parameter recognition methods of mixing artificial bee colony algorithm, the above problem is preferably resolved.
Summary of the invention
In order to overcome the shortcomings of above-mentioned existing method, the purpose of the present invention is to provide a kind of strong robustness, global convergences
Speed is fast, the parameter identification side of the nonlinear dampling system of the search solution mixing ant colony algorithm with high accuracy looked for food based on bacterium
Method.
The object of the present invention is achieved like this:
Parameter identification method based on the nonlinear dampling system for mixing ant colony algorithm that bacterium is looked for food, including walk as follows
It is rapid:
(1) displacement sensor, acceleration transducer are installed for damper, set excited frequency, load sinusoidal excitation
Load；
(2) data sampling rate is set, displacement and acceleration information are received by sensor and is filtered；
(3) artificial bee colony algorithm parameter is initialized, field is generated using the chemotaxis of bacterium and solves, carry out local search；
(4) roulette probability is replaced using Boltzmann probability, and controls the search speed of honeybee；
(5) displacement read, acceleration value, and velocity amplitude is obtained, the fitness value of the solution of search is calculated, when algorithm reaches
The number of iterations then exits；
(6) when honeybee search reaches the number limitation of local search, current solution is saved, and enter Chaos Search state,
When Chaos Search result is better than current solution in regulation Chaos Search numbers range, current solution is updated, otherwise current solution is included in
Introduce taboo list reinitializes honeybee, searches for into next round；
(7) when search reaches termination condition, output parameter recognition result, and equation of motion song is fitted by recognition result
Line, algorithm terminate, and unload sinusoidal loading.
The parameter to be identified of the damper is obtained by hysteretic damping device damping model:
A typical nonlinear dampling system model is established with hysteretic damping device damping model, the movement for establishing system is micro-
Divide equation:
X in above formula0It is the quiet deformation of damper, r is the deformed restoring force of damper, and g is acceleration of gravity；
The nonlinear restoring force of damper is decomposed into the parallel connection of memory section and memoryless part:
Wherein memoryless restoring force can be taken as linear parametric model, i.e.,
Wherein sgn is sign function；
Wherein η such as is at the physical parameter vector of damper to be identified:
η=[a0, a1..., an1, b0, b1.., bn2]
Therefore equation matrix form to be identified are as follows:
Xη=F
In the step (5), according to identification equation calculation search solution fitness value,
According to obtained identification equation, coherence factor is obtained:
Wherein ε represents the residual vector of least-squares estimation, due to ρ2It is sliding limit ysysFunction G (ys), introduce public
Formula:
Fit=-1/lnG (ys)
Wherein:
The fitness function value that identification requires whether is had reached as judgement identification parameter.
Chaos Search in the step (6):
According to x(n+1), d=μ xN, d(1-xN, d)
Chaos sequence is generated, the value of Chaos Variable is mapped to the value range of optimized variable by carrier system,
n∈[1,Nmax], d ∈ [1, D], μ are the control parameters of chaos state, when μ takes 4 Logistic equation completely into
Chaos state.
The beneficial effects of the present invention are:
The present invention has implementation parameter few, global convergence news speed simple with parameter setting, strong robustness, recognition result
The characteristics of precision height etc., the algorithmic procedure identified for least-squares estimation algorithm to nonlinear dampling system parameter are more multiple
Miscellaneous, the problems such as accuracy of identification is not high, more can adequately solve the parameter recognition speed of nonlinear dampling system and asking for precision
Topic.
Detailed description of the invention
Fig. 1 is algorithm flow chart of the invention.
The mechanical model of Fig. 2 hysteretic damping damper.
Fig. 3 dual slope constitutive relation schematic diagram.
Tri- kinds of algorithm contrast and experiments of Fig. 4.
Specific implementation measure
The present invention is described further with reference to the accompanying drawing.
The invention discloses the nonlinear dampling system parameter recognition methods based on mixing artificial bee colony algorithm, establish non-
Linear damping systems parameter model, and the new mixing artificial bee colony algorithm looked for food based on bacterium of one kind is proposed to non-linear resistance
The process that damping system parameter is identified.The present invention includes: to establish identification model, obtains identification equation, provides identification parameter, add
Carry sinusoidal excitation load；Artificial bee colony algorithm parameter is initialized, field is generated using the chemotaxis of bacterium and solves, part is carried out and searches
Rope；Roulette probability is replaced using Boltzmann probability, and controls the search speed of honeybee；According to identification equation calculation search
Solution fitness value, then exited when algorithm reaches the number of iterations；When honeybee search reach local search number limitation and not
More New food source constantly, saves current solution, and enter Chaos Search state, when chaos is searched in regulation Chaos Search numbers range
When hitch fruit is better than current solution, current solution is updated, otherwise current solution is included in introduce taboo list, reinitializes honeybee, and entrance is next
Wheel search；When search reaches termination condition, output parameter recognition result, algorithm terminates.The present invention has implementation parameter few, tool
There are the characteristics of parameter setting is simple, global convergence news are fast, strong robustness, recognition result precision height etc., for least-squares estimation
The problems such as algorithmic procedure that algorithm identifies nonlinear dampling system parameter is complex, and accuracy of identification is not high can more sufficiently
The parameter recognition speed for solving the problems, such as nonlinear dampling system and precision.
Nonlinear dampling system is modeled first, obtains the system motion differential equation of damping system.For movement
Equation suggestion identifies equation, obtains corresponding identification parameter and solution of equation.The solution of Practical Project is by displacement sensor and acceleration
Sensor acquisition obtains, and the solution of emulation experiment is obtained by Runge Kutta algorithm.Mass block quality is obtained, sample rate is set, if
Determine sine excitation frequency, initialization mixing artificial bee colony algorithm, honeybee generates field solution by bacterium foraging behavior and carries out part
Search；When honeybee part repeatedly not more New food source when, into Chaos Search, prevent local optimum；When enter Chaos Search
When also not obtaining new food source, search solution at this time is included in introduce taboo list,
This method comprises the concrete steps that:
(1) parameter to be identified of damper is mainly obtained by hysteretic damping device damping model, and this method is according to mould
The identification parameter that type obtains, the foundation measured as emulation experiment and Practical Project.
Nonlinear dampling model is established, is memory part and non-memory power part, note by nonlinear dampling system decomposition
Power part is recalled using bilinear model；
Hysteretic damping damper is a typical nonlinear system, is modeled herein to the system.Hysteretic damping subtracts
The vibrational system formed after one nominal-mass m of vibration device configuration is as shown in Figure 2, and taking the equipoise of quality m is coordinate origin, then
The differential equation of motion of system is formula (1):
X in above formula0It is the quiet deformation of damper, r is the deformed restoring force of damper, and g is acceleration of gravity.Damper
Nonlinear restoring force can be analyzed to the parallel connection of memory section and memoryless part.Therefore there are formula (2):
Wherein memoryless restoring force can be taken as linear parametric model, up to formula (3)
Wherein sgn is sign function.
Bilinear model can be used to describe in nonlinear restoring force z (t) with memory characteristic.This structure of bilinear model
Relationship is shown in Fig. 3.
Wherein ysIt is displacement limits when damper generates macroslip, ZsIt is the memory restoring force after sliding.It can by Fig. 3
The equation for writing out memory restoring force Z (t) is as follows:
Z (t)=zsh(ys)
In formulaThe peak value for indicating system dynamic respond, has known to Fig. 3 and equation (4)
Memory restoring force z (t) is about dynamic respond y (t) multivalue.
(2) identification equation is established, and nonlinear dampling solution to model is obtained using Runge Kutta algorithm
Measure the quiet deformation x of damper0And the sampled signal f of excitation, responsek,xk, k=1,2 ..., N (N > n1+
n2+ 1) after, such as given ysA value, then the following linear dimensions of damper can be formed by equation (5) and identify problem:
Wherein η is etc. shown in the physical parameter vector form (6) of damper to be identified:
η=[a0, a1..., an1, b0, b1.., bn2] (6)
Problem above is abbreviated as matrix form:
Xη=F (7)
X and F is corresponding observation matrix and vector.Estimated by the least square that equation (7) can find out parameter vector to be identified
It is calculated as:
η=(XTX)-1(XTF) (8)
The residual vector of least-squares estimation are as follows:
ε=Xη-F (9)
Then coherence factor are as follows:
[0 closer to 1, shows that recognition result is more correct by ρ ∈.From identification process above, coherence factor is actually
It is the function for sliding the limit, i.e.,2=G. is for true ysreal, function G (ysreal) maximum value therefore pass through will be provided find a function
The maximum value of G can acquire the actual parameter of damper.
Due to being tested by the way of analog simulation herein, before carrying out algorithm identification, need to obtain non-
The acquisition data of linear system, and the needs for obtaining corresponding data use fourth order Runge-Kutta algorithm shown in equation (11) public
Formula:
Formula 11 gives the general formula of fourth order Runge-Kutta algorithm, K1, K2, and K3, K4 are 1 rank of f function, 2 ranks, and 3
Rank and 4 order derivatives, h is the displacement step-length calculated, for the value pointed out；
Acquired by displacement sensor and acceleration transducer when Practical Project measurement and filter acquisition actual displacement value
And acceleration value, and velocity amplitude is obtained by the integral operation of acceleration, instead of the obtained solution of Runge Kutta algorithm.
(3) quality of mass block is obtained, the rate of setting data acquisition sets the frequency of sinusoidal loading exciting, initialization
Artificial bee colony algorithm parameter generates field using the chemotaxis of bacterium and solves, carries out local search.
It is assumed that the sum of bacterium is Sn, the position of each bacterium represents a possible solution of problem, is represented by D dimension space
In a vectorIf with symbol xi(j) indicate that i-th bacterium becomes medicine by jth time
Position after behavior, then location may be expressed as: next time after chemotaxis step
Wherein C (i) is normal number, indicates the step-length unit that bacterium i moves about forward every time；After then indicating bacterium rolling
Another direction of advance chosen at random.
Based on above analysis, if being replaced in ABC algorithm using bacterial chemotaxis behavior as new local searching strategy
" neighbouring solution generates --- greediness selection " strategy, and so as to improve search performance.For this reason, the neighbouring solution of ABC algorithm generates
Formula can be replaced
Vi=Xi+Δi
Parameter MD therein is the positive integer for being not more than dimension D, and representing each step of honeybee can be simultaneously in MD dimension
Upper its coordinate value of change, wherein the numerical value of MD can be taken as MD=[0.1*D], and symbol [] indicates to be rounded herein, and MD is too small to adaptation
The adjustment capability of angle value is limited, { j1,...,jMDIt is the set for having MD value, each of these entry value jd∈ J be from [1,
D] random dimension serial number that range generates, and it does not repeat each other；K ∈ 1,2 ..., and ne } it is the index value being randomly generated, and
It must satisfy k ≠ i, ne is the sum of food source.
(4) roulette probability is replaced using Boltzmann probability, and controls the search speed of honeybee
The new probability formula of Boltzmann roulette can be expressed as follows with formula
(5) it according to the fitness value of the solution of identification equation calculation search, is then exited when algorithm reaches the number of iterations
Fit=-1/lnG (ys)(15)
(6) when honeybee search reaches the number limitation of local search, current solution is saved, and enter Chaos Search state,
When Chaos Search result is better than current solution in regulation Chaos Search numbers range, current solution is updated, otherwise current solution is included in
Introduce taboo list reinitializes honeybee, searches for into next round
Algorithm parameter value: Np, limit, MD, N is sets,T0,a,G,Nmax。The main thought of Chaos Search is under
Formula:
x(n+1), d=μ xN, d(1-xN, d) (16)
Chaos sequence is generated, then the value of Chaos Variable is mapped to the value range of optimized variable by carrier system
In formula: n ∈ [1, Nmax], d ∈ [1, D] μ is the control parameter of chaos state, and Logistic equation is completely into chaos when μ takes 4
State
(7) when search reaches termination condition, output parameter recognition result, it is fitted equation of motion curve, algorithm terminates,
Unload load.
Based on the nonlinear dampling system parameter recognition methods of mixing artificial bee colony algorithm, the specific steps of which are as follows:
Step 1: installation displacement sensor and acceleration transducer obtain mass block quality, set data sampling rate, setting
Algorithm parameter value: Np, limit, MD, N is arranged in the frequency of load excitings,T0,a,G,Nmax
Step 2: employing the position of bee using Np/2 in formula (11) random initializtion population, and initialize each counter
failurei=0；Calculate fitness value fiti=-1/lnG (ys) formula (14) is used to calculate respective Boltzmann probability Pi；.
Step 3: bee being employed to each, generates new position x with formula (13)iAnd calculate fitness value fiti'.If fiti’<
fiti；Then enable failurei=failurei+ 1 carries out next step；Otherwise failure is enabledi=0 and remember new position i.e. xi=
Vi；Repeat similarly become medicine movement, when alreading exceed Ns times to honeybee to food source does not improve food source into
Enter next step.
Step 4: bee being observed to each, according to respective Boltzmann probability PiIt is worth one food source of roulette selection.
Then with employing as bee in step 3, primary selected food source is exploited.
Step 5: checking and all employ bee.If failurei> limit starts to carry out Chaos Search, according to formula
(16) N is continuously generatedmaxSecondary iteration, and N is generated by formula (13)maxA field solution searches for all field solutions at this time, passes through neck
Domain solution updates current foodstuff source.If more New food source, then do not employ bee to abandon corresponding food i-th after Chaos Search
Material resource position, and use formula (13) random distribution to search space.
Step 6: current algebra g is checked, if being less than maximum cycle G, and optimal solution precision not up to requires, and goes to
Step 3 executes next round circulation.Otherwise it performs the next step rapid.
Step 7: output recognition result, algorithm exit.
Effect of the invention can be further illustrated by following emulation:
1. simulated conditions and parameter setting
Experiment condition:
AMDAthlon(tm)64Processor3000+2.00GHz,2.00GBMicrosoftWindows7ultimat
e6.1.7600Release7600
MATLABversion7.11.0.584(R2010b)32-bit(win32)August16,2010
By the above-mentioned identification step provided, setting sample rate is 30KHz, mass block weight 1000Kg, excitation load frequency
Honeybee populations quantity Np=60 is arranged in rate 50Hz；Local iteration limited number of times limit=200；The dimension MD=of food source variation
3；Food source dimension D=6；Bacterium number of oscillations Ns=3；The press factors T of Boltzmann probability0=100, a=0.995；Repeatedly
Generation number G=2000；Chaos iteration times N max=30, chaos controlling parameter μ=4；Algorithm number of repetition runtime=30；
The comparison algorithm for participating in test has ABC algorithm and HABC algorithm and proposed in this paper identify for nonlinear system parameter to improve
HABC-CS algorithm.
2. the simulation experiment result
Fig. 4 gives under identical experiment environment, the Average Iteration that three kinds of algorithms obtain after algorithm repetitive operation 30 times
Convergence curve.As can be seen from the figure the algorithm of this paper either can in terms of the precision and robustness that convergence rate still solves
Reach higher level, precision and the algorithm for effectively solving the convergence rate reconciliation that nonlinear system parameter identification is encountered are complicated
Degree problem.
Claims (3)
1. a kind of parameter identification method of the nonlinear dampling system for the mixing ant colony algorithm looked for food based on bacterium, feature are existed
In including the following steps:
(1) displacement sensor, acceleration transducer are installed for damper, set excited frequency, load sinusoidal excitation load；
(2) data sampling rate is set, displacement and acceleration information are received by sensor and is filtered；
(3) artificial bee colony algorithm parameter is initialized, field is generated using the chemotaxis of bacterium and solves, carry out local search；
If the sum of bacterium is Sn, the position of each bacterium represents a possible solution of problem, one be expressed as in D dimension space
VectorSymbol xi(j) position of i-th of bacterium after jth time becomes medicine behavior is indicated
It sets, next time after chemotaxis step, location is indicated are as follows:
Wherein C (i) is normal number, indicates the step-length unit that bacterium i moves about forward every time；Then indicate random after bacterium rolls
Another direction of advance chosen；
Neighbouring solution generates formula and replaces with
Vi=Xi+Δi
Parameter MD therein is the positive integer for being not more than dimension D, it can be changed on MD dimension simultaneously by representing each step
Coordinate value, wherein the numerical value of MD is taken as MD=[0.1*D], and symbol [] indicates to be rounded herein, { j1,...,jMDBe one have MD
The set of a value, each of these entry value jd∈ J is the random dimension serial number generated from [1, D] range, and is not repeated each other；
K ∈ 1,2 ..., and ne } it is the index value being randomly generated, and must satisfy k ≠ i, ne is the sum of food source；
(4) roulette probability is replaced using Boltzmann probability, and controls the search speed of honeybee；
(5) displacement, acceleration value are read, and obtains velocity amplitude, calculates the fitness value of the solution of search, when algorithm reaches iteration time
It is several, it exits；The fitness value for calculating the solution of search obtains coherence factor according to obtained identification equation:
Wherein ε represents the residual vector of least-squares estimation, and coherence factor ρ is the function for sliding limit ys, i.e. ρ2=(ys), draws
Enter fitness value:
Fit=-1/lnG (ys)
Wherein:
The fitness function value that identification requires whether is had reached as judgement identification parameter；
(6) when honeybee search reaches the number limitation of local search, save current solution, and enter Chaos Search state, when
When Chaos Search result is better than current solution in regulation Chaos Search numbers range, current solution is updated, otherwise current solution is included in taboo
List reinitializes honeybee, searches for into next round；
(7) when search reaches termination condition, output parameter recognition result, and equation of motion curve is fitted by recognition result,
Algorithm terminates, and unloads sinusoidal loading.
2. a kind of parameter of the nonlinear dampling system of mixing ant colony algorithm looked for food based on bacterium according to claim 1
Recognition methods, it is characterised in that: the parameter to be identified of the damper is obtained by hysteretic damping device damping model:
A typical nonlinear dampling system model is established with hysteretic damping device damping model, establishes the motion side of system
Journey:
X in above formula0It is the quiet deformation of damper, r is the deformed restoring force of damper, and g is acceleration of gravity；
The nonlinear restoring force of damper is decomposed into the parallel connection of memory section and memoryless part:
Wherein memoryless restoring force is taken as linear parametric model, i.e.,
Wherein sgn is sign function；
Wherein η such as is at the physical parameter vector of damper to be identified:
η=[a0,a1,…,an1,b0,b1,..,bn2]
Therefore equation matrix form to be identified are as follows:
X η=F, X and F are observation matrix and vector.
3. a kind of parameter of the nonlinear dampling system of mixing ant colony algorithm looked for food based on bacterium according to claim 1
Recognition methods, it is characterised in that: the Chaos Search in the step (6):
According to x(n+1),d=μ xn,d(1-xn,d)
Chaos sequence is generated, the value of Chaos Variable is mapped to the value range of optimized variable by carrier system,
n∈[1,Nmax], d ∈ [1, D], μ are the control parameters of chaos state, and Logistic equation is completely into chaos when μ takes 4
State.
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