CN103020709B - Based on the one-dimensional water quality model parameter calibration method of artificial bee colony and quanta particle swarm optimization - Google Patents

Based on the one-dimensional water quality model parameter calibration method of artificial bee colony and quanta particle swarm optimization Download PDF

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CN103020709B
CN103020709B CN201210402849.2A CN201210402849A CN103020709B CN 103020709 B CN103020709 B CN 103020709B CN 201210402849 A CN201210402849 A CN 201210402849A CN 103020709 B CN103020709 B CN 103020709B
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water quality
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CN103020709A (en
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陈广洲
刘桂建
汪家权
李如忠
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Anhui Jianzhu University
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Abstract

The invention discloses a kind of one-dimensional water quality model parameter calibration method based on artificial bee colony and quanta particle swarm optimization, it comprises following key step: (1) chooses the river that will study, according to measured value and employing one-dimensional water quality model, work out objective function to be optimized; (2) the general operational factor of algorithm is inputted: population number, iterations, dimension, variable-value scope, objective function to be optimized; (3) one or more computing method choosing ABC, QPSO, QPSO+ABC and ABC+QPSO calculate; (4) if only use one, whether direct judged result meets is optimized requirement; If more than a kind of computing method, whether the result of Integrated comparative result of calculation and evaluation optimum meets the requirement of this suboptimization; (5) if meet the demands, computing terminates, and exports result of calculation and iterativecurve; (6) otherwise, the input parameter of amendment algorithm, recalculates, and the result of calculation after output parameter adjustment and iterativecurve, obtain final optimization pass result.

Description

Based on the one-dimensional water quality model parameter calibration method of artificial bee colony and quanta particle swarm optimization
Technical field
The present invention relates to the optimization application in artificial intelligence, Management Science and Engineering, particularly relate to a kind of one-dimensional water quality model parameter calibration method based on artificial bee colony and quanta particle swarm optimization.
Background technology
Optimization problem is present in real world in a large number, and especially in scientific research and engineer applied field, the effect of optimum theory and technology becomes more and more important.In addition, optimisation technique also has purposes widely in the industry-by-industry of national economy.Solve the needs of the optimization problem of the feature such as extensive, combination, non-linear, discreteness, randomness, multiple goal, promote the development of mathematic programming methods and intelligent optimization algorithm.Colony intelligence optimized algorithm is one of them study hotspot in recent years.
Artificial bee colony algorithm is a kind of Swarm Intelligence Algorithm efficiently, and the gathering honey behavior that it imitates honeybee is searched for.Honeybee carries out different activities according to the respective division of labor, and realizes sharing and exchanging of bee colony information, thus finds the optimum solution of problem.Shown by numerical function optimization and multimodal function optimization, ABC algorithm has better Optimal performance than genetic algorithm, differential evolution algorithm and Particle Swarm Optimization.
Quanta particle swarm optimization is incorporated in basic particle group algorithm by quantum theory, for the deficiency of basic particle group algorithm optimizing, from quantum-mechanical angle, utilize quantum uncertainty principle to describe the motion state of particle, basic particle group algorithm is improved.It is seen as a kind of newly, can to one of probabilistic algorithm that basic particle group algorithm future thrust has an impact.Show through polytype application: the method have travelling speed soon, stronger optimizing performance.
Above-mentioned two kinds of algorithms respectively have advantage, often need to adopt above-mentioned two kinds of algorithms to be optimized computing in production practices.A kind of method wherein can be adopted to calculate result, also can compare two kinds of arithmetic result, decide what to use; In addition, for improving ability of searching optimum further, the mixed method (QPSO+ABC and ABC+QPSO) of these two kinds of methods also can be adopted to carry out optimizing intensive treatment, to obtain better optimum results.
Summary of the invention
The technical problem to be solved in the present invention is to provide a kind of one-dimensional water quality model parameter calibration method based on artificial bee colony and quanta particle swarm optimization.
In order to solve the problems of the technologies described above, the technical solution used in the present invention is: based on the one-dimensional water quality model parameter calibration method of artificial bee colony and quanta particle swarm optimization, artificial bee colony algorithm calls ABC in the following text, and quanta particle swarm optimization calls QPSO in the following text, comprises the following steps:
(1) choose the river that will study, obtain tracer concentration data over time by tracer experiment; According to measured value and employing one-dimensional water quality model ( c = ( M 0 / ( A 4 * pi * D L - * t ) ) * exp ( - ( x - vt ) 2 / ( 4 D L t ) ) ) The minimum principle of calculated value sum of squares of deviations works out objective function to be optimized:
(2) the general operational factor of algorithm is inputted: population number, iterations, dimension, variable-value scope, objective function to be optimized;
(3) one or more computing method choosing ABC, QPSO, QPSO+ABC and ABC+QPSO carry out the calibration calculating of model parameter;
(4) if only adopt the one in above-mentioned algorithm, whether direct judged result meets is optimized requirement; According to two in above-mentioned algorithm kind and above computing method, Integrated comparative result of calculation and evaluate the requirement whether optimum result meets this suboptimization;
(5) if meet the demands, computing terminates, the result of output parameter calibration and the iterativecurve of algorithm;
(6) otherwise, amendment algorithm input parameter, recalculate, output parameter adjustment after result of calculation and iterativecurve, obtain final optimum results.
As preferably, objective function refers to that a class can be converted into the function asking extreme value, the error between the calculated value that the measured value and carrying out according to theory as tested gained calculates.
As preferably, the calculation procedure of artificial bee colony algorithm is as follows:
(1) carry out initialization according to self span of each variable respectively according to population number, carry out dimension merging subsequently, form bee colony initial population x ij, i=1 ..., SN, j=1 ... D, wherein SN represents the quantity of food source, and D is the dimension of variable;
(2) calculate the function fitness value of population, and evaluate population;
(3) gathering honey honeybee (x ij) in food source neighborhood, near its neighborhood, produce new explanation v by formula (1) ij:
v ij＝x ij+φ ij(x ij-x kj)(1)
Wherein, x kexcept x ioutside a solution of random selecting, φ ijbe the random number of a variation range at interval [-a, a], a gets 1 usually, then, applies greedy selection algorithm and determines v iand x iquality;
(4) according to formula (2), according to fitness value (fit i) calculate and separate x iprobable value p i:
p i = fit i / ( Σ i = 1 SN fit i ) - - - ( 2 )
Wherein, for minimization problem, the calculating of fitness value is pressed formula (3) and is calculated:
fit i = 1 / ( 1 + f i ) if f i &GreaterEqual; 0 1 + abs ( f i ) if f i < 0 - - - ( 3 )
Wherein, f ifor target function value;
(5) for observation honeybee, produce new explanation in the neighborhood of the food source selected by it, adopt greedy selection algorithm to compare v iand x iquality;
(6) the solution x abandoned is determined i, adopt the new explanation x ' that formula (4) produces at random ireplace it, it can be used as search bee:
x / ij＝xmin j+rand(0，1)*(xmax j-xmin j)(4)
Wherein, xmin jfor the span lower limit of parameter j, xmax jfor the span upper limit of parameter j;
(7) solution that memory is best at present, if meet ending standard requirement, algorithm stops, and exports result of calculation; Otherwise, forward step (2) to and continue iteration.
As preferably, the new explanation obtained in the calculation procedure 3 of artificial bee colony algorithm and step 5, will carry out range check respectively to each variable range, make it not exceed the interval of himself change.
The invention has the beneficial effects as follows:
Choose artificial bee colony algorithm and this colony intelligence optimized algorithm that two kinds of required input parameters are few, Optimal performance is strong of quanta particle swarm optimization carries out being integrated into a universal computing platform, it has the following advantages:
(1) parameters input is simple, easy to operate; (2) user is by the objective function to be optimized of establishment oneself, can solve the actual optimization problem that it runs into easily, be with a wide range of applications and practical value; (3) user is by changing the parameters of certain algorithm, can observe the affecting laws of this algorithm parameter change to Optimal performance; (4) for same optimization problem, various combination account form can be adopted to calculate, compare Optimal performance situation and the quality of result of calculation, thus select optimum result of calculation for; Particularly two kinds of mixing account form (QPSO+ABC and ABC+QPSO), adopt the optimum results of a kind of front method directly to implant in the initial population of subsequent algorithm and participate in successive iterations and calculate, and enhance the Optimal performance of algorithm.
Accompanying drawing explanation
Below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation.
Fig. 1 is the process flow diagram of the optimized calculation method embodiment that the present invention is based on artificial bee colony algorithm and quanta particle swarm optimization.
Fig. 2 is the iterativecurve figure of the optimized calculation method embodiment A BC that the present invention is based on artificial bee colony algorithm and quanta particle swarm optimization.
Fig. 3 is the iterativecurve figure of the optimized calculation method embodiment QPSO that the present invention is based on artificial bee colony algorithm and quanta particle swarm optimization.
Fig. 4 is the iterativecurve figure of the optimized calculation method embodiment A BC+QPSO that the present invention is based on artificial bee colony algorithm and quanta particle swarm optimization.
Fig. 5 is the iterativecurve figure of the optimized calculation method embodiment QPSO+ABC that the present invention is based on artificial bee colony algorithm and quanta particle swarm optimization.
Embodiment
The present embodiment is the application example of a water quality parameter identification, and Fig. 1 is its process flow diagram.
Analyze river water mass tracing experiment data, determine Longitudinal Dispersion D lduring with mean velocity in section v, many employings describe the analytic solution of the one-dimensional river water mass tracing experiment under instantaneous input tracer agent condition:
( c = ( M 0 / ( A 4 * pi * D L - * t ) ) * exp ( - ( x - vt ) 2 / ( 4 D L t ) ) ) ;
In formula: c is tracer agent mass concentration, M 0for the quality of instantaneous input tracer agent; A is river cross section area; D lfor longitudinal dispersion coefficient of river; X is the distance between sampled point and release position; T is the time; V is cross section of river mean flow rate, and pi represents π, gets 3.14 during calculating.
Objective function is:
min f ( &theta; ) = &Sigma; i = 1 m ( c i - c j ) 2
In formula: c ifor the actual tracer agent mass concentration value observed in the i-th moment; c jthe tracer agent mass concentration value in the i-th moment calculated for utilizing above formula; θ is parameters of river water quality vector to be estimated, i be tracer concentration observation time sequence number (i=1,2 ..., n).Choose suitable parameter value θ, make the sum of squares of deviations of concentration calculated value and concentration observed reading reach minimum, now corresponding parameters of river water quality value is required by problem.
Known M 0=10kg, x=500m, give parameter true value θ 1=D l=3000m 2/ mir, θ 2=v=30m/min and θ 3=A=20m 2time, the raw data c corresponding to different time i, specifically in table 1.
Table 1:c i~ t iraw data correspondence table
t i/min 6 10 12 14 16 20 24 36
c i/(mg·L -1) 0.254 0.583 0.649 0.663 0.642 0.552 0.444 0.197
Arranging population number is 30, and iteration total degree is that the variation range of 300, three parameters is respectively: [0,300000], [0,3000], [0,2000], and objective function is shuizhicanshu, and result of calculation is as follows:
Adopt the result of calculation of ABC: target function value is 9.230009e-007, and variable result to be optimized is followed successively by 3001.46,30.0082,20.0009, and the iterativecurve of output as shown in Figure 2.
Adopt the result of calculation of QPSO: target function value is 9.2109e-007, and variable result to be optimized is followed successively by 3001.81,30.008,20.0001, and the iterativecurve of output as shown in Figure 3.
Adopt the result of calculation of ABC+QPSO: target function value is 9.2109e-007, and variable result to be optimized is followed successively by 3001.81,30.008,20.0001, and the iterativecurve of output as shown in Figure 4.
Adopt the result of calculation of QPSO+ABC: target function value is 9.2109e-007, and variable result to be optimized is followed successively by 3001.81,30.008,20.0001, and the iterativecurve of output as shown in Figure 5.
As follows to the observation and comparison of the concrete iterativecurve of above-mentioned four kinds of methods:
By observing Fig. 2 and Fig. 3, can find out that QPSO is better than ABC in speed of convergence and optimum results; Fig. 4 reflects the mixed running effect of order for ABC+QPSO two kinds of algorithms, shows that QPSO has had certain improvement solving on basis of ABC to result again, obtains more excellent result; Fig. 5 reflects the mixed running effect of order for QPSO+ABC two kinds of algorithms, show the result that QPSO has obtained, and solving of ABC does not improve to some extent to the above results.
In the present embodiment, the variable of artificial bee colony algorithm (ABC) is not search for by identical interval, but searches for according to the interval of self, like this can convergence speedup speed and enhancing optimizing effect.
For convenience of using, in the present embodiment uses, adopt the MATLABGUI technological development optimization computing platform of an interactive interface close friend.This platform is made up of three parts: (1) load module part, for receiving population number, dimension, the bound scope of variable-value and objective function to be optimized; (2) output module: export the optimal objective function value and corresponding variable-value that calculate; (3) iterativecurve display module: the evolution process of target function value with iterations that certain algorithm can be demonstrated real-time dynamicly.Its interactive interface is made up of 2 panels, 9 static text frames, 8 Edit Text frames, 1 coordinate axis control and 1 drop-down menu.By this optimization computing platform, as long as user is aided with simple operations on interface just can solve the complicated optimum problem run in reality.
Above-described embodiment of the present invention, does not form limiting the scope of the present invention.Any amendment done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within claims of the present invention.

Claims (4)

1., based on the one-dimensional water quality model parameter calibration method of artificial bee colony and quanta particle swarm optimization, described artificial bee colony algorithm calls ABC in the following text, and described quanta particle swarm optimization calls QPSO in the following text, comprises the following steps:
(1) choose the river that will study, obtain tracer concentration data over time by tracer experiment; According to measured value and employing one-dimensional water quality model ( c = ( M 0 / ( A 4 * pi * D L * t ) ) * exp ( - ( x - vt ) 2 / ( 4 D L t ) ) ) The minimum principle of calculated value sum of squares of deviations works out objective function to be optimized:
(2) the general operational factor of algorithm is inputted: population number, iterations, dimension, variable-value scope, objective function to be optimized;
(3) one or more computing method choosing ABC, QPSO, QPSO+ABC and ABC+QPSO carry out the calibration calculating of model parameter;
(4) if only adopt the one in above-mentioned algorithm, whether direct judged result meets is optimized requirement; According to two in above-mentioned algorithm kind and above computing method, Integrated comparative result of calculation and evaluate the requirement whether optimum result meets this suboptimization;
(5) if meet the demands, computing terminates, the result of output parameter calibration and the iterativecurve of algorithm;
(6) otherwise, amendment algorithm input parameter, recalculate, output parameter adjustment after result of calculation and iterativecurve, obtain final optimum results.
2. one-dimensional water quality model parameter calibration method according to claim 1, is characterized in that: objective function described in step 1 refers to that a class can be converted into the function asking extreme value.
3. one-dimensional water quality model parameter calibration method according to claim 1, is characterized in that: the calculation procedure of described artificial bee colony algorithm is as follows:
(1) carry out initialization according to self span of each variable respectively according to population number, carry out dimension merging subsequently, form bee colony initial population x ij, i=1 ..., SN, j=1 ... D, wherein SN represents the quantity of food source, and D is the dimension of variable;
(2) calculate the function fitness value of population, and evaluate population;
(3) gathering honey honeybee (x ij) in food source neighborhood, near its neighborhood, produce new explanation v by formula (1) ij:
v ij＝x ij+φ ij(x ij-x kj)(1)
Wherein, x kexcept x ioutside a solution of random selecting, φ ijbe the random number of a variation range at interval [-a, a], a gets 1 usually, then, applies greedy selection algorithm and determines v iand x iquality;
(4) according to formula (2), according to fitness value (fit i) calculate and separate x iprobable value p i:
p i = fit i / ( &Sigma; i = 1 SN fit i ) - - - ( 2 )
Wherein, for minimization problem, the calculating of fitness value is pressed formula (3) and is calculated:
fit i = 1 / ( 1 + f i ) if f i &GreaterEqual; 0 1 + abs ( f i ) if f i < 0 - - - ( 3 )
Wherein, f ifor target function value;
(5) for observation honeybee, produce new explanation in the neighborhood of the food source selected by it, adopt greedy selection algorithm to compare v iand x iquality;
(6) the solution x abandoned is determined i, adopt the new explanation that formula (4) produces at random replace it, it can be used as search bee:
x′ ij＝xmin j+rand(0，1)*(xmax j-xmin j)(4)
Wherein, xmin jfor the span lower limit of parameter j, xmax jfor the span upper limit of parameter j;
(7) solution that memory is best at present, if meet ending standard requirement, algorithm stops, and exports result of calculation; Otherwise, forward step (2) to and continue iteration.
4. one-dimensional water quality model parameter calibration method according to claim 3, it is characterized in that: the new explanation obtained in the calculation procedure 3 of described artificial bee colony algorithm and step 5, range check to be carried out respectively to each variable range, make it not exceed the interval of himself change.
CN201210402849.2A 2012-10-19 2012-10-19 Based on the one-dimensional water quality model parameter calibration method of artificial bee colony and quanta particle swarm optimization Expired - Fee Related CN103020709B (en)

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