CN114580601A - Magnetic dipole target positioning method based on improved intelligent optimization algorithm - Google Patents
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Abstract
The invention belongs to the technical field of magnetic target positioning, and discloses a magnetic dipole target positioning method based on an improved intelligent optimization algorithm, which comprises the following steps: describing the magnetic induction intensity of a target by adopting a magnetic dipole model under a far field condition; constructing a magnetic dipole target positioning nonlinear equation set based on an improved intelligent optimization algorithm; and optimizing by using an improved intelligent optimization algorithm to realize the magnetic dipole target positioning based on the improved intelligent optimization algorithm. The optimization process by using the improved intelligent optimization algorithm comprises the following steps: an initial population is generated through initialization of the good point set, so that the initial population position is more uniform; secondly, adding a particle swarm position updating formula to enhance the information exchange and cooperation mechanism among the particles; in addition, the change probability and the Levy flight are added, so that the activity and the diversity of the particles are enhanced, and the algorithm is prevented from falling into local optimization. The invention has higher positioning precision and higher convergence rate under the condition of low signal-to-noise ratio, and can be used for magnetic target detection.
Description
Technical Field
The invention belongs to the technical field of magnetic target positioning, and particularly relates to a magnetic dipole target positioning method based on an improved intelligent optimization algorithm.
Background
At present, the magnetic target positioning method has important value in the application fields of aviation magnetic detection, robot attitude detection, geomagnetic field navigation, geological exploration, unexploded object detection and the like. When the magnetic target is far enough away from the magnetic sensor, the target can be equivalent to a magnetic dipole, and the magnetic dipole can be used to describe the magnetic induction intensity of the target. The magnetic dipole positioning problem is solved by mainly adopting three methods, namely an analytic method, an optimization method, a sequential filtering method and the like. The analytic method is sensitive to observation noise, and the positioning performance is poor under the condition of low signal-to-noise ratio; the sequential filtering method mainly aims at the positioning problem of a moving target, and the optimization method is the main method for solving the problem of magnetic dipole target positioning based on an improved intelligent optimization algorithm at present.
The optimization algorithm usually obtains the position information of the magnetic target from the measurement data of the magnetic sensor by using the optimization algorithm. Wiegert et al, 2008, proposed a gradient direction derivative method based on a central potential field for a real-time point-by-point localization problem. In 2009, Lihua et al located a magnetic target by using a genetic algorithm based on a single-rotation ellipsoid model, so that online magnetic target location was realized, and a calculation result shows that the method is accurate in location and reliable in judgment. Zhang Dan et al studied the optimization problem of search paths of airborne magnetic probes based on genetic algorithm in 2017, constrained the spatial range of solution according to the prior information of the target, and generated the initial population according to the regular search matrix and the random search matrix, so that the non-inferiority and diversity of individuals are guaranteed. Gao et al used LM algorithm to locate moving magnetic targets in 2018.
The current situation of research at home and abroad aiming at the problem of magnetic dipole target positioning based on the improved intelligent optimization algorithm shows that the optimal value can be easily converged by using the traditional optimization method for the problem of magnetic field three-component positioning with a smaller range, but the traditional optimization algorithm is too sensitive to the initial value and the target positioning performance is difficult to guarantee under the conditions of larger parameter range and more complex target function.
Through the above analysis, the problems and defects of the prior art are as follows: aiming at the conditions that the parameter range is large and the target function is complex, the traditional optimization algorithm is too sensitive to the initial value, and the target positioning performance is difficult to guarantee.
The difficulty in solving the above problems and defects is: the magnetic dipole sub-targets are difficult to locate quickly and accurately under low signal-to-noise ratio conditions.
The significance of solving the problems and the defects is as follows: the invention aims to provide a magnetic dipole positioning method, which is used for solving the problems of reduced magnetic dipole target positioning accuracy and low convergence speed based on an improved intelligent optimization algorithm under the condition of low signal to noise ratio and can be used for analyzing target magnetic induction intensity data measured by a magnetic sensor quickly.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a magnetic dipole target positioning method based on an improved intelligent optimization algorithm.
The invention is realized in such a way, a magnetic dipole target positioning method based on an improved intelligent optimization algorithm comprises the following steps:
step one, adopting a magnetic dipole model to describe the magnetic induction intensity of a target under a far field condition, which is the model basis of the scheme;
constructing a magnetic dipole target positioning nonlinear equation set based on an improved intelligent optimization algorithm, and determining a fitness function for the intelligent optimization algorithm;
and thirdly, optimizing by using an improved intelligent optimization algorithm to realize magnetic dipole target positioning based on the improved intelligent optimization algorithm, which is a key step of the scheme.
Further, in the first step, the specific process of describing the magnetic induction intensity of the target by adopting the magnetic dipole model under the far field condition is as follows:
when the distance between the magnetic sensor and the target is more than 2.5 times of the size of the magnetic target, the magnetic target object is regarded as a magnetic dipole;
the target position of the magnetic dipole in the coordinate system is A (x)0,y0,z0) The coordinates of the fluxgate sensor are B (x, y, z), r is the vector from the origin of the magnetic dipole to the magnetic sensor,
is the magnetic moment vector of the magnetic dipole, m is the target magnetic moment, theta is the geomagnetic inclination angle,
is the magnetic declination. The magnetic induction intensity B generated by the target at the point B is obtained; and in a rectangular coordinate system, developing a magnetic induction intensity B equation.
Further, the magnetic induction intensity B equation generated by the target at the point B is:
further, the magnetic induction B equation is developed as:
in a rectangular coordinate system, developing a magnetic induction intensity B equation to obtain:
wherein mu0A free space permeability of 4 π × 10-7H/m, the above formula is a group consisting of 6In the nonlinear equation set of unknown numbers, at least two measurement points are required to be provided, and the unknown parameters of the target can be estimated only by constructing six equations; under the actual measurement condition, certain errors exist in the measurement of the magnetic induction intensity value, the result obtained by only depending on the data of two monitoring points is not accurate, in order to reduce the errors, the number of the magnetic sensors needs to be increased, the magnetic sensors are converted into a nonlinear optimization problem, and then an optimization algorithm is utilized to solve the problem. .
Further, in the second step, a magnetic dipole target positioning nonlinear equation set based on an improved intelligent optimization algorithm is constructed, and the specific process is as follows:
firstly, a set of unknowns is assumed and substituted into the right half of the B equation of the magnetic induction to obtain a set of estimates of the magnetic induction
The set of unknowns is then evaluated on the criterion of least sum of squared errors, resulting in the following equation:
so that f takes the minimum value
Corresponding unknown quantity
Is the optimal solution of the equation.
Further, in the third step, the optimization process by using the improved intelligent optimization algorithm is as follows:
firstly, initializing to generate an initial population through a good point set, so that the position of the initial population is more uniform;
secondly, adding a particle swarm position updating formula to enhance the information exchange and cooperation mechanism among the particles;
in addition, the probability change and the Levy flight are added, so that a part of particles can change the positions of the particles according to the Levy flight, the activity and the diversity of the particles are enhanced, and the algorithm is prevented from falling into local optimization.
Further, the initial population is generated through the initialization of the good point set, and the specific process is as follows:
suppose GDIs a unit cube of D-dimensional space, assuming r ∈ GDIn the shape of
Deviation of
The set of (c) is called a set of good points, and r is called a good point; wherein C (r, epsilon) is constant and is only related to r, epsilon (epsilon > 0), taking r k1 ≦ k ≦ M where p is the smallest prime number that satisfies (p-D/2) ≧ D, or r k1 ≦ k ≦ M, and { a } is the fractional portion of a; when the calculation function is in GDIn the integration, the error obtained by taking n number of the good points is the smallest relative to the weighted sum formed by the function values of any given n number of the good points.
Further, the adding of the change probability and the Levis flight specifically comprises the following steps:
(1) generating an initial position X by using a good point set initialization method, setting an initial population scale N, a maximum iteration number max _ iter, a population dimension D and a learning coefficient c1,c2The like;
(2) the fitness function is minimized, and the cycle is skipped after the optimal solution, the suboptimal solution and the quarterly optimal solution are obtained by the gray wolf algorithm;
(3) update at each cycle
And
updating the speed and the position according to a position updating formula of a PSO-GWO hybrid algorithm; according to the probability P at the same timecRandomly selecting particles to carry out Levin flight according to 0.5, and jumping out the local optimum according to a position updating formula to update the speed and the position;
(4) judging whether the iteration times are equal to a preset upper limit value or not, and if so, ending the operation; otherwise, jump to (2).
Further, the position update formula of the PSO-GWO hybrid algorithm in (3) is:
the position update formula in (3) is as follows:
by adding change probability PcAnd (0.5), comparing the random number A (rand () set in iteration) at each iteration to judge that the Laey flight strategy is not needed.
It is a further object of the invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of the improved intelligent optimization algorithm based magnetic dipole target localization method.
It is a further object of the present invention to provide a computer readable storage medium, storing a computer program which, when executed by a processor, causes the processor to perform the steps of the improved intelligent optimization algorithm based magnetic dipole target localization method.
The invention further aims to provide an information data processing terminal which is used for realizing the magnetic dipole target positioning method based on the improved intelligent optimization algorithm.
By combining all the technical schemes, the invention has the advantages and positive effects that: the invention selects a mixed algorithm of two intelligent optimization algorithms, namely a particle swarm-wolf mixed optimization algorithm based on Levy flight to research the magnetic dipole target positioning problem based on the improved intelligent optimization algorithm. Aiming at the defect that the particle swarm algorithm and the gray wolf algorithm are easy to fall into local optimization, the improved particle swarm optimization algorithm is provided, and the defect that the particle swarm algorithm and the gray wolf algorithm fall into the local optimization is overcome. The optimization method has the advantages that the initialization of the optimal point set is introduced when the initial population is generated, the diversity and uniformity of the initial population are enhanced, the self-adaptive weight is introduced when the population position is updated so as to meet the optimization requirements of different periods, the vitality and the jumping capacity of the particles of the particle swarm and the gray wolf optimization algorithm can be optimized by adding Levy flight, and the particles can jump out of local optimization.
Drawings
Fig. 1 is a flowchart of a magnetic dipole target positioning method based on an improved intelligent optimization algorithm according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a magnetic dipole model according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a social ranking of a sirius population according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of a two-dimensional population distribution generated by initializing a set of good points according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of a two-dimensional population distribution generated by random initialization according to an embodiment of the present invention.
Fig. 6 is a flowchart of an algorithm provided by an embodiment of the present invention.
Fig. 7 is a schematic diagram of a 1 × 4 node probe array according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of the movement of the target to the position a according to the embodiment of the present invention.
Fig. 9 is a schematic diagram of comparing positioning errors of different algorithms under different signal-to-noise ratios according to an embodiment of the present invention.
FIG. 10 is a graph illustrating the trend of the convergence curves of the three algorithms when the SNR is changed from-5 dB to 35dB at the iteration time of 100 according to the embodiment of the present invention.
In fig. 10: figure a, experiment 1 convergence graph; graph b, experiment 2 convergence graph; fig. c, experiment 3 convergence graph; fig. d, experiment 4 convergence graph; graph e, experiment 5 convergence graph.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a magnetic dipole target positioning method based on an improved intelligent optimization algorithm, and the invention is described in detail below with reference to the accompanying drawings.
The method for positioning a magnetic dipole target based on an improved intelligent optimization algorithm provided by the invention can be implemented by adopting other steps by persons skilled in the art, and the method for positioning a magnetic dipole target based on an improved intelligent optimization algorithm provided by the invention of fig. 1 is only a specific embodiment.
As shown in fig. 1, a magnetic dipole target positioning method based on an improved intelligent optimization algorithm provided by an embodiment of the present invention includes:
s101: describing the magnetic induction intensity of a target by adopting a magnetic dipole model under a far field condition;
s102: constructing a magnetic dipole target positioning nonlinear equation set based on an improved intelligent optimization algorithm;
s103: and optimizing by using an improved intelligent optimization algorithm to realize the magnetic dipole target positioning based on the improved intelligent optimization algorithm.
In S101 provided by the embodiment of the present invention, a specific process of describing the magnetic induction intensity of a target by using a magnetic dipole model under a far-field condition is as follows:
when the distance between the magnetic sensor and the target is more than 2.5 times of the size of the magnetic target, the magnetic target object is regarded as a magnetic dipole;
the target position of the magnetic dipole in the coordinate system is A (x)0,y0,z0) The coordinates of the fluxgate sensor are B (x, y, z), r is the vector from the origin of the magnetic dipole to the magnetic sensor, m is the magnetic moment vector of the magnetic dipole, theta is the geomagnetic inclination angle,
is the magnetic declination.
The magnetic induction intensity B equation generated by the target at the point B is as follows:
in a rectangular coordinate system, developing a magnetic induction intensity B equation to obtain:
wherein mu0A free space permeability of 4 π × 10-7H/m, the above formula is a nonlinear equation system containing 6 unknowns, and at least two measurement points are required to be provided, and six equations are constructed to estimate the unknown parameters of the target; under the actual measurement condition, certain errors exist in the measurement of the magnetic induction intensity value, the result obtained by only depending on the data of two monitoring points is not accurate, in order to reduce the errors, the number of the magnetic sensors needs to be increased, the magnetic sensors are converted into a nonlinear optimization problem, and then an optimization algorithm is utilized to solve the problem.
In S102 provided by the embodiment of the present invention, a magnetic dipole target location nonlinear equation set based on an improved intelligent optimization algorithm is constructed, and the specific process is as follows:
firstly, a set of unknowns is assumed and substituted into the right half of the B equation of the magnetic induction to obtain a set of estimates of the magnetic induction
The set of unknowns is then evaluated on the criterion of least sum of squared errors, resulting in the following equation:
so that f takes the minimum value
Corresponding unknown quantity
Is the optimal solution of the equation.
In S103 provided by the embodiment of the present invention, the optimization process using the improved intelligent optimization algorithm includes:
firstly, initializing to generate an initial population through a good point set, so that the position of the initial population is more uniform;
secondly, adding a particle swarm position updating formula to enhance the information exchange and cooperation mechanism among the particles;
in addition, the probability change and the Levy flight are added, so that a part of particles can change the positions of the particles according to the Levy flight, the activity and the diversity of the particles are enhanced, and the algorithm is prevented from falling into local optimization.
The initial population is generated through the initialization of the good point set, and the specific process is as follows:
suppose GDIs a unit cube of D-dimensional space, assuming r ∈ GDIn the shape of
Deviation of
The set of (a) is called a set of vertices, r is called a vertex; wherein C (r, epsilon) is constant and is only related to r, epsilon (epsilon > 0), taking r k1 ≦ k ≦ M where p is the smallest prime number that satisfies (p-D/2) ≧ D, or r k1 ≦ k ≦ M, and { a } is the fractional part of a. When the calculation function is in GDIn the integration, the error obtained by taking n sweet spots is the smallest relative to the weighted sum of the function values of any given n sweet spots.
The adding of the change probability and the Levy flight comprises the following specific processes:
(1) generating an initial position X by using a good point set initialization method, setting an initial population scale N, a maximum iteration number max _ iter, a population dimension D and a learning coefficient c1,c2The like;
(2) the fitness function is minimized, and the cycle is skipped after the optimal solution, the suboptimal solution and the quarterly optimal solution are obtained by the gray wolf algorithm;
(3) update at each cycle
And
updating the speed and the position according to a position updating formula of a PSO-GWO hybrid algorithm; according to the probability P at the same timecRandomly selecting particles to carry out Levin flight according to 0.5, and jumping out the local optimum according to a position updating formula to update the speed and the position;
(4) and (3) in the case that the iteration stop condition is not reached, updating the speed and the position of the particles according to the third step, then starting the calculation from the second step, and completing the circulation until the termination condition is reached.
The position updating formula of the PSO-GWO hybrid algorithm in the step (3) is as follows:
the position update formula in (3) is as follows:
by adding change probability PcAnd (0.5), comparing the random number A (rand () set in iteration) at each iteration to judge that the Laey flight strategy is not needed.
The technical solution of the present invention will be described in detail with reference to the following specific examples.
1 magnetic dipole target positioning model based on improved intelligent optimization algorithm
1.1 magnetic dipole model
For a magnetic target object, when the distance between the magnetic sensor and the target is more than 2.5 times the size of the magnetic target, the magnetic target object can be considered as a magnetic dipole.
As shown in FIG. 2, the target position of the magnetic dipole in the coordinate system is A (x)0,y0,z0) The coordinates of the fluxgate sensor are B (x, y, z), r is the vector from the origin of the magnetic dipole to the magnetic sensor, m is the magnetic moment vector of the magnetic dipole, and the magnetic induction intensity B generated by the target at the point B is:
in a rectangular coordinate system, the formula (1) is developed to obtain:
wherein mu0A free space permeability of 4 π × 10-7H/m, equation (2) is a nonlinear system of equations containing 6 unknowns, and obviously at least two measurement points are given, so there are at least six equations. However, in the actual measurement situation, there is a certain error in the measurement of the magnetic induction intensity value, and then the result obtained by only relying on the data of two monitoring points is not accurate, and in order to reduce the error, the number of the magnetic sensors is properly increased, and it is assumed that there are 4 magnetic sensors, and the 4 magnetic sensors are converted into a nonlinear optimization problem and then solved by using an optimization algorithm.
1.2 determination of the objective function
For the system of equations in the above section, it can be considered a non-linear least squares problem. First, a set of unknowns is assumed and substituted into the right half of equation (2) to obtain a set of estimates of magnetic induction
The set of unknowns is then evaluated on the criterion of least sum of squared errors, resulting in the following equation:
so that f takes the minimum value
Corresponding unknown quantity
Is the optimal solution of the equation.
2 magnetic dipole target positioning method based on improved intelligent optimization algorithm
2.1 positioning algorithm based on Grey wolf optimization
The gray wolf optimization algorithm is a group intelligent optimization algorithm proposed by Mirjalili et al in 2014. The algorithm is an enlightening algorithm which is provided by simulating the social level and the hunting behavior of the natural wolf group, and the wolf group has a social level system representing the power and the dominance. The system divides the wolf group into α wolf, β wolf, δ wolf, ω wolf, as shown in fig. 3, wherein α wolf is the highest rank wolf group, other wolf needs to obey the command of α wolf, β wolf obeys α wolf and assists α wolf to make decision, δ wolf is the subordinate wolf of β wolf, obeys the command of α wolf and β wolf, ω wolf is the lowest rank wolf to obey the command of other three groups of wolf groups. The wolfsbane colony has the features of hunting, including enclosing, chasing and attacking prey, besides the strict grade.
(1) Surrounding prey
When the gray wolf group finds the prey, the gray wolf can be quickly approached to and surrounded by the prey, and the position of the gray wolf is updated as the following formula (6) (assuming that the search space is d-dimension):
X(t)＝{Xi(t)|i＝1,2,...,d} (4)
X(t+1)＝XP(t)-AD (6)
wherein X (t) represents the t-th generation of ashWolf population position, XP(t) represents the position of the prey of the t-th generation, D represents the distance vector between the wolf population and the prey, and A and C represent coefficient vectors.
A＝2ar1-a (7)
C＝2r2 (8)
In the formulae (7), (8) and (9): r is1，r2Is a uniformly distributed random number from 0 to 1, a is a convergence factor, linearly decreasing from 2 to 0, and max _ iter is the maximum number of iterations.
(2) Hunting article
When hunting, the hunting behavior starts after the gray wolf surrounds the prey, because the α wolf, the β wolf and the δ wolf are more sensitive to the prey, the other gray wolfs will depend on the distance between themselves and the α wolf, the β wolf and the δ wolf, i.e. Dα,Dβ,DδCalculating the step-shifting distances X of the self-heading alpha wolf, beta wolf and delta wolf respectively1,X2,X3And moving towards the inner of the three surrounding rings, and updating the formulas (10), (11) and (12):
X1＝Xα-ADα
X2＝Xβ-ADβ (11)
X3＝Xδ-ADδ
where i ═ 1,2,3, d, X (t +1) represents the location update of the ω wolf.
(3) Attack prey
Hunting articleWhen the movement is stopped, the gray wolf starts to attack the game, and the process is described mathematically as when the value of A is [ -1,1]When the interval is out of range, the search agent searches freely at the current position and the optimal solution of the wolf, and when the value of A is [ -1,1]When the range is within the range, the optimal solution is necessarily found
2.2 positioning Algorithm based on PSO
The PSO algorithm is an optimization algorithm for swarm intelligent random search proposed by foraging behavior of a bird swarm, each particle can be regarded as an individual of a d-dimensional search space, the current position of the particle corresponds to a candidate solution of an optimization nonlinear problem, and the flight process of the particle in the search space is the search process of the individual. The particles, when initialized, have two properties: the position and the speed of the particle in the initialization have an initial speed and a position, the algorithm is iterated every time, and the particle updates the position of the particle according to the experience of the particle and the experience of the adjacent particles and the optimal positions of the particle and the adjacent particles. In addition, each particle has a fitness value corresponding to its own position. Function of degree of adaptation
The smaller the position is, the better the position accuracy is obtained, and the more accurate the positioning is. When the population size is N and the dimension is D, the position of the particle X can be represented as Xi＝(xi1,xi2,...,xid,...,xiD) Wherein x isidRepresenting the d-th component of the i-th dimension, the velocity of the particle X being Vi＝(vi1,vi2,...,vid,...,viD) Wherein v isidThe d-th velocity, the position and velocity of the particle, which represents the i-th dimension, are updated by the following equations (13) (14):
w＝wmax-(t/max_iter)*(wmax-wmin) (15)
wherein j is 1, 2., d,
the extreme values of the individuals are represented,
representing a global extremum, t representing the current number of iterations, c1,c2For learning factors, c is usually set1＝c2＝2，r1，r2The number is a random number which is uniformly distributed from 0 to 1, the formula (15) w is an inertia weight, the larger the weight value is, the stronger the global search capability is, the smaller the value is, the stronger the local search capability is, and the value range is generally (0, 4).
2.3 flight of Levy
Levy flight is a walking method used to describe a random search of the levy distribution. Many studies have shown that in nature many insects and animals behave in accordance with the Levis distribution. The main application of the Rivie flight is a Mantegna algorithm for generating random step length according with the Rivie distribution, and the essence of the method is that the random walk has high probability of large step, so that the diversity of the population can be ensured and the local optimum can be avoided.
The update formula of the position of the levy flight is as follows (16):
in the formula: i is an element of [1,2]Wherein
Is the position of the ith particle at the t-th iteration, which is the initial position,
to representThe position of the location after the update is,
denotes a dot product operation, α denotes a step control amount, Levy (λ) denotes a random search path, and Levy (λ) satisfies the following formula (17):
Levy(λ)～μ＝t-λ,1＜λ≤3 (17)
the step length of the Levy flight belongs to the Levy distribution, and the formula of the step length s is as shown in an expression (18):
wherein, mu and v belong to a normal distribution as follows:
wherein σμ，σvRespectively, the following formulae (21) and (22):
σv＝1 (22)
wherein β is typically 1.5.
2.4 magnetic dipole positioning algorithm based on PSO-GWO mixture
Since the gray wolf population of the gray wolf algorithm follows the command of alpha wolf, beta wolf and delta wolf for hunting, but each individual is independent, useful information is not utilized due to lack of useful information communication between the gray wolf individual and the population, the convergence speed of the algorithm is too low, and the accuracy of the algorithm is not high, the position updating formula in the particle swarm algorithm is introduced into the position updating formula of the gray wolf algorithm, so that the useful information is utilized, and the mixed algorithm has memorability and a cooperation mechanism. In addition, an inertia constant w is introduced to adjust the local optimizing capability and the global optimizing capability of the wolf particle swarm hybrid algorithm, so that the position updating and the wolf distance formula of the hybrid algorithm are as follows (23) (24):
2.5 improved PSO-GWO Algorithm
2.5.1 best Point set initialization
The set of good points is defined as: suppose GDIs a unit cube of D-dimensional space, assuming r ∈ GDIn the shape of
Deviation of
The set of (a) is called a set of good points, and r is called a good point. Wherein C (r, epsilon) is constant and is only related to r, epsilon (epsilon > 0), taking r k1 ≦ k ≦ M where p is the smallest prime number that satisfies (p-D/2) ≧ D, or r k1 ≦ k ≦ M, and { a } is the fractional part of a. Theory proves that when the calculation function is in GDIn the integration, the error obtained by taking n number of the good points is the smallest relative to the weighted sum formed by the function values of any given n number of the good points.
Fig. 4 and 5 show two-dimensional initial population distribution maps of a population size of 100 generated using the best-point set initialization method and the random initialization method, respectively.
As can be seen from the figure, under the condition that 100 points are taken, the optimal point set initialization is more uniform than the population distribution generated by random initialization, and secondly, the population distribution of the optimal point set is irrelevant to the dimension, so that the method can be well adapted to the high-dimensional problem; in addition, the population is obtained each time when the good point set is initializedThe distribution effect is the same, and the stability is high. Thus will GDThe optimal point is mapped to a target solution space, and a more uniform point taking method can be obtained. Because the PSO-GWO hybrid algorithm obtains the optimal solution by the movement of the particles in the solution space, and the local optimum is continuously close to the global optimum through iteration, the algorithm cannot find the global optimum solution if the population is in premature convergence, but the particles can be uniformly distributed in the solution space around the current optimum position of the population through the optimal point set initialization method, the solution space characteristics can be more effectively represented, the initial population keeps good diversity, and the algorithm is prevented from being in the local optimum and finally converges to the global optimum.
2.5.2 Add Individual optimal memory and Levy flights
Since the gray wolf algorithm is easy to fall into local optimum, the distribution of the particles can be improved by adding the experience of individual particle history optimum into GWO algorithm, but the improved PSO-GWO still has the defect of falling into local optimum. The Levy flight combines the search of a short distance and the occasional long-distance step length, can break the aggregation of particles, can improve the activity and the jumping capability of population particles, and fundamentally can improve the defect that the PSO-GWO hybrid algorithm is easy to fall into local optimum. Based on the levitational flight strategy, the position update formula is expressed as the following equation (25):
by adding change probability PcAnd (0.5), comparing the random number A (rand () set in iteration) at each iteration to judge whether the Lewy flight strategy needs to be carried out or not.
The specific steps of the whole improved PSO-GWO algorithm are as follows:
(1) generating an initial position X by using a good point set initialization method, setting an initial population scale N, a maximum iteration number max _ iter, a population dimension D and a learning coefficient c1,c2And the like;
(2) the fitness function is minimized, and the cycle is skipped after the optimal solution, the suboptimal solution and the quarterly optimal solution are obtained by the gray wolf algorithm;
(3) update at each cycle
And
updating the speed and position according to equation (23); according to the probability P at the same timecRandomly selecting particles to carry out Levis flight when the particle size is 0.5, jumping out of the local optimum according to a formula (25), and updating the speed and the position;
(4) judging whether the iteration times are equal to a preset upper limit value or not, and if so, ending the operation; otherwise, jump to (2).
The technical scheme of the invention is described in detail in combination with simulation experiments.
In order to verify the magnetic dipole positioning performance of the PSO-GWO hybrid algorithm based on the Levis flight, a built magnetic dipole target positioning simulation system based on an improved intelligent optimization algorithm is adopted for analysis. As shown in fig. 7, a rectangular coordinate system is established with the sensor node No. 1 as the origin, and the positions of the remaining three magnetic sensors are as shown in fig. 7. Assuming that the magnetic dipole moves to the point a (see fig. 8), giving the position and angle information (see table 1), then substituting into a formula to reversely deduce three-component values of the magnetic induction intensity at each node, taking these coordinate values as the entry parameters of the algorithm, and the parameter estimation accuracy can be measured by the mean square error, where the formula is:
wherein the actual parameter of the magnetic target is assumed to be x, xiFor the estimation of the ith experiment, N is the total number of monte carlo simulations.
The algorithm parameters are set as follows: four magnetic sensors are provided and the positions of the sensors are as shown in the above figure, and the control ranges of the parameters are respectively: x is equal to 0,10],y∈[0,10],z∈[0,10],m∈[0,2000],θ∈[0,π/2],
Learning factor c1＝c2＝c30.5, the parameter of the PSO algorithm is set to c1＝c 22, w is 0.8, the parameters of the PSO-GWO algorithm are set to wmax is 0.9 and wmin is 0.2, where beta in the leigh flight is 1.5, probability of random jump out PcSince the actual sensor measurement data contains noise, the signal-to-noise ratio SNR is set to vary from-5 dB to 35dB every 10dB, the maximum number of iterations max _ iter is 100, and the population size N is 60. The Monte Carlo simulation times are 50, and the root mean square error value is calculated and used for performance comparison of different algorithms.
TABLE 1 parameter values for movement of an object to Point A
The target positioning results obtained by applying the PSO, the GWO and the improved PSO-GWO algorithm provided by the present invention with different signal-to-noise ratios are shown in fig. 9, and it can be seen from fig. 9 that in the case of very low signal-to-noise ratio, the PSO-GWO algorithm can maintain very high accuracy compared with GWO and the PSO algorithm, and when the SNR is 35, the positioning error of the PSO-GWO algorithm can be reduced to 0.01. The solving performance of the PSO-GWO algorithm is better than that of the PSO algorithm and the GWO algorithm no matter the signal-to-noise ratio is low or high.
In addition, fig. 10(a) -10 (e) clearly show the variation trend of the convergence curves of the three algorithms when the signal-to-noise ratio is changed from-5 dB to 35dB at the time of 100 iterations. For each SNR case, the PSO-GWO algorithm has a better convergence speed than the other two algorithms. From the above results, it can be seen that the proposed PSO-GWO is superior to the other two algorithms, both in terms of solution accuracy and convergence speed.
And (4) conclusion: the invention researches a magnetic dipole target positioning method based on an improved intelligent optimization algorithm. The method comprises the steps of initializing a grey wolf particle swarm by using a good point set initialization method, adding a particle cooperation mechanism of a PSO algorithm, improving the utilization rate of the grey wolf algorithm to information, adding change probability and Levy flight to improve the activity of particles and keep the diversity of the particles, enabling the particles to jump out of a local optimal solution, carrying out simulation test under different SNR, comparing with positioning results of the PSO algorithm and GWO algorithm, greatly improving the convergence speed and the solving precision of the improved algorithm, and verifying the effectiveness of improving the PSO-GWO algorithm under the condition of low signal to noise ratio.
It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A magnetic dipole target positioning method based on an improved intelligent optimization algorithm is characterized by comprising the following steps:
step one, describing the magnetic induction intensity of a target by adopting a magnetic dipole model under a far field condition;
constructing a magnetic dipole target positioning nonlinear equation set based on an improved intelligent optimization algorithm;
and step three, optimizing by using an improved intelligent optimization algorithm, and realizing magnetic dipole target positioning based on the improved intelligent optimization algorithm.
2. The method for positioning the magnetic dipole target based on the improved intelligent optimization algorithm according to claim 1, wherein in the step one, the specific process of describing the magnetic induction intensity of the target by using the magnetic dipole model under the far-field condition is as follows:
when the distance between the magnetic sensor and the target is more than 2.5 times of the size of the magnetic target, the magnetic target object is regarded as a magnetic dipole;
the target position of the magnetic dipole in the coordinate system is A (x)0,y0,z0) The coordinates of the fluxgate sensor are B (x, y, z), r is the vector from the origin of the magnetic dipole to the magnetic sensor,
is the magnetic moment vector of the magnetic dipole, m is the target magnetic moment, theta is the geomagnetic inclination angle,
is the magnetic declination. The magnetic induction intensity B generated by the target at the point B; and in a rectangular coordinate system, developing a magnetic induction intensity B equation.
3. The improved intelligent optimization algorithm-based magnetic dipole target positioning method as claimed in claim 2, wherein the magnetic induction intensity B equation generated by the target at the B point is as follows:
4. the improved intelligent optimization algorithm-based magnetic dipole target positioning method according to claim 2, wherein the magnetic induction intensity B equation is developed as follows:
in a rectangular coordinate system, developing a magnetic induction intensity B equation to obtain:
wherein mu0A free space permeability of 4 π × 10-7H/m, the above formula is a nonlinear equation set containing 6 unknowns, and at least two measurement points are required to be provided, six equations are constructed, and the target parameters can be solved; under the actual measurement condition, certain errors exist in the measurement of the magnetic induction intensity value, the result obtained by only depending on the data of two monitoring points is not accurate, in order to reduce the errors, the number of the magnetic sensors needs to be increased, the magnetic sensors are converted into a nonlinear optimization problem, and then an optimization algorithm is utilized to solve the problem.
5. The method for positioning the magnetic dipole target based on the improved intelligent optimization algorithm of claim 1, wherein in the second step, the specific process of constructing the magnetic dipole target positioning nonlinear equation set based on the improved intelligent optimization algorithm comprises the following steps:
first, a set of possible target parameters are substituted into the magnetic dipole model to obtain a set of estimates of the magnetic induction intensity
The set of unknowns is then evaluated on the criterion of least sum of squared errors, resulting in the following equation:
so that f takes the minimum value
Corresponding unknown quantity
Is the optimal solution of the equation.
6. The method for positioning magnetic dipole targets based on the improved intelligent optimization algorithm of claim 1, wherein in the third step, the optimization process by using the improved intelligent optimization algorithm comprises:
firstly, initializing to generate an initial population through a good point set, so that the position of the initial population is more uniform;
secondly, adding a particle swarm position updating formula to enhance the information exchange and cooperation mechanism among the particles;
in addition, the probability change and the Levy flight are added, so that a part of particles can change the positions of the particles according to the Levy flight.
7. The method for positioning the magnetic dipole target based on the improved intelligent optimization algorithm according to claim 6, wherein the specific process of generating the initial population through the initialization of the optimal point set comprises the following steps: gDIs a unit cube of D-dimensional space, assuming r ∈ GDIn the shape of
Deviation of
The set of (a) is called a set of vertices, r is called a vertex; wherein C (r, epsilon) is constant and is only related to r, epsilon (epsilon > 0), taking rk1 ≦ k ≦ M where p is the smallest prime number that satisfies (p-D/2) ≧ D, or rk1 ≦ k ≦ M, and { a } is the fractional portion of a; when the calculation function is in GDWhen the integration is carried out, the error obtained by taking n optimal points is the smallest relative to the weighted sum formed by the function values of any given n points;
the specific process of adding the change probability and the Levy flight is as follows:
(1) generating an initial position X by using a good point set initialization method, setting an initial population scale N, a maximum iteration number max _ iter, a population dimension D and a learning coefficient c1,c2The like;
(2) the fitness function is minimized, and the cycle is skipped after the optimal solution, the suboptimal solution and the quarterly optimal solution are obtained by the gray wolf algorithm;
(3) update at each cycle
And
updating the speed and the position of the population according to a position updating formula of a PSO-GWO hybrid algorithm; according to the probability P at the same timecRandomly selecting particles to carry out Levin flight according to 0.5, and jumping out the local optimum according to a position updating formula to update the speed and the position;
(4) judging whether the iteration times are equal to a preset upper limit value or not, and if so, ending the operation; otherwise, jumping to (2);
the position updating formula of the PSO-GWO hybrid algorithm in the step (3) is as follows:
the position update formula in (3) is as follows:
by adding change probability PcAnd (0.5), comparing the random number A (rand () set in iteration) at each iteration to judge that the Laey flight strategy is not needed.
8. A computer arrangement, characterized in that the computer arrangement comprises a memory and a processor, the memory storing a computer program, which when executed by the processor causes the processor to carry out the steps of the improved intelligent optimization algorithm based magnetic dipole target localization method according to any one of claims 1 to 7.
9. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the improved intelligent optimization algorithm-based magnetic dipole target location method according to any one of claims 1 to 7.
10. An information data processing terminal, characterized in that the information data processing terminal is used for implementing the magnetic dipole target positioning method based on the improved intelligent optimization algorithm of any one of claims 1 to 7.
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