CN115270617B - Underwater constant current element positioning method, system, medium, equipment and terminal - Google Patents
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Abstract
The invention belongs to the technical field of underwater constant current element positioning, and discloses an underwater constant current element positioning method, an underwater constant current element positioning system, an underwater constant current element positioning medium, an underwater constant current element positioning device and an underwater constant current element terminal, wherein a nonlinear equation set of a theoretical value and a measured value is established based on an underwater scalar potential expression generated by a constant current element in a semi-infinite sea area; converting the positioning problem of the constant current element into a solving problem of a nonlinear equation set, establishing an objective function, and converting the solving problem of the equation set into an objective function minimum value optimizing problem; optimizing by utilizing an intelligent optimization algorithm, introducing a parameter self-adaptive strategy and a boundary variation processing mechanism, and establishing a boundary variation self-adaptive differential evolution algorithm; and measuring the underwater scalar potential by using an array sensor, and realizing the positioning of the underwater constant current element by using a boundary variation self-adaptive differential evolution algorithm. The invention can realize the accurate positioning of current elements beyond 8km, lays a foundation for the remote detection and early warning of ship targets, and proves the effectiveness of the method through simulation and experiments.
Description
Technical Field
The invention belongs to the technical field of underwater constant current element positioning, and particularly relates to an underwater constant current element positioning method, an underwater constant current element positioning system, an underwater constant current element positioning medium, an underwater constant current element positioning device and an underwater constant current element positioning terminal.
Background
At present, the detection and positioning of underwater targets such as ships and submarines are always focused on by naval forces of various countries in the world, and at present, inversion calculation is mainly performed on parameters such as positions, intensities, moving speeds and the like by capturing physical field signals such as magnetic fields, sound fields and the like generated by the targets. Under the condition that the technologies of noise reduction, demagnetization and the like are more mature, the detection and positioning of underwater targets are completed by utilizing the underwater electric field to assist the sound field and the magnetic field.
In order to study the underwater electric field characteristics of targets such as ships, submarines and the like, a learner often simplifies the marine environment into an air (insulating medium) -seawater (conductive medium) two-layer layering model. The constant electric field generated by the ships, submarines and the like in the seawater due to corrosion and the like can be understood as that current flows out from one source point and flows into the other sink point, and the current passes through the seawater, so that an underwater electric field is generated. From this mechanism, the field source of a constant electric field can be equivalent to a constant current element. Therefore, the positioning problem of targets such as ships, submarines and the like can be simplified into the positioning problem of constant current elements in semi-infinite sea areas.
At present, a positioning method of constant current elements (also called electric dipoles) in sea water is mostly used for measuring field intensity of an underwater electric field generated by a field source, and then fitting of field source parameters is completed by using a numerical iteration method. For example Lu Xincheng et al have carried out the research work of iteratively fitting the position of an electric dipole source by using the horizontal bisectors of electric fields at two points in seawater, the method is only suitable for quasi-near field (about 2500 m) and horizontal electric dipole positioning, and the equivalent current element direction of the field source is not only the horizontal direction in most cases; the method comprises the steps that (1) Chongqing, zhao Shuang and the like derive a matrix relation from field intensity to field source intensity by using a field distribution matrix expression, further calculate a field source position by using positions of two identical field intensity points, and carry out theoretical deduction only, wherein the size of an applicable space and the noise immunity are not illustrated; the positioning method of the horizontal direct current electric dipole source inverted by the electric field intensity of the Chinese packet et al is also only suitable for positioning the horizontal dipoles within the range of hundreds of meters; du Chuyang et al deduce a transmission matrix of field intensity to field source dipole moment in semi-infinite space, and then measure field intensity of two arbitrary field points to finish inversion of field source parameters.
Such numerical iterative inversion methods have a few short plates: the unknown parameters which can be inverted at the same time are few, and the method depends on initial values and is only suitable for near fields. The existing intelligent optimization algorithm which is rapidly developed can well solve the problem of relying on initial values, such as a method for inverting the position of an electric dipole source by using an N multiplied by N array sensor by Xue Wei and the like, and the problem of relying on initial values is effectively avoided by using a particle swarm algorithm when position iteration is carried out, but the algorithm is not improved enough, so that a plurality of electrode arrays are needed and the positioning range is small (about 10 meters). The equivalent current element of ships, submarines and the like is about hundred ampere meters, scalar potential of tens of nano volts can be generated beyond five kilometers for the current element of hundred ampere meters, the resolution of the current detection electrode can reach the order of magnitude of 10 -9 volts (nV), and the possibility is provided for remote detection and positioning of ships, submarines and the like. With hardware support, the accuracy of positioning is largely determined by the merits of the algorithm. Based on the above, aiming at the problem of remote positioning of constant current elements in any direction in a semi-infinite sea area, a new underwater constant current element positioning method and system are needed to be designed.
Through the above analysis, the problems and defects existing in the prior art are mainly as follows:
(1) The current positioning method of the constant current element or the electric dipole in the sea water is mostly only suitable for positioning the quasi-near field and the horizontal electric dipole, and the equivalent current element direction of the field source is not only the horizontal direction under most conditions.
(2) The current positioning methods of constant current elements or electric dipoles in the sea water are mostly only in principle method level, and the positioning space range and the noise resistance are not further studied.
(3) The existing positioning method of constant current elements or electric dipoles in the seawater mostly adopts a numerical iteration inversion method, and the unknown parameters which can be inverted at the same time are few, and the initial value dependence is strong; an intelligent optimization algorithm is adopted in a small amount, but the algorithm is still in a primary stage, and the algorithm is not improved enough, so that a large number of electrode arrays are needed, the positioning range is small, and the limiting condition is large.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides an underwater constant current element positioning method, an underwater constant current element positioning system, an underwater constant current element positioning medium, an underwater constant current element positioning device and an underwater constant current element positioning terminal, and particularly relates to an underwater constant current element positioning method, an underwater constant current element positioning system, an underwater constant current element positioning medium, an underwater constant current element positioning device and an underwater constant current element positioning terminal based on an improved differential evolution algorithm.
The invention is realized in such a way that the underwater constant current element positioning method comprises the following steps: based on an underwater scalar potential expression generated by a constant current element in a semi-infinite sea area, establishing a nonlinear equation set of a theoretical value and a measured value;
The established nonlinear equation system is utilized to carry out positioning solution of constant current elements, and an objective function is established,
Converting the solving problem of the nonlinear equation set into an objective function minimum optimizing problem; optimizing by using an intelligent optimization algorithm;
introducing a parameter self-adaptive strategy and boundary variation processing, and establishing a boundary variation self-adaptive differential evolution algorithm;
and measuring underwater scalar potential by using an array sensor, and positioning underwater constant current elements by using a boundary variation self-adaptive differential evolution algorithm.
Specifically, the underwater constant current element positioning method comprises the following steps:
step one, establishing a nonlinear equation set of a theoretical value and a measured value based on an underwater scalar potential expression generated by a constant current element in a semi-infinite sea area;
Step two, converting the positioning problem of the constant current element into a solving problem of a nonlinear equation set, establishing an objective function, and converting the solving problem of the nonlinear equation set into a minimum optimizing problem of the objective function;
Step three, optimizing by utilizing an intelligent optimization algorithm, introducing a parameter self-adaptive strategy and a boundary variation processing mechanism, and establishing a boundary variation self-adaptive differential evolution algorithm;
And fourthly, measuring underwater scalar potential by using an array sensor, and realizing the positioning of underwater constant current elements by using a boundary variation self-adaptive differential evolution algorithm.
In the first step, in the semi-infinite sea area, the lower half is the sea area, the conductivity is sigma, the upper half is air, and the permittivity is epsilon; and establishing a space rectangular coordinate system by taking the interface as an xoy plane and taking the vertical downward direction as the positive direction of the z axis, wherein n is the normal vector of the xoy plane unit. Let M 0 in the sea area (position vector R 0＝(x0,y0,z0)) have constant current element, intensity p (p x,py,pz),Μ′0 is symmetry point of M 0 about sea level (position vector R '0＝(x0,y0,-z0)), measuring point M in the sea area, position vector r= (x, y, z), and position vectors relative to M 0 and M' 0 are R and R respectively R′,R＝r-r0＝(x-x0,y-y0,z-z0),R'＝r-r'0＝(x-x0,y-y0,z+z0).
The scalar potential expression generated at M by the current element is found by the mirror method as follows:
wherein, If there is a set u= { M 1,Μ2,...,Μn }, where the position vector of the measurement point M k is R k＝(xk,yk,zk), the position vectors of the relative M 0 and M '0 are R k＝(xk-x0,yk-y0,zk-z0) and R' k＝(xk-x0,yk-y0,zk+z0), respectively, for n different field points (measurement points) in the sea domain, the corresponding scalar potential expression is:
Wherein k=1, 2,3, n. Containing the amperometric parameters, R k and R' k contain the amperometric position parameters (x 0,y0,z0). Now, a system of equations is established:
Further, in the second step, the six parameters p x,py,pz,0x,0 y related to the field source are solved by the nonlinear equation set, so that the problem of positioning the current element is converted into the problem of solving the nonlinear equation set.
In the practical application of the present invention,For the measurement, let:
Taking the modulus value as an objective function:
The solving problem of the nonlinear equation set is converted into the minimum optimizing problem of the objective function, and the constraint condition of p x,py,pz,x0,y0,z0 is defined according to engineering application requirements.
Further, in the third step, the following variables are defined: population number NP, parameter D to be solved, mutation scaling factor F, crossover probability CR and maximum evolution algebra G.
Analyzing a minimum value optimization problem containing D parameters to be solved: let x= [ x 1,x2,...,xi,...,xD]T be the real number vector defined in D-dimensional space, the minimum optimization problem for the D-number of parameters to be solved is to find the optimal solution x best for the vector x for a given objective function H (x), so that the function H (x) reaches a minimum, and each possible solution is called an individual in the population.
For the minimum optimization problem:
minH(x)；
Where x i,min≤xi≤xi,max,xi,min and x i,max are the lower and upper bounds, respectively, of the ith parameter to be solved. The basic differential evolution algorithm (DIFFERENTIAL EVOLUTION, hereinafter DE) solves the following procedure.
At the initial stage, randomly extracting an initial population X 1 containing NP individuals from a search space, wherein the initial population X 1 is represented as follows by a matrix, and the upper right mark represents algebra of the current population;
Where j=1, 2,3,..np represents the j-th individual in the population. DE then enters an evolution cycle, each of which is divided into three steps of mutation, crossover and selection.
(1) Variation: the DE algorithm performs a mutation operation to generate variant individuals, one for each individual in the current populationProducing mutant individuals/>In practice, the DE/rand/1 mutation strategy is chosen and defined as follows:
Wherein k1, k2, k3 are three random integers selected from the set {1,2,.,. NP } that are different from each other and from i; the scaling factor F is a real number within (0, 1), preferably 0.5, for scaling the differential vector
(2) Crossing: in the crossover phase, the DE algorithm generates test individuals according to the following equation
Wherein rang (1) represents a random real number between 0 and 1; jrand denotes an integer randomly selected from the [0, D ] range, which is regenerated before each target individual crosses, jrand is used to ensure thatAt least one parameter ofDifferent.
(3) Selecting: at the position ofAnd test individuals of the next generation/>Better individuals are selected between them. For minimizing optimization problems, the selection operation is defined as follows:
Generating final generation population X G after G generation mutation, crossover and selection operation, and screening out individual with minimum fitness value by using objective function H (X) Each component in the individual is a required parameter.
The parameter adaptive strategy comprises the following steps: the scaling factor F and the crossover rate CR continuously adjust the self according to the mutation success rate so as to optimize the quality of individuals in the current population and enable the individuals in the population to be closer to the optimal solution.
Each individual has its own mutation factor and crossover rate. For individualsThe mutation factor and crossover rate are expressed as F i t and/>, respectivelyThe scale factors and crossover rates of test individuals used to generate the target individuals are represented as NF i t and NF i t, respectivelyIn each generation, NF i t and/>The adjustment of (2) is as follows:
Using modified NF i t and respectively The values complete the variation and crossover of each individual, F i t+1 and/>, associated with each individualThe values of (2) are modified as follows:
According to the adaptive parameter control scheme, the mutation factor and the crossing rate of the algorithm are adaptively adjusted according to the feedback of the searching process. At the same time, randomly selecting an individual in the offspring Performing mutation:
Wherein a 1,a2 and a 3 are real numbers between 0 and 1, and the condition a 1+a2+a3 =1 is satisfied; is the individual with the minimum fitness value in the population; /(I) And/>Representing a random selection from the current population that is different from/>Is a single or two different individuals.
Further, the boundary variation processing mechanism in the third step includes:
The new strategy for variation is:
If the individuals after the two variations still cross the boundary, randomly generating an individual in the solution space to replace the cross-boundary individual; and guiding the child individuals to converge to the vicinity of the optimal solution by using a boundary processing mode so as to obtain a better solution.
The differential evolution algorithm after the parameter adaptive strategy and the boundary variation processing mechanism are introduced is hereinafter referred to as a boundary variation adaptive differential evolution algorithm (boundary variation ADAPTIVE DIFFERENTIAL evolution, BVADE).
Another object of the present invention is to provide an underwater constant current cell positioning system applying the underwater constant current cell positioning method, the underwater constant current cell positioning system comprising:
The nonlinear equation set establishing module is used for establishing a nonlinear equation set of which the theoretical value is related to the measured value based on an underwater scalar potential expression generated by a constant current element in a semi-infinite sea area;
the positioning problem conversion module is used for converting the positioning problem of the constant current element into a solving problem of a nonlinear equation set, establishing an objective function and converting the problem of square equation set solution into an objective function minimum value optimization problem;
the BVADE algorithm construction module is used for optimizing by utilizing an intelligent optimization algorithm, namely, introducing a parameter self-adaptive strategy and a boundary variation processing mechanism to establish a boundary variation self-adaptive differential evolution algorithm;
And the constant current element positioning module is used for measuring underwater scalar potential by using an array sensor and then realizing the positioning of the underwater constant current element by using a boundary variation self-adaptive differential evolution algorithm.
Another object of the present invention is to provide a computer device, the 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 underwater constant current cell positioning method.
Another object of the present invention is to provide a computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the underwater constant current cell positioning method.
Another object of the present invention is to provide an information data processing terminal for implementing the underwater constant current cell positioning system.
In combination with the above technical solution and the technical problems to be solved, please analyze the following aspects to provide the following advantages and positive effects:
first, aiming at the technical problems and the difficulty of solving the problems in the prior art, the technical scheme to be protected, results, data and the like in the research and development process are closely combined, and how to solve the technical problems and some creative technical effects brought after the problems are deeply analyzed in detail. The specific description is as follows:
The invention starts from an underwater scalar potential expression generated by a semi-infinite constant current element, converts the positioning problem of the current element into a solving problem of a nonlinear equation set, establishes an objective function, and further converts the solving problem into an objective function minimum value optimizing problem; on the basis, aiming at the problem that the initial value dependence is strong when the former person is in parameter fitting, a differential evolution algorithm (DE) is proposed to finish positioning; in order to solve the problems that the differential evolution algorithm is easy to fall into a local optimal solution and the global optimal solution has poor convergence, a boundary variation self-adaptive differential evolution algorithm (BVADE) is further provided to obtain a more accurate positioning effect. Simulation and experimental results show that the noise immunity of a positioning algorithm can be greatly enhanced by introducing an operator self-adaptive strategy and a boundary secondary variation processing mechanism, the positioning accuracy is obviously improved, the underwater scalar potential is measured by using an array sensor, and the positioning of the underwater constant current element can be accurately completed by using a BVADE algorithm.
The invention establishes a nonlinear equation set with a theoretical value related to a measured value by means of scalar potential expression generated by a constant current element in a semi-infinite sea area, converts the positioning problem of the current element into a solving problem of the nonlinear equation set, establishes an objective function, converts the problem of the solving of the equation set into an objective function minimum value optimizing problem, and optimizes by utilizing an intelligent optimizing algorithm; through research on a DE algorithm, aiming at the problems that the algorithm falls into a local optimal solution and a global optimal solution and has poor convergence, a parameter self-adaptive strategy and a boundary variation processing mechanism are introduced, a BVADE algorithm is provided, the positioning precision is improved, the noise immunity is enhanced, and the applicability of the method is illustrated through simulation; and finally simulating a semi-infinite conductive medium space and a constant current element in a laboratory, inverting the position parameters through actual measurement potential, and comparing theoretical values to prove the practicability of the method.
Secondly, the technical scheme is regarded as a whole or from the perspective of products, and the technical scheme to be protected has the following technical effects and advantages:
The invention utilizes the array sensor to detect the underwater scalar potential, and then the method for obtaining the current element parameter based on the boundary variation self-adaptive differential evolution algorithm intelligent optimization lays a foundation for the remote detection and early warning of the ship target. The method can realize accurate positioning of current elements beyond 8km, and the effectiveness of the method is proved through simulation and experiments.
Simulation experiment results show that if scalar potential measurement values of the array electrodes can be accurately obtained, the field source positioning can be accurately completed by means of the algorithm of the invention. Meanwhile, the underwater constant current element positioning method provided by the invention also has the application prospect of underwater weapon explosion point control, underwater robot positioning and the like.
Thirdly, as inventive supplementary evidence of the claims of the present invention, the following is also presented: the invention is mainly used for military applications. The method can be used for electric field positioning of underwater targets, so that early warning and striking are carried out on the invasion targets.
The technical scheme of the invention improves the defects of the prior art scheme, improves the positioning precision, expands the positioning range and gradually leads the underwater electric field positioning technology to be practical.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for positioning underwater constant current elements provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of a semi-infinite sea area according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the result of the NSSDE inversion with a signal-to-noise ratio of 30dB provided by the embodiment of the invention;
FIG. 4 is a flowchart of a boundary variation process according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of the result of the BVADE inversion with a signal-to-noise ratio of 30dB provided by the embodiment of the invention;
FIG. 6 is a schematic diagram of an experimental setup provided in an embodiment of the present invention;
FIG. 7 is a schematic representation of laboratory inversion results provided by an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Aiming at the problems existing in the prior art, the invention provides an underwater constant current element positioning method, an underwater constant current element positioning system, an underwater constant current element positioning medium, an underwater constant current element positioning device and an underwater constant current element positioning terminal, and the underwater constant current element positioning method, the underwater constant current element positioning device and the underwater constant current element positioning terminal are described in detail below with reference to the accompanying drawings.
1. The embodiments are explained. In order to fully understand how the invention may be embodied by those skilled in the art, this section is an illustrative embodiment in which the claims are presented for purposes of illustration.
As shown in fig. 1, the underwater constant current element positioning method provided by the embodiment of the invention comprises the following steps:
S101, establishing a nonlinear equation set of a theoretical value and a measured value based on an underwater scalar potential expression generated by a constant current element in a semi-infinite sea area;
S102, converting a positioning problem of a constant current element into a solving problem of a nonlinear equation set, establishing an objective function, and converting a problem of a square equation set solution into a minimum value optimizing problem of the objective function;
s103, optimizing by utilizing an intelligent optimization algorithm, introducing a parameter self-adaptive strategy and a boundary variation processing mechanism, and establishing a boundary variation self-adaptive differential evolution algorithm;
S104, measuring underwater scalar potential by using an array sensor, and realizing positioning of underwater constant current elements based on a boundary variation self-adaptive differential evolution algorithm.
The invention introduces a self-adaptive strategy and a boundary crossing secondary variation mechanism to improve the differential evolution algorithm, and provides a boundary variation self-adaptive differential evolution algorithm (BVADE) to enhance the searching capability and convergence of the algorithm and make up for a numerical iteration method and a short plate of a common intelligent optimization algorithm. The underwater constant current element positioning method provided by the embodiment of the invention specifically comprises the following steps:
1. Problem model
The basic idea of the method is to convert the constant current element positioning problem into a solving problem of a nonlinear equation set and further into an objective function minimum value optimization problem based on BVADE algorithm.
In the semi-infinite sea area shown in fig. 2, the lower half is sea area, the conductivity is sigma, the upper half is air, and the permittivity is epsilon; and establishing a space rectangular coordinate system by taking the interface as an xoy plane and taking the vertical downward direction as the positive direction of the z axis, wherein n is the normal vector of the xoy plane unit. Let M 0 in the sea area (position vector R 0＝(x0,y0,z0)) have constant current element, intensity p (p x,py,pz),Μ′0 is symmetry point of M 0 about sea level (position vector R '0＝(x0,y0,-z0)), measuring point M in the sea area, position vector r= (x, y, z), and position vectors relative to M 0 and M' 0 are R and R respectively R′,R＝r-r0＝(x-x0,y-y0,z-z0),R'＝r-r'0＝(x-x0,y-y0,z+z0).
The scalar potential expression generated at M by the current element is found by the mirror method as follows:
Wherein q=diag (1, -1). If there is a set u= { M 1,Μ2,...,Μn }, where the position vector of the measurement point M k is R k＝(xk,yk,zk), the position vectors of the relative M 0 and M '0 are R k＝(xk-x0,yk-y0,zk-z0) and R' k＝(xk-x0,yk-y0,zk+z0), respectively, for n different field points (measurement points) in the sea domain, the corresponding scalar potential expression is:
Where k=1, 2,3,..n. p= (p x,py,pz) contains the current element strength parameter, R k and R' k contain the current element position parameter (x 0,y0,z0). Now, a system of equations is established:
The six parameters p x,py,pz,x0,y0,z0 related to the field source are solved by the step (3), so that the positioning problem of the current element is converted into the solving problem of the nonlinear equation system.
In the practical application of the present invention,For the measurement, let:
Taking the modulus value as an objective function:
The solving problem of the nonlinear equation set (3) is converted into the minimum optimizing problem of the objective function (4), and the constraint condition of p x,py,pz,x0,y0,z0 is defined according to engineering application.
2. Improved differential evolution algorithm
2.1 Basic DE algorithm
The DE algorithm is an intelligent optimization algorithm based on population, proposed by American scholars Rainer and Storn Kennethprice in 1995, adopts mutation, crossover and selection operation to simulate gene mutation in the biological evolution process, and reserves highly adaptive individuals to obtain an optimal solution, and has the characteristics of simple coding, good convergence and strong robustness.
The following variables are first defined: population number NP, parameter D to be solved, mutation scaling factor F, crossover probability CR and maximum evolution algebra G.
Consider a minimum optimization problem that contains D parameters to be solved: let x= [ x 1,x2,...,xi,...,xD]T be the real number vector defined in D-dimensional space, the minimum optimization problem of the D-number of parameters to be solved is to find the optimal solution x best of the vector x for a given objective function H (x) so that the function H (x) reaches the minimum. And each possible solution is called an individual in the population.
For the minimum optimization problem:
minH(x)；
where x i,min≤xi≤xi,max,xi,min and x i,max are the lower and upper bounds, respectively, of the ith parameter to be solved. The basic DE algorithm solving flow is as follows.
In the initial stage, an initial population X 1 (the superscript right representing the algebra of the current population) containing NP individuals is randomly extracted from the search space and represented by a matrix as follows:
Where j=1, 2,3,..np represents the j-th individual in the population. The DE then enters an evolution cycle, each of which is divided into three steps of mutation, crossover and selection.
The first step is mutation. The DE algorithm performs a mutation operation to generate variant individuals, specifically, for each individual in the current populationProducing mutant individuals/>In practice, a number of mutation strategies can be chosen, of which DE/rand/1 is the most widely used strategy, defined as follows:
Where k1, k2, k3 are three random integers selected from the set {1,2,..np } which are different from each other and from i. The scaling factor F is a real number within (0, 1) for scaling the differential vector In this strategy, 0.5 is typically taken.
The second step is the crossover. In the crossover phase, the DE algorithm generates test individuals according to the following equation
Wherein rang (1) represents a random real number between 0 and 1; jrand represents an integer randomly selected from the [0, D ] range, which is regenerated before each target individual crossing, jrand is used to ensureAt least one parameter and/>Different.
The third step is the selection, i.e. inAnd test individuals of the next generation/>Better individuals are selected between them. For minimizing optimization problems, the selection operation is defined as follows:
Generating final generation population X G after G generation mutation, crossover and selection operation, and screening out individual with minimum fitness value by using objective function H (X) Each component in the individual is the required parameter. Because the initial population is selected with randomness and global property, the algorithm overcomes the problem that many iterative algorithms rely on initial values. However, in general, the objective function has multiple extreme points, so that the computer easily falls into a locally optimal solution during the searching process, and the deviation between the result and the theoretical value is large, which is a limitation of the basic DE algorithm, and the problem needs to be solved starting from the parameter adaptive link, and a parameter adaptive strategy is provided herein, specifically as follows.
2.2 Parameter adaptive strategy
The scaling factor F and the crossing rate CR are extremely important control parameters of the DE algorithm, and the advantages and disadvantages of the algorithm performance are largely determined by the control parameters. In order to ensure that the algorithm still has better convergence and accuracy when dealing with complex objective functions with multiple extrema, a new parameter self-adaptive strategy is provided, and the core idea is that F and CR continuously adjust themselves according to mutation success rate so as to optimize the quality of individuals in the current population and enable the individuals in the population to be closer to an optimal solution. The specific operation is as follows.
Each individual has its own mutation factor and crossover rate. For individualsThe mutation factor and crossover rate are expressed as F i t and/>, respectivelyThe scale factors and crossover rates of test individuals used to generate the target individuals are represented as NF i t and NF i t, respectivelyIn each generation, NF i t and/>The adjustment of (2) is as follows:
Using modified NF i t and respectively The values complete the variation and crossover for each individual. Furthermore, F i t+1 and/>, associated with each individualThe values of (2) are modified as follows:
according to the adaptive parameter control scheme, the mutation factor and the crossing rate of the algorithm can be adaptively adjusted according to the feedback of the searching process.
At the same time, in order to increase the convergence rate, a body is randomly selected from the offspringThe mutation is carried out by the following specific method:
Wherein a 1,a2 and a 3 are real numbers between 0 and 1, and the condition a 1+a2+a3 =1 is satisfied; is the individual with the minimum fitness value in the population; /(I) And/>Representing a random selection from the current population that is different from/>Is a single or two different individuals. The searching strategy is used for improving the population quality by utilizing the information of the optimal individuals in the current population so as to accelerate the convergence rate.
2.3 Boundary variation handling mechanism
In the DE algorithm, a common boundary processing method is a boundary absorption method or a random regeneration process. The first method is relatively simple to process, if overflow individuals are more, offspring are easy to gather towards boundaries, searching of an optimal solution is affected, and the second method is too strong in randomness, and algorithm convergence is affected. In order to further enhance the convergence of the global optimal solution, a boundary variation processing mechanism is added in parameter self-adaptive algorithm iteration, and a BVADE algorithm is provided.
The BVADE algorithm provides a new boundary processing method, and the method is performed on individuals exceeding the search boundary, and then two mutation opportunities are completed, if the individuals still exceed the boundary, the individuals are randomly generated in the solution space to replace, so that the aggregation of the individuals to the boundary is avoided, and the randomness of the processing is reduced. The new strategy for variation is:
if the individuals after the two variations still cross the boundary, randomly generating an individual in the solution space to replace the cross-boundary individual.
The specific flow is shown in fig. 4.
Such a boundary processing approach may guide the child individuals to converge near the optimal solution to obtain a more optimal solution.
The underwater constant current element positioning system provided by the embodiment of the invention comprises:
The nonlinear equation set establishing module is used for establishing a nonlinear equation set of which the theoretical value is related to the measured value based on an underwater scalar potential expression generated by a constant current element in a semi-infinite sea area;
the positioning problem conversion module is used for converting the positioning problem of the constant current element into a solving problem of a nonlinear equation set, establishing an objective function and converting the problem of square equation set solution into an objective function minimum value optimization problem;
The BVADE algorithm construction module is used for optimizing by utilizing an intelligent optimization algorithm, introducing a parameter self-adaptive strategy and a boundary variation processing mechanism, and providing a boundary variation self-adaptive differential evolution algorithm;
And the constant current element positioning module is used for measuring underwater scalar potential by using an array sensor and realizing the positioning of the underwater constant current element by using a boundary variation self-adaptive differential evolution algorithm.
2. Evidence of the effect of the examples. The embodiment of the invention has a great advantage in the research and development or use process, and has the following description in combination with data, charts and the like of the test process.
1. Comparison with simulation results of existing algorithms
In the invention, in order to improve the convergence of the global optimal solution of the differential evolution algorithm, a boundary variation mechanism is further introduced, and finally, a boundary variation self-adaptive differential evolution algorithm (BVADE) is formed so as to obtain a more accurate positioning effect. In order to judge the improved algorithm effect, the simulation comparison is particularly carried out on the positioning effect of the global neighborhood search differential positioning algorithm (self-ADAPTIVE DIFFERENTIAL evolution with globe neighborhood search, NSSDE hereinafter) under the same condition. The NSSDE algorithm is a parameter self-adaptive differential evolution algorithm without introducing a boundary variation mechanism.
It is assumed that an array sensor is used to perform positioning simulation on a constant current element at the open sea, as follows.
In the semi-infinite sea area shown in fig. 3, it is assumed that there is a group of 1×10 array measuring electrode sensors near the origin, the ordinate interval is 300m, the abscissa is randomly generated in the (0, 300) m range, the placement depth range (measuring point z coordinate range) is (80, 100) m, and the electrode layout is mainly array, but has a certain randomness; the constant current element is positioned at P (7400,2800,150) m, is about 3 times as long as the arrangement length of the electrode array from the center of the measuring electrode array, has intensity of (60,80,10) A.m and is used for simulating an equivalent field source for generating a stable and constant electric field by a ship; seawater conductivity was taken to be σ=3.0S/m. Scalar potential of the current element at 10 measuring electrodes can be obtained according to the formula (1), the simulation uses the obtained scalar potential value plus random noise with a certain signal-to-noise ratio as a measured value, and the signal-to-noise ratio S is defined as follows:
wherein, Is the theoretical average value of 10 electrode potentials,/>Is the noise amplitude. Then 50 inversions were completed by NSSDE algorithm, the result is shown in FIG. 3, average position/>Average intensity size/>Positional deviation/>And intensity deviation/>The results are shown in Table 1.
Table 1 NSSDE algorithm simulation test results
As can be seen from the data in Table 1, the error of the inversion result is smaller and is 1.22% when no noise exists by using NSSDE algorithm, but as the noise intensity increases, the positioning error obviously increases and exceeds 10%, which indicates that the noise immunity of the algorithm is poor; the intensity deviation of the current element is smaller when no noise exists, and the error is larger when the noise is larger than 40dB, and the intensity of the current element is of great significance for the identification of the ship size, so that only the intensity is subjected to error analysis, and the direction error is not analyzed.
As can be seen from fig. 3, after adding 30dB noise, the inversion point is scattered far from the theoretical position, so that the positioning error is larger, which means that the algorithm convergence is weaker, therefore, the NSSDE algorithm positioning accuracy is greatly affected by noise, and the noise immunity is poor.
And under the same condition, the simulation positioning is performed based on BVADE algorithm, and the noise intensity is increased to be larger. The average of 50 inversion results is recorded as shown in table 2.
Table 2 BVADE algorithm simulation test results
The s=30 dB inversion provided by the embodiment of the invention (BVADE) is shown in fig. 5.
As can be seen from table 2, after the boundary variation processing mechanism is introduced, the noise immunity and positioning accuracy of the algorithm are obviously improved, and the algorithm is obtained through data analysis: ① When the noise is below 20dB, the positioning error is smaller and reaches within 5% by using the method; ② The intensity deviation of the current element is smaller and reaches within 5 percent. This shows that if the scalar potential measurement value of the array electrode can be obtained more accurately, the accurate positioning of the constant current element in the semi-infinite sea area can be completed by combining BVADE algorithm with the array electrode.
2. Experiment verification
In order to examine the practicability of completing constant current element positioning by using an array type measuring electrode and BVADE algorithm, a positioning experiment is carried out in a laboratory. Brine (sigma=1.7S/m, depth 0.5 m) is contained in a hard plastic cuboid water tank (size is 2.2mx1.5mx0.8m) to simulate an air-seawater two-layer parallel layered medium space, a pair of platinum sheet electrodes are used for simulating current elements, scalar potential of 10 positions on a certain depth plane in seawater is measured, and then the positions and the intensities of the current elements are inverted, so that the feasibility of the inversion method is proved.
Fig. 6 is a schematic layout of the experimental apparatus. The intersection point of the diagonal lines of the liquid level is taken as an origin, the liquid level is an xoy plane, the vertical downward direction is the positive direction of the z axis, and the x axis and the y axis are respectively parallel to the two walls of the water tank, so that a rectangular coordinate system is established. A pair of platinum sheet surfaces were placed parallel to the x-axis with a center point line parallel to the x-axis, a spacing of 0.015m, and a constant current i=500 mA was applied to simulate a field source. The scalar potential of 10 positions was measured using a solid Ag-AgCl measurement electrode, with a spacing of about 5-7 cm per dot. The measurements were collected with a digital memory recorder.
In order to reduce boundary influence caused by the tank wall, the current element and the measuring plane are far away from the tank wall as far as possible and are close to the liquid level. The current element position in the experiment is P 0 (0,0,0.13) m; the measurement position selects 5 positions on two lines of z=0.266 m, y=0.3 m and y=0.25 m on the depth plane. The average was taken over 50 inversions and the results are shown in table 3 and fig. 7.
Table 3 BVADE algorithm inversion experiment results
The positioning error in a laboratory by using the method is calculated to be 4.08%, and the intensity error of the current element is calculated to be 3.04%. Considering errors in electrode size, spatial position measurement and the like in experiments and the influence of background noise, the experimental result can be considered to be more consistent with the theoretical result, and the practicability of inverting the position of the constant current element by using the array electrode and BVADE algorithm can be illustrated.
It should be noted that the embodiments of the present invention can be realized in 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 special purpose design hardware. Those of ordinary skill 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 as provided on a carrier medium such as a magnetic disk, CD or DVD-ROM, a programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present invention and its modules may be implemented by hardware circuitry, such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., as well as software executed by various types of processors, or by a combination of the above hardware circuitry and software, such as firmware.
The above description is merely illustrative of the embodiments of the present invention, and the present invention is not limited thereto, but any modifications, equivalents, improvements and modifications made by those skilled in the art within the scope of the present invention disclosed herein, are intended to be included within the scope of the present invention.
Claims (9)
1. The underwater constant current element positioning method is characterized by comprising the following steps of:
Based on an underwater scalar potential expression generated by a constant current element in a semi-infinite sea area, establishing a nonlinear equation set of a theoretical value and a measured value; the established nonlinear equation system is utilized to carry out positioning solution of constant current elements, and an objective function is established,
Converting the solving problem of the nonlinear equation set into an objective function minimum optimizing problem; optimizing by utilizing an intelligent optimization algorithm, introducing a parameter self-adaptive strategy and boundary variation processing, and establishing a boundary variation self-adaptive differential evolution algorithm;
measuring underwater scalar potential by using an array sensor, and positioning underwater constant current elements by using a boundary variation self-adaptive differential evolution algorithm;
in optimizing the optimized objective function by using the intelligent optimization algorithm, the following variables are defined: population number NP, parameter D to be solved, mutation scaling factor F, crossover probability CR and maximum evolution algebra G;
analyzing a minimum value optimization problem containing D parameters to be solved: let x= [ x 1,x2,...,xi,...,xD]T be the real number vector defined in D-dimensional space, the minimum optimization problem of the D-number of parameters to be solved is to find the optimal solution x best of the vector x for a given objective function h (x), so that the function h (x) reaches the minimum, and each possible solution is called an individual in the population;
for the minimum optimization problem:
minΗ(x)；
Wherein, x i,min≤xi≤xi,max,xi,min and x i,max are the lower bound and the upper bound of the ith parameter to be solved respectively; the basic DE algorithm solving flow is as follows;
At the initial stage, randomly extracting an initial population X 1 containing NP individuals from a search space, wherein the initial population X 1 is represented as follows by a matrix, and the upper right mark represents algebra of the current population;
Where j=1, 2,3,..np represents the j-th individual in the population; DE enters an evolution cycle, each cycle being divided into three steps of variation, crossover and selection;
(1) Variation: the DE algorithm performs a mutation operation to generate variant individuals, one for each individual in the current population Producing mutant individuals/>In practice, a number of mutation strategies were chosen, of which DE/rand/1 is the most widely used strategy, defined as follows:
Wherein k1, k2, k3 are three random integers selected from the set {1,2,.,. NP } that are different from each other and from i; the scaling factor F is a real number within (0, 1), 0.5 is taken for scaling the differential vector
(2) Crossing: in the crossover phase, the DE algorithm generates test individuals according to the following equation
Wherein rang (1) represents a random real number between 0 and 1; jrand denotes an integer randomly selected from the [0, D ] range, which is regenerated before each target individual crosses, jrand is used to ensure thatAt least one parameter and/>Different;
(3) Selecting: at the position of And test individuals of the next generation/>Selecting better individuals; for minimizing optimization problems, the selection operation is defined as follows:
Generating final generation population X G after G generation mutation, crossover and selection operation, and screening out individuals with minimum fitness value by using an objective function H (X) Each component in the individual is a sought parameter;
The parameter adaptive strategy comprises the following steps: the scaling factor F and the crossing rate CR continuously adjust the self according to the mutation success rate so as to optimize the quality of individuals in the current population and enable the individuals in the population to be more close to the optimal solution;
each individual has its own mutation factor and crossover rate; for individuals The mutation factor and crossover rate are expressed as F i t and/>, respectivelyThe scale factors and crossover rates of test individuals used to generate the target individuals are expressed as NF i t and/>, respectivelyIn each generation, NF i t and/>The adjustment of (2) is as follows:
Using modified NF i t and respectively The values complete the variation and crossover of each individual, F i t+1 and/>, associated with each individualThe values of (2) are modified as follows:
according to the self-adaptive parameter control scheme, the mutation factor and the crossing rate of an algorithm are self-adaptively adjusted according to feedback of a searching process; at the same time, randomly selecting an individual in the offspring Performing mutation:
Wherein a 1,a2 and a 3 are real numbers between 0 and 1, and the condition a 1+a2+a3 =1 is satisfied; is the individual with the minimum fitness value in the population; /(I) And/>Representing a random selection from the current population that is different from/>Is a single or two different individuals.
2. The underwater constant current cell positioning method as claimed in claim 1, wherein in a semi-infinite sea area, a lower half is a sea area, conductivity is σ, an upper half is air, and permittivity is ε; establishing a space rectangular coordinate system by taking the interface as an xoy plane and taking the vertical downward direction as the positive direction of the z axis, wherein n is the unit normal vector of the xoy plane; let M 0 in sea area have constant current element, the intensity is p (p x,py,pz),Μ′0 is symmetry point of M 0 about sea level, the measuring point M is in sea area, the position vector is r= (x, y, z), the position vectors relative to M 0 and M' 0 are R and R respectively R′,R＝r-r0＝(x-x0,y-y0,z-z0),R'＝r-r'0＝(x-x0,y-y0,z+z0).
3. The underwater constant current cell positioning method as claimed in claim 2, wherein the scalar potential expression generated at M of the current cell is found by a mirror image method as follows:
Wherein q=diag (1, -1); if there is a set u= { M 1,Μ2,...,Μn }, where the position vector of the measurement point M k is R k＝(xk,yk,zk), the position vectors of the relative M 0 and M' 0 are R k＝(xk-x0,yk-y0,zk-z0) and R k′＝(xk-x0,yk-y0,zk+z0), the corresponding scalar potential expression is:
Wherein k=1, 2,3,; p= (p x,py,pz) contains the current element strength parameter, R k and R k' contain the current element position parameter (x 0,y0,z0); now, a system of equations is established:
4. The underwater constant current element positioning method as claimed in claim 1, wherein in the positioning solution of the constant current element by using the established nonlinear equation set, six parameters p x,py,pz,x0,y0,z0 related to the field source are solved by the equation set, and the positioning problem of the current element is converted into the solving problem of the nonlinear equation set;
in the practical application of the present invention, For the measurement, let:
Taking the modulus value as an objective function:
The solving problem of the nonlinear equation set is converted into a minimum optimizing problem of the objective function, and the constraint condition of p x,py,pz,x0,y0,z0 is defined according to engineering application.
5. The method for positioning an underwater constant current cell according to claim 2, wherein the boundary variation processing comprises:
The new strategy for variation is:
If the individuals after the two variations still cross the boundary, randomly generating an individual in the solution space to replace the cross-boundary individual; and guiding the child individuals to converge to the vicinity of the optimal solution by using a boundary processing mode so as to obtain a better solution.
6. An underwater constant current cell positioning system applying the underwater constant current cell positioning method as claimed in any one of claims 1 to 5, characterized in that the underwater constant current cell positioning system comprises:
The nonlinear equation set establishing module is used for establishing a nonlinear equation set of which the theoretical value is related to the measured value based on an underwater scalar potential expression generated by a constant current element in a semi-infinite sea area;
the positioning problem conversion module is used for converting the positioning problem of the constant current element into a solving problem of a nonlinear equation set, establishing an objective function and converting the solving problem of the equation set into an objective function minimum value optimization problem;
The BVADE algorithm construction module is used for optimizing by utilizing an intelligent optimization algorithm, introducing a parameter self-adaptive strategy and a boundary variation processing mechanism, and establishing a boundary variation self-adaptive differential evolution algorithm;
And the constant current element positioning module is used for measuring underwater scalar potential by using an array sensor and realizing the positioning of the underwater constant current element by using a boundary variation self-adaptive differential evolution algorithm.
7. 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 underwater constant current cell positioning method as claimed in any one of claims 1 to 5.
8. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the underwater constant current cell positioning method according to any one of claims 1 to 5.
9. An information data processing terminal, characterized in that the information data processing terminal is adapted to implement an underwater constant current cell positioning system as claimed in claim 6.
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