CN114065512B - NSGA-II algorithm-based induction magnetometer coil parameter multi-objective optimization method - Google Patents
NSGA-II algorithm-based induction magnetometer coil parameter multi-objective optimization method Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 16
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 claims abstract description 15
- 230000004907 flux Effects 0.000 claims abstract description 12
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- 239000010949 copper Substances 0.000 claims description 5
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- 238000003199 nucleic acid amplification method Methods 0.000 claims description 4
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Abstract
The invention relates to an induction magnetometer coil parameter multi-objective optimization method based on NSGA-II algorithm, which comprises the following steps: A. taking the copper wire diameter, the magnetic core length, the magnetic flux collector diameter and the coil turns of the induction magnetometer as decision variables, and determining constraint conditions of the decision variables; B. establishing a multi-objective optimization model with minimum weight and minimum noise at 1Hz as optimization targets; C. defining individual dominance relations in the evolved population; D. and solving the multi-objective optimization model by adopting a multi-objective optimization algorithm NSGA-II to realize optimization. According to the NSGA-II algorithm-based multi-objective optimization method for the coil parameters of the induction magnetometer, the coil parameters of the induction magnetometer can be reasonably calculated, and the weight and the noise level of the probe can be simultaneously optimized.
Description
Technical Field
The invention belongs to the technical field of induction magnetometers, and particularly relates to an induction magnetometer coil parameter multi-objective optimization method based on an NSGA-II algorithm.
Background
The induction magnetometer converts the changed magnetic signals into changed electric signals according to Faraday electromagnetic induction law, and outputs the changed electric signals through an amplifying circuit to be used for measuring information in a specific frequency band. Because of its application in seismic precursor monitoring, special demands are placed on its weight and noise level. Therefore, in order to ensure the working performance, the coil parameters of the induction magnetometer need to be optimally designed.
The weight and the noise level of the induction magnetometer are two mutually restricted variables, and when the induction magnetometer has a lower noise level, the induction magnetometer can bring about larger weight; as the weight changes to a smaller one, the noise level also changes to a greater trend. The research shows that the multi-objective optimization can reasonably calculate the coil parameters of the induction magnetometer, and the weight and the noise level of the probe can be simultaneously optimized. If a multi-target optimization method for the coil parameters of the induction magnetometer can be developed, the induction magnetometer has wide application prospect and potential application value.
Disclosure of Invention
The invention aims to provide an induction magnetometer coil parameter multi-objective optimization method based on NSGA-II algorithm, so as to solve the problem of reasonably calculating the coil parameter of the induction magnetometer, and simultaneously optimize the weight and the noise level.
The invention aims at realizing the following technical scheme:
An induction magnetometer coil parameter multi-objective optimization method based on NSGA-II algorithm comprises the following steps:
A. taking the copper wire diameter, the magnetic core length, the magnetic flux collector diameter and the coil turns of the induction magnetometer as decision variables, and determining constraint conditions of the decision variables;
B. establishing a multi-objective optimization model with minimum weight and minimum noise at 1Hz as optimization targets;
C. defining individual dominance relations in the evolved population;
D. And solving the multi-objective optimization model by adopting a multi-objective optimization algorithm NSGA-II to realize optimization.
Further, in step B, the multi-objective optimization model is characterized by minimizing a first objective function and a second objective function, and the built multi-objective optimization model is:
minf(1)＝G(dcu,l,D,N)
minf(2)＝NEMI1Hz(dcu,l,D,N) (1)
The constraint conditions are as follows:
In the formula (1), f (1) is a weight calculation formula of the induction magnetometer, f (2) is an equivalent noise level calculation formula of the induction magnetometer under 1Hz, D cu, l, D and N are decision variables respectively representing the diameter of a copper wire, the length of a magnetic core, the diameter of a magnetic flux collector and the number of turns of a coil.
Further, f (1) is represented by formula (3):
Where ρ w is the density of copper wire, ρ p is the density of permalloy, d w＝dcu+2ti,ti is the thickness of copper wire insulation layer, d 0 is the magnetic flux collector thickness, t is the hollow core thickness (difference between inner and outer diameters), and d is the outer diameter of the hollow core.
Further, f (2) is represented by formula (4):
Wherein e n is pre-amplification circuit short-circuit voltage noise, i n is pre-amplification circuit current noise, R is resistance of an induction coil of the induction magnetometer, L is induction coil inductance, ω=2pi f, f is 1Hz, e R is induction coil thermal noise, and μ a is effective magnetic permeability of a magnetic core.
Further, the calculation formula of R is as formula (5):
further, the calculation formula of L is as formula (6):
Further, the calculation formulas of e R are formula (7), formula (8) and formula (9):
T＝1.37×10-23J/K (8)
k＝249 (9)。
further, the calculation formula of μ a is formulas (10), (11) and (12):
further, step D, the specific steps are as follows:
D1, initializing variable information of copper wire diameter, magnetic core length, magnetic flux collector diameter and coil turn number, and setting evolution algebra gen=1;
d2, judging whether a first generation sub population is generated, and if so, enabling an evolution algebra Gen=2; otherwise, non-dominant ordering and selection are carried out on the initial population, gaussian intersection and mutation are carried out, so that a first generation sub population is generated, and the evolution algebra Gen=2;
d3, merging the parent population and the offspring population into a new population;
D4, judging whether a new parent population is generated, if not, calculating an objective function of an individual in the new population, and executing operations such as rapid non-dominant sorting, congestion degree calculation, elite strategy and the like to generate the new parent population; otherwise, entering the next step;
d5, selecting, crossing and mutating the generated parent population to generate a child population;
d6, judging whether Gen is equal to the maximum evolution algebra, if not, the evolution algebra Gen=Gen+1 and returning to the step D3; otherwise, outputting the optimization result, and ending the algorithm operation.
Compared with the prior art, the invention has the beneficial effects that:
The multi-objective optimization method for the coil parameters of the induction magnetometer based on the NSGA-II algorithm can reasonably calculate the coil parameters of the induction magnetometer, and achieves the purposes of meeting the minimum weight requirement and achieving lower equivalent noise level.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 shows an induction magnetometer coil parameter multi-objective optimization method based on NSGA-II algorithm.
Detailed Description
The present invention will be further described with reference to specific examples, which are given in detail on the basis of the present technology, but the scope of the present invention is not limited to the following examples.
The invention provides an induction magnetometer coil parameter multi-objective optimization method based on NSGA-II algorithm, which comprises the following steps:
Step 1, the aim of seeking the minimum weight and the minimum noise of the induction magnetometer is converted into an optimization problem comprising two targets by utilizing the optimization idea: minimizing the weight of the induction magnetometer and minimizing NEMI (equivalent noise level) of the induction magnetometer at 1 Hz.
And 2, establishing a multi-objective optimization model of the corresponding induction magnetometer, wherein the multi-objective optimization model is characterized by minimizing a first objective function and a second objective function.
And 3, defining individual dominance relations in the evolution population.
And 4, solving the induction magnetometer multi-objective optimization model obtained in the step 3 by adopting a multi-objective optimization algorithm NSGA-II.
The embodiment of the invention provides an NSGA-II-based induction magnetometer coil parameter multi-objective optimization method, which optimizes the weight and noise level of an induction magnetometer by applying the idea of multi-objective optimization. The solving deficiency of the traditional method is overcome by utilizing the multi-objective optimization method, and meanwhile, the multi-objective optimization method can ensure that the noise level is minimum under the condition of minimum weight.
In the embodiment of the invention, the induction magnetometer multi-objective optimization model established in the step 2 is as follows:
minf(1)＝G(dcu,l,D,N)
minf(2)＝NEMI1Hz(dcu,l,D,N) (1)
The constraint condition is that
In the formula (1), f (1) is a weight calculation formula of the induction magnetometer, f (2) is an equivalent noise level calculation formula of the induction magnetometer under 1Hz, D cu, l, D and N are decision variables respectively representing the diameter of a copper wire, the length of a magnetic core, the diameter of a magnetic flux collector and the number of turns of a coil.
The formula of the induction magnetometer weight G is shown in formula (3), and the induction magnetometer weight G can be divided into 3 parts, namely copper wire weight, magnetic flux collector weight and hollow magnetic core weight, wherein ρ w is the density of copper wires, ρ p is the density of permalloy, d w＝dcu+2ti,ti is the thickness of a copper wire insulating layer, d 0 is the thickness of a magnetic flux collector, t is the thickness (difference between inner diameter and outer diameter) of the hollow magnetic core, and d is the outer diameter of the hollow magnetic core.
Equation (4) is a calculation formula of equivalent noise level of the induction magnetometer under 1Hz
Wherein e n is short-circuit voltage noise of the pre-amplifying circuit, i n is current noise of the pre-amplifying circuit, R is resistance of an induction coil of the induction magnetometer, and a calculation formula is shown as formula (5); l is inductance of the induction coil, and a calculation formula is shown as formula (6); ω=2pi f, where f takes 1Hz; e R is the thermal noise of the induction coil, and the calculation formulas are formula (7), formula (8) and formula (9); the effective magnetic permeability of the mu a magnetic core is calculated by the formulas (10) (11) (12);
T＝1.37×10-23J/K (8)
k＝249 (9)
Note that the above is only a preferred embodiment of the present invention and the technical principle applied. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, while the invention has been described in connection with the above embodiments, the invention is not limited to the embodiments, but may be embodied in many other equivalent forms without departing from the spirit or scope of the invention, which is set forth in the following claims.
Claims (1)
1. The induction magnetometer coil parameter multi-objective optimization method based on NSGA-II algorithm is characterized by comprising the following steps:
A. taking the copper wire diameter, the magnetic core length, the magnetic flux collector diameter and the coil turns of the induction magnetometer as decision variables, and determining constraint conditions of the decision variables;
B. establishing a multi-objective optimization model with minimum weight and minimum noise at 1Hz as optimization targets;
C. defining individual dominance relations in the evolved population;
D. Solving the multi-objective optimization model by adopting a multi-objective optimization algorithm NSGA-II to realize optimization;
and B, the multi-objective optimization model is characterized by minimizing a first objective function and a second objective function, and the established multi-objective optimization model is as follows:
minf(1)＝G(dCu,l,D,N)
minf(2)＝NEMI1Hz(dCu,l,D,N) (1)
The constraint conditions are as follows:
In the formula (1), f (1) is a weight calculation formula of the induction magnetometer, f (2) is an equivalent noise level calculation formula of the induction magnetometer under 1Hz, D Cu, l, D and N are decision variables respectively representing the diameter of a copper wire, the length of a magnetic core, the diameter of a magnetic flux collector and the number of turns of a coil;
The f (1) is shown as a formula (3):
Wherein ρ w is the density of copper wire, ρ p is the density of permalloy, d w＝dCu+2ti,ti is the thickness of copper wire insulation layer, d 0 is the thickness of magnetic flux collector, t is the thickness of hollow magnetic core, i.e. the difference between inner and outer diameters, d is the outer diameter of hollow magnetic core;
the f (2) is shown as a formula (4):
Wherein e n is pre-amplification circuit short-circuit voltage noise, i n is pre-amplification circuit current noise, R is resistance of an induction coil of the induction magnetometer, L is induction coil inductance, ω=2pi f, f is 1Hz, e R is induction coil thermal noise, and μ a is effective magnetic permeability of a magnetic core;
the calculation formula of R is shown as formula (5):
the calculation formula of L is shown as formula (6):
the calculation formulas of e R are formula (7), formula (8) and formula (9):
T＝1.37×10-23J/K (8)
k＝249 (9)；
The calculation formula of μ a is formulas (10), (11) and (12):
step D, the specific steps are as follows:
D1, initializing variable information of copper wire diameter, magnetic core length, magnetic flux collector diameter and coil turn number, and setting evolution algebra gen=1;
d2, judging whether a first generation sub population is generated, and if so, enabling an evolution algebra Gen=2; otherwise, non-dominant ordering and selection are carried out on the initial population, gaussian intersection and mutation are carried out, so that a first generation sub population is generated, and the evolution algebra Gen=2;
d3, merging the parent population and the offspring population into a new population;
D4, judging whether a new parent population is generated, if not, calculating an objective function of an individual in the new population, and executing rapid non-dominant sorting, congestion degree calculation and elite strategy operation to generate the new parent population; otherwise, entering the next step;
d5, selecting, crossing and mutating the generated parent population to generate a child population;
d6, judging whether Gen is equal to the maximum evolution algebra, if not, the evolution algebra Gen=Gen+1 and returning to the step D3; otherwise, outputting the optimization result, and ending the algorithm operation.
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