CN111126549A - Double-star spectrum fitting method based on strategy improved goblet and sea squirt intelligent algorithm - Google Patents
Double-star spectrum fitting method based on strategy improved goblet and sea squirt intelligent algorithm Download PDFInfo
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Abstract
The invention discloses a strategy-based double-star spectrum fitting method for improving a goblet and sea squirt intelligent algorithm, which comprises the steps of firstly, setting an observation spectrum band to be fitted in a theoretical spectrum asteroid sample library under a double-star model; and then optimizing the observation spectrum to be fitted in a theoretical spectrum astrology sample library by using a strategy improved ascidian intelligent algorithm to obtain the optimal fitting spectrum. The chaotic mapping and reverse learning method is applied to population initialization, so that the initial position distribution of population individuals is more uniform, the population diversity is more obvious, and the problem of premature convergence in the early stage of the traditional algorithm is favorably solved; the position of the food source is updated by adopting a random walk strategy, so that a local convergence trap can be skipped, and the global optimization performance of the algorithm is further enhanced; the strategy-improved goblet and ascidian intelligent algorithm has the advantages of higher convergence speed, smoother convergence, and more benefit for jumping out of local precocious, and when the strategy-improved goblet and ascidian intelligent algorithm is applied to double-star spectrum fitting, the fitting speed is higher, and the fitting precision is higher.
Description
Technical Field
The invention belongs to the technical field of big data processing, and particularly relates to a mass double-star spectral data fitting method based on a strategy improved goblet ascidian intelligent algorithm.
Background
The spectra of the galaxy or galaxy are mainly from stars. The spectrum of the galaxy contains a large amount of galaxy physical information, and how to quickly and accurately analyze the observation spectrum of the galaxy to obtain the estimation of the related physical parameters of the galaxy is the key for researching the evolution formation of the galaxy. With the development of the sky patrol technology, more and more high-quality astrology observation spectrum data are collected. The star synthesis method is a process of comparing integral characteristics of a star, such as a spectrum and the like, with an observed or theoretical star model to determine the star components and physical parameters forming the star system. Research shows that the ratio of double stars in the galaxy exceeds 50%, and the synthesis of double stars is of great significance for physical research of celestial bodies and is listed as one of six challenges for the synthesis of galaxy in decades of the future. The spectral fitting is the key of the star family synthesis method, and is to estimate the relevant parameter information of the star family by fitting by using the calculable characteristic quantity (such as spectral distribution and the like) of the star family. Particularly, the model spectrum which is most approximate to the observed spectrum is found from the model spectrum library, and the essence of the star spectrum fitting is that the model spectrum library is pairedSearching the corresponding parameter space to find the minimum value χ of the fitted observation spectrum2=∑[(fobλ-fthλ)2ωλ]Corresponding model spectrum, where fobλAnd fthλObserved and theoretical spectra, respectively, and ω λ is the weight of the wavelength λ, the best result corresponding to min (χ)2) In most cases, ω isλ=1/Eoλ 2Indicating the use of the observation error, ωλFixed values can also be assigned according to special requirements, which is essentially an optimization problem that is data-scale and the objective function is not easily derived.
In recent years, the hair-style search algorithm is widely concerned by academia and industry by virtue of unique global optimization capability, and the hair-style search algorithm is generally considered to have a larger chance of finding a global optimal solution than the traditional optimization method, so that various meta-heuristic algorithms are proposed to fit the parameters of the two-star spectrum model.
The traditional method for fitting the double-star spectrum adopts a grid search method, and the performance of the method is mainly caused by the mass rule of spectrum data, so that the efficiency is low, and the global optimization capability is insufficient. Experiments show that fitting a full spectral range on a personal computer by using a full grid search method takes about 7.5 hours. The existing fitting method combining a heuristic intelligent algorithm adopts a Metropolis Simulated Annealing algorithm (SA) and a Markov chain, although the Simulated Annealing algorithm starts from any initial point, if a sufficiently long Markov chain is generated according to a certain condition, the algorithm converges on a global minimum point with a probability of 1.0, however, in actual operation, because the length and the operation time of the Markov chain are limited, the algorithm usually shows stronger local search capability, but poorer global search capability, and the final convergence result is greatly influenced by the initial value. The standard goblet sea squirt Algorithm (Salp Swarm Algorithm) proposed in 2017 by Seyedali Mirjalii and Amir H.Gandomi et al is an intelligent bionic optimization Algorithm simulating the foraging group of the goblet sea squirt. Compared with a simulated annealing method, the metaheuristic algorithm based on the population has advantages over the metaheuristic algorithm based on the monomer. The search process starts with a randomly generated population. 2. Multiple populations can share information within the search space, avoiding locally optimal solutions. 3. The search capability of the multi-population-based meta-heuristic algorithm is superior to that of the individual-based meta-heuristic algorithm. However, the standard goblet ascidian algorithm can achieve fast convergence in a population-optimal mode based on the goblet ascidian chain, but has disadvantages in global search diversity, is easily trapped in local precocity on the multi-peak problem due to limitations of population diversity and disadvantages of a food source updating mechanism, is not easy to jump out of a local optimal trap, has low convergence speed and low precision, and is not easy to find a global estimation parameter with better fitting degree.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide the strategy-based improved goblet and sea squirt intelligent algorithm double-star spectrum fitting method which is less in iteration times, high in convergence speed and high in precision and is not easy to fall into local precocity.
The technical scheme adopted by the invention is as follows:
a strategy-based double-star spectrum fitting method for improving a goblet and ascidian intelligent algorithm specifically comprises the following steps:
step 1: preprocessing an observation spectrum to be fitted, and setting a theoretical spectrum asteroid sample library of the observation spectrum to be fitted under the two-star model according to an observation spectrum band to be fitted;
step 2: and (3) optimizing the observed spectrum to be fitted in the step 1 in a theoretical spectrum astrology sample library by applying a strategy improved ascidian intelligent algorithm to obtain an optimal fitting spectrum.
The step 2 specifically comprises the following substeps:
step 2.1: population initialization and real number encoding of population individuals
Initializing individual variables and related parameters in a population, and encoding real numbers of individuals in the population, wherein the population X ═ { X ═ XiI ═ 1,2,3, … …, N }, population individuals Xi={XidD is 1,2,3, … …, D }, N is the number of the population, D is the dimension of the search space, and F is the food source of the chain of goblet sea squirts;
mapping individual population by using a chaotic mapping function formula (6) in a mode of formula (7), performing inverse learning on the population by using a formula (8) after the mapping is finished,
Xid=Xmibd+yid*(Xmaxd-Xmind) (7)
OXid=Xmin d+Xmax d-Xid(8)
in equation (6), the chaotic mapping function generates a chaotic sequence y ═ y in the D-dimensional spaced,d=1,2,……,D},yd={yid,i=1,2,……,N};
In the formula (7), N is the number of the population, Xmind is the lower bound of the search, Xmaxd is the upper bound of the search, D is the dimensionality of the search space, and the maximum search iteration number is defined as L;
in formula (8), the reversed population OX ═ OXiI 1,2, … …, N }, reverse population individuals OXi={OXid,d=1,2,……,D};
Step 2.2: the adaptation value of the observed spectrum is calculated using equation (5),
x2=∑[(fobλ-fthλ)2ωλ](5)
in the formula (5), fobλIs an observed spectrum, fthλIs a theoretical spectrum, and ωλIs the weight of wavelength λ; sorting the adaptive values obtained in the formula (5) to find the minimum adaptive value and assigning the minimum adaptive value to a food source F as the current food adaptive value;
step 2.3: updating the current food adaptation value, i.e. the food source F, according to the formula (4) and the random walk strategy, and keeping according to the elite strategy,
in the formula (4), xnIs the position after the nth step, αiIs a step-size control factor, siIs derived from Cauchy distributed random numbers;
step 2.4: population location update
Calculating individual adaptation values in the population, assigning the individual position corresponding to the optimal adaptation value to a food source F, defining the first half part of the population as a band team goblet sea squirt, and guiding the population to move to the optimal solution, wherein the position updating mode is formula (2),
wherein, thereinIs the position of the first band team goblet sea squirt in dimension j, FjIs the position of the j-th food source, c2, c3 are random numbers of (0-1), ubjIs the upper search bound, lb, of the j-th dimension search spacejIs the lower search boundary of the j-th dimension search space, l is the current iteration number, c1 is the iteration factor, and is determined by the formula (1);
the second half of the population is defined as the following casaia ecteinascidae, the position updating mode is formula (3),
in the formula (3), Xi jIs the location of the ith following Hyacinus goblet in the jth search space, Xi-1 jIs the position of the ith-1 following halymenia crustacean in the jth dimension search space;
step 2.5: after the positions of all the ascidians in the population are updated, correcting the population according to the searched upper bound and the searched lower bound to obtain the adaptive value of each individual in the updated population; comparing the updated adaptive value of each individual in the population with the current food adaptive value, and if the individual with the better adaptive value is superior to the current food adaptive value, taking the individual position of the kava sylvestris with the better adaptive value as a new food position, namely assigning the position corresponding to the optimal individual adaptive value to a food source F;
and 2.6, judging whether the maximum iteration times or the termination condition is reached, if the maximum iteration times or the termination condition is reached, terminating the algorithm, and outputting the optimal individual position to obtain the optimal fitting spectrum.
Compared with the prior art, the invention has the following advantages: the random number generated by the chaotic mapping function and the reverse learning method are applied to population initialization, so that the initial position distribution of population individuals is more uniform, the population diversity is more obvious, and the problem of premature convergence in the early stage of the traditional algorithm is favorably solved; the position of the food source is updated by adopting a random walk strategy, so that a local convergence trap can be skipped, and the global optimization performance of the algorithm is further enhanced; the strategy-improved goblet and ascidian intelligent algorithm has the advantages of higher convergence speed, smoother convergence, and more benefit for jumping out of local precocious, and when the strategy-improved goblet and ascidian intelligent algorithm is applied to double-star spectrum fitting, the fitting speed is higher, and the fitting precision is higher.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a convergence curve of the algorithm without adding the adaptive inertia factor;
FIG. 3 is an algorithm convergence curve for increasing the adaptive inertia factor;
FIG. 4 is an algorithm convergence curve for a population of 500 individuals;
in fig. 2-4, the vertical axis is the adaptation value (fit), the horizontal axis is the iteration number (iteration), and the title is the total time consumption (total times);
FIG. 5 is a two-star spectral fit curve;
in fig. 5, the vertical axis represents the relative value of the spectral radiant flux (flux) at a wavelength 5500, the horizontal axis represents the spectral wavelength (λ), Z is 0.017 is the abundance of the metal 0.017, redshift is 0.003586 is the red shift 0.003586, dashed, dotted, solid represent the spectral energy distribution of the star group containing 2,3 and 6 components, respectively.
Detailed Description
For better understanding of the technical solution of the present invention, the following detailed description of the technical solution of the present invention is provided with reference to the accompanying drawings and specific examples:
with reference to fig. 1 to 5, a strategy-based improved goblet and sea squirt intelligent algorithm double-star spectrum fitting method specifically includes the following steps:
step 1: preprocessing an observation spectrum to be fitted, and setting a theoretical spectrum asteroid sample library of the observation spectrum to be fitted under the two-star model according to an observation spectrum band to be fitted;
and 2, optimizing the observed spectrum to be fitted in the step 1 in a theoretical spectrum astrology sample library by applying a strategy improved ascidian intelligent algorithm to obtain an optimal fitting spectrum.
The step 2 specifically comprises the following substeps:
step 2.1: population initialization and real number encoding of population individuals
Initializing individual variables and related parameters in a population, and encoding real numbers of individuals in the population, wherein the population X ═ { X ═ XiI ═ 1,2,3, … …, N }, population individuals Xi={XidD is 1,2,3, … …, D }, N is the number of the population, D is the dimension of the search space, and F is the food source of the chain of goblet sea squirts;
mapping individual population by using a chaotic mapping function formula (6) in a mode of formula (7), performing inverse learning on the population by using a formula (8) after the mapping is finished,
Xid=Xmind+yid*(Xmaxd-Xmind) (7)
OXid=Xmin d+Xmax d-Xid(8)
in equation (6), the chaotic mapping function generates a chaotic sequence y ═ y in the D-dimensional spaced,d=1,2,……,D},yd={yid,i=1,2,……,N};
In the formula (7), N is the number of the population, Xmind is the lower bound of the search, Xmaxd is the upper bound of the search, D is the dimensionality of the search space, and the maximum search iteration number is defined as L;
in formula (8), the reversed population OX ═ OXiI 1,2, … …, N }, reverse population individuals OXi={OXid,d=1,2,……,D};
Step 2.2: the adaptation value of the observed spectrum is calculated using equation (5),
χ2=∑[(fobλ-fthλ)2ωλ(5)
in the formula (5), fobλIs an observed spectrum, fthλIs a theoretical spectrum, and ωλIs the weight of wavelength λ;
sorting the adaptive values obtained in the formula (5) to find the minimum adaptive value and assigning the minimum adaptive value to a food source F; in the specific application, real number codes of each individual of the goblet sea squirt population are mapped to an observation spectrum library to be fitted, so that the sample number of the observation spectrum library to be fitted is coded by using the individual position of the goblet sea squirt; carrying in (5) calculating individual adaptive values, arranging the adaptive values in a descending order, and assigning the individual position corresponding to the minimum adaptive value to a food source F as a current food adaptive value;
step 2.3: updating the current food adaptation value, i.e. the food source F, according to the formula (4) and the random walk strategy, and keeping according to the elite strategy,
in the formula (4), xnIs the position after the nth step, αiIs a step-size control factor, siIs derived from Cauchy distributed random numbers;
step 2.4: population location update
Calculating individual adaptation values in the population, assigning the individual position corresponding to the optimal adaptation value to a food source F, defining the first half part of the population as a band team goblet sea squirt, and guiding the population to move to the optimal solution, wherein the position updating mode is formula (2),
wherein, thereinIs the position of the first band team goblet sea squirt in dimension j, FjIs the position of the j-th food source, c2, c3 are random numbers of (0-1), ubjIs the upper search bound, lb, of the j-th dimension search spacejIs the lower search boundary of the j-th dimension search space, l is the current iteration number, c1 is the iteration factor, and is determined by the formula (1);
further, preferably, the inertia of the food source F is adjusted by the formula (9),
wherein it is consistent with l in definition, and is the current iteration number, and ω (it) is the inertia factor corresponding to the current iteration number, and acts on formula F (2)jBefore: the original FjItem replacement is ω (it) × FjIncreasing an adaptive exponential inertia factor omega (it) to make the algorithm convergence smoother and more efficient; specifically, the formula is shown as follows:
the second half of the population is defined as the following casaia ecteinascidae, the position updating mode is formula (3),
in the formula (3), Xi jIs the location of the ith following Hyacinus goblet in the jth search space, Xi-1 jIs the position of the ith-1 following halymenia crustacean in the jth dimension search space;
step 2.5: after the positions of all the ascidians in the population are updated, correcting the population according to the searched upper bound and the searched lower bound to obtain the adaptive value of each individual in the updated population; comparing the updated adaptive value of each individual in the population with the current food adaptive value, and if the individual with the better adaptive value is superior to the current food adaptive value, taking the individual position of the kava sylvestris with the better adaptive value as a new food position, namely assigning the position corresponding to the optimal individual adaptive value to a food source F;
and 2.6, judging whether the maximum iteration times or the termination condition is reached, if the maximum iteration times or the termination condition is reached, terminating the algorithm, and outputting the optimal individual position to obtain the optimal fitting spectrum.
Example 1
A simulation experiment is carried out on the strategy improved ascidian intelligent algorithm, the experiment platform is Python, the operating system is Windows, the memory capacity is 8GB, and the CPU model is i 5-85000. Selecting and selecting test function (Sphere function) F1x (-100,100), taking the search space dimension D of 30, initializing the number of individual goblet sea squirt populations to be 50, and obtaining a convergence curve shown in figure 2 by testing; the convergence curve after the food source is added with the adaptive inertia factor is shown in fig. 3, and the convergence is smoother after the adaptive inertia factor is added, so that the algorithm is more favorable for jumping out of local precocity; in addition, the convergence curve is shown in fig. 4 after the number of initialized ascidian population is increased to 500, the convergence rate of the algorithm is obviously increased, and the time consumption is reduced from 23.459s to 2.11 s.
Example 2
A strategy improved ascidian intelligent algorithm is adopted to carry out fitting experiments on observed spectra (the observed spectral data and theoretical spectral data used in the experiments are both existing data), an experiment platform is Python, an operating system is Windows, the memory capacity is 8GB, and the CPU model is i 5-85000. The fitting curve obtained by fitting the observed spectrum (number: spec-0266-.
Claims (3)
1. A strategy-based double-star spectrum fitting method for improving a goblet and ascidian intelligent algorithm is characterized by comprising the following steps:
step 1: setting an observation spectrum band to be fitted in a theoretical spectrum asteroid sample library under a double-star model;
and 2, optimizing the observed spectrum to be fitted in the step 1 in a theoretical spectrum astrology sample library by applying a strategy improved ascidian intelligent algorithm to obtain an optimal fitting spectrum.
2. The method as claimed in claim 1, wherein the step 2 comprises the following steps:
step 2.1: population initialization and real number encoding of population individuals
Initializing individual variables and related parameters in a population, and encoding real numbers of individuals in the population, wherein the population X ═ { X ═ XiI ═ 1,2,3, … …, N }, population individuals Xi={XidD is 1,2,3, … …, D, N is the number of the population, D is the dimension of the search space;
mapping individual population by using a chaotic mapping function formula (6) in a mode of formula (7), performing inverse learning on the population by using a formula (8) after the mapping is finished,
Xid=Xmind+yid*(Xmaxd-Xmind) (7)
OXid=Xmind+Xmaxd-Xid(8)
in equation (6), the chaotic mapping function generates a chaotic sequence y ═ y in the D-dimensional spaced,d=1,2,……,D},yd={yid,i=1,2,……,N};
In the formula (7), N is the number of the population, Xmind is the lower bound of the search, Xmaxd is the upper bound of the search, and D is the dimension of the search space;
in formula (8), the reverse population OX={OXiI 1,2, … …, N }, reverse population individuals OXi={OXid,d=1,2,……,D};
Step 2.2: the adaptation value of the observed spectrum is calculated using equation (5),
χ2=Σ[(fobλ-fthλ)2ωλ](5)
in the formula (5), fobλIs an observed spectrum, fthλIs a theoretical spectrum, and ωλIs the weight of wavelength λ; sorting the adaptive values obtained in the formula (5) to find the minimum adaptive value and assigning the minimum adaptive value to a food source F as the current food adaptive value;
step 2.3: updating the current food adaptation value, i.e. the food source F, according to the formula (4) and the random walk strategy, and keeping according to the elite strategy,
in the formula (4), xnIs the position after the nth step, αiIs a step-size control factor, siIs derived from Cauchy distributed random numbers;
step 2.4: population location update
Calculating individual adaptation values in the population, assigning the individual position corresponding to the optimal adaptation value to a food source F, defining the first half part of the population as a band team goblet sea squirt, and guiding the population to move to the optimal solution, wherein the position updating mode is formula (2),
wherein, thereinIs the position of the first band team goblet sea squirt in dimension j, FjIs the position of the j-th food source, c2, c3 are random numbers of (0-1), ubjIs the upper search bound, lb, of the j-th dimension search spacejIs the lower search bound of the j-th dimension search space, L is the current iteration number, and L is the maximumSearching iteration times, wherein c1 is an iteration factor and is determined by formula (1);
the second half of the population is defined as the following casaia ecteinascidae, the position updating mode is formula (3),
in the formula (3), Xi jIs the location of the ith following Hyacinus goblet in the jth search space, Xi-1 jIs the position of the ith-1 following halymenia crustacean in the jth dimension search space;
step 2.5: after the positions of all the ascidians in the population are updated, correcting the population according to the searched upper bound and the searched lower bound to obtain the adaptive value of each individual in the updated population; comparing the updated adaptive value of each individual in the population with the current food adaptive value, and if the individual with the better adaptive value is superior to the current food adaptive value, taking the individual position of the kava sylvestris with the better adaptive value as a new food position, namely assigning the position corresponding to the optimal individual adaptive value to a food source F;
and 2.6, judging whether the maximum iteration times or the termination condition is reached, if the maximum iteration times or the termination condition is reached, terminating the algorithm, and outputting the optimal individual position to obtain the optimal fitting spectrum.
3. The method as claimed in claim 2, wherein the inertia of the food source F in step 2.4 is adaptively adjusted by formula (9),
wherein it is consistent with l, both are the current iteration times, and ω (it) is the inertia corresponding to the current iteration timesFactor acting on formula (2) FjBefore: the original FjItem replacement is ω (it) × FjSpecifically, the formula is shown as follows:
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