CN115169229A - Annealing type particle swarm method for nonlinear inversion - Google Patents
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Abstract
The invention discloses an annealing type particle swarm method for nonlinear inversion, which comprises the following steps: step 1: obtaining multi-beam echo intensity data, and extracting an angle response curve from the multi-beam echo intensity data; step 2: defining basic parameters of the annealing type particle swarm algorithm, wherein the basic parameters comprise constant parameters and variable parameters, and the variable parameters comprise the number of sub-populations, the number of particles contained in the sub-populations and the like; and step 3: generating a first random function and a second random function with different value ranges, and performing random initialization on the speed and the initial position of the particles based on the two random functions; and 4, step 4: and (3) taking the GSAB model formula as a fitting function of the angle response curve to carry out multiple iterations to obtain the optimal solution (namely the optimal position) of the whole population, and taking the optimal solution as a fitted GSAB model parameter. The invention improves the population diversity of the particle swarm algorithm, can dynamically set the number of the sub-populations and the sizes of the sub-populations, and realizes the generalization of the algorithm and the improvement of the algorithm performance.
Description
Technical Field
The invention relates to the technical field of inversion processing, in particular to an annealing type particle swarm method for nonlinear inversion.
Background
The Particle Swarm Optimization (Particle Swarm Optimization) algorithm was first proposed by Kennedy and Eberhart (1995) and belongs to one of the group intelligence algorithms (Zhang Yudong, 2015). The algorithm is inspired by foraging behaviors of birds, is simple in structure, easy to implement, few in parameters, convenient to use (Tianxinghua and the like, 2020), has obvious advantages in solving complex optimization problems, and is widely concerned once being put forward.
Particle swarm algorithms also have certain disadvantages, such as easy premature convergence. Therefore, the scholars propose a great deal of targeted improvement ways to improve the performance of the algorithm. The improvement of the basic particle swarm algorithm mainly has two directions: the method comprises the following steps of firstly, optimally setting inertia weight (Hujiaxiu and the like, 2006; arzilian and the like, 2009; liyan and the like, 2020) and acceleration factor (Ratnaweera and the like, 2004); secondly, adjustment of algorithm mechanisms, such as rare bone particle swarm optimization algorithm (Haibo Zhang et al, 2011), particle migration based method (Ma Gang et al, 2012), dynamic heterogeneous particle swarm algorithm (Shiqin Yang et al, 2017), adaptive particle swarm optimization algorithm (Feng Qian et al, 2020), and combination of particle swarm algorithm and other ideas/algorithms, such as chaos ideas (Qi Wu et al, 2013; king Shawu et al, 2016 Xiangli Xia et al, 2020), fuzzy ideas (Yau-Tarng Juang et al, 2010), simulated annealing ideas (Sun Yi et al, 2020, tianxinghua et al, 2020), and self-correcting and dimension-by-dimension learning ideas (Zhang Yuan et al, 2021), etc. are adopted. These different improvements all improve the performance of the basic particle swarm algorithm to some extent.
As an intelligent optimization algorithm, the particle swarm algorithm is widely applied to the research of geological inversion, wherein the applications in the field of geophysical are more, and the particle swarm algorithm comprises seismic exploration (Liuliufeng and the like 2014; zhang and the like 2018), electromagnetic exploration (Chengculong and the like 2014), well logging (PanpaoZhi and the like 2016), rock physics (Liu and the like 2018), remote sensing (Dingsheng and the like 2010), mapping (Liusheng and the like 2018) and the like, and the improvement on the particle swarm algorithm is not lacked. In addition, the method has certain applications in geological (Zhangjiang Yang, etc., 2019) and ocean fields, such as segmentation of side-scan sonar images by quantum-swarm optimization (Zhao Jianhu, etc., 2016), division of substrate types by combining the particle-swarm optimization and BP neural networks, and the like (Chenjia, etc., 2017).
As an intelligent optimization algorithm, the basic particle swarm algorithm has the defect of easy premature convergence, so that the algorithm is easy to converge to a local minimum value. However, most of the current researchers improve the particle swarm optimization algorithm by aiming at the outstanding problem that the particle swarm optimization is easy to early-mature and converge, and the simulated annealing algorithm is mostly used. The simulated annealing algorithm can improve the global optimization capability of the whole algorithm, and is a better improvement mode. However, it must be pointed out that, in the existing algorithm, the information exchange between the particles of the whole population is insufficient, which results in low diversity of the population; and the particles do not store historical optimal positions, resulting in missing some better solutions that were found; and the particles in the whole sub-population are updated in the same way, so that the searching form is single. Generally speaking, the intelligent level of the existing products is still slightly insufficient, the information exchange capability of each particle in the population is not strong, the efficiency and the precision of the algorithm still need to be further improved, and the method is not enough to be applied to the field of marine geophysical, especially the multi-beam-based substrate type division.
The relevant references are as follows:
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[3] tianxinghua, zhangjie, liyang.2020. Adaptive annealing type particle swarm algorithm [ J ] based on chaotic mapping, complex system and complexity science, 17 (1): 45-54.
[4] Hujian, once created, 2006 PSO Algorithm [ J ] with random inertial weights, computer simulation, 21 (8): 164-167.
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[6] Li Yan, chen Qian 2020, research on particle swarm optimization algorithm based on nonlinear decrement of inertial weight [ J ]. University of Shaanxi science and technology, 38 (3): 166-171.
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[14]Xiangli Xia,Shijin Li.2020.Research on improved chaotic particle optimization algori thm based on complex function[J].Frontiers in Physics,8.
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[16] Sunyi, chilobrachys, 2020 analysis and improvement of particle swarm algorithm under semi-supervised clustering objective [ J ]. Academic newspaper of Beijing postal and telecommunication university, 43 (5): 21-26.
[17] Zhang Ziyuan, zhang Jun, jiwei Dong et al 2021 particle swarm algorithm [ J ] small microcomputer system 42 (5): 919-926 with self-correcting and dimension-by-dimension learning ability.
[18] Liu Li Feng, sun Zandon, korea, etc. 2014, research on fuzzy neural network carbonate rock fluid identification method by quantum particle swarm [ J ]. Geophysical science, 3): 991-1000.
[19] Zhang Ice, liu Gou, guo Zhi Qi et al 2018. Inversion of anisotropic shale reservoir parameters [ J ] geophysical report based on statistical petrophysical models 61 (6): 2601-2617.
[20] Chengdulong, limingxing, xiaoshouli, etc. 2014, mine transient electromagnetic particle swarm optimization inversion research under the condition of full space [ J ]. The report of geophysical science 57 (10): 3478-3484.
[21] 2016.CEC ratio method in the logging evaluation of polio sandstone reservoir, such as Pengbao, liu Si Hui, huang Bu, etc. [ J ] takes sea-tower basin X sunken polio sandstone reservoir as example, geophysical report, 59 (5): 1920-1926.
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[25] Zhang Jiang Yang, sun Zhen, qiun, etc. 2019. Bounce zone three-dimensional effective elastic thickness inversion based on particle swarm optimization [ J ]. Geophysical science, 62 (12): 4738-4749.
[26] Zhao Jian Hu, wang Xiao, zhang hong Mei et al, 2016, neutral set of side scan sonar image segmentation and Quantum Sum-Suo Algorithm [ J ] Proc. Memo, 45 (8): 935-942,951.
[27] Chenjiangbing, wu Zi Ying, zhao Dingneng, etc. 2017, PSO-BP submarine acoustic substrate classification method based on particle swarm optimization algorithm [ J ] oceanographic newspaper 39 (9): 51-57.
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[31]Yang Y.,He G.,Ma J.,et al.Acoustic quantitative analysis of ferromanganese nodules and cobalt-rich crusts distribution areas using EM122 multibeam backscatter data from deep-sea basin to seamount in Western Pacific Ocean.[J].Deep-Sea Research Part I,2020,Oceanographic Research Papers,161.
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Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an annealing type particle swarm method for nonlinear inversion, which can solve the problems that a particle swarm algorithm is applied to seabed sediment division and algorithm performance is improved.
The technical scheme for realizing the purpose of the invention is as follows: an annealing type particle swarm method for nonlinear inversion comprises the following steps:
step 1: obtaining multi-beam echo intensity data, extracting an angle response curve from the multi-beam echo intensity data, wherein the angle response curve represents echo intensity values of the same substrate type under different incidence angles;
step 2: defining basic parameters of the annealing type particle swarm algorithm, wherein the basic parameters comprise constant parameters and variable parameters, the number of the sub-populations, the number of particles contained in the sub-populations and the like are different, the updating modes of the particles of the sub-populations are different, and the dimensionality of the particles is the number of GSAB model parameters;
and step 3: generating a first random function and a second random function with different value ranges, and randomly initializing the speed and the position of the particles according to the first random function and the second random function;
and 4, step 4: calculating a fitting function of the angle response curve, calculating a fitting value of the angle response curve by the fitting function according to the position of each particle in the sub-population by using a GSAB model formula, and returning the mean square error of the angle response curve and the actual angle response curve, wherein the GSAB model formula is as follows:
BS(θ)＝10log[A·exp(-θ 2 /2B 2 )+C·cos D θ+E·exp(-θ 2 /2F 2 )]
wherein BS (theta) represents the echo intensity corresponding to the sea bottom incidence angle theta, A represents the maximum amplitude of specular reflection, B represents the angle range parameter of the specular reflection region, C represents the average echo intensity level under the oblique incidence angle, D represents the angle attenuation amount of the echo intensity, E represents the maximum value of the instantaneous echo intensity, F is 1/2 of the angle range of the echo intensity,
calculating the fitting errors of the optimal solutions of all the sub-populations, returning the positions of the particles with the minimum fitting errors in all the sub-populations, and taking the positions as the optimal solutions of the whole population in the iteration;
calculating the fitting difference of each particle by combining the current position of the particle according to the GSAB model formula, comparing the fitting difference with the last position, taking the last position with the fitting difference smaller than the last position as a final position, judging whether to accept the current new position according to Metropolis acceptance criteria if the fitting difference of the current position is larger than the last position,
calculating the optimal position of each sub-population, comparing the optimal solutions of all the sub-populations to obtain the optimal position of the whole population in the iteration,
and then, cooling according to a rapid annealing mode, stopping iteration after multiple iterations when the maximum iteration times is reached or the precision meets the preset requirement, outputting the position of the optimal particles of the whole population, and taking the optimal particles as the fitted GSAB model parameters.
Further, the constant parameters include Boltzmann constant, pi.
Further, the variable parameters further include an initial temperature, a total number of particles, a maximum number of iterations, a maximum velocity of the particles, and a search range of the particles.
Further, the initial temperature is 1000, the total number of particles is 120, the number of sub-populations is 3, the dimension of the particles is 6, the maximum number of iterations is 100, and the maximum velocity of the particles is 0.1.
Further, in the step 3, the value of the first random function is in the range of [0,1], and the value of the second random function is in the range of [ -1,1 ].
The invention has the beneficial effects that: according to the invention, by introducing the sub-populations and giving the sub-populations different particle updating modes, the diversity of the whole population is improved, the generalization of the algorithm can be realized by dynamically setting the number of the sub-populations and the sizes of the sub-populations, and the improvement of the algorithm performance can be realized by coupling different types of sub-populations. And the annealing type particle swarm algorithm is applied to fitting of the GSAB model, so that the classification of the seabed sediment types is realized.
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FIG. 1 is a schematic flow chart of the present invention.
Detailed description of the preferred embodiments
The invention will be further described with reference to the accompanying drawings and specific embodiments:
as shown in fig. 1, an annealing type particle swarm method for nonlinear inversion comprises the following steps:
step 1: obtaining multi-beam echo intensity data, and extracting an angle response curve from the multi-beam echo intensity data, wherein the angle response curve represents echo intensity values of the same substrate type under different incidence angles.
The multi-beam echo intensity data is typically comprised of angle and echo intensity data pairs. Wherein the range of variation of the angle is determined by the opening angle of the multi-beam. Since the edge beam data quality is generally poor, the angular response curve is not necessarily exactly the same as the beam opening angle range. Taking the example of ocean clay deposition as applied in this example, the angular response curve has an angular range of [ -55,55] in degrees. The range of the open angle of the echo intensities is [ -52.260, -11.312], in dB, and the data interval of the angle is 0.01. For a certain angle, at least one echo intensity corresponds to it, in other words, there may be several different echo intensities corresponding to it, which also explains the problem that the fitting of the angular response curve is a non-linear inversion from one angle.
Step 2: and defining basic parameters of the annealing type particle swarm optimization, wherein the basic parameters comprise constant parameters and variable parameters. The constant parameters comprise Boltzmann constants, pi and the like, and the variable parameters comprise initial temperature, total number of particles, number of sub-populations, dimensions of the particles, maximum iteration times, maximum speed of the particles, search range of the particles and the like.
In this embodiment, the initial temperature is selected to be a large value, which is 1000 in the method, in order to ensure that the annealing process can converge to a global optimum. The total number of the particles and the number of the sub-populations can be dynamically adjusted according to the type of the target function and the experimental result, so that a better convergence effect is achieved. The total number of particles in the method is 120, and the number of the sub-populations is 3. The dimension of the particle is 6 because the GSAB model parameters that need to be inverted are 6. The maximum number of iterations is 100, and can be increased or decreased according to experimental results. The maximum speed of the particles is 0.1, so that the particles have certain initial speed and certain flight capacity, the search fineness is ensured, and the particles can be properly adjusted according to an experimental result and a search range. Since the GSAB model parameter values that need to be inverted have different search ranges, the search range is different for each dimension. Namely, the 6 model parameters respectively correspond to 6 different search ranges, which are respectively [ -30, -15], [0.5,5.0], [ -50, -20], [1 x 10^ (-4), 3.0], [ -50, -20], [0.5, 30].
Compared with the conventional annealing type particle swarm algorithm, the sub-populations are provided in the step, and for different sub-populations, the updating modes of the particles of the sub-populations are different when the annealing type particle swarm algorithm is applied. For a particular sub-population, the speed and position update of all particles within the sub-population is fixed, consistent with the basic particle swarm algorithm.
In the embodiment, 3 sub-populations are adopted, and the acceleration factor and the inertia weight of the first sub-population are constants; the acceleration factor of the second sub-population is a constant, and the inertia weight is linearly decreased; and the third sub-population adopts a PSO-TVAC mode and is a sub-population with a time-varying acceleration factor and a varying inertia weight. In the third sub-population, the acceleration factor c1 is decreased from 2.5 to 0.5 along with the increase of the iteration times; the acceleration factor c2 is increased by a value of 2.5 from 0.5, and the inertial weight is linearly decreased to 0.4 from 0.9. In the actual use process, the quantity of the sub-population and the particle updating mode can be adjusted, so that the particle updating mode is more diversified, and the diversity of the whole population is improved.
And step 3: a first random function with a value in the range of [0,1] and a second random function with a value in the range of [ -1,1] are generated. The purpose of generating the two random functions is to perform random initialization on the speed and the position of all particles in the population, and the random initialization is realized by calling in the initialization process of each particle, so that the position of each particle in the random distribution in the search range and the speed of each particle in the random distribution in the upper and lower speed limit ranges are obtained.
And 4, step 4: calculating a fitting function of the angle response curve, calculating a fitting value of the angle response curve by the fitting function according to the position of each particle in the sub-population by using a GSAB model formula, and returning the mean square error of the angle response curve and the actual angle response curve, wherein the GSAB model formula is as follows:
BS(θ)＝10log[A·exp(-θ 2 /2B 2 )+C·cos D θ+E·exp(-θ 2 /2F 2 )]
wherein BS (theta) represents the echo intensity corresponding to the sea bottom incidence angle theta, A represents the maximum amplitude of the specular reflection, the value of which is related to the reflection coefficient of the fluid-solid interface and the sea surface roughness, B represents the angle range parameter of the specular reflection area, which reflects the roughness of the interface, C represents the average echo intensity level under the oblique incidence angle, the value of which increases with the increase of the frequency, the sea bottom roughness, the wave impedance and the volume heterogeneity, D represents the angle attenuation amount of the echo intensity, which shows a high value on the soft and smooth sedimentary interface, E represents the maximum value of the instantaneous echo intensity, F is 1/2 of the angle range of the echo intensity, and E and F are parameters which are increased on the basis of the original four-parameter GSAB model. The range of variation of these six parameters (a-F) is different for different substrate (seafloor surface sediment) types. According to the echo intensity values (angle response curves) under different incidence angles, 6 parameters of A, B, C, D, E and F can be calculated by utilizing a particle swarm algorithm, so that an actual angle response curve is fitted, and the division of the substrate types is realized.
And according to the GSAB model formula, calculating an objective function value (namely fitting difference) of each particle by combining the current position of the particle, and comparing the objective function value with the historical optimal position. And if the fitting difference of the current position is smaller than that of the last position, and the current position is considered to be superior to the last position, taking the current position as the historical optimal position of the child. And if the fitting difference of the current position is larger than the last position, judging whether to accept the current new position according to Metropolis acceptance criteria. The Metropolis acceptance criterion is the content of the simulated annealing algorithm, belongs to the prior art, and is not described herein.
And when each particle in each sub-population completes the process of updating, comparing and determining a new position once, calculating the optimal position of each sub-population, comparing the optimal solutions of all the sub-populations, and taking the position of the particle with the minimum fitting error in all the sub-populations as the optimal solution of the whole population in the iteration, wherein one iteration is considered to be completed. And then, cooling is carried out according to a rapid annealing mode, the related rapid annealing method is the prior art, and details are not repeated herein, and the rapid annealing method is selected for cooling, so that the convergence of the algorithm can be ensured, and the convergence speed can be improved to a certain extent. And when the maximum iteration times are reached or the precision meets the preset requirement, stopping iteration, outputting the position of the optimal particle of the whole population, and taking the position as a fitted GSAB model parameter.
According to the invention, by introducing the sub-populations and giving different particle updating modes to the sub-populations, the diversity of the whole population is improved, the generalization of the algorithm can be realized by dynamically setting the number of the sub-populations and the sizes of the sub-populations, and the improvement of the algorithm performance is realized by coupling different types of sub-populations. And a historical optimal position is introduced, and in the basic particle swarm algorithm, the historical optimal position searched by the particles is not stored, so that certain better solutions are lost, and the whole iterative process is slowed down. By introducing the method, the historical optimal position searched by each particle can be stored and the subsequent searching of the particles is guided, so that the searching efficiency is improved. The method introduces the idea of simulated annealing, judges whether to receive a new position according to the probability for each iteration of each sub-population, increases the capability of the particles to jump out of local minimum, and improves the global optimization capability of the algorithm. The method applies the annealing type particle swarm algorithm to the fitting of the GSAB model, further realizes the classification of the seabed sediment types, and provides a new method.
The invention can be well integrated on marine environment monitoring and detecting equipment, provides a rapid field processing method for seabed sediment type division, and provides a data basis for subsequent identification of seabed shallow surface layer geological structure, hidden deposit searching and the like.
The embodiments disclosed in this description are only an exemplification of the single-sided characteristics of the invention, and the scope of protection of the invention is not limited to these embodiments, and any other functionally equivalent embodiments fall within the scope of protection of the invention. Various other changes and modifications to the above-described embodiments and concepts will become apparent to those skilled in the art from the above description, and all such changes and modifications are intended to be included within the scope of the present invention as defined in the appended claims.
Claims (5)
1. An annealing type particle swarm optimization method about nonlinear inversion is characterized by comprising the following steps of:
step 1: obtaining multi-beam echo intensity data, and extracting an angle response curve from the multi-beam echo intensity data, wherein the angle response curve represents echo intensity values of the same substrate type under different incidence angles;
step 2: defining basic parameters of the annealing type particle swarm algorithm, wherein the basic parameters comprise constant parameters and variable parameters, the variable parameters comprise the number of sub-populations, the number of particles contained in the sub-populations and the like, the updating modes of the particles of the sub-populations are different, and the dimension of the particles is the number of GSAB model parameters;
and step 3: generating a first random function and a second random function with different value ranges, and randomly initializing the speed and the position of the particles according to the first random function and the second random function;
and 4, step 4: calculating a fitting function of the angle response curve, calculating a fitting value of the angle response curve by the fitting function according to the position of each particle in the sub-population by using a GSAB model formula, and returning the mean square error of the angle response curve and the actual angle response curve, wherein the GSAB model formula is as follows: BS (θ) =10log [ A ] & exp (- θ) 2 /2B 2 )+C·cos D θ+E·exp(-θ 2 /2F 2 )]
Wherein BS (theta) represents the echo intensity corresponding to the sea bottom incidence angle theta, A represents the maximum amplitude of specular reflection, B represents the angle range parameter of the specular reflection region, C represents the average echo intensity level under the oblique incidence angle, D represents the angle attenuation amount of the echo intensity, E represents the maximum value of the instantaneous echo intensity, and F is 1/2 of the angle range of the echo intensity,
calculating the fitting errors of the optimal solutions of all the sub-populations, returning the positions of the particles with the minimum fitting errors in all the sub-populations, and taking the positions as the optimal solutions of the whole population in the iteration;
calculating the fitting difference of each particle by combining the current position of the particle according to the GSAB model formula, comparing the fitting difference with the last position, taking the last position with the fitting difference smaller than the last position as the final position, if the fitting difference of the current position is larger than the last position, judging whether to accept the current new position according to Metropolis acceptance criteria,
calculating the optimal position of each sub-population, comparing the optimal solutions of all the sub-populations to obtain the optimal position of the whole population in the iteration,
and then, cooling according to a rapid annealing mode, stopping iteration after multiple iterations when the maximum iteration times is reached or the precision meets the preset requirement, outputting the position of the optimal particles of the whole population, and taking the optimal particles as the fitted GSAB model parameters.
2. The method for population of annealed species for nonlinear inversion in accordance with claim 1, wherein the constant parameters comprise Boltzmann constants, pi.
3. The method of annealing-type particle swarm for nonlinear inversion according to claim 1, wherein the variable parameters further comprise initial temperature, total number of particles, maximum number of iterations, maximum velocity of particles, and search range of particles.
4. The method for population of annealed particles in connection with nonlinear inversion as recited in claim 1, wherein the initial temperature is 1000, the total number of particles is 120, the number of sub-populations is 3, the dimension of the particles is 6, the maximum number of iterations is 100, and the maximum velocity of the particles is 0.1.
5. The method for nonlinear-inversion-based annealing-type particle swarm optimization according to claim 1, wherein in the step 3, the value of the first random function is in the range of [0,1], and the value of the second random function is in the range of [ -1,1 ].
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