Stochastic Particle Swarm Optimization Algorithm Research Articles

Simulation and evaluation study of atmospheric aerosol nonsphericity as a function of particle size

Aerosol nonsphericity causes great uncertainty in radiative forcing assessments and climate simulations. Although considerable studies have attempted to quantify this uncertainty, the relationship between aerosol nonsphericity and particle size is usually not considered, thus reducing the accuracy of the results. In this study, a coupled inversion algorithm combining an improved stochastic particle swarm optimization algorithm and angular light scattering is used for the nonparametric estimation of aerosol nonsphericity variation with particle size, and the optimal sample selection method is employed to screen the data. Based on the verification of inversion accuracy, the variation of aerosol aspect ratio with particle size based on the ellipsoidal model in global regions has been obtained from Aerosol Robotic Network (AERONET) data, and the effect of nonsphericity on radiative forcing and dry deposition has been studied. The results show that the aspect ratio increases with particle size in all regions, with the maximum ranging from 1.4 to 1.8 in the desert, reflecting the differences in aerosol composition at different particle sizes. In radiation calculations, considering aerosol nonsphericity makes the aerosol cooling effect weaker and surface radiative fluxes increase, but hardly changes the aerosol absorption, with maximum differences of 9.22% and 22.12% at the bottom and top of the atmosphere, respectively. Meanwhile, the differences in radiative forcing between aspect ratios as a function of particle size and not varying with particle size are not significant, averaging less than 2%. Besides, the aspect ratio not varying with particle size underestimates the deposition velocity of small particles and overestimates that of large particles compared to that as a function of particle size, with maximum differences of 7% and 4%, respectively.

Extracting stellar emissivity via a machine learning analysis of MSX and LAMOST catalog data

Many astronomical studies model stars like radiating blackbodies with unit emissivity. Their conclusions should be reconsidered if the stellar spectral emissivity, ${ϵ}_{\ensuremath{\lambda}}$, were to be proven to be appreciably smaller. However, determining ${ϵ}_{\ensuremath{\lambda}}$ from raw observational data poses serious technical challenges. Here, using a machine learning technique, we implemented an inverse model for calculating the stellar spectral radiation flux in a given spectral band emissivity. Radiation flux data in some spectral bands serve as input to determine the unknown model parameters. To this purpose, we chose 411 stars (361 from the Midcourse Space Experiment (MSX) catalog and 50 from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) catalog) as training samples of a stochastic particle swarm optimization algorithm. The mean values of the emissivity estimates thus obtained deviate significantly from the ideal blackbody value. Knowledge of the model parameters then enabled us to calculate the radiation fluxes in other spectral bands to compare with the existing observational data and thus validate our approach. Finally, based on the trained algorithm, we discuss our predictions for spectral bands where astronomical data are unavailable. Besides providing direct evidence against modeling stars as emitting blackbodies, our conclusions also call for more direct investigations of the stellar emissivity.

APPLICATION OF STOCHASTIC PARTICLE SWARM OPTIMIZATION ALGORITHM FOR NONINVASIVE DETERMINATION OF TEMPERATURE-DEPENDENT THERMAL PROPERTIES OF BIOLOGICAL TISSUE

The knowledge of thermal properties of biological tissue is of great importance to medical diagnosis and thermotherapy. In this study, an inverse model based on stochastic particle swarm optimization (SPSO) algorithm and sensitivity analysis is developed to determine the temperature-dependent thermal properties of one-dimensional biological tissue. The noninvasive determination task is formulated as an inverse problem which is solved by the SPSO algorithm from the knowledge of surface temperature measurements. A logistic mapping strategy is introduced to improve the quality of the initial particle swarm. Retrieval results demonstrate that the developed inverse technique is robust to determine the temperature-dependent thermal conductivity, specific heat and blood perfusion rate of biological tissue. The maximum relative error of the simultaneous determination results is less than 0.8%. The maximum determination error is 1.15% when a 3% random deviation is considered. Meanwhile, the present SPSO algorithm is proved to be more efficient and accurate than other intelligent algorithms. Considering the convergence accuracy and computational time, the population size of the SPSO algorithm is suggested to be M = 80.

An algorithm for solving FEVM problem based on SPSO algorithm

To solve fuzzy expected value model problem that widely exists in fuzzy programming field, a new hybrid intelligence algorithm based on Stochastic Particle Swarm Optimization (SPSO) algorithm is put forward in this article. Fuzzy simulation is used to get training samples for multi-layer (BP) Back Propagation artificial neural networks and multi-layer BP artificial neural networks is used to approximate fuzzy expected value function when SPSO algorithm is used to find the optimal value, the trained multi-layer BP artificial neural networks is used to calculate fuzzy expected function’s fitness value and detail steps are designed. Compared with the hybrid intelligence algorithm based on the classical Genetic Algorithm, the proposed algorithm overcomes some defects, such as taking a long time, computing complexity, easy being immersed in local extremum. The results are justified with the help of two numerical illustrations for fuzzy expected value model problem, the effectiveness of our new approach is demonstrated and it has determinate practical value.

Probabilistic convergence analysis of the stochastic particle swarm optimization model without the stagnation assumption

As a stochastic optimization algorithm, it is more reasonable for particle swarm optimization (PSO) to study the probabilistic convergence. In this study, we analyze its convergence with probability 1 using the theory of probabilistic metric space. Firstly, we assume that the personal best of the particle and global best of the particle swarm are updated during the run; however, we do not assume that the personal best of the particle and global best of the particle swarm must be independent of the position of the particle. Such an assumption is more pragmatic and could be implemented in all PSO variants. Then, we develop a stochastic recurrence relation of the state of a particle under this assumption. Finally, we derive a sufficient condition that ensures the stochastic PSO algorithm is τ-convergent with probability 1. In addition, we analyze the impact of the parameters in the unstable range on the individual iterations. Although these parameters could not guarantee the long-term convergence, their impact significantly influences the exploration ability of PSO; thus, it is crucial to understand them. Based on this analysis, we propose a novel strategy for balancing the exploitation and exploration abilities of the PSO algorithm.

Application of improved decentralized fuzzy inference methods for estimating the thermal boundary condition of participating medium

The decentralized fuzzy inference method (DFIM) was applied to estimate the time-dependent heat flux of 1D participating medium. The direct problem concerned on coupled radiation and conduction heat transfer in the medium was solved by the finite volume method and discrete ordinate method. The simulated boundary temperature was served as input for the inverse analysis. The inverse problem was formulated as an optimization approach. Three improved decentralized fuzzy inference methods (IDFIMs) were developed to accelerate the convergence rate and enhance the estimation accuracy. Five kinds of time-dependent heat fluxes were considered to test the performance of the present inverse technique. No prior information on the functional forms of the unknown boundary conditions was needed for the inverse analysis. All retrieval results showed that the incident heat flux of participating medium can be accurately estimated by DFIMs. The proposed IDFIMs achieved better performance than the original DFIM in terms of computational accuracy and efficiency. Moreover, a comparison between the IDFIM and other optimization techniques was conducted. The proposed IDFIM was proved to be more efficient and accurate than conjugate gradient method, Levenberg-Marquardt method, stochastic particle swarm optimization algorithm and genetic algorithm.

Inversion of stellar spectral radiative properties based on multiple star catalogues

The spectral flux density of stars can indicate their atmospheric physical properties. A detector can obtain any band flux density at the design stage. However, the band flux density is confirmed and fixed in the process of operation because of the restriction of filters. Other band flux densities cannot be obtained through the same detector. In this study, a computational model of stellar spectral flux density is established based on basic physical parameters which are effective temperature and angular parameter. The stochastic particle swarm optimization algorithm is adopted to address this issue with appropriately chosen values of the algorithm parameters. Four star catalogues are studied and consist of the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST), Wide-field Infrared Survey Explorer (WISE), Midcourse Space Experiment (MSX), and Two Micron All Sky Survey (2MASS). The given flux densities from catalogues are input parameters. Stellar effective temperatures and angular parameters are inverted using the given flux densities according to SPSO algorithm. Then the flux density is calculated according to Planck's law on the basis of stellar effective temperatures and angular parameters. The calculated flux density is compared with the given value from catalogues. It is found that the inversion results are in good agreement for all bands of the MSX and 2MASS catalogues, whereas they do not agree well in some bands of the LAMOST and WISE catalogues. Based on the results, data from the MSX and 2MASS catalogues can be used to calculate the spectral flux density at different wavelengths of given wavelength ranges. The stellar flux density is obtained and can provide data support and an effective reference for detection and recognition of stars.

Application of stochastic particle swarm optimization algorithm to determine the graded refractive index distribution in participating media

Inverse estimation of the refractive index distribution in one-dimensional participating media with graded refractive index (GRI) is investigated. The forward radiative transfer problem is solved by the Chebyshev collocation spectral method. The stochastic particle swarm optimization (SPSO) algorithm is employed to retrieve three kinds of GRI distribution, i.e. the linear, sinusoidal and quadratic GRI distribution. The retrieval accuracy of GRI distribution with different wall emissivity, optical thickness, absorption coefficients and scattering coefficients are discussed thoroughly. To improve the retrieval accuracy of quadratic GRI distribution, a double-layer model is proposed to supply more measurement information. The influence of measurement errors upon the precision of estimated results is also investigated. Considering the GRI distribution is unknown beforehand in practice, a quadratic function is employed to retrieve the linear GRI by SPSO algorithm. All the results show that the SPSO algorithm is applicable to retrieve different GRI distributions in participating media accurately even with noisy data.

Apparent directional spectral emissivity determination of semitransparent materials**Project supported by the National Natural Science Foundation of China (Grant Nos. 51476043 and 51576053) and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51421063).

An inverse estimation method and corresponding measurement system are developed to measure the apparent spectral directional emissivities of semitransparent materials. The normal spectral emissivity and transmissivity serve as input for the inverse analysis. Consequently, the refractive index and absorption coefficient of the semitransparent material could be retrieved by using the pseudo source adding method as the forward method and the stochastic particle swarm optimization algorithm as the inverse method. Finally, the arbitrary apparent spectral directional emissivity of semitransparent material is estimated by using the pseudo source adding method given the retrieval refractive index and absorption coefficient. The present system has the advantage of a simple experimental structure, high accuracy, and excellent capability to measure the emissivity in an arbitrary direction. Furthermore, the apparent spectral directional emissivity of sapphire at 773 K is measured by using this system in a spectral range of 3 μm–12 μm and a viewing range of 0°–90°. The present method paves the way for a new directional spectral emissivity measurement strategy.

Inverse Transient Radiative Analysis in Two-Dimensional Turbid Media by Particle Swarm Optimizations

Three intelligent optimization algorithms, namely, the standard Particle Swarm Optimization (PSO), the Stochastic Particle Swarm Optimization (SPSO), and the hybrid Differential Evolution-Particle Swarm Optimization (DE-PSO), were applied to solve the inverse transient radiation problem in two-dimensional (2D) turbid media irradiated by the short pulse laser. The time-resolved radiative intensity signals simulated by finite volume method (FVM) were served as input for the inverse analysis. The sensitivities of the time-resolved radiation signals to the geometric parameters of the circular inclusions were also investigated. To illustrate the performance of these PSO algorithms, the optical properties, the size, and location of the circular inclusion were retrieved, respectively. The results showed that all these radiative parameters could be estimated accurately, even with noisy data. Compared with the PSO algorithm with inertia weights, the SPSO and DE-PSO algorithm were demonstrated to be more effective and robust, which had the potential to be implemented in 2D transient radiative transfer inverse problems.

Consensus analysis for a class of stochastic PSO algorithm

Most of the existing results mainly concentrate on the convergence analysis and stability analysis of Particle Swarm Optimization (PSO) in the presence of ω∈[0, 1]. However, few existing works discuss the convergence and the stability of time-varying stochastic PSO swarm system from the perspective of the consensus. This paper firstly proposes an improved consensus protocol on the basis of the velocity and position equations of the canonical PSO algorithm, and transforms the dynamical PSO system into one new linear discrete-time system including random variables. Finally several important theorems concerning the mean square consensus are provided according to the existing important results of nonnegative random matrices, stability theory of large-scale system, etc. Furthermore, the boundary of consensus region is given to better select the parameters in PSO algorithm. Finally, numerical simulation results chiefly discuss the convergence analysis of each particle and demonstrate the effectiveness of the above-mentioned theorems.

Calculation of Parameters of Crop Water Production Function of Jensen Model Based on Stochastic Particle Swarm Optimization Algorithm

In this paper, Stochastic Particle Swarm Optimization Algorithm (SPSO) is introduced to calculate parameters of crop water production function directly. SPSO is an improvement of the standard PSO, compared with which, it can be guaranteed to converge to the global optimization solution with probability one in theory, and speed up the convergence. The dimension of space of a particulate is determined by the phases of crop growth and development period in SPSO, and the sensitive index , an important parameter of crop water production function, is regarded as optimized variable to be calculated directly. This method can eliminate some problems existing in linear regression method, such as biased estimate and distortion of result and it can search the global optimization value more easily than the PSO. Through example analysis, we can see that the SPSO is better than PSO in accuracy and calculation speed.

A Two-Stage Scheme for Plate Damage Identification Based on Lock-in Thermography and Dynamic Analysis

This paper presents a two-stage scheme of damage identification for plate-type structure. In the first stage, probable damaged regions and their relative severities can be detected based on lock-in thermography technique. In the second stage, the relation between the damage level and its corresponding natural frequencies of the plate is constructed by means of Kriging surrogate model based on dynamic analysis. The inverse problem of damage quantification over the surrogate model is then solved by using a robust stochastic particle swarm optimization algorithm. Experimental study on a double-damaged plate demonstrates the feasibility and effectiveness of the proposed scheme.

Retrieve properties of participating media by different spans of radiative signals using the SPSO algorithm

The numerical model of a short-pulse laser propagating in participating media was analysed based on the complete transport theory described as the transient radiative transfer equation (TRTE). The finite volume method was used to solve the TRTE for any dimensional problem. Radiative signals are transmitted signals and reflected signals caused by time-domain laser pulse and signal results were compared with the benchmark results obtained by the reverse Monte Carlo method. Moreover, sensitivity analysis has been presented with different thickness, short pulse width and optical properties. In order to estimate the optical parameters effectively, some criteria for choosing more sensitive spans of the measured signals have been obtained based on the sensitivity analysis. Furthermore, different sampling spans and peak values of radiative signals were used as measurement data for inverse analysis by using the stochastic particle swarm optimization algorithm. Firstly, the different sampling times of transmittance and reflectance signals were, respectively, used as the measurement data to reconstruct optical properties (scattering coefficients and absorption coefficients) of one-dimensional participating media. After that, the maximums of the signals for inverse analysis with different albedos were investigated and the properties of different cases were estimated and listed.

Identification of 5-Axis Machine Tools Feed Drive Systems for Contouring Simulation

An identification technique is introduced for identifying closed loop transfer function of machine tool’s feed drive systems to be used in simulation of the tracking and contouring performance of Computer Numerical Controlled (CNC) machine tools. The identification is performed from air-cutting tests utilizing only standard G-codes containing linear motion commands. A general transfer function model is derived for representing the closed loop tracking response of the feed drive system. The model considers the drive to be controlled by commonly used controller schemes such as P-PI Cascade, PID or the Sliding Mode Controller (SMC) with feed-forward dynamic and friction compensation. The parameters of the model transfer function are fitted tominimize the discrepancy between the actual and predicted axis position on the axis. In order to guarantee the stability of the identified model transfer function, bounds on the pole locations are imposed. The resultant constrained non-linear optimization problem is solved efficiently using the Particle Swarm Optimization (PSO) method. For achieving reliable convergence of the stochastic PSO algorithm, a parameter tuning strategy is presented. Simulation and experimental studies show that the identified feed drive model captures the fundamental dynamics of the drives system accurately for simulating their closed loop response. Combined with the kinematics of the machine, contouring errors of 5-axis CNC machine tools during simultaneous multi-axis motion are predicted.

Inverse Problem of Absorption Coefficients for One-dimensional Non-uniform Medium

Inverse radiation problem for one-dimensional non-uniform medium has been investigated. A stochastic particle swarm optimization algorithm (SPSO) with a stochastic selection is adopted to estimate the absorption coefficients in a one-dimensional absorbing, emitting medium. The directional radiative intensities simulated by discrete ordinate method are served as input for the inverse problems. The performances of this algorithm on the accuracy of estimation are examined. Numerical results show that the proposed algorithm can guarantee the convergence of the global optimization solution, and is proved to be fast. The absorption coefficients could be estimated accurately.

Particle Swarm Optimization for Scattering Coefficients in One-Dimensional Non-Uniform Media

Inverse problem of scattering coefficients in one-dimensional non-uniform medium has been investigated. A stochastic particle swarm optimization algorithm (SPSO) with a stochastic selection is adopted to estimate the absorption coefficients in a one-dimensional absorbing, emitting and scattering medium. The directional radiative intensities simulated by discrete ordinate method are served as input for the inverse problems. The performances of this algorithm on the accuracy of estimation are examined. Numerical results show that the proposed algorithm can guarantee the convergence of the global optimization solution, and is proved to be fast. The distribution of scattering coefficients could be estimated accurately.

Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization

As a part of resolving optical properties in atmosphere radiative transfer calculations, this paper focuses on obtaining aerosol optical thicknesses (AOTs) in the visible and near infrared wave band through indirect method by gleaning the values of aerosol particle size distribution parameters. Although various inverse techniques have been applied to obtain values for these parameters, we choose a stochastic particle swarm optimization (SPSO) algorithm to perform an inverse calculation. Computational performances of different inverse methods are investigated and the influence of swarm size on the inverse problem of computation particles is examined. Next, computational efficiencies of various particle size distributions and the influences of the measured errors on computational accuracy are compared. Finally, we recover particle size distributions for atmospheric aerosols over Beijing using the measured AOT data (at wavelengths λ=0.400, 0.690, 0.870, and 1.020 μm) obtained from AERONET at different times and then calculate other AOT values for this band based on the inverse results. With calculations agreeing with measured data, the SPSO algorithm shows good practicability.