Simultaneous estimation of the temperature and heat rate distributions within the combustion region by a new inverse radiation analysis

A new inverse radiation analysis is presented for estimating the heat rate and temperature distributions in the combustion region from the information of the temperature and heat flux profiles of wall elements in the system. The Monte Carlo method is employed to solve the radiative heat transfer equation. The inverse radiation problem is posed as a minimization problem of the least squares criterion, which is solved by the conjugate gradient method. The performance of the present technique of inverse analysis is evaluated and the effects of the errors of the absorption coefficient, emissivity and convective heat transfer coefficient on the inverse analysis are investigated. The results show that the present technique is robust and yields accurate estimation even with noisy measurement.     

Regularized variable metric method versus the conjugate gradient method in solution of radiative boundary design problem

In this paper, an appropriate distribution of the heating elements’ strengths in a radiation furnace is estimated using inverse methods so that a pre-specified temperature and heat flux distribution is attained on the design surface. Minimization of the sum of the squares of the error function is performed using the variable metric method (VMM), and the results are compared with those obtained by the conjugate gradient method (CGM) established previously in the literature. It is shown via test cases and a well-founded validation procedure that the VMM, when using a “regularized” estimator, is more accurate and is able to reach at a higher quality final solution as compared to the CGM. The test cases used in this study were two-dimensional furnaces filled with an absorbing, emitting, and scattering gas.     

A new inverse approach for the equivalent gray radiative property of a non-gray medium using a modified zonal method and the complex-variable-differentiation method

Non-gray radiative properties of an absorbing, emitting, non-gray participating medium significantly increase the difficulty of solving the radiative transfer equation. This paper presents a new inverse approach for the equivalent gray radiative property of a non-gray medium. In this approach, the unknown equivalent gray radiative properties are treated as the optimization variables, and the errors to be minimized are the differences between the calculated temperatures and the measured ones. The measured data are simulated by solving the direct problem, in which a modified zonal method together with the Edwards exponential wide-band model is employed. In the inverse problem, the sensitivity coefficients are first calculated by the complex-variable-differentiation method, and then the least-square method and the Newton-Raphson iterative method are employed to minimize the target function. The effectiveness and efficiency of the inverse problem are demonstrated in an example, and another case is given to show the accuracy and potential of the proposed algorithm. The effects of the measurement error and the number of measurement points on the accuracy of the inverse analysis are also investigated in detail.     

The DORT solution in acoustic inverse scattering problem of a small elastic scatterer

The DORT (French acronym for Décomposition de l’Opérateur de Retournement Temporel) method is a novel approach for active detection and focusing of acoustic waves on the targets in the scattering medium. This technique involves the determination of the invariant of the time-reversal operator obtained by measurement of the scattering data in a pulse-echo mode. In this paper, a proposed approach based on the DORT method is developed to solve the acoustic inverse scattering problem of a small metallic scatterer. The proposed approach not only estimates the position of the scatterer, but also determines the physical properties of an unknown metallic scatterer such as the shape (cylinder or sphere), the material (density), and the size (radius) in an anisotropic scattering case. Theoretical and numerical simulation results are also studied and investigated to show that the proposed approach can simultaneously characterize all those properties of an unknown metallic scatterer. Moreover, the advantage of the proposed approach is to avoid the complex iterative scheme in solving the direct scattering problem and results in smaller computational load and faster implementation.     

Estimation of emissivities in a two-dimensional irregular geometry by inverse radiation analysis using hybrid genetic algorithm

An inverse radiation analysis is presented for estimating the wall emissivities for an absorbing, emitting, scattering media in a two-dimensional irregular geometry with diffusely emitting and reflecting opaque boundaries from the measured temperatures. The finite-volume method was employed to solve the radiative transfer equation for 2D irregular geometry. The hybrid genetic algorithm which contains local optimization algorithm was adopted to estimate wall emissivities by minimizing an objective function, while reducing computation time. It was found that an increase in the standard deviation in measurements significantly deteriorated the estimation of wall emissivities. Thus, a very accurate measurement was required in inverse radiation for better estimation of wall emissivities, especially, in a high temperature environment.     

Closed form solution to a second order boundary value problem and its application in fluid mechanics

The Adomian decomposition method is used by many researchers to investigate several scientific models. In this Letter, the modified Adomian decomposition method is applied to construct a closed form solution for a second order boundary value problem with singularity.     

Application of multi-phase particle swarm optimization technique to inverse radiation problem

The multi-phase particle swarm optimization (MPPSO) technique is applied to the inverse radiation problem in the present paper. The directional radiative intensities are served as the measurement data to estimate the radiative source term, optical thickness, scattering albedo, and phase function in one-dimensional semitransparent plane-parallel media by the inverse simulation. To check the performance and accuracy in retrieval, a comparison is presented between three PSO methods, i.e. the MPPSO, the standard PSO, and the Stochastic PSO. The results confirm the potential of the proposed approach MPPSO and show its effectiveness and superiority over the other two PSO algorithms. Furthermore, the effects of swarm size, searching space, phase change frequency, and velocity-reinitializing frequency on the convergence velocity and computational accuracy of MPPSO are also investigated.     

The solution of inverse radiation problems using an efficient computational technique

In our previous work (Park, Kim, JQSRT 58 (1) (1997) 115), an efficient computational technique for solving the radiative transfer equations for participating media has been devised, which is as accurate as the S₄ method but consumes much less computer time. In the present investigation, we employ this technique to solve an inverse radiation problem of determining the time-varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three-dimensional participating media where radiation and conduction occurs simultaneously. The present technique is found to identify the strength of the heat source efficiently without a priori information about the unknown function to be estimated.     

Benchmark numerical solutions for radiative heat transfer in two-dimensional medium with graded index distribution

In graded index media, the ray goes along a curved path determined by Fermat principle. Generally, the curved ray trajectory in graded index media is a complex implicit function, and the curved ray tracing is very difficult and complex. Only for some special refractive index distributions, the curved ray trajectory can be expressed as a simple explicit function. Two important examples are the layered and the radial graded index distributions. In this paper, the radiative heat transfer problems in two-dimensional square semitransparent with layered and radial graded index distributions are analyzed. After deduction of the ray trajectory, the radiative heat transfer problems are solved by using the Monte Carlo curved ray-tracing method. Some numerical solutions of dimensionless net radiative heat flux and medium temperature are tabulated as the benchmark solutions for the future development of approximation techniques for multi-dimensional radiative heat transfer in graded index media.     

非定常输运问题适应于消息传递并行编程环境的香农熵计算方法

在多计算步的非定常输运问题的蒙特卡罗模拟中,为自动调整每一步的样本数以获得较高的计算效率,可以有多种准则.一种可选的方法是在每一步每隔若干样本监测一次系统中未死亡粒子属性分布对应的香农熵的收敛情况以决定何时停止追加样本,此种方法需要在每一步频繁计算香农熵值.由于在MPI消息传递并行编程环境下香农熵的经典计算方法必须广播大量的数据,导致每一步的计算时间随香农熵计算频率的提高而快速增大,这显然是不能满足实际需求的.本文提出了一种适应于消息传递并行编程环境的香农熵计算新方法,该方法计算得到的香农熵值并不等价于经典方法,但二者之间的差别会随着样本数的增加而趋于零.新方法的最大优势是高频计算香农熵值的时间代价大为降低,为最终实现基于香农熵收敛判断的每步样本数的自动调整奠定了必要的基础.     

Manipulation with heterogeneity within a species population formulated as an inverse problem

Dependence of the evolutionary dynamics on the population’s heterogeneity has been reliably recognized and studied within the frame of evolutionary optimization theory. As the causal relation between the heterogeneity and dynamics of environment has been revealed, the possibility to influence convergence rate of evolutionary processes by purposeful manipulation with environment emerges.For the above purposes we formulate the task as the inverse problem meaning that desired population heterogeneity, quantified by Tsallis information entropy, represents the model’s input and dynamics of environment leading to desired population heterogeneity is looked for. Here the presented abstract model of evolutionary motion within the inverse model of replicating species is case-independent and it is relevant for the broad range of phenomena observed at cellular, ecological, economic and social scales. We envision relevance of the model for anticancer therapy, in which the effort is to circumvent heterogeneity as it typically correlates with the therapy efficiency.     

深穿透粒子输运问题的自适应抽样方法

屏蔽计算中的深穿透问题一直是蒙特卡罗计算的一个难题,研究了一种发射点作为驿站的随机游动机制,推导了相应的自适应抽样方法。其主要优势在于,在蒙特卡罗方法求解粒子输运的同时,利用已经获得的信息,自适应地控制各次抽样数,不断完善计算进程。通过对碰撞点引进重要性函数,实现发射点作为驿站的重要性抽样,并结合自适应控制达到最佳抽样状态。数值结果表明:基于发射点作为驿站的自适应抽样方法,在一定程度上克服了深穿透计算中估计值偏低现象。相应的重要函数抽样方法获得了满意的结果。     

Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite-difference Newton method

An inverse radiation problem was considered to estimate boundary conditions such as temperature distribution and emissivity in axisymmetric absorbing, emitting, and scattering medium, given the measured incident radiative heat fluxes. The finite-volume method was employed to solve a direct radiative transfer equation for a two-dimensional axisymmetric geometry. Various parameter estimators, such as conjugate-gradient method, hybrid genetic algorithm, and finite-difference Newton method, were employed to solve the inverse problems, while discussing their performances in terms of estimation accuracy and computational efficiency. Based on this, we proposed, as a best inverse analysis tool, a new combined method that adopted the hybrid genetic algorithm as an initial value selector and used the finite-difference Newton method as a parameter estimator.     

An inverse radiative transfer problem of simultaneously estimating profiles of temperature and radiative parameters from boundary intensity and temperature measurements

A parallel-plane space filled with absorbing, emitting, isotropically scattering, gray medium is studied in this paper. The boundary intensity and boundary temperature profiles are calculated for the inverse analysis. For the simultaneous estimation of temperature, absorption and scattering coefficient profiles in the medium, the sum of residuals of boundary intensity and temperature after being weighted by a balance factor is minimized through using a Newton-type iteration algorithm and the least-squares method. To avoid over-updating for the parameters, the relative updating magnitude during the iteration process is constrained not to be >0.5. It is shown that the boundary intensity measurement alone is not enough to estimate simultaneously the temperature (source) and the radiative properties (both absorption and scattering coefficients) when the measurement data contain sensitive random errors. The boundary temperature measurement can serve as a necessary supplementation to the boundary intensity to make this kind of inverse radiative transfer problem resolvable. It was shown that a compensation relationship between absorption and scattering coefficients makes it difficult to fix them accurately. Parabolic profiles for the three parameters are used to validate the estimation method. When the optical thickness approaches 4.0, the results for the radiative properties are not acceptable, although the result for temperature profile is reasonable. This means the method needs further improvements.     

A numerical procedure for estimation of the melt depth in laser material processing

In this study, an algorithm based on conjugate gradient method (CGM) is applied to estimate the unknown time dependent melt depth during laser material processing in liquid phase. The determination of the melt depth is treated as a one-dimensional, transient, inverse heat conduction problem (IHCP). It is assumed that no prior information is available for the functional form of the unknown melt depth, but it can be estimated by an inverse analysis with temperature measurements near the heated surface. The algorithm has been applied to aluminum, titanium and fused quartz and accurate melting depth and temperature distributions can also be returned. In addition, this methodology can also be applied to solve other problems such as calculating the cutting forces in nanomachining by atomic force microscopy (AFM), and estimating the heat sources in a X-ray lithographic process.     

Inverse problem of ship propeller cavitationnoise radiation

I.IntroductionInthecourseofnavigation,shipsinevitablyproducevariouskindsofnoiseradiation,whichbringusimportantinformation.Ononehand,manyresearchersdevotethemselvestothestudyofthetime-frequency-amplitudedomaincharacteristicsoftheshipnoiseradiationfield,whichistheregularmethodforstudyingthenoiseradiation,i.e.,thedirectproblem.ontheotherhand,theyareworkinghardatmakinguseofthelloiseradiationtoinferthestateofshipnavigationandtheconditionofthemainaPparatusonboard,etc.,andthisistheinverseproblemofthe…     

蒙特卡罗方法在解微分方程边值问题中的应用

介绍了蒙特卡罗方法的基本原理以及随机数的产生方法。基于蒙特卡罗方法的思想,结合有限差分方法,建立了求解微分方程边值问题的随机概率模型,并以第一类边界条件的拉普拉斯方程和一个给定初值及边界条件的非稳态热传导方程为数值算例,研究了蒙特卡罗方法在求解微分方程边值问题中的应用。结果表明:利用蒙特卡罗方法,不仅可以有效解决给定边界条件的微分方程,对于给定初值条件的微分方程,也可以从时域有限差分方程出发,采用蒙特卡罗方法进行求解。数值模拟和对误差的理论分析均表明,增加蒙特卡罗试验中的模拟粒子点数,可以提高计算结果的精度。     

Variational Monte Carlo analysis of Bose--Einstein condensation in a two-dimensional trap

The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas--Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度,畴壁动力学由此成为研究的重点。本文采用动力学蒙特卡罗模拟方法,对二维Ising模型磁畴界面的非平衡动力学展开数值研究。系统初态设为半正半负,即由完全有序但自旋取向完全相反的两部分组成,其间的磁畴壁随时间生长。通过对磁化标度形式的分析,发现畴壁内外的动力学标度形式虽然相同,但临界指数在数值上却存在很大差异,相差一个 =1,这是由初始条件导致的。     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度,畴壁动力学由此成为研究的重点.本文采用动力学蒙特卡罗模拟方法,对二维Ising模型磁畴界面的非平衡动力学展开数值研究.系统初态设为半正半负,即由完全有序但自旋取向完全相反的两部分组成,其间的磁畴壁随时间生长.通过对磁化标度形式的分析,发现畴壁内外的动力学标度形式虽然相同,但临界...