轴对称介质内辐射源项反演算法

结合Abel变换和离散坐标法,提出了一种基于CCD相机采集的单幅辐射图像重建轴对称发射-吸收介质内辐射源项分布的反演算法。通过在求解辐射正问题得到的准确值的基础上,添加随机噪声模拟试验测量数据,分析了网格数目、辐射源项分布形式、吸收系数和测量误差对算法反演精度的影响。测试结果表明:该算法对测量误差不敏感,在有测量误差的情况下也能够准确的重建介质内的辐射源项分布。     

用射线踪迹法解黑表面矩形介质耦合换热

本文用射线踪迹-节点分析法研究了二维黑体表面矩形、各向同性散射半透明介质内辐射与导热瞬态耦合换热。采用全隐格式的有限差分法离散二维瞬态微分能量方程,用辐射传递系数来表示辐射源项,结合谱带模型并采用射线踪迹法求解辐射传递系数。采用Patankar线性化方法将辐射源项及不透明边界条件线性化,并采用附加源项法处理边界条件,运用ADI方法求解名以上的线性化方程组,从而解得二维矩形介质内的瞬态温度分布。     

各向异性介质辐射特性参数联合反演

本文基于BP神经网络方法结合蒙特卡洛和BEER定律辐射传输模拟方法建立了联合反演各向异性散射介质的辐射特性参数模型。首先采用半球透射率结合半球反射率反演模型反演了各向同性介质的吸收系数和散射系数,在此基础上增加准直透射率,建立了联合反演各向异性介质的吸收系数、散射系数和散射不对称因子三参数联合反演模型。反演结果表明该模型能准确反演出介质辐射特性参数,具有实用意义。此外,为了检验测量误差对模型的反演准确性的影响,分别在不同程度测量误差情况下进行反演,结果显示测量误差对散射不对称因子反演值影响较大。     

多孔介质预混燃烧中辐射属性影响的敏感性分析

建立了惰性多孔介质中预混合燃烧的数学模型,采用辐射传递的有限体积法求解固相能量方程中的辐射源项,研究多孔介质热辐射在燃烧系统中的作用,考察辐射属性(吸收系数和散射反照率)对轴向温度场和辐射热流量影响的敏感性。研究表明,辐射属性参数波动对预测结果影响明显,固体热辐射在多孔介质预混燃烧中的影响不可忽略。     

激光脉冲在各向异性散射介质内的瞬态热效应

本文考察了激光脉冲在吸收、发射、各向异性散射介质内引起的瞬态热效应。将激光脉冲辐射在介质内的传递过程分为两个子过程：发射－衰减－反射过程和吸收－散射过程。用光线踪迹法结合节点分析导出辐射传递系数和辐射源项,用控制容积法解瞬态能量方程。检验结果表明,本文的计算方法准确。在此基础上,考察了散射特性、初始温度对激光脉冲响应的影响。     

表面不透明三层漫反射散射性介质耦合换热

本文采用射线踪迹、节点分析法研究了三层吸收、各向同性散射性介质层内的一维辐射和导热瞬态耦合换热,复合层表面不透明漫反射,介质层交界面半透明漫反射,且半透明漫反射交界面的反射率采用Fresnel反射定律确定。采用一层和二层辐射能量传递模型跟踪辐射能量在三层介质内的传递,从而推导出辐射传递系数。运用辐射传递系数求解辐射源项,在辐射对流边界条件下、采用全隐格式求解瞬态能量方程,并从机理上研究了辐射和导热耦合换热过程。     

辐射模型和弥散效应对多孔介质内燃烧影响的数值模拟

本文根据气固两相局部非热平衡假设,建立了甲烷/空气预混气在惰性多孔介质内的一维层流燃烧数学模型。分别采用附加导热、Rossland模型和二通量法模型求解固体能量方程中的辐射源项,研究了热辐射模型和弥散效应对多孔介质内燃烧火焰结构的影响。结果表明,多孔固体表面辐射的影响不可忽略,辐射模型对火焰温度的预测影响显著,而弥散效应对气体温度的分布及反应热影响则较小。     

一维平板内介质和表面的辐射特性参数同时反演方法EI北大核心CSCD

考虑了实际物体表面BRDF的影响,利用方向半球反射率、方向半球透射率、法向反射率和法向透射率等光谱数据,同时反演了一维平板内介质和表面的辐射特性参数。将该方法用于吸收散射、强散射和强吸收三种介质的辐射特性参数反演,反演结果与给定初值较吻合。     

基于光角度散射法的弥散介质多种辐射参数联合反演研究

本文基于光角度散射法,对弥散介质多种辐射特性参数进行了联合反演。此外,本文还提出了一种基于敏感度分析和主成分分析的测量角度优化筛选方案,用以寻找反演精准度较高的测量角度。研究表明:采用角度散射法对弥散介质多种辐射特性测量参数进行联合反演时,对于前向散射占优或者后向散射占优弥散介质,优化测量角度范围分别推荐为(0°,40°]和[140°,180°);与随机测量角度相比,优化筛选的测量角度能确保反演结果精度,且在5%的随机测量误差下,仍能获得合理的反演结果。     

一维平板内介质和表面的辐射特性参数同时反演方法

考虑了实际物体表面BRDF的影响,利用方向半球反射率、方向半球透射率、法向反射率和法向透射率等光谱数据,同时反演了一维平板内介质和表面的辐射特性参数。将该方法用于吸收散射、强散射和强吸收三种介质的辐射特性参数反演,反演结果与给定初值较吻合。     

Solution of the inverse radiative load problem in a two-dimensional system

An inverse radiation analysis is presented for estimating the temperature and the heat load distributions of the heating surface from the temperature and the heat flux measurements of the heated object. The Monte Carlo method is employed to solve the direct radiation problem. The inverse radiation problem is solved using the conjugate gradient and singular value decomposition methods. The measured data are simulated by adding random errors to the exact solution of the direct problem. The effects of the measurement errors on the accuracy of the inverse analysis are investigated. The study shows that the heat load distribution of the heating surface can be estimated accurately for the exact and noisy data. And the conjugate gradient method is better than the singular value decomposition method since the former can obtain more accurate results if the measurement errors are the same.     

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.     

半透明介质中辐射传递方程的反演计算及数值模拟

本文介绍了一侧为半透明、另一侧为非透明界面时一维半透明介质的辐射强度计算式。采用辐射与导热复合换热模型计算半透明介质内温度场。利用已知的温度场求半透明介质的辐射强度一正问题计算。将此辐射强度代入辐射反问题计算模型，引入测量误差，采用Ｃｈａｈｉｎｅ方法及演半透明介质内温度场一反问题计算。数值模拟表明，本文所采用的辐射反演法具有较高的精度及稳定性。     

Inverse radiation problem of temperature distribution in one-dimensional isotropically scattering participating slab with variable refractive index

In this paper, an inverse analysis is performed for estimation of source term distribution from the measured exit radiation intensities at the boundary surfaces in a one-dimensional absorbing, emitting and isotropically scattering medium between two parallel plates with variable refractive index. The variation of refractive index is assumed to be linear. The radiative transfer equation is solved by the constant quadrature discrete ordinate method. The inverse problem is formulated as an optimization problem for minimizing an objective function which is expressed as the sum of square deviations between measured and estimated exit radiation intensities at boundary surfaces. The conjugate gradient method is used to solve the inverse problem through an iterative procedure. The effects of various variables on source estimation are investigated such as type of source function, errors in the measured data and system parameters, gradient of refractive index across the medium, optical thickness, single scattering albedo and boundary emissivities. The results show that in the case of noisy input data, variation of system parameters may affect the inverse solution, especially at high error values in the measured data. The error in measured data plays more important role than the error in radiative system parameters except the refractive index distribution; however the accuracy of source estimation is very sensitive toward error in refractive index distribution. Therefore, refractive index distribution and measured exit intensities should be measured accurately with a limited error bound, in order to have an accurate estimation of source term in a graded index medium.     

Inverse radiation problem in one-dimensional slab by time-resolved reflected and transmitted signals

A time-domain inverse approach is proposed for estimating the distribution of absorbing and scattering coefficients in one-dimensional inhomogeneous media. The temporal reflected and transmitted signals are detected when an ultra-short pulse irradiates on the boundary of semi-transparent scattering media. Forward computation and inverse algorithm employ the least-squares finite element method and conjugate gradient method, respectively. As the prevalent diffusion approximation is not employed in our model, the present approach can be extended to more comprehensive application. The investigation about detected signals indicates that the reflected signals play a significant role in reconstructing optical properties; the signals in early sampling time are more important than those at long-time logarithm slope, and so, more attention should be paid to the early signals in the solution of inverse radiation problem. Three different inverse radiation problems are investigated to show the ability of the present approach to deal with the two-layer, three-layer and continuous inhomogeneous media. The effect of measured errors on the accuracy of reconstruction is investigated by adding artificial random errors. The results indicate that accurate reconstruction depends on not only precise numerical simulation but also quality of detected data.     

A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem

In this paper, a meshless regularization method of fundamental solutions is proposed for a two-dimensional, two-phase linear inverse Stefan problem. The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions. Furthermore, the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution. Therefore, regularization is necessary in order to obtain a stable solution. Numerical results for several benchmark test examples are presented and discussed.     

基于无导数优化方法的数值模式误差估计

初始场误差和模式误差是制约数值预报准确率的两个关键因素,本文主要考虑利用历史观测资料实现时空演变的模式误差的估计问题.通过把模式误差综合考虑成为准确模式中的未知项,把历史资料看作是带有未知项的准确模式的特解,构造了求解时空演变的模式误差项的反问题及其最优控制问题.给出了一个解决最优控制问题的无导数优化方法,该方法的优点是不需要建立原数值模式的切线性模式与伴随模式,它只需在增加一个外强迫项的基础上运行原数值模式即可实现模式误差项的最优估计.关于Burgers方程的算例表明,无论模式的初始状态是否准确已知,无导数优化方法都能有效解决时空演变的模式误差的最优估计问题,它为实际业务模式利用历史数据提取模式误差信息并显著地改进预报效果提供了一种方便可行的数值方法与理论依据.     

An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

Model error is one of the key factors restricting the accuracy of numerical weather prediction(NWP). Considering the continuous evolution of the atmosphere, the observed data(ignoring the measurement error) can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers’ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.     

On optimal solution error covariances in variational data assimilation problems

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively. The quasi-Newton BFGS algorithm is adapted to construct the covariance matrix of the optimal solution error using the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. Preconditioning is applied to reduce the number of iterations required by the BFGS algorithm to build a quasi-Newton approximation of the inverse Hessian. Numerical examples are presented for the one-dimensional convection–diffusion model.     

Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The data contain errors (observation and background errors), hence there will be errors in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can often be approximated by the inverse Hessian of the cost functional. Here we focus on highly nonlinear dynamics, in which case this approximation may not be valid. The equation relating the optimal solution error and the errors of the input data is used to construct an approximation of the optimal solution error covariance. Two new methods for computing this covariance are presented: the fully nonlinear ensemble method with sampling error compensation and the ‘effective inverse Hessian’ method. The second method relies on the efficient computation of the inverse Hessian by the quasi-Newton BFGS method with preconditioning. Numerical examples are presented for the model governed by Burgers equation with a nonlinear viscous term.