Backward Monte Carlo Method Research Articles

Simulating skylight polarization patterns using the backward Markov Chain Monte Carlo method

Skylight polarization patterns provide valuable information for atmospheric measurements, polarized remote sensing and navigation applications. However, efficiently and accurately modeling polarized radiative transfer in atmospheric scattering remains challenging. We propose a backward Markov chain Monte Carlo (B-MCMC) method to simulate skylight polarization patterns by constructing a Markov chain in parameter space to track photons from the sensor to the top-of-atmosphere (TOA). The results show that the B-MCMC model significantly improves the computational efficiency by a factor of 8-10 while retaining the computational accuracy compared with Monte Carlo simulations. The experiments show that in cloudy skies, the skylight polarization pattern is generally weakened, in the field of skylight polarization detection and application, long wavelengths should be used in clear weather and blue-violet light should be used in cloudy weather, which corresponds to a larger degree of polarization (DOP) and facilitates the acquisition of polarization information. Finally, the aerosol optical depth (AOD) has an important effect on the skylight polarization, as the AOD increases, the DOP decreases, and the decreasing trend will be more and more obvious, when the AOD is above 0.3, the maximum DOP will not exceed 0.5, which is verified by the division of focal plane (DOFP) polarization measurement device.

Three-dimensional inhomogeneous temperature tomography of confined-space flame coupled with wall radiation effect by instantaneous light field

Optical tomography has been demonstrated to be a powerful tool for the three-dimensional (3D) measurement of the dynamic characteristics of turbulent flame. Many practical visualizations of reaction flows require imaging through optical windows on the combustor, which have complex interactions with wall temperature, reflection characteristics, and limited optical access, which may seriously influence the imaging quality. Previous work focused on unconfined flame imaging, and lacked the study of the multiple reflection effects of the wall and the tomographic reconstruction within a wide temperature range. To solve these problems, the effect of chamber wall radiation on the photothermal information is analyzed in the forward problem, and the flame temperature with wall radiation is reconstructed in the inverse problem. In the forward problem, the light field acquisition model of spontaneous emission of the confined flame is developed through the backward Monte Carlo method based on the radiation distribution factor, which can comprehensively consider the essential effects such as radiative attenuation, wall reflection, medium scattering interference, and limited optical access. The recorded light field signals indicate that the reflection pattern and transfer mechanism of the wall material could affect the contribution of radiative source terms in different discrete domains to the detected energy. A novel tomography algorithm, namely, the adaptive threshold segmentation iterative regularization (ATSIR) method, has been proposed to extend the temperature range of tomography. The key of this method is to carry out a two-step reconstruction of the high and low-temperature regions through the temperature threshold, and introduce the prior smoothing information to alleviate the ill-posedness of tomography. The visualization results show that the well-established algorithms (e.g., least-square QR-factorization and regularization) have lower reconstruction quality for the combustion field within a wide temperature range, even if the regularization term is added. However, the proposed ATSIR method has the advantages of better suppression of fluctuations, smaller reconstruction error, and stronger anti-noise ability. The detailed analysis of the radiative transfer mode and 3D temperature visualization of the combustion field in a confined space can provide a valuable guideline for the safety design of the engine combustion chamber and fuel utilization.

Backward Monte Carlo method for simulating spectral radiation characteristics of boost-gliding vehicle

The boost-gliding hypersonic vehicle possesses unique features of high Mach number, high stealth, and high maneuverability, becoming a new air defense threat. The detection of its spectral radiation characteristics is one of the early warning ways. The study of spectral radiation characteristics is essentially a process of solving the Radiative Transfer Equation (RTE). Backward Monte Carlo Method (BMCM) is the most accurate method to solve the RTE compared with other methods, such as the Finite Volume Method and Line-Of-Sight method. In this study, numerical simulations of spectral radiation characteristics of an HTV2-shaped aircraft, at three trajectory points of 70 km, 50 km, and 30 km, are conducted using the BMCM. The incoming flow around the aircraft is calculated by a two-temperature OpenFOAM solver. In particular, a long-range detection model for the BMCM is developed to improve simulation efficiency. The absorption coefficients are calculated by the Line-By-Line method. Eventually, a code termed Plume Work Station-Radiation is developed to obtain spectral radiation intensities of an HTV2-shaped aircraft in the range of 1−15μm. Simulation results indicate that the high-temperature aircraft surface makes a vital contribution to the total spectral radiation characteristics, while the external flow field only has a finite contribution at some sensitive bands. The spectral radiation intensity at 50 km is the highest among the three trajectory points. An intersection point appears between the spectral radiation intensities of 70 km and 30 km due to the localized high-temperature surface at 70 km. The wavelength of the intersection point varies with the detector direction, which is attributed to the variation of the projected area of the high-temperature surface with the detector direction.

Model of Spectral and Directional Radiative Transfer in Complex Urban Canopies with Participating Atmospheres

Thermal heat transfers, including solar and infrared radiation in cities, are key processes for studying urban heat islands, outdoor human thermal comfort, energy consumption, and production. Thus, accurate radiative transfer models are required to compute the solar and infrared fluxes in complex urban geometry accounting for the spectral and directional properties of the atmosphere and city fabric materials. In addition, these reference models may be used to evaluate existing parametrization models of radiative heat transfer and to develop new ones. The present article introduces a new reference model for outdoor radiative exchange based on the backward Monte Carlo method. The integral formulations of the direct and scattered solar, and the terrestrial infrared radiative flux densities are presented. This model can take into account the ground (e.g., roads, grass), different types of buildings and vegetation (e.g., trees consisting of opaque leaves and trunks) with their spectral and directional (Lambertian and specular) reflectivity of materials. Numerical validations of the algorithm are presented against the results of a state-of-the-art model based on the radiosity method for the particular case of an infinitely long street canyon. In addition, the convergence of urban solar radiation budgets is studied for a selection of urban complex geometries including or not the window glazing. Good convergence is found for all geometries, even in the presence of rare events due to specular reflections.

The effect of the round jet parameters on infrared radiation characteristics

In this study, the effects of nozzle size, CO2 and H2O molar fraction, pressure, and temperature on the infrared characteristics of round jets are studied. The backward Monte Carlo method is used to calculate the spectral radiation characteristics and infrared images. The results show that kλ is insensitive to the molar fraction of the species, and it is slightly more sensitive to pressure. Temperature has the greatest effect on the kλ. In addition, the effects of characteristic length of the jet, molar fraction of the species, and pressure on the infrared characteristics are similar. (1) When the characteristic optical thickness of the jet is thick enough, with the increasing of above parameters, the spectral radiance increases at 3 ∼ 3.6 μm and 4.6 ∼ 5 μm, while it decreases around 4.3 μm. The magnitude of the two radiance peaks near 4.1 μm and 4.4 μm remain almost unchanged. However, the peak position moves to both sides. (2) Otherwise, there will be only one radiance peak in 4.1 ∼ 4.4 μm. The height of radiance peak decreases with the decrease of characteristic optical thickness.

A backward Monte Carlo method for fast-ion-loss simulations

This paper presents a novel scheme to improve the statistics of simulated fast-ion loss signals and power loads to plasma-facing components in fusion devices. With the so-called backward Monte Carlo method, the probabilities of marker particles reaching a chosen target surface can be approximately traced from the target back into the plasma. Utilizing the probabilities as a priori information for the well-established Forward Monte Carlo method, statistics in fast-ion simulations are significantly improved. For testing purposes, the scheme has been implemented to the ASCOT suite of codes and applied to a realistic ASDEX upgrade configuration of beam-ion distributions

A New Approach to Solve Inverse Boundary Design of a Radiative Enclosure With Specular–Diffuse Surfaces

Abstract The maintenance of uniform temperature distribution affects the efficiency in most industrial applications. In this study, a novel strategy has been developed for inverse radiative boundary design problems in radiant enclosures with participating medium. This study presents the Backward Monte Carlo method to investigate the inverse boundary design of an enclosure composed of specular and diffuse surfaces. A new optimized Monte Carlo method is proposed to determine the temperature distribution of heaters to achieve desirable prescribed uniform heat flux on the design surfaces. The proposed approach is highly efficient and simple to implement with appropriate results. The evaluated heat fluxes on design surfaces and temperature distribution of heaters are compared with the case where the reradiating walls are assumed to be perfectly diffuse. In the proposed approach, for a specific range of specularity, the absorptivity of the reradiating surfaces does not affect the temperature distribution of heaters. Compared to the diffuse walls, the specular walls have a more uniform temperature distribution and heat flux of heaters. This finding will provide insight into solar furnaces design to enhance temperature uniformity, making specular surfaces suitable in many industrial applications.

Generalized source term multiflux method coupled with Runge-Kutta ray tracing technique for arbitrary radiative intensity of graded-index media.

The generalized source term multiflux method (GSMFM) combined with Runge-Kutta ray tracing technique is developed to calculate arbitrary directional radiative intensity of graded-index media. In this method, the finite volume method is employed to solve source terms along the curved ray path determined by the Fermat principle. Runge-Kutta ray tracing technique is adopted to obtain the ray trajectory numerical solution in graded-index media. And the GSMFM is used to solve radiative intensity to be expected. One-dimensional and two-dimensional radiative heat transfer problems are investigated to verify the performance of this method. The numerical results show that the accuracy of the GSMFM is close to that of backward Monte Carlo (BMC) method, while the efficiency of GSMFM is much higher than that of the BMC. Therefore, the GSMFM developed can be considered as a promising method to solve arbitrary radiative intensity in graded-index media.

Thermal emission of a two-dimensional semitransparent medium with discrete distributions of graded index

The backward Monte Carlo method combined with the discrete Runge-Kutta ray-tracing technique (DRKRT) is developed to simulate the thermal emission of a two-dimensional medium with discrete distributions of graded index. Refractive index and its gradient are retrieved by the moving least quare approximation. The comparison between the results predicted by the (DRKRT) and those in references shows excellent agreement, which confirms the validity of the present method. The DRKRT can be also applied to discrete distributions of graded index, given at nonuniform grids, or with data errors. For discrete distributions of nonlinear refractive index with large gradient, the accuracy of the DRKRT decreases at peaks of the apparent thermal emission, which requires finer grids.

Robust long-term interest rate risk hedging in incomplete bond markets

AbstractPricing ultra-long-dated pension liabilities under the market-consistent valuation is challenged by the scarcity of the long-term market instruments that match or exceed the terms of pension liabilities. We develop a robust self-financing hedging strategy which adopts a min–max expected shortfall hedging criterion to replicate the long-dated liabilities for agents who fear parameter misspecification. We introduce a backward robust least squares Monte Carlo method to solve this dynamic robust optimization problem. We find that both naive and robust optimal portfolios depend on the hedging horizon and the current funding ratio. The robust policy suggests taking more risk when the current funding ratio is low. The yield curve constructed by the robust dynamic hedging portfolio is always lower than the naive one but is higher than the model-based yield curve in a low-rate environment.

The backward Monte Carlo method for semiconductor device simulation

A backward Monte Carlo method for the numerical solution of the semiconductor Boltzmann equation is presented. The method is particularly suited to simulate rare events. The general theory of the backward Monte Carlo method is described, and several estimators for the contact current are derived from that theory. The transition probabilities for the construction of the backward trajectories are chosen so as to satisfy the principle of detailed balance. This property guarantees stability of the numerical method and allows for a clear physical interpretation of the estimators. A symmetric sampling method which generates wave vectors always in pairs symmetric to the origin can be shown to yield zero current exactly as thermal equilibrium is approached. The properties of the different estimators are evaluated by simulation of an n-channel MOSFET. Quantities varying over many orders of magnitude can be resolved with ease. Such quantities are the drain current in the sub-threshold region, the high-energy tail of the carrier distribution function, and the so-called acceleration integral which varies over 30 orders in the example shown.

Tomography-based analysis of apparent directional spectral emissivity of high-porosity nickel foams

The apparent radiative behaviors of open cell nickel foams and their dependency on textural features and intrinsic optical properties are numerically investigated in the limit of geometrical optics. Five realistic nickel foams with high porosity from 0.87 to 0.97 and pore density from 10 to 40 PPI were used as samples. First, the representations of foams and their microstructures were obtained by using computed tomography and scanning electron microscope techniques. Second, a Backward Monte Carlo method that employed the realistic representations and their intrinsic optical properties facilitated the computation of the apparent directional spectral emissivity. The apparent emissivity and its dependency on textural features and intrinsic optical properties were subsequently investigated based on a specially defined Representative Elementary Volume. It was noted that at pore scale, the non-homogenized apparent emissivity fields can vary according to the local compositions near to the foam surface (solid strut and void space) and the void pore behaves somewhat like a “black cavity” for thermal radiation. For open cell foams composed of low emittance nickel struts, high-porosity cell network may increase the intrinsic emissivity by a maximum of nearly 4 times. A predictive relationship was established that links the homogenized apparent emissivity to the open porosity and the intrinsic emissivity of solid struts. These findings will provide a deeper understanding of both the non-homogenized and homogenized radiative behaviors of open cell foams.

Identification of radiative properties for heterogeneous materials at high temperature

In porous ceramics used as thermal barriers, it is necessary to determine whether radiative heat transfer is significant compared to energy transport by conduction. In order to address this problem in a first approach only radiative heat transfer is considered through an isothermal semi-transparent ceramic. The emphasis is placed here on the method to estimate the radiative properties. It is based on an identification technique that combines spectrometric emission power measurements at high temperature together with a Backward Monte Carlo Method (BMCM).Absorption and scattering spectral coefficients of a SiO2 fibrous ceramic are presented as an example of the output of the technique.

Backward and forward Monte Carlo method for vector radiative transfer in a two-dimensional graded index medium

In vector radiative transfer, backward ray tracing is seldom used. We present a backward and forward Monte Carlo method to simulate vector radiative transfer in a two-dimensional graded index medium, which is new and different from the conventional Monte Carlo method. The backward and forward Monte Carlo method involves dividing the ray tracing into two processes backward tracing and forward tracing. In multidimensional graded index media, the trajectory of a ray is usually a three-dimensional curve. During the transport of a polarization ellipse, the curved ray trajectory will induce geometrical effects and cause Stokes parameters to continuously change. The solution processes for a non-scattering medium and an anisotropic scattering medium are analysed. We also analyse some parameters that influence the Stokes vector in two-dimensional graded index media. The research shows that the Q component of the Stokes vector cannot be ignored. However, the U and V components of the Stokes vector are very small.

Inverse boundary design solution in a combined radiating-free convecting furnace filled with participating medium containing specularly reflecting walls

In this paper, an inverse boundary design problem of combined natural convection-radiation considering specular reflectivity and participating media is solved. The aim of this paper is to find the strength of heaters in a step-like enclosure to produce the desired temperature and heat flux distribution on the design surface. The finite volume method for transition flow (which causes a faster convergence) is used as the direct solver of the energy and momentum equations. The SIMPLE algorithm is utilized to satisfy pressure–velocity coupling in order to solve the free convection heat transfer. Also, the backward Monte Carlo method is employed in order to be able to compute the distribution factors and carry out the radiant exchange calculations. Finally, the goal function which is defined on the basis of square root error is minimized by means of a conjugate gradients method. The effects of variation of specularity ratio for specular surfaces are investigated to compare the results for diffuse and specular surfaces in the enclosure considering radiation and free convection. The effects of variation of range of parameters such as the Rayleigh number, temperature ratio, radiation conduction parameter and the specularity ratio on the relative root mean square and heat flux are investigated and results are compared. The results demonstrate the efficiency and the accuracy of the proposed method.

Solution of radiative inverse boundary design problem in a combined radiating-free convecting furnace

In this paper an inverse boundary design problem of combined natural convection–radiation is solved. The aim of this paper is to find the strength of heaters in a step-like enclosure to produce desired temperature and heat flux distribution on the design surface. The finite volume method for transition flow (which causes a faster convergence) is used as the direct solver of the energy and momentum equations. The SIMPLE algorithm is utilized to satisfy pressure–velocity coupling in order to solve the free convection heat transfer. Also, the backward Monte Carlo method is employed in order to be able to compute the distribution factors and carry out the radiant exchange calculations. Finally, the goal function which is defined on the basis of square root error is minimized by means of conjugate gradients method. The effects of variation of range of parameters such as the Rayleigh number, temperature ratio, radiation conduction parameter and the emissivity coefficient of insulated surfaces on the relative root mean square and heat flux are investigated and results are compared. The results demonstrate the efficiency and the accuracy of the proposed method.

A Novel, Noniterative Inverse Boundary Design Regularized Solution Technique Using the Backward Monte Carlo Method

In this paper, the inverse radiation boundary problem is solved using a simplified backward Monte Carlo method (MCM) for cases in which radiation is the dominant mode of heat transfer (i.e., radiative equilibrium). For an N-surface enclosure, N2 radiative transfer factors are required to carry out the radiant exchange calculations. In this paper, it is shown that when the enclosure is comprised of some adiabatic surfaces (as is nearly always the case in radiative furnaces), this number can be reduced considerably. This reduction in the required number of distribution factors causes a clear simplification in the formulation of the inverse problem and a substantial reduction in the computational time. After presenting the formulation for the inverse problem, standard test cases are solved to demonstrate the efficiency and the accuracy of the proposed method.

Radiative transfer modelling inside thermal protection system using hybrid homogenization method for a backward Monte Carlo method coupled with Mie theory

A backward Monte Carlo method for modelling the spectral directional emittance of fibrous media has been developed. It uses Mie theory to calculate the radiative properties of single fibres, modelled as infinite cylinders, and the complex refractive index is computed by a Drude-Lorenz model for the dielectric function. The absorption and scattering coefficient are homogenised over several fibres, but the scattering phase function of a single one is used to determine the scattering direction of energy inside the medium. Sensitivity analysis based on several Monte Carlo results has been performed to estimate coefficients for a Multi-Linear Model (MLM) specifically developed for inverse analysis of experimental data. This model concurs with the Monte Carlo method and is highly computationally efficient. In contrast, the surface emissivity model, which assumes an opaque medium, shows poor agreement with the reference Monte Carlo calculations.

On the treatment of non-optimal regularization parameter influence on temperature distribution reconstruction accuracy in participating medium

The choice of the regularization parameter plays a very important role in the inverse radiation problem of temperature distribution in participating medium and in practice the regularization parameter is not easy to determine accurately, which can directly affect the reconstruction accuracy and introduce errors into reconstruction results. This paper presents the alleviation of non-optimal regularization parameter influence on the temperature distribution reconstruction accuracy in participating medium using coupled methods, i.e., two kinds of regularization method (least square QR decomposition (LSQR) method and truncated singular value decomposition (TSVD) method) coupled with genetic algorithm (GA). The radiative heat transfer was described by the backward Monte Carlo method for its efficiency. Two kinds of temperature distributions with one peak and two peaks are considered. The results show that GA can still improve the accuracy of solutions even though the optimal regularization parameters are used in the coupled methods (LSQR-GA and TSVD-GA). GA can also reduce the temperature reconstruction errors due to the non-optimal choice of the regularization parameter and improve the accuracy of the reconstruction results in the coupled methods. Moreover, the coupled methods can even reach the same or better solutions accuracy for some samples with non-optimal regularization parameter, compared with the accuracy of solutions obtained by the single LSQR method or TSVD method with the optimal regularization parameter. This study demonstrates that the coupled method can alleviate non-optimal regularization parameter influence and obtain more accurate results for the inverse radiation problem of temperature distribution in participating medium.

Experimental reconstructions of flame temperature distributions in laboratory-scale and large-scale pulverized-coal fired furnaces by inverse radiation analysis

Two-dimensional (2-D) and three-dimensional (3-D) temperature distributions in laboratory-scale and large-scale pulverized-coal fired furnaces were reconstructed experimentally by means of CCD cameras through the inverse radiation analysis. The reconstruction technique was developed based on the backward Monte Carlo method. The reconstruction matrix equation was solved by the least square QR decomposition (LSQR) method. The numerical reconstructions were utilized for checking the validity of inverse method before each experimental reconstruction. The experimental reconstruction results were compared with those in references. The temperature distributions for both laboratory-scale and large-scale pulverized-coal fired furnaces can be numerically reconstructed well, and the experimentally reconstructed temperature distributions can reasonably reproduce the main features of actual temperature distributions in the pulverized-coal fired furnaces. The reconstruction technique also has a good ability of on-line temperature distributions reconstruction and monitoring, and will be useful for the combustion diagnostics and control of pulverized-coal fired power plant.