Automated Variance Reduction Applied to Nuclear Well-Logging Problems

The application of the Automated Variance Reduction Generator (ADVANTG) code to accelerate MCNP neutron transport calculations in fusion-relevant geometries is presented. The ADVANTG code generates variance-reduction parameters using the Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) methods based on deterministic transport calculations performed by the discrete ordinates code Denovo. The aim of ADVANTG is to reduce the MCNP computational time by automating the process of variance-reduction parameter generation. ADVANTG was tested on a simplified model of a JET-like tokamak that in spite of its simplicity retains all the major characteristics of such a tokamak. The performance of the nuclear data libraries provided with ADVANTG and of various other ADVANTG/Denovo settings on variance-reduction efficiency was tested. Several cases using deuterium-deuterium or deuterium-tritium (D-T) volumetric (plasma) sources and 252Cf or D-T point neutron sources were analyzed to find guidelines for successful use of the code for fusion applications. Additionally, the use of ADVANTG as a tool to identify major neutron pathways from the neutron source to the detector is demonstrated.

The immense size and complex geometry of the ITER experimental fusion reactor require the development of special techniques that can accurately and efficiently perform neutronics simulations with minimal human effort. This paper shows the effect of the hybrid Monte Carlo (MC)/deterministic techniques—Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS)—in enhancing the efficiency of the neutronics modeling of ITER and demonstrates the applicability of coupling these methods with computer-aided-design-based MC. Three quantities were calculated in this analysis: the total nuclear heating in the inboard leg of the toroidal field coils (TFCs), the prompt dose outside the biological shield, and the total neutron and gamma fluxes over a mesh tally covering the entire reactor. The use of FW-CADIS in estimating the nuclear heating in the inboard TFCs resulted in a factor of ˜275 increase in the MC figure of merit (FOM) compared with analog MC and a factor of ˜9 compared with the traditional methods of variance reduction. By providing a factor of ˜21 000 increase in the MC FOM, the radiation dose calculation showed how the CADIS method can be effectively used in the simulation of problems that are practically impossible using analog MC. The total flux calculation demonstrated the ability of FW-CADIS to simultaneously enhance the MC statistical precision throughout the entire ITER geometry. Collectively, these calculations demonstrate the ability of the hybrid techniques to accurately model very challenging shielding problems in reasonable execution times.

Hybrid biasing approaches for global variance reduction

Analysis of inconsistent source sampling in monte carlo weight-window variance reduction methods

The hybrid Monte Carlo (MC)/deterministic techniques - Consistent Adjoint Driven Importance Sampling (CADIS) and Forward Weighted CADIS (FW-CADIS) - enable the full 3-D modeling of very large and complicated geometries. The ability of performing global MC calculations for nuclear parameters throughout the entire ITER reactor was demonstrated. The 2 m biological shield (bioshield) reduces the total prompt operational dose by six orders of magnitude. The divertor cryo-pump port results in a peaking factor of 120 in the prompt operational dose rate behind the bioshield of ITER. The equatorial port, plugged by 2 m of shielding, increases the prompt dose rate behind the bioshield by a factor of 47. The peak values of the prompt dose rates at the back surface of the bioshield were 240 μSv/hr and 94 μSv/hr corresponding to the regions behind the divertor cryo-pump port and the equatorial port, respectively.

Radiation dose rate distributions of spent fuel dry casks estimated with MAVRIC based on detailed geometry and continuous-energy models

The solid fuel thorium molten salt reactor (TMSR-SF1) is a 10-MWth fluoride-cooled pebble bed reactor. As a new reactor concept, one of the major limiting factors to reactor lifetime is radiation-induced material damage. The fast neutron flux (E > 0.1 MeV) can be used to assess possible radiation damage. Hence, a method for calculating high-resolution fast neutron flux distribution of the full-scale TMSR-SF1 reactor is required. In this study, a two-step subsection approach based on MCNP5 involving a global variance reduction method, referred to as forward-weighted consistent adjoint-driven importance sampling, was implemented to provide fast neutron flux distribution throughout the TMSR-SF1 facility. In addition, instead of using the general source specification cards, the user-provided SOURCE subroutine in MCNP5 source code was employed to implement a source biasing technique specialized for TMSR-SF1. In contrast to the one-step analog approach, the two-step subsection approach eliminates zero-scored mesh tally cells and obtains tally results with extremely uniform and low relative uncertainties. Furthermore, the maximum fast neutron fluxes of the main components in TMSR-SF1 are provided, which can be used for radiation damage assessment of the structural materials.

<sec>Monte Carlo method is an ideal way to simulate criticality, shielding and nuclear detection. JMCT is a multipurpose 3D Mont Carlo (MC) neutron-photon-electron and coupled neutron /photon /electron transport code which is developed by IAPCM. The program is developed based on the combinatorial geometry parallel infrastructure JCOGIN and has the most functions of general Monte Carlo particle transport code, including the various variance reduction techniques. In addition, some new algorithms, such as Doppler broadening on-the-fly (OTF), uniform tally density (UTD), consistent adjoint driven importance sampling (CADIS), fast criticality search of boron concentration (FCSBC), the domain decomposition (DD), the two-level parallel computation of MPI and OpenMP, etc. have been developed, where the number of geometry zones, materials, tallies, depletion zones, memories and period of random number are big enough to simulate various extremely complicated problems. Also the JMCT is hybrid the discrete ordinate SN program JSNT to generate source biasing factors and weight window parameters for deep-penetration shielding problems. The input is based on the CAD modeling, and the result is a visualized output. The JMCT can provide technology support for radiation shielding design, reactor physics and criticality safe analysis. Especially, the JMCT is coupled depletion and thermal-hydraulic code for simulating the reactor feedback effect, including depletion, thermal feedback. In recent years, new function of γ-ray spectrum analysis has been developed. </sec><sec>In this paper, the working principles of timing measure are introduced. The advanced calibration count is developed for distinguishing between inelastic γ-ray and capture γ-ray based on time bin tally. On the other hand, when neutron collides with nuclide, the secondary photon is labeled into the primary line photon and primary continuous photon, where energy of primary line photon does not change with the incident neutron energy, such as carbon spectral-line at 4.43 MeV and oxygen spectral-line at 6.13 MeV. The element components of detected object can be determined by the primary line photon. On the other hand, expect value estimator (EVE) is used to produce the secondary photons. The advantage of EVE does not leak any event even with a small probability which is important for detecting the hide exploder. However the shortage of the EVE results in producing a great number of photons with small weight. If all of these small weight photons are simulated one by one, a great amount of computation time and memory will be consumed. For avoiding this case, a new algorithm is design by coupling EVE and DE (direct estimator). The all of secondary photons from EVE only make the direct tally take a little computing time, then end the photon history and return to the DE production photon model (one photon production at most). Final, the total tally is a summation of EVE direct tally and DE scattering tally. The use of new algorithm to realize the analysis of γ-ray spectrum will increase only a little computing time. The numerical tests are done by using own Monte Carlo code JMCT. The correctness and validity of the algorithm are shown preliminarily.</sec>

Nowadays, there is a problem of a lack of computer power to conduct high-precision reactor analysis. There are several factors that increase the excessive computational load and make it difficult to calculate nuclear reactor full-scale models using Monte Carlo method. Among them is the large neutron-flux attenuation, which is observed in deep penetration problems. Various reduction techniques are used to increase the efficiency of Monte Carlo calculations in such tasks. It allows to reduce the statistical uncertainty of the functional evaluation without increasing the number of neutron histories. This work is devoted to study and testing of variance reduction techniques in the deep penetration problem. To demonstrate the possibility of using non-analogue Monte Carlo modeling a test problem was formulated. To quantify the efficacy of applying the variance reduction methods, FOM characteristic is considered, which is a function of the relative error in a flux estimate and the computational time of the simulation. The article considers non-analogue techniques implemented in the MCU (Monte Carlo Univarsal) and OpenMC codes. As part of the study, a module of the OpenMC code was developed that allows to automatically generate weight windows. It is shown that variance reduction techniques increase the calculation efficiency by several times, particularly, the weight windows method in OpenMC make it possible to achieve a 7-fold increase in the efficiency of neutron flux estimation with the same number of simulated histories. The formulated recommendations can be used in the calculation of innovative nuclear reactors full-scale models.

An analytic approach to calculate variance reduction under analog and biased Monte Carlo simulation of deep-penetration problems is presented. Within the framework of this formulation, the variance reduction characteristics of exponential biasing and a recently proposed scheme that couples exponential biasing to scattering angle biasing are studied. The advantages and disadvantages of the coupled scheme over exponential biasing on deep-penetration problems with varying scattering probability and anisotropy are clearly illustrated.

The surrogate model-based sampling method has been an active area of research due to its evident efficiency over direct sampling method. The fusion of the adaptive kriging (AK) model with the adaptive radial-based importance sampling (ARBIS) method is developed as an improvement of the AK model combined with Monte Carlo simulation (MCS) method especially for estimating the small failure probabilities. In the AK–ARBIS method, the number of candidate samples in each updating process of the kriging model is reduced through partitioning the whole MCS sample domain into different subdomains and removing the samples inside the last subdomain from the participating candidate sampling pool, which can avoid the time-consuming matrix operation involved in kriging predictions in order to find the best training sample in each updating step. In the existing AK–ARBIS method, kriging model stops updating according to the learning function-based stopping criterion, which cannot directly reflect the error of the estimated failure probability. In this regard, this paper proposes the error-based stopping criterion (ESC) enhanced AK–ARBIS method, where the processes of finding the optimal hypersphere and accurately identifying the sign of candidate samples are decoupled in order to successfully embed the ESC. In addition to embedding the ESC into the AK–ARBIS method, two target-oriented candidate sampling reduction strategies are investigated, respectively, to improve the efficiency of finding the optimal hypersphere and accurately identifying the sign of the participating candidate samples. Based on the candidate sampling pool reduction strategies and ESC, both the computational time and the required number of calls to the real limit state function are reduced over the existing AK–ARBIS method. Three case studies are analyzed to demonstrate the accuracy and efficiency of the proposed enhanced AK–ARBIS method, especially for estimating the small failure probabilities.

A new global variance reduction technique based on pseudo flux method

One-way coupling often occurs in multi-dimensional models in finance. In this paper, we present a dimension reduction technique for Monte Carlo (MC) methods, referred to as drMC, that exploits this structure for pricing plain-vanilla European options under an N-dimensional one-way coupled model, where N is arbitrary. The dimension reduction also often produces a significant variance reduction.The drMC method is a dimension reduction technique built upon (i) the conditional MC technique applied to one of the factors which does not depend on any other factors in the model, and (ii) the derivation of a closed-form solution to the conditional partial differential equation (PDE) that arises via Fourier transforms. In the drMC approach, the option price can be computed simply by taking the expectation of this closed-form solution. Hence, the approach results in a powerful dimension reduction from N to one, which often results in a significant variance reduction as well, since the variance associated with the other factors in the original model are completely removed from the drMC simulation. Moreover, under the drMC framework, hedging parameters, or Greeks, can be computed in a much more efficient way than in traditional MC techniques. A variance reduction analysis of the method is presented and numerical results illustrating the method’s efficiency are provided.

The shielding analysis of the spent fuel dry storage cask TN-32 is carried out using the continuous-energy Monte Carlo neutron- and photon-transport code MCS developed by the Computational Reactor Physics and Experiment laboratory of the Ulsan National Institute of Science and Technology. The shielding analysis involves the transport simulation of the decay neutrons and gammas emitted by the spent fuel to obtain the neutron and gamma dose rate values outside of the cask. This deep-penetration problem is solved by means of weight window population control as variance reduction. The TN-32 cask calculations are repeated with the MCNP6 Monte Carlo code for verification purpose and a good agreement within three standard deviations is observed between MCS and MCNP6. The neutron dose rate on the cask surface and 2 m away from the cask can be calculated with MCS, whereas the photon dose rate calculation for positions outside of the cask will be further improved by employing more sophisticated variance reduction techniques.

This paper develops importance resampling into a variance reduction technique for Monte Carlo integration. Importance resampling is a sample generation technique that can be used to generate more equally weighted samples for importance sampling. This can lead to significant variance reduction over standard importance sampling for common rendering problems. We show how to select the importance resampling parameters for near optimal variance reduction. We demonstrate the robustness of this technique on common global illumination problems and achieve a 10%-70% variance reduction over standard importance sampling for direct lighting. We conclude that further variance reduction could be achieved with cheaper sampling methods.