Monte Carlo Simulation Time Research Articles

Prediction of Long-Term Offshore Structural Responses Based on Nonlinear Wave Modeling

Wind-generated random wave loads are the dominant loads to consider for maintaining the reliability of fixed offshore structures. Based on probabilistic techniques, the inherent randomness of the wave loading can be used to predict extreme offshore structural response, which is Gaussian in nature. However, researchers have found that the hydrodynamic component and structural dynamics substantially impact the frequency spectrum, leading to a non-Gaussian stochastic offshore structural response. A finite-memory non-linear system (FMNSNL) has been proven to be an efficient approach to evaluate the non-Gaussian stochastic offshore structural response compared to the conventional method, Monte Carlo time simulation. However, the analysis has been conducted based on short-term distribution only. The most satisfactory analysis is based on long-term distribution. Hence, further investigation in this paper will evaluate the long-term probability distribution of extreme offshore structural responses. As a result, a 100-year extreme offshore structural response prediction achieves 80% to 96% accuracy compared to the Monte Carlo time simulation. The probability distribution has been evaluated using the Gumbel distribution function throughout this investigation. Still, there is a little deviation at the tail end of the distribution between the simulated response values and the fitted line. A different distribution function, such as the Generalised Extreme Value (GEV) distribution, is advised for future work.

An Improved Version of ETS-Regression Models in Calculating the Fixed Offshore Platform Responses

An offshore structural design should accurately calculate wave loads and structural responses acting on slender cylinders. The hydrodynamic drag-dominated force was always challenging, hence the hydrodynamic wave loading became a complex solution; it led to a nonlinear relation between the wave force and responses caused by the diffracted and radiated waves, which was included in Morison’s equation. For more consistency in the structural assessment, the linearised drag–inertia force was considered in model development, such as an improved version of the efficient time simulation regression (ETS-Reg) procedure that was introduced. The study aimed to improve the prediction of structural responses using the predetermined linear, polynomial, and cubic regression models. These simulations were performed focusing on high sea state conditions without wave-induced current effects. In order to evaluate the level of accuracy, the recent ETS-Reg models were compared and validated using the Monte Carlo time simulation (MCTS) method. An amended ETS-Reg model, known as the ETS-RegLR model, was also compared with the previous results obtained using the conventional ETS-Reg models (ETS-RegSE), leading to better structural response calculations.

Extreme response prediction for fixed offshore structures by efficient time simulation regression procedures. Part 2: model validation

ABSTRACT The major component of environmental loadings on offshore structures is the wave-induced loads. The time-domain analysis has been commonly preferred to assess offshore structures because it provides considerable benefits to the practicing engineer without losing accuracy. However, such assessments are high computational demands and time costs due to complex numerical procedures in completing the hydrodynamic loadings on the offshore structures. Moreover, a huge number of simulations is required to increase the accuracy, leading to a long processing time. Hence, a simplified analysis-based time domain is introduced by applying direct calculation procedures to overcome this issue. It refers to an efficient time simulation regression method called the ETS-Reg SE model. The result of the Monte Carlo Time Simulation (MCTS) will be used to compare the performance of the ETS-Reg SE model’s output. Provided with reasonable accuracy, the ETS-Reg SE model offered a more efficient approach to optimal and costeffective structural analysis.

Efficient derivation of extreme non-Gaussian stochastic structural response using the finite-memory nonlinear system (FMNS NL ). Part 1: model development

ABSTRACT For offshore structural design, the load due to wind-generated random waves is usually the most important source of loading. The most accurate method that is commonly used to evaluate the offshore structural response on the subjected load is the Monte Carlo time simulation which can account for all sorts of nonlinearities without introducing any approximations. However, it is computationally very demanding due to its complex procedure. A simple method using finite-memory nonlinear system (FMNS) has been introduced. The method is, however, only applicable based on the linear wave analysis. Hence, by taking advantage on the efficiency of FMNS method, a new model needs to be developed by apply the FMNS method with a nonlinear wave analysis for a more reliable result. The most appropriate model can then be used to determine the probability distribution of response extreme values with great efficiency and accuracy.

Scatter correction based on adaptive photon path-based Monte Carlo simulation method in Multi-GPU platform

Monte Carlo (MC)-based simulation is the most precise method in scatter correction for Cone-beam CT (CBCT). Nonetheless, the existing MC methods cannot be fully applied in clinical due to its low efficiency. The traditional MC simulations perform calculations via a particle-by-particle scheme, which leads to high computation costs because abundant photons do not reach the X-ray detector in transport. The conventional approaches cannot control where the particle ends. Hence, it unavoidably waste lots of time in transporting numerous photons that have no contribution to the signal at the detector, yielding a low computational efficiency. To solve the problem, an innovative GPU-based Metropolis MC (gMMC) method was proposed. Compared with the traditional ones, the Metropolis based algorithm utilizes a path-by-path sampling method. The method can automatically control each particle path and eventually accelerate the convergence. In this paper, we firstly take planning CT image as prior information because of its precise CT value, and utilize gMMC to estimate scatter signal. Then the scatter signals are removed from the raw CBCT projections. Afterwards, FDK reconstruction is performed to obtain the corrected image,some accelerating strategies including reducing photon history number, pixels sampling, projection angles sampling and reconstructed image down-sampling achieve adaptive fast CBCT image reconstruction. For having high computational efficiency, we implemented the whole workflow on a 4-GPU workstation. In order to verify the feasibility of the the method, the experiment of several cases are conducted including simulation, phantom, and real patient cases. Results indicate that the image contrast becomes better, the scatter artifacts are eliminated. The maximum error (emax), the minimum error (emin), the 95th percentile error (e95%), average error (¯e) are reduced from 264, 56, 14 and 21 HU to 28, 10, 3 and 7 HU in full-fan case, and from 387, 5, 19 and 95 HU to 39, 2, 2 and 6 HU in the half-fan case. In terms of computation time, the MC simulation time of all cases is within 2.5 seconds, and the total time is within 15 seconds.

Monte Carlo study on optimal breast voxel resolution for dosimetry estimates in digital breast tomosynthesis

Digital breast tomosynthesis (DBT) is currently used as an adjunct technique to digital mammography (DM) for breast cancer imaging. Being a quasi-3D image, DBT is capable of providing depth information on the internal breast glandular tissue distribution, which may be enough to obtain an accurate patient-specific radiation dose estimate. However, for this, information regarding the location of the glandular tissue, especially in the vertical direction (i.e. x-ray source to detector), is needed. Therefore, a dedicated reconstruction algorithm designed to localize the amount of glandular tissue, rather than for optimal diagnostic value, could be desirable. Such a reconstruction algorithm, or, alternatively, a reconstructed DBT image classification algorithm, could benefit from the use of larger voxels, rather than the small sizes typically used for the diagnostic task. In addition, the Monte Carlo (MC) based dose estimates would be accelerated by the representation of the breast tissue with fewer and larger voxels. Therefore, in this study we investigate the optimal DBT reconstructed voxel size that allows accurate dose evaluations (i.e. within 5%) using a validated Geant4-based MC code. For this, sixty patient-based breast models, previously acquired using dedicated breast computed tomography (BCT) images, were deformed to reproduce the breast during compression under a given DBT scenario. Two re-binning approaches were applied to the compressed phantoms, leading to isotropic and anisotropic voxels of different volumes. MC DBT simulations were performed reproducing the acquisition geometry of a SIEMENS Mammomat Inspiration system. Results show that isotropic cubic voxels of 2.73 mm size provide a dose estimate accurate to within 5% for 51/60 patients, while a comparable accuracy is obtained with anisotropic voxels of dimension 5.46 × 5.46 × 2.73 mm3. In addition, the MC simulation time is reduced by more than half in respect to the original voxel dimension of 0.273 × 0.273 × 0.273 mm3 when either of the proposed re-binning approaches is used. No significant differences in the effect of binning on the dose estimates are observed (Wilcoxon–Mann–Whitney test, p-value > 0.4) between the 0° the 23° (i.e. the widest angular range) exposure.

Contributon-Based Mesh-Reduction Methodology for Hybrid Deterministic-Stochastic Particle Transport Simulations Using Block-Structured Grids

In neutral-particle transport shielding problems, variance-reduction methods are used in Monte Carlo (MC) simulations to bias the progression of tracked particles toward user-defined detectors or regions of interest. These biasing techniques allow for converged results in areas that would otherwise be poorly sampled due to low neutron or gamma fluxes relative to the fixed source. One widely used state-of-the-art methodology in shielding simulations is the Consistent Adjoint-Driven Importance Sampling (CADIS) method, which is a hybrid transport methodology that uses deterministic adjoint solutions to define weight window (WW) targets for particle splitting, rouletting, and source biasing during MC. However, for large problems, the WW data can require prohibitively large amounts of memory (tens to hundreds of gigabytes). This can make the simulation not feasible with the available computational resources, or it can restrict execution to a small fraction of nodes with large enough memory, thus significantly reducing the available resources and increasing the turnaround time needed to complete intended analyses.A novel methodology and data structure have been developed and implemented within the MONACO and MAVRIC sequences of the Scale 6.1 code package that greatly reduces memory requirements for storing WW maps by orders of magnitude. The data structure is accompanied with an algorithm that determines mesh reduction through coarsening and refinement using contributon response theory. Large memory savings are achieved by using separate block-structured grids for each energy group. The implementation of this methodology leads to a fractional increase in biased MC simulation time due to tracking particles through a more complex data structure storing the WW targets. For large shielding problems, enhanced parallelism enabled by memory reduction more than compensates for the decline in biased MC performance resulting in an effective speedup in solution time. Here, the improvements and drawbacks in the methodology are demonstrated on the relatively small but well-known Pool Critical Assembly shielding benchmark. The methodology showed a reduction in memory of from 163 to 194 times, with only a limited slowdown in biasing efficiency between 1% and 9%.

Comparison of Various Spectral Models for the Prediction of the 100-Year Design Wave Height

Offshore structures are exposed to random wave loading in the ocean environment, and hence the probability distribution of the extreme values of their response to wave loading is required for their safe and economical design. In most cases, the dominant load on offshore structures is due to wind-generated random waves where the ocean surface elevation is defined using appropriate ocean wave energy spectra. Several spectral models have been proposed to describe a particular sea state that is used in the design of offshore structures. These models are derived from analysis of observed ocean waves and are thus empirical in nature. The spectral models popular in the offshore industry include Pierson-Moskowitz spectrum and JONSWAP spectrum. While the offshore industry recognizes that different methods of simulating ocean surface elevation lead to different estimation of design wave height, no systematic investigation has been conducted. Hence, the aim of this study is to investigate the effects of predicting the 100-year responses from various wave spectrum models. In this paper, the Monte Carlo time simulation (MCTS) procedure has been used to compare the magnitude of the 100-year extreme responses derived from different spectral models. Additionally, the linear random wave theory (LRWT) was implemented to simulate the offshore structural responses due to random wave loading. The models have been tested for three different environmental conditions represented by Hs = 15m, 10m and 5m respectively. The accuracy of the predictions of the 100-year responses from Pierson-Moskowitz and JONSWAP spectrums will then be investigated.

Use of a radial projection to reduce the statistical uncertainty of spot lateral profiles generated by Monte Carlo simulation.

Monte Carlo (MC) simulation has been used to generate commissioning data for the beam modeling of treatment planning system (TPS). We have developed a method called radial projection (RP) for postprocessing of MC‐simulation‐generated data. We used the RP method to reduce the statistical uncertainty of the lateral profile of proton pencil beams with axial symmetry. The RP method takes advantage of the axial symmetry of dose distribution to use the mean value of multiple independent scores as the representative score. Using the mean as the representative value rather than any individual score results in substantial reduction in statistical uncertainty. Herein, we present the concept and step‐by‐step implementation of the RP method, as well as show the advantage of the RP method over conventional measurement methods for generating lateral profile. Lateral profiles generated by both methods were compared to demonstrate the uncertainty reduction qualitatively, and standard error comparison was performed to demonstrate the reduction quantitatively. The comparisons showed that statistical uncertainty was reduced substantially by the RP method. Using the RP method to postprocess MC data, the corresponding MC simulation time was reduced by a factor of 10 without quality reduction in the generated result from the MC data. We concluded that the RP method is an effective technique to increase MC simulation efficiency for generating lateral profiles for axially symmetric pencil beams.

All-Region Statistical Model for Delay Variation Based on Log-Skew-Normal Distribution

In this paper, we propose a single probability density function for the distributions of the delay in the presence of the process variation for different regions of operation. The delay variation model is inspired by considering the analytical current models for each operating region. Based on these models, we suggest using the log-skew-normal distribution for modeling the delay variation for a wide range of supply voltages from the subthreshold to above-threshold regions. To assess the accuracy of the proposed delay distribution, the mean, standard deviation, skewness, 99th percentile, and yield of the proposed distribution are compared with those of the normal and log-normal distributions using the Monte Carlo (MC) simulations for different circuits in both bulk and FinFET technologies. The results show a higher accuracy for the proposed distribution in all regions of operation. Also, the proposed model enables us to obtain the $3 {\sigma } $ yield of the distribution using up to 3.4 times less MC simulation time.

Towards control of carbon nanotube synthesis process using prediction-based fast Monte Carlo simulations

Precise control of the lengths of carbon nanotube (CNT) and other nanostructures is important for various industrial applications. However, time-resolution (∼1min) of current in situ measurements does not allow control of lengths to within 20nm. We present an approach to combine intermittent in situ measurements with length estimates from a fast atomistic Monte Carlo (MC) simulation of CNT synthesis. The MC simulation time was reduced by >70% through prediction of the nonlinear and nonstationary growth increments, and initialization of relaxation process (the most computationally intensive step in MC simulations) with the near-optimum predicted positions, leading to one of the longest (∼194nm) CNTs from atomistic simulations. A utility function of growth predictions was defined so that its maximization specified the end-point of the synthesis process. Extensive simulation studies indicate that the approach can be used to control CNT lengths to within 1nm of specifications.

Efficient construction of irregular codes with midterm block length and near-Shannon performance

In this study, the authors propose a new method for constructing irregular low-density parity-check codes (LDPC codes) with midterm or short block lengths. It is a Monte-Carlo simulation-based optimisation procedure called downhill simplex which uses progressive edge growth method for Tanner graph construction in cost function evaluations. It outperforms the density evolution (DE) method in both efficiency and performance. The efficiency of the authors' proposal mostly depends on the Monte-Carlo simulation time which owing to the midterm block lengths is relatively small compared to the time delay of the conventional DE method. Simulation results show that for block length of 3200 and a relatively low code rate 3/8, LDPC codes constructed using the authors' proposal noticeably outperform those constructed with DE method by more than 0.2 dB in the entire signal to noise ratio (SNR) range under AWGN channel.

Simulation of dynamic recrystallization in solder interconnections during thermal cycling

In the present study, an algorithm, combining the Potts model based Monte Carlo (MC) and finite element methods, is developed in order to predict the dynamic recrystallization of tin in tin-rich lead-free solder interconnections during thermal cycling. A correlation between real time and MC simulation time is established. The phenomenon that intermetallic particles provide favorable sites for nucleation of new tin grains in solder matrix is also simulated. It is demonstrated that the present algorithm predicts the incubation period of the recrystallization as well as the growth tendency of the recrystallized regions, in a way consistent with the experimental findings. This quantitative description of the microstructural changes will contribute significantly to the reliability studies of solder interconnections.

MO‐D‐224A‐06: Fast Monte Carlo‐Based Computation of ASi‐EPID Dose Images for IMRT Treatment Field Through Phantom

Purpose: During‐treatment IMRT dosimetric verification can be accomplished with exit dose portal dosimetry; however, differential beam hardening and patient scatter radiation results in inaccuracies in invariant kernel‐based calculation methods. The purpose of this study is to develop an accurate, yet efficient Monte‐Carlo (MC) based algorithm to predict during treatment dosimetric aSi‐EPID images to compare with measured images for plan delivery quality assurance. Method and Materials: To compute EPID images, the VMC++ MC algorithm is used to transport particles through the patient geometry. Particles exiting the patient are scored into 19 energy‐differential fluence‐matrices at the EPID surface. Computed EPID images are generated by summing the contributions of each fluence‐matrix convolved with MC generated mono‐energetic energy deposition kernels. Kernel‐based method validation was performed for open, MLC‐blocked, intensity test‐pattern and a prostate‐IMRT field with and without a 20 cm thick phantom by comparing with full MC computation of EPID images. Additionally, the prostate‐IMRT plan was computed through a pelvic phantom. A cone‐beam CT of the pelvic phantom was used for dose computation particle transport. Comparison metrics include image profiles and gamma‐metric evaluation. Results: For the test fields, kernel‐based methods had >95% of voxels with γ<1 for 1 %, 1mm criteria and >99.1% with a 2%, 2mm criteria with respect to the MC‐calculated fields. For the pelvic phantom, 92.6% of pixels had γ<1 for 1%, 1mm criteria. The systematic discrepancy(∼0.5%) is well below the statistical uncertainty(∼3%). Conclusion: The kernel‐based convolution method is comparable in accuracy with full MC while requiring substantially less computation time than a full MC EPID simulation. Image computation time is independent of MC statistical precision and adds <1min to the MC simulation time. Comparison of measured images with MC‐computed portal images may be a practical method to perform during‐treatment dose validation. Conflict of Interest: Supported in‐part by Varian Medical Systems.

FEM simulation on microstructure of DC flash butt welding for an ultra-fine grain steel

Finite element method (FEM) was used to simulate the process of a direct current (DC) flash butt welding (FBW) processing. In the simulation thermal–electrical coupling and flash process are considered. Element live-death method was adopted to simulate metal melting and metal loss during the flash process. Then, the temperature field of the welded joint was computed. In addition, a Monte Carlo (MC) simulation technology was utilized to investigate the Austenite grain growth in the heat affected zone (HAZ) of the FBW for the ultra-fine grain steel. On the basis of the result of the temperature field, an experimental data-based (EDB) model proposed by Gao was used to establish the relation between the MC simulation time and real time in the grain growth kinetics simulation. Moreover, thermal pinning was considered due to the effect of temperature gradient on HAZ grain growth of welded joint. The simulations give out the grain size distribution in HAZ of the FBW welded joint for the ultra-fine grain steel and effect of grain growth due to temperature gradient.

On the Monte Carlo simulation of curvature-driven growth

The kinetics of shrinking of an island grain embedded in a matrix as a function of the grain boundary properties is simulated using a Monte Carlo (MC)technique where the probability of switching of a grain boundary site is scaled according to the product of the boundary energy and mobility. Careful investigation of the simulation results shows that the correct implementation is one where the MC simulation time, the time of visit to a grain boundary site during the simulation is scaled according to the product of the boundary energy and mobility. Simulations in which the site is visited all the time, but the flip probability is scaled according to the product of the boundary energy and mobility, do not yield the correct results expected for curvature-driven boundary migration. The mechanistic differences between the two approaches are described.