Improve Simulation Efficiency Research Articles

Bragg peak characteristics of proton beams within therapeutic energy range and the comparison of stopping power using the GATE Monte Carlo simulation and the NIST data

AbstractPurpose:To examine detail depth dose characteristics of ideal proton beams using the GATE Monte Carlo technique.Methods:In this study, in order to improve simulation efficiency, we used pencil beam geometry instead of parallel broad-field geometry. Depth dose distributions for beam energies from 5 to 250 MeV in a water phantom were obtained. This study used parameters namedRpeak,R90,R80,R73,R50, full width at half maximum (FWHM), width of 80–20% distal fall-off (W(80–20)) and peak-to-entrance ratio to represent Bragg peak characteristics. The obtained energy–range relationships were fitted into third-order polynomial formulae. The present study also used the GATE Monte Carlo code to calculate the stopping power of proton pencil beams in a water cubic phantom and compared results with the National Institute of Standards and Technology (NIST) standard reference database.Results:The study results revealed deeper penetration, broader FWHM and distal fall-off and decreased peak-to-entrance dose ratio with increasing beam energy. Study results for monoenergetic proton beams showed thatR73can be a good indicator to characterise a range of incident beams. These also suggest FWHM is more sensitive thanW(80–20)distal fall-off in finding initial energy spread. Furthermore, the difference between the obtained stopping power from simulation and NIST data almost in all energies was lower than 1%.Conclusion:Detail depth dose characteristics for monoenergetic proton beams within therapeutic energy ranges were reported. These results can serve as a good reference for clinical practitioners in their daily practice.

Enhanced sampling based on slow variables of trajectory mapping

Most current enhanced sampling (ES) algorithms attempt to bias a potential energy surface based on preset slow collective variables to improve simulation efficiency. However, due to difficulty in obtaining slow variables in complex molecular systems, approximate slow variables are usually applied in ES, which often fail to achieve the expected high efficiency and sufficient accuracy when reconstructing equilibrium properties. In this paper, we demonstrate that the trajectory mapping (TM) technique has the potential to provide the required slow variables for ES.We illustrate the application of a typical ES algorithm (metadynamics) based on the slow variables constructed from the TM in a hairpin peptide system. In this system, both the equilibrium properties and slow dynamics are accurately obtained within approximately two to three orders of magnitude shorter simulation time than in regular molecular dynamics simulation.

Identifying time-varying hydrological model parameters to improve simulation efficiency by the ensemble Kalman filter: A joint assimilation of streamflow and actual evapotranspiration

Hydrological model parameters are essential for model simulation, which may vary with time owing to climatic variations and human activities. As a result, the implementation of stationary parameters may lead to inaccurate streamflow simulation. Actual evapotranspiration (ET) is a crucial component of hydrological cycles with an important influence on regional climate characteristics. Our aim was to investigate an appropriate way to estimate time-varying parameters using streamflow and ET observations, and to explore the how the simulation efficiency would change when ET data were added into assimilation. Data assimilation techniques can automatically adjust hydrological model parameters according to changing conditions. The ensemble Kalman filter (EnKF) technique was used to assimilate observations into a two-parameter monthly water balance model. Four data assimilation schemes were designed and applied in a synthetic experiment and 173 catchments in USA, including: (1) sole assimilation of streamflow to update both parameters, (2) joint assimilation of streamflow and ET to simultaneously update parameters, (3) sole assimilation of ET first to update parameter C (measuring evapotranspiration), and then subsequently joint assimilation of streamflow and ET to update parameter SC (measuring water storage capacity), and (4) sole assimilation of ET to update parameter C, and then sole assimilation of streamflow to update parameter SC. The four schemes were compared in terms of deterministic and probabilistic model performances, and model parameter correlations. The results indicated that: (1) the estimation of parameter C can be improved by assimilating ET observations into the model, and the time-varying model parameters obtained by adding ET data into assimilation led to a significant enhancement in deterministic streamflow and ET prediction, (2) among the three joint assimilation schemes, the deterministic model simulation performances were similar, while the ensemble predictions were more reliable in scheme 2. The joint assimilation of streamflow and ET to update both parameters in one step, i.e., scheme 2, outperformed the other two schemes in parameter SC estimation and model performance, (3) the ability to enhance simulation accuracy and to weaken correlations between parameters was more significant in humid catchments. The joint assimilation was helpful for the application of multiple sources of information into a hydrological simulation.

Advanced EMT and Phasor-Domain Hybrid Simulation With Simulation Mode Switching Capability for Transmission and Distribution Systems

Conventional electromagnetic transient (EMT) and phasor-domain hybrid simulation approaches presently exist for transmission system level studies. Their simulation efficiency is generally constrained by the EMT simulation. With an increasing number of distributed energy resources and nonconventional loads being installed in distribution systems, it is imperative to extend the hybrid simulation application to include distribution systems and integrated transmission and distribution systems. Meanwhile, it is equally important to improve the simulation efficiency as the modeling scope and complexity of the detailed system in the EMT simulation increases. To meet both requirements, this paper introduces an advanced EMT and phasor-domain hybrid simulation approach. This approach has two main features: first, a comprehensive phasor-domain modeling and simulation framework which supports positive-sequence, three-sequence, three-phase, and mixed three-sequence/three-phase representations and second, a robust and flexible simulation mode switching scheme. The developed scheme enables simulation switching from hybrid simulation mode back to pure phasor-domain dynamic simulation mode to achieve significantly improved simulation efficiency. The proposed method has been tested on integrated transmission and distribution systems. The results show that with the developed simulation switching feature, the total computational time is significantly reduced compared to running the hybrid simulation for the whole simulation period while maintaining good simulation accuracy.

Nonadiabatic dynamics simulation method for transition metal complexes: Theory, developments, and applications

Excited-state related properties of transition metal complexes have received much attention in recent years due to their potential applications in the field of energy, material and biology. To fully understand the underlying mechanism, we always need to resort to ultrafast time-resolved spectroscopies as well as reliable ab initio nonadiabatic dynamics simulations. However, nonadiabatic dynamics simulation methods that are suitable for investigating excited-state dynamics of transition metal complexes still demand further developments to improve simulation efficiency and accuracy. In this short review, we have shortly present some recent developments of non-adiabatic dynamics methods that are suitable for investigating excited state properties of transition metal complexes, mainly including Multi-Configuration Time Dependent Hartree (MCTDH) and mixed quantum-classical surface hopping methods. In addition, we have introduced our recently developed TD-DFT-based generalized trajectory surface hopping method in which an efficient algorithm of computing nonadiabatic couplings is realized. In combination with the classical path approximation, this newly developed method can effectively simulate internal conversion and intersystem crossing processes of transition metal complexes on an equal footing. With this newly developed method, we have systematically investigated the early-time ultrafast excited-state dynamics of three Ir(III) complexes bearing distinct ligands. The ISC rates estimated by our simulations are 65, 81 and 140 fs, which agree quite well with experimentally measured ca. 80, 80 and 110 fs. These Ir(III) complexes show similar macroscopic phenomena, i.e., ultrafast IC and ISC, their microscopic excited-state relaxation dynamics are individually different, for example, electron and hole transfer dynamics. These new insights for excited-state dynamics of Ir(III) complexes could be helpful for rationally designing Ir-containing compounds with excellent photoluminescence performance. In addition, we have also investigated the ultrafast intersystem crossing process of Au(I) naphthalene derivatives. We have found that (1) ultrafast and sub-picosecond intersystem crossing processes are mainly caused by small energy gaps and large spin-orbit couplings between S1 and T n . (2) Adding the second gold(I)-phosphine group does not increase spin-orbit couplings between S1 and T n but decrease their values remarkably, which implies that heavy-atom effects are state-specific, not-universal. (3) The position at which the second gold(I)-phosphine group is attached has remarkable influence on electronic structures of S1 and T n and their relative energies, which affect energy gaps and spin-orbit couplings between S1 and T n and eventually modulate intersystem crossing rates from S1 to T n . This work exemplifies that different isomers of a compound could have distinct excited-state relaxation dynamics. Above simulation results not only agree pretty well with experiments, but also provide valuable insights into excited-state relaxation dynamics for these transition-metal-containing complexes. In one word, our present developments have established an efficient and accurate simulation tool for investigating excited-state dynamics of transition metal complexes.

Qing Mu ; Jun Liang ; Xiaoxin Zhou ; Gen Li ; Xing Zhang

With wider applications of power electronic devices in modern power systems, simulation using traditional electromechanical and electromagnetic simulation tools suffer from low speed and imprecision. Multi-rate technologies can greatly improve simulation efficiency by avoiding simulating the entire system using a small time-step. However, the drawbacks of the current synchronization mechanisms is that they introduce numerical errors and numerical instabilities in multi-rate parallel simulations. An improved multi-rate parallel technology, node splitting interface (NSI), is proposed to reduce errors and enhance simulation stability. A new synchronization mechanism is used to avoid prediction and signal delays. Theoretical analyses are carried out to prove the convergence and absolute stability of the proposed NSI algorithm. This algorithm is particularly suitable for simultaneously investigating long term dynamics of DC grids and fast transients of power electronic converters.

Accurate parametrization and methodology for selection of pertinent single diode photovoltaic model with improved simulation efficiency

An accurate model of photovoltaic (PV) panel is indispensable for simulations studies. In general, the PV circuit parameters for simulation studies are extracted from the manufacturer’s data sheet under different environmental conditions. The PV characterizing equations are nonlinear and requires a more involved computation. This paper presents a fast convergent third order Newton-type method to solve such nonlinear equations and thereby, to accurately parameterize any of the possible PV circuit models. The applicability and suitability of the proposed method are demonstrated through modeling of multi and mono-crystalline PV cells. Further an algorithm to evaluate the efficacy of the available methods and the proposed method is presented. PV characteristics of the suitable circuit model at various levels of temperature and irradiation are also examined. Finally, the effectiveness of the developed method is comprehensively assessed through comparison with the most recent and available effective techniques by considering various performance indices based on current-voltage, power-voltage curves and experimental data is carried out.

Unified Modeling Method for Large Space Structures Using Absolute Nodal Coordinate

A unified rigid-flexible coupled modeling method for large flexible space structures is proposed based on absolute nodal coordinate formulation (ANCF). The explicit formulas of gravitational potential energy and generalized gravitational force are developed, which are simple to use and apply to all ANCF elements. First, the shape functions of all kinds of ANCF elements are written as a unified form by using the Kronecker product. Then, the equations of motion are derived through Hamilton’s principle. A Taylor series expansion is adopted to obtain the explicit expression of gravitational potential energy. Also, a simplified model of the gravitational force is proposed to improve simulation efficiency. Finally, two case studies are presented to validate the proposed modeling method, including a two-dimensional Euler–Bernoulli beam in elliptic orbits and a thin plate in a circular orbit. The effects of orbital eccentricity on the orbital and attitude accuracies of the proposed method, the mutual effects between the attitude motion and structural vibrations, and the effects of the flexibility on the attitude controller of the beam are also investigated. Simulation results show that the proposed modeling method takes gravitational force as well as gravity gradient torque into account accurately. The simplified model is recommended because of its accuracy and time efficiency.

Numerical simulation of aneurysmal haemodynamics with calibrated porous-medium models of flow-diverting stents

Modelling flow-diverting (FD) stents as porous media (PM) markedly improves the efficiency of computational fluid dynamics (CFD) simulations in the study of intracranial aneurysm treatment. Nonetheless, the parameters of PM models adopted for simulations up until now were rarely calibrated to match the represented FD structure. We therefore sought to evaluate the PM parameters for a representative variety of commercially available stents, so characterising the flow-diversion behaviours of different FD devices on the market.We generated fully-resolved geometries for treatments using PED, Silk+, FRED, and dual PED stents. We then correspondingly derived the calibrated PM parameters—permeability (k) and inertial resistance factor (C2)—for each stent design from CFD simulations, to ensure the calibrated PM model has identical flow resistance to the FD stent it represents. With each of the calibrated PM models respectively deployed in two aneurysms, we studied the flow-diversion effects of these stent configurations.This work for the first time reported several sets of parameters for PM models, which is vital to address the current knowledge gap and rectify the errors in PM model simulations, thereby setting right the modelling protocol for future studies using PM models. The flow resistance parameters were strongly affected by porosity and effective thickness of the commercial stents, and thus accounted for in the PM models. Flow simulations using the PM stent models revealed differences in aneurysmal mass flowrate (MFR) and energy loss (EL) between various stent designs.This study improves the practicability of FD simulation by using calibrated PM models, providing an individualised method with improved simulation efficiency and accuracy.

A Multirate EMT Co-Simulation of Large AC and MMC-Based MTDC Systems

This paper proposes a novel multirate co-simulation method to improve simulation efficiency of large-scale AC plus multiterminal DC (MTDC) grids. In this method, the whole system is partitioned into different AC and MTDC subsystems. They each are simulated with different time steps according to their requirements of accuracy. Unlike the existing methods where simplified models are adopted, the proposed approach fully reserves both the detailed behavior of converters and the nonlinear dynamics of large-scale AC systems. To realize the coordination between different subsystems, updating and discretization of the interface models are significant to guarantee the overall numerical accuracy and stability of the co-simulation method. Accordingly, the interface models of the partitioned AC and DC networks are represented by time-varying Thevenin and Norton equivalents. To eliminate the aliasing or time-delay errors, their parameters are derived using moving-window prediction, stepwise correction, and averaging techniques. A numerical oscillation suppression algorithm is developed for the discretization of the interface model. Thus, numerical stability is well guaranteed. The variables inside each subsystem as well as the interfaces, which are derived by augmented network equations (ANEs), are calculated simultaneously. The rate ratio of large AC and MTDC systems is determined based on our proposed criterion of electromagnetic transient simulation accuracy. The effectiveness of the cosimulation method is validated on a practical system integrating large AC and modular-multilevel-converter-based MTDC grids.

Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

Stochastic process design kits for photonic circuits based on polynomial chaos augmented macro-modelling

Fabrication tolerances can significantly degrade the performance of fabricated photonic circuits and process yield. It is essential to include these stochastic uncertainties in the design phase in order to predict the statistical behaviour of a device before the final fabrication. This paper presents a method to build a novel class of stochastic-based building blocks for the preparation of Process Design Kits for the analysis and design of photonic circuits. The proposed design kits directly store the information on the stochastic behaviour of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using these macro-models, only a single deterministic simulation is required to compute the stochastic moments of any arbitrary photonic circuit, without the need of running a large number of time-consuming circuit simulations thereby dramatically improving simulation efficiency. The effectiveness of the proposed approach is verified by means of classical photonic circuit examples with multiple uncertain variables.

A Hybrid Simulation Approach for Fast and Accurate Timing Analysis of Multi-Processor Platforms Considering Communication Resources Conflicts

In the early design phase of embedded systems, discrete-event simulation is extensively used to analyse time properties of hardware-software architectures. Improvement of simulation efficiency has become imperative for tackling the ever increasing complexity of multi-processor execution platforms. The fundamental limitation of current discrete-event simulators lies in the time-consuming context switching required in simulation of concurrent processes. In this paper, we present a new simulation approach that reduces the number of events managed by a simulator while preserving timing accuracy of hardware-software architecture models. The proposed simulation approach abstracts the simulated processes by an equivalent executable model which computes the synchronization instants with no involvement of the simulation kernel. To consider concurrent accesses to platform shared resources, a correction technique that adjusts the computed synchronization instants is proposed as well. The proposed simulation approach was experimentally validated with an industrial modeling and simulation framework and we estimated the potential benefits through various case studies. Compared to traditional lock-step simulation approaches, the proposed approach enables significant simulation speed-up with no loss of timing accuracy. A simulation speed-up by a factor of 14.5 was achieved with no loss of timing accuracy through experimentation with a system model made of 20 functions, two processors and shared communication resources. Application of the proposed approach to simulation of a communication receiver model led to a simulation speed-up by a factor of 4 with no loss of timing accuracy. The proposed simulation approach has potential to support automatic generation of efficient system models.

Electromagnetic Field and Radio Frequency Circuit Co-Simulation for Magnetic Resonance Imaging Dual-Tuned Radio Frequency Coils.

Electromagnetic (EM) field simulation plays a key role in the design of magnetic resonance imaging radio frequency (RF) coils. However, the values of the components in tuning and matching circuits often need to be iterated repeatedly in the conventional simulation method in order to achieve optimal scattering parameters. This leads to a time-consuming optimization to tune and match RF coils, particularly dual-tuned coils that are comprised of multiple lumped elements. A method combining EM field simulation and circuit simulation was employed in this paper, which can dramatically improve simulation efficiency for the optimization of the values of the lumped elements and corresponding EM field distribution. A systematical theoretical analysis of the co-simulation method was presented. To validate the accuracy and efficiency of the co-simulation method, a comparison study was conducted between the conventional simulation and the proposed co-simulation approaches.

MBAR-enhanced lattice Monte Carlo simulation of the effect of helices on membrane protein aggregation

We study the effect of helical structure on the aggregation of proteins using a simplified lattice protein model with an implicit membrane environment. A recently proposed Monte Carlo approach, which exploits the proven statistical optimality of the MBAR estimator in order to improve simulation efficiency, was used. The results show that with both two and four proteins present, the tendency to aggregate is strongly expedited by the presence of amphipathic helix (APH), whereas a transmembrane helix (TMH) slightly disfavours aggregation. When four protein molecules are present, partially aggregated states (dimers and trimers) were more common when the APH was present, compared with the cases where no helices or only the TMH is present.

Characteristic methods and Roe’s method for the incompressible two-fluid model for stratified pipe flow

This article examines the use of characteristic methods in stratified two-phase pipe flow simulations for obtaining non-dissipative flow predictions. A Roe scheme and several methods based on the principle of characteristics are presented for the two-fluid model. The main focus is finding numerically efficient ways of capturing wave dynamics and flow regime transitions through direct simulation. Capturing flow regime transitions both effciently and precisely necessitates schemes which remain stable in a numerical sense, yet predicts wave growth once the flow conditions turn unstable. Characteristic methods offer the possibility of simulating hyperbolic systems without numerical dissipation. These methods do however lack certain fundamental conservation properties. Challenges related to information scattering and clustering in space and time, particularly around shocks, are also an issue in some method variants. Hybridisations with the finite volume method are proposed which overcome these shortcomings. All methods are compared, evaluating predictions on the onset of linear wave growth and simulations of non-linear, discontinuous roll-waves. The following observations are made: 1. Characteristic methods are excellent at predicting the onset of linear hydrodynamic instability, even with a small number of computational nodes. 2. Dissipative errors in finite volume methods and characteristic hybrids will be closely linked to the CFL number. The Roe scheme and the characteristic hybrids give very little dissipation error as the CFL number approaches unity. This then becomes a question of numerical stability. 3. Adapting dynamic grid cells, moving along with the characteristics information drift, greatly improves simulation efficiency by allowing for longer time steps. Dynamic grid cells are also useful for alleviating the need for interpolation in characteristic methods.On the whole, the performance of the characteristic hybridisations are similar to that of the Roe scheme at large CFL numbers. Characteristic hybridisations perform somewhat better in predicting linear instability while the Roe scheme is better suited for the shock fronts found in the roll-wave flow regime. These method easily out-perform the more basic upwind and Lax–Friedrich schemes.

TU-AB-BRC-08: Egs_brachy, a Fast and Versatile Monte Carlo Code for Brachytherapy Applications

Purpose: To introduce egs_brachy, a new, fast, and versatile Monte Carlo code for brachytherapy applications. Methods: egs_brachy is an EGSnrc user-code based on the EGSnrc C++ class library (egs++). Complex phantom, applicator, and source model geometries are built using the egs++ geometry module. egs_brachy uses a tracklength estimator to score collision kerma in voxels. Interaction, spectrum, energy fluence, and phase space scoring are also implemented. Phase space sources and particle recycling may be used to improve simulation efficiency. HDR treatments (e.g. stepping source through dwell positions) can be simulated. Standard brachytherapy seeds, as well as electron and miniature x-ray tube sources are fully modelled. Variance reduction techniques for electron source simulations are implemented (Bremsstrahlung cross section enhancement, uniform Bremsstrahlung splitting, and Russian Roulette). TG-43 parameters of seeds are computed and compared to published values. Example simulations of various treatments are carried out on a single 2.5 GHz Intel Xeon E5-2680 v3 processor core. Results: TG-43 parameters calculated with egs_brachy show excellent agreement with published values. Using a phase space source, 2% average statistical uncertainty in the PTV ((2mm)3 voxels) can be achieved in 10 s for 100 125I or 103Pd seeds in a 36.2 cm3 prostate PTV, 31 s for 64 103Pd seeds in a 64 cm3 breast PTV, and 56 s for a miniature x-ray tube in a 27 cm3 breast PTV. Comparable uncertainty is reached in 12 s in a (1 mm)3 water voxel 5 mm away from a COMS 16mm eye plaque with 13 103Pd seeds. Conclusion: The accuracy of egs_brachy has been demonstrated through benchmarking calculations. Calculation times are sufficiently fast to allow full MC simulations for routine treatment planning for diverse brachytherapy treatments (LDR, HDR, miniature x-ray tube). egs_brachy will be available as free and open-source software to the medical physics research community. This work is partially funded by the Canada Research Chairs program, the Natural Sciences and Engineering Research Council of Canada, and the Ontario Ministry of Research and Innovation (Ontario Early Researcher Award).

Functional Modeling of Symmetrical Multipulse Autotransformer Rectifier Units for Aerospace Applications

This paper aims to develop a functional model of symmetrical multipulse autotransformer rectifier units (ATRUs) for more-electric aircraft (MEA) applications. The ATRU is seen as the most reliable way readily to be applied in the MEA. Interestingly, there is no model of ATRUs suitable for unbalanced or faulty conditions at the moment. This paper is aimed to fill this gap and develop functional models suitable for both balanced and unbalanced conditions. Using the fact that the dc voltage and current are strongly related to the voltage and current vectors at the ac terminals of ATRUs, a functional model has been developed for the asymmetric ATRUs. The developed functional models are validated through simulation and experiment. The efficiency of the developed model is also demonstrated by comparing with corresponding detailed switching models. The developed functional model shows significant improvement of simulation efficiency, especially under balanced conditions.

A modified Monte Carlo “Local Importance Function Transform” method

The Local Importance Function Transform (LIFT) method uses an approximation of the contributon transport problem to bias a forward Monte-Carlo (MC) source-detector simulation (Turner, 1996; Turner and Larsen, 1997a,b). Local (cell-based) biasing parameters are calculated from an inexpensive deterministic adjoint solution and used to modify the physics of the forward transport simulation. In this paper, we develop a new expression for the LIFT biasing parameter, which depends on a cell-average adjoint current-to-scalar flux (J*/ϕ*) ratio. This biasing parameter differs significantly from the original expression, which uses adjoint cell-edge scalar fluxes to construct a finite difference estimate of the flux derivative; the resulting (original LIFT) biasing parameters exhibit spikes in magnitude at material discontinuities, causing the method to lose efficiency in problems with high spatial heterogeneity. The new J*/ϕ* expression, while more expensive to obtain, generates biasing parameters that vary smoothly across the spatial domain. The result is an improvement in simulation efficiency. A representative test problem has been developed and analyzed to demonstrate the advantage of the updated biasing parameter expression with regards to solution figure of merit (FOM). For reference, the two variants of the LIFT method are compared to a similar variance reduction method developed by Depinay (1997) and Depinay et al. (2006), as well as MC with deterministic adjoint weight windows (WW).

Efficient Splitting Simulation for Blackout Analysis

The analysis of severe blackouts has become an essential part of transmission grid planning and operation. This may include evaluation of rare-event probabilities, which can be difficult to estimate. While simulation offers flexibility to model large complex systems, efficiency remains a big concern when estimating very small probabilities. This paper presents an effective simulation technique to evaluate rare-event probabilities associated with cascading blackouts in an electric grid. We test our technique on an IEEE 118-bus electric network and show that it can dramatically improve simulation efficiency. We also demonstrate that the proposed technique can effectively locate vulnerable links. These are links whose failures lead to the highest probabilities of a blackout event.