Fast statistical circuit analysis with finite-point based transistor model

In this paper. The effect of intradie process variations oy the delay of tapered buffers designed in static CMOS logic style is analyzed in depth. An analytical delay model accounting for the dependency of variations on transistor sizing, load and input capacitance requirement is derived for the single stage. Then, this model is extended to the case of N-stage tapered buffers. The closed-form delay expressions includin. The contribution of intradie variations permit to gain an insight int. The impact of process variations oy the performance of tapered buffers. Monte Carlo simulations on a 90-nm technology including layout parasitica are performed to validat. The analysis. Results are shown to agree well wit. The expressions derived, thereby confirmin. The validity oy the underlying assumptions, as well at the suitability oy the proposed models for design purposes. © 2009 IEEE.

The paper analyzes the possibilities of using statistical simulation in the macroeconomic risks measurement. At the level of the whole world, macroeconomic risks are, due to the excessive imbalance, significantly increased. Using analytical statistical methods and Monte Carlo simulation, the authors interpret the collected data sets, compare and analyze them in order to mitigate potential risks. The empirical part of the study is a qualitative case study that uses statistical methods and Monte Carlo simulation for managing macroeconomic risks, which is the central theme of this work. Application of statistical simulation is necessary because the system, for which it is necessary to specify the model, is too complex for an analytical approach. The objective of the paper is to point out the previous need for consideration of significant macroeconomic risks, particularly in terms of the number of the unemployed in the society, the movement of gross domestic product and the country’s credit rating, and the use of data previously processed by statistical methods, through statistical simulation, to analyze the existing model of managing the macroeconomic risks and suggest elements for a management model development that will allow, with the lowest possible probability and consequences, the emergence of the recent macroeconomic risks. The stochastic characteristics of the system, defined by random variables as input values defined by probability distributions, require the performance of a large number of iterations on which to record the output of the model and calculate the mathematical expectations. The paper expounds the basic procedures and techniques of discrete statistical simulation applied to systems that can be characterized by a number of events which represent a set of circumstances that have caused a change in the system’s state and the possibility of its application in the field of assessment of macroeconomic risks. The method has no limitations. It can be used to study very complex systems by using special computer programs. The method uses reasonable estimates for important economic inputs to determine a set of results, not only one outcome at one point in time, yet there is a multiple-possibilities estimation of a certain risk performance, regarding the range of economic variables used in the model. Attempt to influence and influence itself on certain macroeconomic risks, in today’s economy, occupies one of the primary imperatives of the world, therefore, this paper deals with the mutual correlation and application of statistical simulations in macroeconomic risks measurement in order to better prevention and remediation.

International audience

In this thesis a new method for the analysis of power transients in a nuclear reactor is developed, which is more accurate than the present state-of-the-art methods. Transient analysis is important tool when designing nuclear reactors, since they predict the behaviour of a reactor during changing conditions, such as a control-rod movement, induced by an operator, or an accident scenario. The current methods for transient analysis apply deterministic solvers to calculate the neutronic response, but not only do these deterministic solvers always need to discretise the problem, they also often apply more fundamental approximations such as homogenization or diffusion. Therefore a stochastic method is needed, which only has a statistical uncertainty. A challenge for applying the Monte Carlo method on transient analysis, is the different types of particles which must be simulated in a single simulation. It is common for a neutronics calculation to simulate the prompt neutrons, however the simulation of precursors is new. The main challenge when simulating precursors lies in their long lifetime, which is seconds, whereas the prompt neutrons have a lifetime of microseconds. This has been solved by dividing the transient problem into time intervals and forcing the precursors to produce a delayed neutron is all time intervals. This will ensure prompt-neutron chains in all intervals. The prompt neutrons will form prompt-neutron chains, which poses another challenge for the Monte Carlo method. The chain length of these prompt neutrons varies a lot and the can also split into many branches, which averages out in a real power reactor, but is difficult to simulate on a computer. To improve the chain-length statistics, a new variance reduction technique is developed, which dictates that a single neutron will emerge from each interaction. This emerging neutron can be the result of a scattering event or a fission event. Finally, a dynamic simulation scheme, which can run in parallel, has been devised, simulating all time intervals consecutively. Also, a method for sampling the initial conditions is created and this scheme is implemented in a purpose-built Monte Carlo code and in a general-purpose Monte Carlo code. The two codes have been tested in several cases and they behave as expected, agreeing with deterministic method where expected, but deviating when the deterministic methods are no longer valid. In order to simulate realistic transients in a power reactor, feedback has to be taken into account. To achieve this, the dynamic Monte Carlo method has been coupled to a thermal-hydraulics code, using an explicit scheme. The results of this coupled simulation are compared to a state-of-the-art coupled diffusion calculation in a NURISP-benchmark calculation and the results agree well, except for a small deviation towards the end. The exact source of this deviation should be further investigated, but the difference is small, when realising that there is already a deviation in the steady-state results. The results demonstrate the feasibility of performing a fully dynamic transient analysis, using only Monte Carlo for the neutronics part of the calculation. Transients can now be calculated, with detailed modelling of any complex geometry and with continuous energy, which is especially useful for newly developed reactor types and one-of-a-kind research reactors.

This paper introduces a Switched-current Analysis Program (SIAP) that can perform both transient and frequency domain analysis of switched-current (SI) circuits. The program uses sparse matrices to reduce storage requirements and computation time. Transient analysis is performed using the large signal MOSFET model and the frequency domain analysis uses the small signal MOSFET model that includes all parasitic capacitance. All devices are modeled in a manner comparable with HSPICE and include almost all nonidealities, such as nonideal switches, clock feedthrough, channel-length modulation and transistor parasitic capacitors. Multiple inputs are allowed in both the transient and frequency domain analysis, thus differential circuits can be easily analyzed.

Monte Carlo (MC) simulation is the most frequently used method to numerically model the light propagation in biological tissues because of its high flexibility and precision. Although MC simulation is assumed to be capable of achieving any desired precision, larger number of photons are always necessary for more precise simulation, leading to its major limitation of intensive computation. In this work, the authors present a way to adapt generative adversarial networks (GAN) to accelerate MC simulation. The pix2pix network, a variant of GAN, was investigated to reconstruct precise MC simulation results from the results roughly modeled by small amount of photons, thus the computation time was expected to be significantly saved. The proposed method was tested on single-layer embedded tumor models to derive the absorption distribution maps. The results demonstrate that the absorption distribution maps reconstructed from the simulation of only 10000 photons were very similar to those modeled by using 1000000 photons, based on the criterion of peak signal to noise ratio (PSNR) and percentage difference of power coupling efficiencies, and the simulation process was proved to be accelerated by approximately 102 times. For the first time, GAN was adapted to save computation time of MC simulation of light propagation. By achieving MC simulation with acceptable quality, the proposed method can speed up the computation by hundreds of times.

The remaining useful life (RUL) estimation is an important metric that helps in condition-based maintenance. Damage data obtained from the diagnostics techniques are often noisy, and the RUL estimated from the data is less reliable. Estimating the probabilistic RUL by quantifying the uncertainty in the predictive model parameters using the noisy data increases confidence in the predicted values. In this work, Bayesian inference is used to inversely quantify the uncertainty in the model parameters of the predictive damage model in adhesively bonded joints, and quantified parameter uncertainty is represented by a probability distribution function (PDF). It is difficult to obtain a closed-form solution for the RUL from the PDF of model parameters due to the nonlinearity of the damage models. Instead, statistical simulations are used to generate the model parameter samples from the PDF, and the RUL is estimated from the samples. In the statistical simulations, the predictive damage model is evaluated for each parameter sample. Using a physics-based model as the predictive model increases computational time, which makes the statistical techniques to be computationally expensive. It is essential to reduce the computational time to estimate the RUL in a feasible time. In this work, real-time probabilistic RUL estimation is demonstrated in adhesively bonded joints using the Sequential Monte Carlo (SMC) sampling method and cloud-based computations. The SMC sampling method is an alternative to traditional Markov Chain Monte Carlo (MCMC) methods, which enables generating statistical parameter samples in parallel. The parallel computational capabilities of the SMC methods are exploited by running the SMC simulation on multiple cloud calls. This approach is demonstrated by estimating fatigue RUL in the adhesively bonded joint. The accuracy of probabilistic RUL estimated by SMC is validated by comparing it with RUL estimated by the MCMC and the experimental values. The SMC simulation is run on the cloud and the computational speedup of the SMC is demonstrated.

At the multiplexer of an ATM network, the admissible cell loss probability is less than 10−12 for some service categories. Ordinary Monte Carlo (MC) simulation requires considerable computation time to obtain such a small probability. The importance sampling (IS) technique is effective in accclerating the MC simulation. In an IS simulation, the underlying distribution is biased so as to generate more samples in the target event. In order to achieve a fast simulation, it is important to have a simulation distribution that yields an estimate with minimum variance. This is called the optimal simulation distribution. In this paper, we investigate the survivor function P(Q > q) of a stationary queue length Q in ATM queuing and obtain an IS estimate of P(Q > q) at about 10−2 by means of the optimal simulation distribution. Conventional methods [1, 2] for determining the optimal distribution require a lot of computation time. We apply the large deviation theory to this problem to obtain the optimal simulation distribution analytically and carry out an IS simulation. We present some numerical results for M/D/1 and 2-state MMPP/D/1 which demonstrate that our estimates are obtained in a very small computation time and are accurate when compared to MC simulation. © Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(12): 28–37, 1997

Monte Carlo (MC) simulations are often used in calculations of radiation transport to enable accurate prediction of radiation-dose, even though the computation is relatively time-consuming. In a typical MC simulation, significant computation time is allocated to following non-important events. To address this issue, variance reduction techniques (VRTs) have been suggested for reducing the statistical variance for the same computation time. Among the available MC simulation codes, electron gamma shower (National Research Council of Canada) (EGSnrc) is a general-purpose coupled electron-photon transport code that also features an even-handed, rich set of VRTs. The most well-known VRTs are the photon splitting, Russian roulette (RR), and photon cross-section enhancement (XCSE) techniques. The objective of this work was to determine the optimal combination of VRTs that increases the simulation speed and the efficiency of simulation, without compromising its accuracy. Selection of VRTs was performed using EGSnrc MC User codes, such as cavity and egs_chamber, for simulating various ion chamber geometries using 6 MV photon beams and 1.25 MeV 60Co photon beams. The results show that the combination of XCSE and RR yields the highest efficiency for ion-chamber dose calculations inside a 30 cm × 30 cm × 30 cm water phantom. Hence, properly selecting a different VRT without altering the underlying physics increases the efficiency of MC simulations for ion-chamber dose calculation.

Global interconnects are widely acknowledged as a limiting factor in future on-chip designs. Novel interconnect driving techniques like multi-level signaling have been proposed to improve performance of on-chip interconnects. This paper presents the impact of process-induced parameter variation on multi-level signaling system for on-chip interconnects. The effects of parameter variations is analyzed by Monte Carlo simulations and parameter sensitivity analyses. Monte Carlo analyses show that the threshold voltage, effective gate length and supply voltage are the key parameters that influence interconnect delay and total average power. It also shows that the interconnect delay and total average power with multi-level signaling for 10 mm line in 100 nm technology are normally distributed with a standard deviation of around 7.8% and 14.55% respectively. Individual parameter sensitivity analyses show that the total average power is most influenced by threshold voltage and is least influenced by drain/source parasitic resistance and thickness of oxide. The impact of different technologies, which include 180 nm, 130 nm and 100 nm are analyzed and it can be seen that the impact of individual device variation on delay and power reduces as technology scaled down. Yield of high performance and low power bins in 180 nm technology under process variations is 30%, yield of high performance bins is 23.2% and yield of low power bins is 36.1%.

Gate oxide breakdown is a major cause of reliability failures in future nanometer-scale CMOS designs. This paper develops an analysis technique that can predict the probability of a functional failure in a large digital circuit due to this phenomenon. Novel features of the method include its ability to account for the inherent resilience in a circuit to a breakdown event, while simultaneously considering the impact of process variations. Based on standard process variation models, at a specified time instant, this procedure determines the circuit failure probability as a lognormal distribution. Experimental results demonstrate this approach is accurate compared with Monte Carlo simulation, and gives 4.7-5.9× better lifetime prediction over existing methods that are based on pessimistic area-scaling models.

On the performance of digital systems in α-[formula omitted] fading and non-Gaussian noise channels

In this paper, we investigate the impact of process variation on soft error vulnerability with Monte Carlo analysis. Our simulation results show that Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">critical</sub> variation (3sigma/mean) of four types of storage circuits caused by process variation can be as large as 13.6%. We also propose an empirical model to estimate the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">critical</sub> variation caused by gate length and threshold voltage variations. Simulation results show that this simple model is very accurate. Based on this model, the dependence of Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">critical</sub> variation on gate length variation, threshold voltage variation, and correlation between gate lengths is studied, using 70 nm SRAM as benchmark circuit.

Statistical mechanical calculations with the extended reference interaction site model (XRISM) and Monte Carlo simulations are performed on fluid CF4. The parameters of a five‐center (12‐6) Lennard Jones potential with added point charges are deduced. The results are compared with total atom pair correlation functions recently determined by neutron diffraction experiments at three supercritical densities. Apart from the good agreement between experimental and theoretical results, we found that depending on the method used, different potentials are able to describe the investigated system. The atom pair correlation functions and angular distribution functions indicate a completely disordered arrangement of the molecules in fluid CF4 with no significant short‐range orientational order except for very close distances. The comparison of the results with former Reverse Monte Carlo (RMC) simulations allows the conclusion that the RMC method is an effective tool, equivalent to the well established Monte Carlo and XRISM methods, in determining the microscopic structure of fluid CF4, but without the exact knowledge of intermolecular potentials.

The distribution of ratios of energy scattered by the medium or reflected by the boundary surface (DRESOR) method can provide radiative intensity with high directional resolution, but also suffers the common drawbacks of the Monte Carlo method (MCM), i.e., it is time-consuming and produces unavoidable statistical errors. In order to overcome the drawbacks of the MCM, the so-called equation-solving DRESOR (ES-DRESOR) method, an equation-solving method to calculate the DRESOR values differently from the MCM used before, was proposed previously. In this method, a unit blackbody emission is supposed within a small zone around a specified point, while there is no emission elsewhere in a plane-parallel, emitting, absorbing, and isotropically scattering medium with transparent boundaries. The set of equations for the DRESOR values based on two expressions for the incident radiation was set up and solved successfully. In this paper, the ES-DRESOR method is extended to a one-dimensional system with diffusely reflecting boundaries. The principle and formulas are given. Several examples with different parameters are taken to examine the performance of the proposed method. The results showed that all the DRESOR values obtained using the ES-DRESOR method agree well with those got using MCM. The average relative error for the intensity obtained by the ES-DRESOR method is 9.446 × 10−6, lower by over 1 order of magnitude than the 2.638 × 10−4 obtained by the MCM under the same conditions. More importantly, the CPU time for computing the DRESOR values, which ranges from several hundred seconds to several thousand seconds using the MCM, is reduced to 0.167 s using the ES-DRESOR method. The computation time is shortened by about 3 orders of magnitude. The overall performance of the ES-DRESOR method is excellent.