Rapid Uncertainty Propagation for High-Fidelity Prognostics Using SROMPy and Python

This paper presents a novel statistical approach, referred to as the stochastic reduced order model (SROM) method, to predict the statistics of crosstalk in the presence of multiple uncertainty sources. In this paper, the cable is modelled using a three-conductor transmission line, and the SROM method is applied to obtain the statistics of crosstalk subject to two independent uncertain sources. Compared with the conventional Monte Carlo (MC) method, it is found that the SROM method can produce accurate statistics of crosstalk using a small computational cost. The Stochastic Collocation (SC) method is also implemented to validate the efficacy of the SROM method. Since the implementation of the SROM method is non-intrusive, the application of this method to other uncertainty-embedded electromagnetic compatibility (EMC) problems is straightforward.

Stochastic analysis of a three phase composite using variational asymptotic based homogenization technique coupled with stochastic reduced order model

This paper introduces a novel statistical method, referred to as the stochastic reduced order model (SROM) method, to predict the variability of cable crosstalk subject to a range of parametric uncertainties. The SROM method is a new member of the family of stochastic approaches to quantify propagated uncertainty in the presence of multiple uncertainty sources. It is nonintrusive, accurate, efficient, and stable, thus could be a promising alternative to some well-established methods, such as the Stochastic Galerkin and stochastic collocation (SC) methods. In this paper, the SROM method is successfully applied to obtain the statistics of cable crosstalk subject to single and multiple uncertainty sources. The statistics of uncertain cable parameters is first accurately approximated by SROM, i.e., pairs of very few samples with known probabilities, such that the uncertain input space is well represented. Then, a deterministic solver is used to produce the samples of cable crosstalk with the corresponding probabilities, and finally the uncertainty propagated to the crosstalk is quantified with good accuracy. Compared to the conventional Monte-Carlo simulation, the statistics of crosstalk obtained by the SROM method converge much faster by orders of magnitude. Also, the computational cost of the SROM method is shown to be small and can be tuned flexibly depending on the accuracy requirement. The SC method based on tensor product sampling strategy is also implemented to validate the efficacy of the SROM method.

Propagation of uncertainty in nasal spray in vitro performance models using Monte Carlo simulation: Part I. model prediction using Monte Carlo Simulation

Propagation of Uncertainty in Nasal Spray In Vitro Performance Models Using Monte Carlo Simulation: Part II. Error Propagation During Product Performance Modeling

In this paper, Monte Carlo Simulation (MCS) method was used as an uncertainty assessment tool for air flow, net thrust measurement. Uuncertainty sources of the net thrust measurement were analyzed, and the probability distribution characteristics of each source were discussed. Detailed MCS methodology was described including the effect of the number of simulation. Compared to the conventional sensitivity coefficient method, the MCS method has advantage in the uncertainty assessment. The MCS is comparatively simple, convenient and accurate, especially for complex or nonlinear measurement modeling equations. The uncertainty assessment result by MCS was compared with that of the conventional sensitivity coefficient method, and each method gave different result. The uncertainties in the net thrust measurement by the MCS and the conventional sensitivity coefficient method were 0.906% and 1.209%, respectively. It was concluded that the first order Taylor expansion in the conventional sensitivity coefficient method and the nonlinearity of model equation caused the difference. It was noted that the uncertainty assessment method should be selected carefully according to the mathematical characteristics of the model equation of the measurement.

How to effectively compute the reliability of a thermal–hydraulic nuclear passive system

Blackbody (BB) cavities as standard radiation sources are used in calibration for various infrared (IR) instruments in IR detection, imaging, material emissivity measuring etc. A surface pitted with cell-like mini cavities as honeycombs whose radiant characteristics is evaluated by Monte Carlo method (MCM) is applied to develop a new surface BB. To improve the precision of MCM, make it more reliable, three requisite factors are considered. First, set up correct physical model in which the radiation of a surface comes from light emitting points across the surface consistently. Second, the uniformity of random number generators are investigated, which is the precondition for the MCM simulation. Third, to perform simulating with tremendous sampling number, after all light points and their rays are tracked, the statistical results become stable, fluctuate slightly, which increase the exactitude of MCM. To implement MCM simulation, every ray of the IR lights is tracked, the position of a light point, the direction of a ray, the state that if the ray is absorbed or reflected at a reflecting point etc. are all regarded as random variables which are sampled by random number according to their probability distribution. The effective emissivity of the surface is evaluated statistically via tracking numerous rays which involves setting up the ray equation, and coordinates transformation etc. The relationships between the accuracy of computation results and simulating model, sampling method, uniformity of pseudo-random number, and sampling number have been discussed. The results show the surface with honeycombs can provide a consistent radiation near to be a diffuse emitter even the material of the surface including spectral components, and the MCM simulating results provide the criteria for surface BB design.

Physics-informed deep learning: A promising technique for system reliability assessment

Monte Carlo (MC) simulation methods are widely used to solve complex engineering and scientific problems. Unlike other deterministic methods, MC methods use statistical sampling to produce approximate solutions. As the processed sample size N growths, the uncertainty of the solution is reduced. It is well known that the mean-square approximation error decreases as 1/N. However, for large problems like high-dimensional integrations and computationally intensive simulations, MC methods may take months or even years to obtain a solution with acceptable tolerance. The Super-Efficient (SE) Monte Carlo simulation method, originated by Umeno, produces a solution whose approximation error decreases as fast as 1/N2. However, it only applies to a small class of problems possessing certain properties. We describe an approximate SE Monte Carlo simulation method that is applicable to a wider class of problems than the original SE method, and yields a convergence rate as fast as 1/Na for 1<a<2.

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state (SLS) of single piles. This contributes to conducting the SLS reliability-based design (RBD) of piles. Based on a two-parameter, hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index (βsls) is obtained using the mean value first order second moment (MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation (MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement (slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety (FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of dierent observation or measurement operators on the update.

Given the importance of uncertainty quantification in various domains, fully propagating uncertainty from model parameters to response functions is essential. While the typical deterministic uncertainty propagation (UP) method makes assumptions about the probability distribution (PD) of model parameters and the linearity of response functions (as do some half-stochastic methods), the Total Monte Carlo (TMC) method allows for fully propagating the PDs of parameters to response functions without prior assumptions. However, performing independent simulations with sampled parameters leads to a significant computational burden in TMC. The present work proposes to combine the certified Reduced-Order Model (ROM) and TMC to significantly enhance the computational efficiency without compromising the advantages of TMC. Using the accurate and efficient ROM-TMC method, the full UP is performed for the three-dimensional International Atomic Energy Agency benchmark. Nonlinearity with respect to certain parameters is observed even in such a simple benchmark. Moreover, it is shown that the fully propagated PDs of keff cannot be described by a common distribution. The numerical results highlight the importance of full UP, which can be efficiently achieved with the proposed ROM-TMC method.

Equilibrium modeling of U(VI) speciation in high carbonate groundwaters: Model error and propagation of uncertainty

The effect of uncertainties on performance predictions of a helicopter is studied in this article. The aeroelastic parameters such as the air density, blade profile drag coefficient, main rotor angular velocity, main rotor radius, and blade chord are considered as uncertain variables. The propagation of these uncertainties in the performance parameters such as thrust coefficient, figure of merit, induced velocity, and power required are studied using Monte Carlo simulation and the first-order reliability method. The Rankine—Froude momentum theory is used for performance prediction in hover, axial climb, and forward flight. The propagation of uncertainty causes large deviations from the baseline deterministic predictions, which undoubtedly affect both the achievable performance and the safety of the helicopter. The numerical results in this article provide useful bounds on helicopter power requirements.