Probabilistic Analysis Approach Research Articles

Multi-aircraft Conflict Detection and Resolution Based on Probabilistic Reach Sets

In this brief, a novel scheme to multi-aircraft conflict detection and resolution is introduced. A key feature of the proposed scheme is that uncertainty affecting the aircraft future positions along some look-ahead prediction horizon is accounted for via a probabilistic reachability analysis approach. In particular, ellipsoidal probabilistic reach sets are determined by formulating a chance-constrained optimization problem and solving it via a simulation-based method called scenario approach . Conflict detection is then performed by verifying if the ellipsoidal reach sets of different aircraft intersect. If a conflict is detected, then the aircraft flight plans are redesigned by solving a second-order cone program resting on the approximation of the ellipsoidal reach sets with spheres with constant radius along the look-ahead horizon. A bisection procedure allows one to determine the minimum radius such that the ellipsoidal reach sets of different aircraft along the corresponding new flight plans do not intersect. Some numerical examples are presented to show the efficacy of the proposed scheme.

Probabilistic analysis of fatigue life for asphalt mixtures using the viscoelastic continuum damage approach

Fatigue cracking is one of the most serious distress modes affecting the serviceability of asphalt pavement structures. The inherent variability of asphaltic materials exhibited in fatigue test results, especially for specimens acquired from field pavements, makes the task of accurately predicting the material’s fatigue characteristics rather difficult. The problem is further exacerbated by the combined impact of a large number of factors, including loading conditions, material heterogeneity, ageing, construction quality and others. For these reasons, notable uncertainty is associated with the predicted fatigue life from laboratory tests based on the use of phenomenological models, which adopt deterministic input parameters despite the varying levels of uncertainty embedded in them. To investigate the effect of inherent uncertainty associated with asphalt mixtures on their fatigue life prediction, a probabilistic analysis approach is evidently needed. In this study, probabilistic analysis was applied to the fatigue life prediction model deduced from the viscoelastic continuum damage theory, based on testing various types of asphalt mixtures. The outcome of the analysis is a newly developed approach with the ability to predict the fatigue performance of asphalt mixtures at more consistent and reliable levels than current practice permits.

A probabilistic bias analysis for misclassified categorical exposures, with application to oral anti-hyperglycaemic drugs.

The effect of drug exposure misclassification generally receives little attention in pharmacoepidemiological research. In this paper, we illustrate a probabilistic bias analysis approach for misclassified categorical exposures and apply it in a database study of oral anti-hyperglycaemic drugs (OADs). A cohort study based on the Health Search Database general-practice database was carried out by including 12 640 adult (≥40 years) patients newly treated with OADs during 2003-2010. The proportion of days covered by OADs prescriptions during the first year of follow-up was evaluated for each individual, either by means of the prescribed daily dose or the defined daily dose. The effect of misclassification on hypothetical OAD-outcome association profiles was assessed through the proposed probabilistic bias analysis approach, taking advantage of available exposure validation data. During the first year of follow-up, the average (SD) number of months with OADs available was 7 (4) months and 5 (3) months according to the prescribed daily dose and defined daily dose metrics, respectively. Probabilistic bias analysis results based on validation data suggest that the effect of misclassification is complex, as conventional exposure-outcome association estimates may be of greater or lower magnitude than their misclassification-adjusted values. Misclassification should be taken into account in database studies on the safety of prescribed medications. To this aim, investigators should take advantage of external exposure validation data in sensitivity analysis approaches such as ours. Copyright © 2016 John Wiley & Sons, Ltd.

Sensitivity analysis and probabilistic re-entry modeling for debris using high dimensional model representation based uncertainty treatment

Well-known tools developed for satellite and debris re-entry perform break-up and trajectory simulations in a deterministic sense and do not perform any uncertainty treatment. The treatment of uncertainties associated with the re-entry of a space object requires a probabilistic approach. A Monte Carlo campaign is the intuitive approach to performing a probabilistic analysis, however, it is computationally very expensive. In this work, we use a recently developed approach based on a new derivation of the high dimensional model representation method for implementing a computationally efficient probabilistic analysis approach for re-entry. Both aleatoric and epistemic uncertainties that affect aerodynamic trajectory and ground impact location are considered. The method is applicable to both controlled and un-controlled re-entry scenarios. The resulting ground impact distributions are far from the typically used Gaussian or ellipsoid distributions.

Probabilistic seismic stability analysis of slope at a given site in a specified exposure time

This paper presents a probabilistic approach for seismic stability analysis of a slope at a given site in a specified exposure time. For a probabilistic seismic stability analysis, the ground motion parameter, in terms of the peak ground acceleration (PGA), at a given site in a specified exposure time of interest (say, 30years) is treated as a random variable, and the PGA distribution at the given site is derived based on the USGS National Seismic Hazard Maps data. Further, the spatial variability of the soil property is simulated herein by a random field, and the fluctuation of the groundwater level is simulated by a random variable. Within the probabilistic framework, a deterministic model for evaluating the slope stability is required; here, a pseudo-static analysis is adopted and implemented through 2D finite difference program FLAC version 7.0. In the face of the uncertainties in the input parameters, the performance or safety of the slope is expressed as a failure probability; within the proposed probabilistic analysis framework, a recently developed sampling method is adopted for the uncertainties propagation through the deterministic solution model. This probabilistic analysis framework is demonstrated with an illustrative example of a two-layer earth slope. Finally, a parametric study is undertaken to investigate how the failure probability of the slope (at a given site in a specified exposure time) is affected by the uncertain factors such as the earthquake-induced ground motion and the spatial variability of soil property. The study results demonstrate the versatility and effectiveness of the proposed framework for probabilistic seismic stability analysis of slope at a given site in a specified exposure time.

Probabilistic analysis of shield-driven tunnel in multiple strata considering stratigraphic uncertainty

Subsurface formations with multiple soil/rock strata are a common geological condition for shield-driven tunnel (i.e., tunnel constructed using shield-driven machines) construction. The excavation face, under such conditions, often encounters a frequently changing stratigraphic configuration that consists of various lithological units. Furthermore, due to a lack of direct and continuous observations of the subsurface region, it is difficult to predict the stratigraphic profile along the entire excavation path with a high degree of certainty. Such a widely changing and uncertain excavation environment may lead to wide variation in the state of stress and deformation of the tunnel structure along the longitudinal direction. This poses a challenge for design engineers in obtaining accurate performance evaluations or reasonable design outcomes for tunnel construction in subsurface ground with multiple strata. This paper aims to address this challenge by presenting a stochastic geological modeling framework for uncertainty quantification of stratigraphic profiles using sparsely located observation information from geotechnical site investigations. In the proposed modeling framework, the underground soil stratigraphic profile is regarded as a Markov random field with specific energy functions, which is able to describe the inherent anisotropic and non-stationary spatial correlation of lithological units in the subsurface stratigraphic structure. By incorporating the developed stochastic geological modeling framework with a finite element simulation of the tunnel excavation, a probabilistic analysis approach is established to evaluate the effects of stratigraphic uncertainty on the structural performance of a shield-driven tunnel.

Bayesian wavelet PCA methodology for turbomachinery damage diagnosis under uncertainty

Centrifugal compressor often suffers various defects such as impeller cracking, resulting in forced outage of the total plant. Damage diagnostics and condition monitoring of such a turbomachinery system has become an increasingly important and powerful tool to prevent potential failure in components and reduce unplanned forced outage and further maintenance costs, while improving reliability, availability and maintainability of a turbomachinery system. This paper presents a probabilistic signal processing methodology for damage diagnostics using multiple time history data collected from different locations of a turbomachine, considering data uncertainty and multivariate correlation. The proposed methodology is based on the integration of three advanced state-of-the-art data mining techniques: discrete wavelet packet transform, Bayesian hypothesis testing, and probabilistic principal component analysis. The multiresolution wavelet analysis approach is employed to decompose a time series signal into different levels of wavelet coefficients. These coefficients represent multiple time-frequency resolutions of a signal. Bayesian hypothesis testing is then applied to each level of wavelet coefficient to remove possible imperfections. The ratio of posterior odds Bayesian approach provides a direct means to assess whether there is imperfection in the decomposed coefficients, thus avoiding over-denoising. Power spectral density estimated by the Welch method is utilized to evaluate the effectiveness of Bayesian wavelet cleansing method. Furthermore, the probabilistic principal component analysis approach is developed to reduce dimensionality of multiple time series and to address multivariate correlation and data uncertainty for damage diagnostics. The proposed methodology and generalized framework is demonstrated with a set of sensor data collected from a real-world centrifugal compressor with impeller cracks, through both time series and contour analyses of vibration signal and principal components.

Large-scale climate patterns and precipitation in an arid endorheic region: linkage and underlying mechanism

The interactions between a range of large-scale climate oscillations and their quantitative links with precipitation are basic prerequisites to understand the hydrologic cycle. Restricted by the current limited knowledge on underlying mechanisms, statistical methods (e.g. correlation methods) are often used rather than a physical-based model. However, available correlation methods generally fail to explain the interactions among a wide range of climate oscillations and associated effects on the water cycle. This study presents a new probabilistic analysis approach by means of a state-of-the-art Copula-based joint probability distribution to characterize the aggregated behaviors for large-scale climate patterns and their connections to precipitation. We applied this method to identify the complex connections between climate patterns (westerly circulation (WEC), El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO)) and seasonal precipitation over a typical endorheic region, the Tarim River Basin in central Asia. Results show that the interactions among multiple climate oscillations are non-uniform in most seasons and phases. Certain joint extreme phases can significantly trigger extremes (flood and drought) owing to the amplification effect among climate oscillations. We further find that the connection is mainly due to the complex effects of climatic and topographical factors.

Point process approach to modeling and analysis of general cascading failure models

Abstract A cascading failure is a failure in a system of interconnected parts in which the failure of a part can trigger the failure of successive parts. Although an initial and introductory approach for probabilistic modeling and analysis of the cascading failures was suggested in the literature, any general framework and fundamental results have yet to be reported. In this paper, applying the point process approach, we suggest a general framework for modeling and analysis of the cascading failures. Furthermore, a new concept of 'information-based residual lifetime' will be defined and discussed.

Stochastic Multidisciplinary Analysis with High-Dimensional Coupling

This paper presents a novel approach for efficient uncertainty quantification and propagation in multidisciplinary analysis with a large number of coupling variables. The proposed methodology has three elements: Bayesian network, copula-based sampling, and principal component analysis. The Bayesian network represents the joint distribution of multiple variables through marginal distributions and conditional probabilities, and it updates the distributions based on new data. This paper uses this concept to develop a novel approach for probabilistic multidisciplinary analysis, that is, inference of distributions of the coupling variables by enforcing the interdisciplinary compatibility condition (which is treated similar to data for updating). The Bayesian network is built using only a few iterations of the coupled multidisciplinary analysis, without iterating until convergence. A copula-based sampling technique is employed for efficient sampling from the joint and conditional distributions. Further savings are achieved through dimension reduction using principal component analysis. A mathematical example and an aeroelastic analysis of an aircraft wing are used to demonstrate the proposed probabilistic multidisciplinary analysis methodology.

Stochastic Small-Signal Stability Analysis of Grid-Connected Photovoltaic Systems

As the penetration level of photovoltaic (PV) generators into the grid is rapidly increasing, the effect of a variable PV power output on the stability of power systems cannot be ignored. Due to the stochastic characteristics of PV power generation, deterministic analysis approaches are not able to fully reveal the impact of high-level PV integration. This paper investigates the impact of the stochastic PV generation on the dynamic stability of grid-connected PV systems by using a probabilistic small-signal analysis approach. The sensitivity of the critical eigenvalue to the variation of solar irradiance is obtained. With the knowledge of the sensitivity relationship and the statistics of solar irradiance data, the probability density function (pdf) of the real part of the critical eigenvalue is approximated by Gram–Charlier expansion. This pdf is then used to calculate the probability of the stochastic small-signal stability of a power system. The impacts of important system parameters on the stochastic stability of the system are also analyzed. It has been found that these system parameters can significantly affect the stochastic stability of the system. Results of Monte Carlo and time-domain simulations of the grid-connected system verify the effectiveness of the proposed stochastic stability analysis method.

Direct Dynamic Kinetic Analysis and Computer Simulation of Growth of Clostridium perfringens in Cooked Turkey during Cooling.

This research applied a new 1-step methodology to directly construct a tertiary model that describes the growth of Clostridium perfringens in cooked turkey meat under dynamically cooling conditions. The kinetic parameters of the growth models were determined by numerical analysis and optimization using multiple dynamic growth curves. The models and kinetic parameters were validated using independent growth curves obtained under various cooling conditions. The results showed that the residual errors (ε) of the predictions followed a Laplace distribution that is symmetric with respect to ε=0. For residual errors, 90.6% are within ±0.5 Log CFU/g and 73.4% are ±0.25 Log CFU/g for all growth curves used for validation. For relative growth <1.0 Log CFU/g, 88.9% of the residual errors are within ±0.5 Log CFU/g, and 63.0% are within ±0.25 Log CFU/g. For relative growth of <2.0 Log CFU/g, 92.7% of the residual errors are within ±0.5 Log CFU/g, and 70.3% are within ±0.25 Log CFU/g. The scale and distribution of residual errors clearly suggests that the models and estimated kinetic parameters are reasonably accurate in predicting the growth of C. perfringens. Monte Carlo simulation was used to estimate the probabilities of >1.0 and 2.0 Log CFU/g relative growth of C. perfringens in the final products at the end of cooling. This probabilistic process analysis approach provides a new alternative for estimating and managing the risk of a product and can help the food industry and regulatory agencies assess the safety of cooked meat in the event of cooling deviation.

Probabilistic Approach for Analysis of Strength of Ceramics With Different Porous Structure Based on Movable Cellular Automaton Modeling

Movable cellular automaton method which is a computational method of particle mechanics is applied to simulating uniaxial compression of 3D porous ceramic specimens. Pores were considered explicitly by removing automata selected randomly from the original fcc packing. Distribution of pores in space, their size and the total fraction were varied. For each values of porosity there were generated several represented specimens with individual pore position in space. The resulting values of elastic modulus and strength of the specimens were scattered and well described by the Weibull distribution. We showed that to reveal dependence of the elastic and strength properties on porosity it is much better to consider not average of the values for the specimens of the same porosity, but the mathematical expectation of the corresponding Weibull distribution. It is shown that relation between mechanical properties of the material and its porosity depends significantly on pore structure. Namely, percolation transition from closed porosity to interconnected pores strongly manifests itself on strength dependence on porosity. Thus, the curve of strength versus porosity fits different equations for different kind of pore structure. Composite ceramics which pores are filled by plastic filler shows the similar behavior.

Probabilistic back analysis based on Bayesian and multi-output support vector machine for a high cut rock slope

Uncertainty of geomechanical parameters is an important consideration for rock engineering and has a very important influence on safety evaluation, design, and construction. Back analysis is a common method of determining geomechanical parameters but traditional deterministic back analysis cannot allow for consideration of this uncertainty. In this study, a new probabilistic back analysis method is proposed that integrates Bayesian methods and a multi-output support vector machine (B–MSVM). In this B–MSVM back analysis method, Bayesian was used to deal with the uncertainty of geomechanical parameters and a multi-output support vector machine (MSVM) was adopted to build the relationships between displacements and those parameters. The proposed method was applied to a high abutment rock slope at the Longtan hydropower station, China. At Longtan, the uncertainty of the two types of geomechanical parameters, Young's modulus and lateral pressure coefficients of in situ stress, were modeled as random variables. Based on the parameters identified by probabilistic back analysis, the computed displacements agreed closely with the measured displacement data monitored in the field. The result showed that B–MSVM presented the uncertainty of the geomechanical parameters reasonably. Further study indicated that the performance of B–MSVM could be improved greatly by updating field monitoring information regularly. The proposed method provides a significant new approach for probabilistic back analysis and contributes to the determination of realistic geomechanical parameters.

Assessment of rock slope stability using GIS-based probabilistic kinematic analysis

Instability in a rock slope is highly dependent on unfavorable orientations of the discontinuities in the rock mass. Therefore, kinematic analysis has been used to analyze the structural condition of unfavorably oriented discontinuities using the stereographic projection method. In this analysis, the orientation of a discontinuity is compared with the slope orientation and friction angle by plotting the orientation of a discontinuity onto a stereonet. This stereonet-based kinematic analysis assumes that a uniform slope orientation and a tightly clustered orientation of the discontinuities exist. However, the slope orientation, represented by the slope aspect and slope angle, cannot be uniform if the slope faces are rugged, as in many natural rock slopes, or if the slope was created by deficient blasting. Moreover, the orientation of discontinuities measured in the field is often scattered, even in a same discontinuity set. However, such variations cannot be included in traditional kinematic analysis and representative values of the slope orientation and mean orientation of a discontinuity are used, which creates uncertainties. To overcome these problems, a GIS-based methodology using grid-based data on the slope orientation data and a probabilistic approach is proposed. To take into account variations in the slope orientation, a digital elevation model (DEM) of the slope face was used and the topographic data of the slope face was derived from the DEM. The slope faces were divided into 2×2m2pixels, and the orientation of the slope face was evaluated based on the grid cells. In addition, the orientation of a discontinuity was treated as a random variable, thereby accounting for natural variability, and a probabilistic analysis approach was adopted to deal with uncertainties and variability. Therefore, a grid-based probabilistic analysis module for the kinematic analysis was developed and used on a cell-by-cell basis to predict instability in spatially distributed slope faces. This probabilistic kinematic analysis was performed in a GIS environment because GIS provides an excellent platform for management and manipulation of raster-based spatial data. We applied this approach to the spatially distributed steep rock slopes in the Baehuryeong area, Korea, located along a tortuous mountain road.

A probabilistic approach for a cost-benefit analysis of oil spill management under uncertainty: A Bayesian network model for the Gulf of Finland

Large-scale oil accidents can inflict substantial costs to the society, as they typically result in expensive oil combating and waste treatment operations and have negative impacts on recreational and environmental values. Cost-benefit analysis (CBA) offers a way to assess the economic efficiency of management measures capable of mitigating the adverse effects. However, the irregular occurrence of spills combined with uncertainties related to the possible effects makes the analysis a challenging task. We develop a probabilistic modeling approach for a CBA of oil spill management and apply it in the Gulf of Finland, the Baltic Sea. The model has a causal structure, and it covers a large number of factors relevant to the realistic description of oil spills, as well as the costs of oil combating operations at open sea, shoreline clean-up, and waste treatment activities. Further, to describe the effects on environmental benefits, we use data from a contingent valuation survey. The results encourage seeking for cost-effective preventive measures, and emphasize the importance of the inclusion of the costs related to waste treatment and environmental values in the analysis. Although the model is developed for a specific area, the methodology is applicable also to other areas facing the risk of oil spills as well as to other fields that need to cope with the challenging combination of low probabilities, high losses and major uncertainties.

A proposed probabilistic seismic tsunami hazard analysis methodology

We expand on existing probabilistic tsunami hazard analysis (PTHA) approaches by presenting a methodology wherein the epistemic uncertainties associated with tsunami timing, generation, and propagation are separated from aleatory uncertainties. The contributions of epistemic and aleatory uncertainties to the overall uncertainty in tsunami hazard are evaluated through a two-level Monte Carlo analysis. The total epistemic uncertainty contribution defines the variance of the tsunami inundation hazard distribution. Through Bayesian inference, the available catalog of tsunami runup data is used to refine the hazard estimate, where the prior distribution is weighted by epistemic uncertainties. The general PTHA framework is further modified to include a hazard function accounting for peak water elevation, velocity, duration of inundation, and warning time. We carry out a formal sensitivity analysis of the tsunami generation and propagation on the feasible model parameter space using the multi-objective generalized sensitivity analysis algorithm. Parameters showing a significant influence on tsunami hazard include the tidal elevation, moment magnitude (M w), the Gutenberg–Richter (G–R) distribution β parameter, epicenter location, and the rake angle. Parameters showing minimal influence on tsunami hazard include the G–R maximum seismic moment magnitude (M max) parameter, strike angle, dip angle, seismic depth and Manning’s roughness. As a proof of concept, the methodology is applied to a case study of tsunami hazard posed to National Oceanic and Atmospheric Administration Station 9411406 (Oil Platform Harvest, CA, USA) by seismic sources along the Aleutian Islands, AK.

Thermal response test for shallow geothermal applications: a probabilistic analysis approach

Abstract Background Thermal Response Test (TRT) is an onsite test used to characterize the thermal properties of shallow underground, when used as heat storage volume for shallow geothermal application. It is applied by injecting/extracting heat into geothermal closed-loop circuits inserted into the ground. The most common types of closed loop are the borehole heat exchangers (BHE), horizontal ground collectors (HGC), and energy piles (EP). The interpretation method of TRT data is generally based on a regression technique and on the calculation of thermal properties through different models, specific for each closed loop and test conditions. Methods A typical TRT record is a graph joining a series of experimental temperatures of the thermal carrier fluid. The proposed geostatistical approach considers the temperature as a random function non-stationary in time, with a given trend, therefore the record is considered as a ‘realization’, one of the possible results; the random nature of the test results is transferred to the fluctuations and a variogram modeling can be applied, which may give many information on the TRT behavior. Results In this paper, a nested probabilistic approach for TRT output interpretation is proposed, which can be applied for interpreting TRT data, independently of the different methodologies and technologies adopted. In the paper, for the sake of simplicity, the probabilistic approach is applied to the ‘infinite line source’ (ILS) methodology, which is the most commonly used for BHE. Conclusions The probabilistic approach, based on variogram modeling of temperature residuals, is useful for identifying with robust accuracy the time boundaries (initial time t 0 and the final time t f) inside which makes temperature regression analysis possible. Moreover, variograms are used into the analysis itself to increase estimation precision of thermal parameter calculation (ground conductivity λ g, ground capacity c g, borehole resistance R b). Finally, the probabilistic approach helps keep under control the effect of any cause of result variability. Typical behaviors of power, flows, and temperatures and of their interaction with the specific closed-loop circuit and geo-hydrological system are deepened by variogram analysis of fluctuations.

Translating online customer opinions into engineering characteristics in QFD: A probabilistic language analysis approach

Online opinions provide informative customer requirements for product designers. However, the increasing volume of opinions make them hard to be digested entirely. It is expected to translate online opinions for designers automatically when they are launching a new product. In this research, an exploratory study is conducted, in which customer requirements in online reviews are manually translated into engineering characteristics (ECs) for Quality function deployment (QFD). From the exploratory study, a simple mapping from keywords to ECs is observed not able to be built. It is also found that it will be a time-consuming task to translate a large number of reviews. Accordingly, a probabilistic language analysis approach is proposed, which translates reviews into ECs automatically. In particular, the statistic concurrence information between keywords and nearby words is analyzed. Based on the unigram model and the bigram model, an integrated impact learning algorithm is advised to estimate the impacts of keywords and nearby words respectively. The estimated impacts are utilized to infer which ECs are implied in a given context. Using four brands of printer reviews from Amazon.com, comparative experiments are conducted. Finally, an illustrative example is shown to clarify how this approach can be applied by designers in QFD.

Efficient Allocation of Resources for Defense of Spatially Distributed Networks Using Agent-Based Simulation.

This article presents ongoing research that focuses on efficient allocation of defense resources to minimize the damage inflicted on a spatially distributed physical network such as a pipeline, water system, or power distribution system from an attack by an active adversary, recognizing the fundamental difference between preparing for natural disasters such as hurricanes, earthquakes, or even accidental systems failures and the problem of allocating resources to defend against an opponent who is aware of, and anticipating, the defender's efforts to mitigate the threat. Our approach is to utilize a combination of integer programming and agent-based modeling to allocate the defensive resources. We conceptualize the problem as a Stackelberg "leader follower" game where the defender first places his assets to defend key areas of the network, and the attacker then seeks to inflict the maximum damage possible within the constraints of resources and network structure. The criticality of arcs in the network is estimated by a deterministic network interdiction formulation, which then informs an evolutionary agent-based simulation. The evolutionary agent-based simulation is used to determine the allocation of resources for attackers and defenders that results in evolutionary stable strategies, where actions by either side alone cannot increase its share of victories. We demonstrate these techniques on an example network, comparing the evolutionary agent-based results to a more traditional, probabilistic risk analysis (PRA) approach. Our results show that the agent-based approach results in a greater percentage of defender victories than does the PRA-based approach.