Probabilistic Insights Research Articles

Hybrid nonlinear probabilistic model using Monte Carlo simulation and hybrid support vector regression for evaporation predictions

This study presents a hybrid model combining Support Vector Regression (SVR) with the Gray Wolf Optimizer (GWO) for evaluating evaporation dynamics. The model was tested using 50 years of meteorological data from Zabol and Chabahar stations in Iran, and compared against standard SVR. Results show that the SVR-GWO significantly outperforms SVR, reducing predictive errors by over 41% on average. For Zabol, the SVR-GWO markedly improved performance, particularly in July where R2 increased from 0.867 to 0.973. The model more closely matched observed statistics, especially for mean and standard deviation, though challenges remain in reproducing higher-order statistics. Interestingly, 5,000 functions evaluation proved nearly as effective as 500,000 suggesting computational efficiency. This integrated approach, incorporating Monte Carlo simulations and kernel density estimation, provides valuable probabilistic insights into evaporation dynamics, offering a promising tool for drought vulnerability assessment and water resources planning in regions with complex climatic patterns.

Mechanism design optimization through CAD-based Bayesian optimization and quantified constraints

This study addresses the challenge of mechanism design optimization, particularly focusing on the energy efficiency and design space of reciprocating mechanisms. The research question centers on how to effectively utilize Computer-Aided Design (CAD) simulations alongside Bayesian optimization (BO) and a constrained design space to streamline the design optimization process, overcoming the limitations of traditional kinematic and dynamic analysis methods. The objective is to investigate and develop a novel optimization framework that integrates CAD-based simulations with a BO approach. To achieve this, the study employs a methodological approach. At first, the feasibility of a chosen mechanism design is evaluated through a sequence of CAD-motion simulations to quantify the (in)feasibility of this design. When this design appears to be feasible, a CAD-based design evaluation method is started, in which the objective value is extracted by a sequence of CAD-motion simulations. In this paper, we advocate the use of non-parametric Gaussian processes to build a surrogate model of the objective function and the feasible design space constrained by static and dynamic constraints. The main research results demonstrate that the proposed CAD-based Bayesian optimization framework can effectively identify optimal design parameters that minimize the root mean square (RMS) torque while adhering to specified static and dynamic constraints. This optimization approach significantly reduces the complexity associated with analytic methods, making it scalable to more complex mechanisms and implementable by machine builders. In conclusion, the study successfully develops a novel optimization framework that leverages CAD-based simulations and Bayesian optimization to streamline the design process of mechanisms. The results of an emergency ventilator case study with three design parameters show a reduction of the RMS torque with 71% after 255 CAD-based design evaluations. Moreover, the results demonstrate the effectiveness of incorporating constraints into the design optimization process and the usage of Bayesian optimization (BO), providing insights into the obtained optimum. This approach offers probabilistic insights into the expected improvement of the optimum, highlighting that the full optimization potential is utilized in a computationally efficient manner.

From certainty to chance: probabilistic insights into quantum control

This study introduces an innovative control methodology designed specifically for quantum physical systems. It bridges a critical gap by accounting for the full spectrum of uncertainties and noise that could affect the time evolution of these systems. In contrast to conventional methods, our pioneering approach utilizes probability density functions (pdfs) to characterize quantum dynamics, providing a more detailed and accurate description of their temporal behavior. We propose a strategy that seeks to minimize the discrepancy between the actual pdf, which encapsulates the combined dynamics of the quantum system and an external electric field, and a desired pdf that aligns with the system’s intended outcomes. This strategy marks a significant shift from traditional quantum control techniques. Initially, we present a solution for controlling quantum systems defined by general pdfs. This solution is then demonstrated on quantum systems described by Gaussian pdfs, with an in-depth account of the resulting optimized controller’s structure. The study culminates with practical demonstrations, showcasing the approach’s efficacy and practicality, thus endorsing its potential as a formidable instrument in quantum control.Graphical abstract

Deep learning solutions for smart city challenges in urban development

In the realm of urban planning, the integration of deep learning technologies has emerged as a transformative force, promising to revolutionize the way cities are designed, managed, and optimized. This research embarks on a multifaceted exploration that combines the power of deep learning with Bayesian regularization techniques to enhance the performance and reliability of neural networks tailored for urban planning applications. Deep learning, characterized by its ability to extract complex patterns from vast urban datasets, has the potential to offer unprecedented insights into urban dynamics, transportation networks, and environmental sustainability. However, the complexity of these models often leads to challenges such as overfitting and limited interpretability. To address these issues, Bayesian regularization methods are employed to imbue neural networks with a principled framework that enhances generalization while quantifying predictive uncertainty. This research unfolds with the practical implementation of Bayesian regularization within neural networks, focusing on applications ranging from traffic prediction, urban infrastructure, data privacy, safety and security. By integrating Bayesian regularization, the aim is to, not only improve model performance in terms of accuracy and reliability but also to provide planners and decision-makers with probabilistic insights into the outcomes of various urban interventions. In tandem with quantitative assessments, graphical analysis is wielded as a crucial tool to visualize the inner workings of deep learning models in the context of urban planning. Through graphical representations, network visualizations, and decision boundary analysis, we uncover how Bayesian regularization influences neural network architecture and enhances interpretability.

Interpretable Tracking and Detection of Unstable Approaches Using Tunnel Gaussian Process

Approach and landing are phases of flight with the highest accident risk. Advanced instruments and procedures have been developed to provide precise navigation for a stabilized approach and landing. With the proliferation of sensing techniques, real-time 4D trajectories can be captured at higher spatial-temporal resolution and enable data-driven decision-making for air traffic controllers (ATCO). This research attempts to augment the existing rule-based stable approach criteria using data-driven and interpretable tunnel Gaussian process (TGP) models to probabilistically characterize the 4D approach and landing parameters. The TGP explicitly and continuously models the underlying distribution of approach and landing parameters and their interrelations. In addition, it provides a comprehensible probabilistic description of anomalies in approach and landing parameters. Based on the trained TGP, we infer the landing parameters of go-around tracks recorded by the advanced surface movement guidance and control system (A-SMGCS) and analyze their adherence to stabilized approach criteria. Empirical results show that anomalous scores were in line with the factors (as reported to ATCOs) in all go-around data in the test dataset, between 0.5 NM (missed approach point) to 7.6 NM from the touchdown threshold, and provides better probabilistic insights of non-compliance, comparing to existing work. Hence, the proposed TGP can provide a ground-based safety net for the compliance of stable approaches. Furthermore, the proposed TGP-based anomaly tracking methods can be directly applied to other types of landing systems (e.g., GNSS landing system and RNAV approaches).

A Machine Learning Predictive Model for Determining Daily Exchange Rate Movement in Sierra Leone

"Prophet is an advanced machine learning tool designed for accurate time series forecasting. Utilizing a Bayesian additive regression model, it employs statistical techniques to analyze historical data and capture underlying patterns, trends, seasonality, and holiday effects. With its ability to handle uncertainties, anomalies, missing data, outliers, and changes in trends or seasonality, Prophet is a versatile solution for both univariate and multivariate time series analyses. In the context of the Sierra Leone currency market, our analysis using Prophet reveals valuable insights into the nominal exchange rates between the Leones and the dollar. On an annual basis, there is an observed upward trend in the nominal exchange rates. Weekly patterns indicate that the Leones tends to experience a slight depreciation on Tuesdays, while showing marginal stabilization or appreciation on Fridays. Additionally, the model highlights a tendency for marginal appreciation in the Leones from April to June, with a slight depreciation around September to October. These findings provide crucial information for risk management, economic planning, and decision-making in the Sierra Leone currency market. By understanding the identified trends in the Leones dollar exchange rates, stakeholders can make informed decisions regarding investments, currency trading, and overall economic strategies. This knowledge contributes to improving investor confidence and enables effective measures for mitigating risks. In summary, Prophet's Bayesian-based forecasting model offers probabilistic insights into future predictions, empowering decision-makers with accurate forecasts and valuable knowledge for strategic planning and risk management. "

Simulation and detection of wind power ramps and identification of their causative atmospheric circulation patterns

The relationship between wind power ramp events and their causative weather systems remains poorly understood, despite its importance to the development of ramp forecasting procedures. Results from previous studies linking ramp events and weather systems have proven difficult to generalize and methodologies used may be difficult to duplicate, especially in cases of measured data scarcity. Accordingly, this paper proposes a flexible methodology for investigating this link between ramps and weather systems in instances of measured data scarcity. A historic wind power time-series is firstly simulated by applying stochastic variations to numeric weather prediction (NWP) reanalysis data. Ramps events are identified within the time-series using a swinging door algorithm. Temporal regularities in ramp statistics are identified as these provide probabilistic insights into ramp occurrences. Finally, ramps are linked to a set of atmospheric circulation archetypes. These archetypes are identified by applying self-organizing maps as a classification procedure to historic NWP data. The proposed methodology is demonstrated through a case study considering a wind farm in South Africa. It is found that mean power and power variability differ significantly as a function of atmospheric circulation, and that thermally driven land-sea breeze interaction can be a primary mechanism for ramp events.

Probabilistic insights on a soil slope in San Francisco and a rock slope in Hong Kong

ABSTRACTTwo slopes are analysed probabilistically, emphasising the insights and sensitivity information obtainable from the design point of the first-order reliability method (FORM). The first case was an underwater slope in San Francisco Bay Mud that failed during excavation. The second case was a rock slope in Hong Kong which had been identified as being potentially unstable. Insights from FORM-based reliability analysis and reliability-based design (RBD) are presented, and RBD’s ability to overcome some of the limitations of partial factor design approaches are discussed.

Implementation of probabilistic assessments to support the ASTRID decay heat removal systems design process

Abstract ASTRID, the Advanced Sodium Technological Reactor for Industrial Demonstration, is a GenIV technological demonstrator. Its purpose will be to demonstrate the progress made in the field of Sodium Fast Reactor (SFR) technology on an industrial scale by qualifying innovative options, especially relative to safety and operability. To support the ASTRID design process during the conceptual design phase, probabilistic assessments have been developed since 2012. They are based on the conventional Fault Tree (FT)/Event Tree (ET) approach and on the determination of the minimal decay heat removal (DHR) systems requirement. Limited to a period of one week, without repair of component malfunctions, their goal is to provide probabilistic insights in the assessment of various design choices and to supplement the deterministic approach in the objective of continuous safety improvements throughout the design process. Nevertheless, the conventional FT/ET “static approach”, developed for PWRs, appears to be inadequate for SFRs in the objectives of assessing the global risk and contributing to the demonstration of the practical elimination of the situation “loss of DHR function” for longer periods of time. Since DHR systems have to operate during long mission times, PSA modelling must consider the repair possibility, adapt the systems requirement to decay heat evolution and take into account all available systems at any time. Therefore, different dynamic probabilistic approaches are developed in a prospective way to comply with the safety demonstration. A first calculation will be performed by the end of the decade to support the demonstration of practical elimination of the DHR function of ASTRID.

Perturbation analysis in finite LD-QBD processes and applications to epidemic models.

SummaryIn this paper, our interest is in the perturbation analysis of level‐dependent quasi‐birth‐and‐death (LD‐QBD) processes, which constitute a wide class of structured Markov chains. An LD‐QBD process has the special feature that its space of states can be structured by levels (groups of states), so that a tridiagonal‐by‐blocks structure is obtained for its infinitesimal generator. For these processes, a number of algorithmic procedures exist in the literature in order to compute several performance measures while exploiting the underlying matrix structure; among others, these measures are related to first‐passage times to a certain level L(0) and hitting probabilities at this level, the maximum level visited by the process before reaching states of level L(0), and the stationary distribution. For the case of a finite number of states, our aim here is to develop analogous algorithms to the ones analyzing these measures, for their perturbation analysis. This approach uses matrix calculus and exploits the specific structure of the infinitesimal generator, which allows us to obtain additional information during the perturbation analysis of the LD‐QBD process by dealing with specific matrices carrying probabilistic insights of the dynamics of the process. We illustrate the approach by means of applying multitype versions of the susceptible‐infective (SI) and susceptible‐infective‐susceptible (SIS) epidemic models to the spread of antibiotic‐sensitive and antibiotic‐resistant bacterial strains in a hospital ward.

Two Applications of Random Spanning Forests

We use random spanning forests to find, for any Markov process on a finite set of size n and any positive integer m le n, a probability law on the subsets of size m such that the mean hitting time of a random target that is drawn from this law does not depend on the starting point of the process. We use the same random forests to give probabilistic insights into the proof of an algebraic result due to Micchelli and Willoughby and used by Fill and by Miclo to study absorption times and convergence to equilibrium of reversible Markov chains. We also introduce a related coalescence and fragmentation process that leads to a number of open questions.

Fine cophasing of segmented aperture telescopes with ZELDA, a Zernike wavefront sensor in the diffraction-limited regime

Context. Segmented aperture telescopes require an alignment procedure with successive steps from coarse alignment to monitoring process in order to provide very high optical quality images for stringent science operations such as exoplanet imaging. The final step, referred to as fine phasing, calls for a high sensitivity wavefront sensing and control system in a diffraction-limited regime to achieve segment alignment with nanometric accuracy. In this context, Zernike wavefront sensors represent promising options for such a calibration. A concept called the Zernike unit for segment phasing (ZEUS) was previously developed for ground-based applications to operate under seeing-limited images. Such a concept is, however, not suitable for fine cophasing with diffraction-limited images. Aims. We revisit ZELDA, a Zernike sensor that was developed for the measurement of residual aberrations in exoplanet direct imagers, to measure segment piston, tip, and tilt in the diffraction-limited regime. Methods. We introduce a novel analysis scheme of the sensor signal that relies on piston, tip, and tilt estimators for each segment, and provide probabilistic insights to predict the success of a closed-loop correction as a function of the initial wavefront error. Results. The sensor unambiguously and simultaneously retrieves segment piston and tip-tilt misalignment. Our scheme allows for correction of these errors in closed-loop operation down to nearly zero residuals in a few iterations. This sensor also shows low sensitivity to misalignment of its parts and high ability for operation with a relatively bright natural guide star. Conclusions. Our cophasing sensor relies on existing mask technologies that make the concept already available for segmented apertures in future space missions.

AN INTEGRATED RISK INFORMED DECISION MAKING IN THE NUCLEAR INDUSTRY

The regulatory body, established to ensure safety of nuclear facilities, is expected to make right decisions and provide appropriate regulations for the nuclear industry. The traditional manner of its activity has been based on a deterministic approach to safety analyses. However, increased maturity of Probabilistic Safety Assessment (PSA) makes it complementary to deterministic studies. The new IAEA concept, described in this article, is to apply an integrated approach by combining both deterministic and probabilistic insights with other requirements affecting the decision making process.

Enhancing Performance of Random Testing through Markov Chain Monte Carlo Methods

In this paper, we propose a probabilistic approach to finding failure-causing inputs based on Bayesian estimation. According to our probabilistic insights of software testing, the test case generation algorithms are developed by Markov chain Monte Carlo (MCMC) methods. Dissimilar to existing random testing schemes such as adaptive random testing, our approach can also utilize the prior knowledge on software testing. In experiments, we compare effectiveness of our MCMC-based random testing with both ordinary random testing and adaptive random testing in real program sources. These results indicate the possibility that MCMC-based random testing can drastically improve the effectiveness of software testing.

Level 1 probabilistic safety assessment to support the design of the CEA 2400 MWth gas-cooled fast reactor

As part of the design of a 4th generation reactor, the integration of safety in the early phase of the concepts is expected. To date, probabilistic insights are increasingly employed in the safety demonstration in combination with the deterministic approach (e.g. to identify the sequences of complex failures, to justify the categorization of situations) and used, even at an early stage of design, to identify the reliability of systems and equipment to handle the safety objectives (expressed in terms of core damage frequency targets). Within this frame, the CEA has undertaken to assess the benefit of developing a probabilistic model to support the design of the 2400MWth gas-cooled fast reactor.In the building process of this level 1 probabilistic safety assessment, a first phase consisted in making a preliminary model that took only into account families of initiating events that were defined for the design of the decay heat removal dedicated loops, namely the loss of coolant accidents (representative of medium pressure situations) and loss of off-site power/station black-out transients (representative of high pressure situations). Owing to the results obtained with this preliminary L1PSA model, it emerged that an increased reliability of the DHR function in high pressure conditions (i.e. characterized by IEs not associated to the loss of integrity of the helium pressure boundary) is suitable to reduce the overall core damage frequency. The track was therefore chosen to require the use of normal loops as first line of provision of the DHR function, possibly including components or particular operating modes related to the secondary and tertiary circuits. In addition, this final L1PSA model is characterized by success criteria based on transient calculations performed with the CATHARE2 code and to a perimeter extended to all representative internal IEs at full operating power.This paper presents the building process and the main results related to these two successive L1PSA models. Finally, useful insights are translated into GFR design improvements that are leading to an overall CDF at full operating power that satisfies nowadays with the probabilistic target defined for 3rd generation reactors, being at least the objective for 4th generation reactors.

Methodology for Fire PSA during design process

Abstract Fire PSA is an essential part of a full scope level 1 PSA. Cable fires play an important role in fire PSA. Usually, cable routing is therefore modeled in detail. During the design of new nuclear power plants the information on cable routing is not yet available. However, for the use of probabilistic safety insights during the design and for licensing purposes a fire PSA may be requested. Therefore a methodology has been developed which makes use of the strictly divisional separation of redundancies in the design of modern nuclear power plants: cable routing is not needed within one division but replaced by the conservative assumption that all equipment fails due to a fire in the concerned division; critical fire areas are defined where components belonging to different divisions may be affected by a fire. For the determination of fire frequencies a component based approach is proposed. The resulting core damage frequencies due to fire are conservative.

Risk-informed design guidance for future reactor systems

Future reactor designs face an uncertain regulatory environment. It is anticipated that there will be some level of probabilistic insights in the regulations and supporting regulatory documents for Generation-IV nuclear reactors. Central to current regulations are design basis accidents (DBAs) and the general design criteria (GDC), which were established before probabilistic risk assessments (PRAs) were developed. These regulations implement a structuralist approach to safety through traditional defense in depth and large safety margins. In a rationalist approach to safety, accident frequencies are quantified and protective measures are introduced to make these frequencies acceptably low. Both approaches have advantages and disadvantages and future reactor design and licensing processes will have to implement a hybrid approach. This paper presents an iterative four-step risk-informed methodology to guide the design of future-reactor systems using a gas-cooled fast reactor emergency core cooling system as an example. This methodology helps designers to analyze alternative designs under potential risk-informed regulations and to anticipate design justifications the regulator may require during the licensing process. The analysis demonstrated the importance of common-cause failures and the need for guidance on how to change the quantitative impact of these potential failures on the frequency of accident sequences as the design changes. Deliberation is an important part of the four-step methodology because it supplements the quantitative results by allowing the inclusion in the design choice of elements such as best design practices and ease of online maintenance, which usually cannot be quantified. The case study showed that, in some instances, the structuralist and the rationalist approaches were inconsistent. In particular, GDC 35 treats the double-ended break of the largest pipe in the reactor coolant system with concurrent loss of offsite power and a single failure in the most critical place as the DBA for the emergency core cooling system. Seventeen out of the 45 variations that we considered violated this DBA, but passed the probabilistic screening criteria. Using PRA techniques, we found that the mean frequency of this accident was very low, thus indicating that deterministic criteria such as GDC 35 must be reassessed in the light of risk insights.

A method for risk-informed safety significance categorization using the analytic hierarchy process and bayesian belief networks

Abstract A risk-informed safety significance categorization (RISSC) is to categorize structures, systems, or components (SSCs) of a nuclear power plant (NPP) into two or more groups, according to their safety significance using both probabilistic and deterministic insights. In the conventional methods for the RISSC, the SSCs are quantitatively categorized according to their importance measures for the initial categorization. The final decisions (categorizations) of SSCs, however, are qualitatively made by an expert panel through discussions and adjustments of opinions by using the probabilistic insights compiled in the initial categorization process and combining the probabilistic insights with the deterministic insights. Therefore, owing to the qualitative and linear decision-making process, the conventional methods have the demerits as follows: (1) they are very costly in terms of time and labor, (2) it is not easy to reach the final decision, when the opinions of the experts are in conflict and (3) they have an overlapping process due to the linear paradigm (the categorization is performed twice—first, by the engineers who propose the method, and second, by the expert panel). In this work, a method for RISSC using the analytic hierarchy process (AHP) and bayesian belief networks (BBN) is proposed to overcome the demerits of the conventional methods and to effectively arrive at a final decision (or categorization). By using the AHP and BBN, the expert panel takes part in the early stage of the categorization (that is, the quantification process) and the safety significance based on both probabilistic and deterministic insights is quantified. According to that safety significance, SSCs are quantitatively categorized into three categories such as high safety significant category (Hi), potentially safety significant category (Po), or low safety significant category (Lo). The proposed method was applied to the components such as CC-V073, CV-V530, and SI-V644 in Ulchin Unit 3 NPP in South Korea. The expert panel consisted of two probabilistic safety assessments (PSA) experts and one system design expert. Before categorizing the components, the design basis functions, simplified P and IDs, and the Fussell-Vesely (FV) importance and the Risk Achievement Worth (RAW) of the PSA were prepared for the experts' evaluations. By using this method, we could categorize the components quantitatively on the basis of experts' knowledge and experience in an early stage.

ICONE11-36432 USNRC Operating Experience Program Activities and Use of Probabilistic Risk Assessment Methods and Insights

ICONE11-36432 USNRC Operating Experience Program Activities and Use of Probabilistic Risk Assessment Methods and Insights

A simple options training model

Options pricing can be based on sophisticated stochastic differential equation models. However, many traders, expert in their art of trading, develop their skills and intuitions based on loose analogies to such models and on games designed to tune their trading skills, not unlike the state of affairs in many disciplines. An analysis of one such game reveals some simple but relevant probabilistic insights into the nature of options trading often not discussed in most texts.