Deterministic Methods Research Articles

On polling directions for randomized direct-search approaches: application to beam angle optimization in intensity-modulated proton therapy

AbstractDeterministic direct-search methods have been successfully used to address real-world challenging optimization problems, including the beam angle optimization (BAO) problem in radiation therapy treatment planning. BAO is a highly non-convex optimization problem typically treated as the optimization of an expensive multi-modal black-box function which results in a computationally time consuming procedure. For the recently available modalities of radiation therapy with protons (instead of photons) further efficiency in terms of computational time is required despite the success of the different strategies developed to accelerate BAO approaches. Introducing randomization into otherwise deterministic direct-search approaches has been shown to lead to excellent computational performance, particularly when considering a reduced number (as low as two) of random poll directions at each iteration. In this study several randomized direct-search strategies are tested considering different sets of polling directions. Results obtained using a prostate and a head-and-neck cancer cases confirmed the high-quality results obtained by deterministic direct-search methods. Randomized strategies using a reduced number of polling directions showed difficulties for the higher dimensional search space (head-and-neck) and, despite the excellent mean results for the prostate cancer case, outliers were observed, a result that is often ignored in the literature. While, for general global optimization problems, mean results (or obtaining the global optimum once) might be enough for assessing the performance of the randomized method, in real-world problems one should not disregard the worst-case scenario and beware of the possibility of poor results since, many times, it is only possible to run the optimization problem once. This is even more important in healthcare applications where the mean patient does not exist and the best treatment possible must be assured for every patient.

Hidden Variable Models in Text Classification and Sentiment Analysis

In this paper, we are proposing extensions to the multinomial principal component analysis (MPCA) framework, which is a Dirichlet (Dir)-based model widely used in text document analysis. The MPCA is a discrete analogue to the standard PCA (it operates on continuous data using Gaussian distributions). With the extensive use of count data in modeling nowadays, the current limitations of the Dir prior (independent assumption within its components and very restricted covariance structure) tend to prevent efficient processing. As a result, we are proposing some alternatives with flexible priors such as generalized Dirichlet (GD) and Beta-Liouville (BL), leading to GDMPCA and BLMPCA models, respectively. Besides using these priors as they generalize the Dir, importantly, we also implement a deterministic method that uses variational Bayesian inference for the fast convergence of the proposed algorithms. Additionally, we use collapsed Gibbs sampling to estimate the model parameters, providing a computationally efficient method for inference. These two variational models offer higher flexibility while assigning each observation to a distinct cluster. We create several multitopic models and evaluate their strengths and weaknesses using real-world applications such as text classification and sentiment analysis.

Democratising complex system modelling

In the contemporary context of an acute need for sustainability and swift response to imminent crises such as global warming, pandemics and economic system disruptions, the focus on responsible decision making, ethical risk assessment and mitigation at all organizational levels is an overarching goal. Our aim is to introduce a deterministic method for investigating the stability of complex systems, in order to find the most important elements of such systems and their impact on different scenarios. The novelty of the current approach lies in its compact format and intuitive nature, designed to accommodate a limited amount of computational resources. The proposed modelling method involves the mapping of complex systems from a diversity of disciplines (economic markets, resource management domain and the community impact of suburbanisation) onto a sequence of chemical reactions and involving a subsequent mathematical analysis. Mapping the results back onto the use cases shows that one can retrieve a considerable amount of detail, making the modelling strategy general enough to be adaptable and scalable while also detailed enough to provide valuable insights for practical scenarios.

Random Responses of Shield Tunnel to New Tunnel Undercrossing Considering Spatial Variability of Soil Elastic Modulus

This paper investigates the effect of spatial variability of soil elastic modulus on the longitudinal responses of the existing shield tunnel to the new tunnel undercrossing using a random two-stage analysis method (RTSAM). The Timoshenko–Winkler-based deterministic method considering longitudinal variation in the subgrade reaction coefficient and the random field of the soil elastic modulus discretized by the Karhunen–Loeve expansion method are combined to establish the RTSAM. Then, the proposed RTSAM is applied to carry out a random analysis based on an actual engineering case. Results show that the increases in the scale of fluctuation and the coefficient of variation of the soil elastic modulus lead to higher variabilities of tunnel responses. A decreasing pillar depth and mean value of the soil elastic modulus and an increasing skew angle strengthen the effect of the spatial variability of the soil elastic modulus on tunnel responses. The variabilities of tunnel responses under the random field of the soil elastic modulus are overestimated by the Euler–Bernoulli beam model. The results of this study provide references for the uncertainty analysis of the new tunneling-induced responses of the existing tunnel under the random field of soil properties.

Fair group decisions via non-deterministic proportional consensus

AbstractAre there group decision methods which (i) give everyone, including minorities, an equal share of effective decision power even when voters act strategically, (ii) promote consensus and equality, rather than polarization and inequality, and (iii) do not favour the status quo or rely too much on chance? We describe two non-deterministic group decision methods that meet these criteria, one based on automatic bargaining over lotteries, the other on conditional commitments to approve compromise options. Using theoretical analysis, agent-based simulations and a behavioral experiment, we show that these methods prevent majorities from consistently suppressing minorities, which can happen in deterministic methods, and keeps proponents of the status quo from blocking decisions, as in other consensus-based approaches. Our simulations show that these methods achieve aggregate welfare comparable to common voting methods, while employing chance judiciously, and that the welfare costs of fairness and consensus are small compared to the inequality costs of majoritarianism. In an incentivized experiment with naive participants, we find that a sizable fraction of participants prefers to use a non-deterministic voting method over Plurality Voting to allocate monetary resources. However, this depends critically on their position within the group. Those in the majority show a strong preference for majoritarian voting methods.

GeosPIn: A MATLAB library for Geostatistical Petrophysical Inversion

Petrophysical inversion of seismic data is one of the key components of seismic reservoir characterization. The goal of petrophysical inversion is to estimate petrophysical properties of reservoir rocks, such as porosity, volumes of minerals or lithologies, and water and hydrocarbon saturations from seismic data. This process can be performed by combining seismic AVO modeling and rock physics relations with deterministic or probabilistic inverse theory methods, either in a two-step approach based on seismic AVO inversion and rock physics inverse mapping or in a single loop step that includes both. We present a comprehensive MATLAB library named Geostatistical Petrophysical Inversion (GeosPIn). The novelty of the library lies in a single-loop geostatistical inversion method based on the Probability Field Simulation (PFS) and the Ensemble Smoother Multiple Data Assimilation (ES-MDA), and its implementation for applications to 3D datasets. The library also includes a Bayesian petrophysical inversion based on the two-step approach for comparison. We illustrate the main algorithms, explain the structure of the source codes, and demonstrate the library applications through 1D and 3D examples.

Effect of Nucleation Heterogeneity on Mineral Precipitation in Confined Environments

AbstractThe formation of new mineral phases in confined environments, especially in porous media, is crucial for various geological processes like mineralization and diagenesis. The nucleation and precipitation of minerals are initiated at the microscale through fluid‐rock interaction, where dissolution of primary phases leads to supersaturated conditions and nucleation and growth of secondary ones. Previous research has focused primarily on either precipitation or nucleation, without fully exploring their combined impact. Our study introduces a computational framework that integrates classical nucleation theory with the micro‐continuum method. We validated our model by comparing with experiments, and discovered that different surface nucleation rate changes the mode of precipitation from a preferential to uniform precipitate textures. Furthermore, our study uncovered that the conventional deterministic precipitation method tends to underestimate the permeability of the porous matrix. In contrast, the new framework significantly improves model accuracy by incorporating preferential precipitation and heterogeneous nucleation.

Application of artificial intelligence in mine ventilation: a brief review

In recent years, there has been a notable integration of artificial intelligence (AI) technologies into mine ventilation systems. A mine ventilation network presents a complex system with numerous interconnected processes, some of which pose challenges for deterministic simulation methods. The utilization of machine learning techniques and evolutionary algorithms offers a promising avenue to address these complexities, resulting in enhanced monitoring and control of air parameter distribution within the ventilation network. These methods facilitate the timely identification of resistance faults and enable prompt calculation of ventilation parameters during emergency scenarios, such as underground explosions and fires. Furthermore, evolutionary algorithms play a crucial role in the advancement of methods for visual analysis of ventilation systems. However, it is essential to acknowledge that the current utilization of AI technologies in mine ventilation is limited and does not encompass the full spectrum of challenging-to-formalize problems. Promising areas for AI application include analyzing changes in air distribution caused by unaccounted thermal draft and gas pressure, as well as developing novel approaches for calculating shock losses. Moreover, the application of AI technologies in optimizing large-scale mine ventilation networks remains an unresolved issue. Addressing these challenges holds significant potential for enhancing safety and efficiency in mine ventilation systems.

Synthesis of Elliptically Shaped Aperiodic Antenna Arrays Subject to Complex Design Constraints

AbstractState‐of‐the‐art conformal array pattern synthesis techniques typically suffer from a significant computational burden. This article builds upon the auxiliary array pattern synthesis technique, allowing the technique to work on elliptical contours. This deterministic method is both computationally efficient and capable of handling complex design cases with additional design constraints. In order to highlight the versatility and applicability, the method has been applied to an elliptical arc array comprised of Rampart antennas and an elliptical ring array using dipole elements. The results have been validated through full‐wave electromagnetic simulations, as well as physical measurements. Both arrays presented show good agreement with the proposed synthesis technique. Highlighting the ability to satisfy additional design constraints, such as enforcing a minimal element spacing or having a controlled beamformer‐network complexity.

Multi-objective branch-and-bound for the design-for-control of water distribution networks with global bounds

This study investigates a design-for-control (DfC) problem formulation for the joint minimization of pressure-induced leakage, maximization of resilience, and minimization of cost in water distribution networks (WDN). The DfC problem, which consists in simultaneously installing new valves and/or pipes and optimizing valve control settings, results in a challenging optimization problem belonging to the class of non-convex multi-objective mixed-integer non-linear programs (MOMINLP). Due to their complex mathematical structure, multi-objective WDN design-for-control problems have previously been solved using general-purpose evolutionary algorithms or local deterministic methods, which do not provide guarantees on the quality of the returned solutions. While branch-and-bound (BB) frameworks have been proposed to approximate the Pareto fronts of MOMINLPs with global bounds, they rely on the availability of attainable solutions which, for WDN design-for-control problems, can be hard to identify. Moreover, in the absence of general-purpose solvers, the performance of multi-objective BB implementations depends, for a given application, on the choice of adequate branching and lower bounding strategies. In this study, we investigate a multi-objective BB algorithm based on tailored branching, lower bounding and additional upper bounding strategies to efficiently approximate the Pareto front of WDN design-for-control problems with bounds of ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon$$\\end{document}-non-dominance. The proposed algorithm is applied to the optimal DfC of two case study networks and is shown to outperform alternative solution methods.

Assessing seismic soil liquefaction susceptibility and hazard zonation in Bihar, India: a comparative study of deterministic method

Assessing seismic soil liquefaction susceptibility and hazard zonation in Bihar, India: a comparative study of deterministic method

Deterministic direct design method for a spherical-aberration-free singlet lens with reduced coma

Deterministic direct design method for a spherical-aberration-free singlet lens with reduced coma

Risks to Human Health from Mercury in Gold Mining in the Coastal Region of Ecuador

Artisanal and small-scale gold mining (ASGM) plays a crucial role in global gold production. However, the adoption of poor mining practices or the use of mercury (Hg) in gold recovery processes has generated serious environmental contamination events. The focus of this study is assessing the concentration of Hg in surface waters within the coastal region of Ecuador. The results are used to conduct a human health risk assessment applying deterministic and probabilistic methods, specifically targeting groups vulnerable to exposure in affected mining environments. Between April and June 2022, 54 water samples were collected from rivers and streams adjacent to mining areas to determine Hg levels. In the health risk assessment, exposure routes through water ingestion and dermal contact were considered for both adults and children, following the model structures outlined by the U.S. Environmental Protection Agency. The results indicate elevated Hg concentrations in two of the five provinces studied, El Oro and Esmeraldas, where at least 88% and 75% of the samples, respectively, exceeded the maximum permissible limit (MPL) set by Ecuadorian regulations for the preservation of aquatic life. Furthermore, in El Oro province, 28% of the samples exceeded the MPL established for drinking water quality. The high concentrations of Hg could be related to illegal mining activity that uses Hg for gold recovery. Regarding the human health risk assessment, risk values above the safe exposure limit were estimated. Children were identified as the most vulnerable receptor. Therefore, there is an urgent need to establish effective regulations that guarantee the protection of river users in potentially contaminated areas. Finally, it is important to continue investigating the contamination caused by human practices in the coastal region.

Control of Discrete Event Systems by Using Symbolic Transition Model: An Application to Power Grids

AbstractIn this paper, a new symbolic modeling framework is proposed for the control of discrete event systems (discrete controller synthesis). Reactive infinite-state systems are generally dynamic systems with inputs and outputs. Modeling the outputs in existing symbolic modeling methods for reactive infinite-state systems has not been extensively discussed in the literature. It is crucial to realistically model the outputs and obtain reliable controllers. One of the main contributions and innovations in this study is the ability to symbolically model their output. In this direction, symbolic transition models are offered, where events are defined as guarded symbolic transitions. The framework considers input/output reactive infinite-state systems to satisfy safety and optimization objectives. Effective algorithms and safety control policies are offered to solve the safety control problem (i.e., satisfy the safety objective) for input/output infinite-state systems. Another contribution in this work provides optimization targets within a given cost function based on state transitions, without specifying the target states. The framework is then applied to power grids to demonstrate the effectiveness of the symbolic transition models and experimentally evaluate the new control algorithms. The results showed that the approach is very effective compared to other approaches found in the literature. The computation times required to achieve both safety and optimization objectives are obtained relatively quickly compared to other deterministic methods found in the literature.

A Deterministic Calibration Method for the Thermodynamic Model of Gas Turbines

Performance adaptation is an effective way to improve the accuracy of gas turbine performance models. Although current performance adaptation methods, such as those using genetic algorithms or evolutionary computation to modify component characteristic maps, are useful for finding good solutions, they are essentially searching methods and suffer from long computation time. This paper presents a novel approach that can achieve good performance adaptation with low time complexity and without using any searching method. In this method, the actual component performance parameters are first estimated using engine measurements at different operating conditions. For each operating condition, some scaling factors are introduced and calculated to indicate the difference between the actual and predicted component performance parameters. Afterward, an interpolating algorithm is adopted to synthesize the scaling factors for modifying all major component maps. The adapted component maps are then able to make the engine model match all the gas path measurements and achieve the required accuracy of the engine performance model. The proposed approach has been tested with a model high-bypass turbofan engine using simulated data. The results show that the proposed performance adaptation approach can effectively improve the model’s accuracy. Specifically, the prediction errors can be reduced from about 9% to about 0.6%. In addition, this approach has much less computational complexity compared to other optimization-based counterparts.

Mathematical simulation of duration and frequency of water consumption by various water dispensers

Water flow rates calculated by using deterministic models and methods do not describe the real variability in the water supply operation. This problem can be solved by mathematical simulation. The stochastic nature of the water consumption process implies involves random variables with certain distribution laws describing the main process components, namely intensity, duration and frequency.This paper discusses the mathematical simulation of the duration and frequency of water consumption by the most common types of water dispensers (kitchen sink and bathtub faucets (shower cubicle), toilet bowl with flush tank, washing machine and dishwasher).Purpose: The aim of this work is to evaluate and substantiate theoretical laws of the water consumption by the most common types of water dispensers as well as the frequency (probability) of their daily use.Research findings: The duration and frequency are determined for water consumed by various water dispensers using water supply systems of buildings. The empirical data are analyzed. Mathematical simulation method is proposed and justified for the water consumption process.

Optimal operation of the dam reservoir in real time based on generalized structure of group method of data handling and optimization technique

The historical data on water intake into the reservoir is collected and used within the framework of a deterministic optimization method to determine the best operating parameters for the dam. The principles that have been used to extract the best values of the flow release from the dam may no longer be accurate in the coming years when the inflow to dams will be changing, and the results will differ greatly from what was predicted. This represents this method’s main drawback. The objective of this study is to provide a framework that can be used to guarantee that the dam is running as efficiently as possible in real time. Because of the way this structure is created, if the dam’s inflows change in the future, the optimization process does not need to be repeated. In this case, deep learning techniques may be used to restore the ideal values of the dam’s outflow in the shortest amount of time. This is achieved by accounting for the environment’s changing conditions. The water evaluation and planning system simulator model and the MOPSO multi-objective algorithm are combined in this study to derive the reservoir’s optimal flow release parameters. The most effective flow discharge will be made feasible as a result. The generalized structure of the group method of data handling (GSGMDH), which is predicated on the results of the MOPSO algorithm, is then used to build a new model. This model determines the downstream needs and ideal release values from the reservoir in real time by accounting for specific reservoir water budget factors, such as inflows and storage changes in the reservoir. Next, a comparison is drawn between this model’s performance and other machine learning techniques, such as ORELM and SAELM, among others. The results indicate that, when compared to the ORELM and SAELM models, the GSGMDH model performs best in the test stage when the RMSE, NRMSE, NASH, and R evaluation indices are taken into account. These indices have values of 1.08, 0.088, 0.969, and 0.972, in that order. It is therefore offered as the best model for figuring out the largest dam rule curve pattern in real time. The structure developed in this study can quickly provide the best operating rules in accordance with the new inflows to the dam by using the GSGMDH model. This is done in a way that makes it possible to manage the system optimally in real time.

A framework for modelling the probability of flooding under levee breaching

AbstractLevees aim to provide protection during floods, however, these structures can breach, causing significant damage. Flood maps that include levee breaching are often limited to deterministic methods. Where probabilistic breaching is done, it often requires computationally expensive Monte Carlo simulations and an understanding of the geotechnical levee properties that are often limited. In this paper, we combine existing fragility curves and empirical breaching equations with a framework for automating levee breaching in catchments with limited geotechnical information. This method can be adapted and applied to existing 2D flood models to determine the probability of inundation, given that a breach occurs. This ultimately allows for greater emergency responses and land use planning to reduce the flood risk faced by our communities. The method was applied to four case study catchments. The results showed that including levee breaching in one catchment led to an average increase in the inundated area by 48.2% and a tripling in the potentially exposed area. However, breaching in some locations reduced the inundation extent by 12%, illustrating the potential for fuse plug levees and floodways as a flood mitigation strategy. This strategy has seen successful usage internationally. Further investigation is recommended to consider whether these mitigation strategies should be enacted.

Analysis of climate-meteorological and technological factors affecting electricity consumption of mining enterprises

Electricity consumption of mining enterprises depends on many factors. The influence of factors on the process of electricity consumption is complex and diverse, and it is impossible to describe it within the framework of deterministic methods, due to the uncertainty of the conditions that determine the influence of factors. These factors include mining geological, mining technological, climate-meteorological, energetic, organizational, operational and others. Energy consumption regimes of mining enterprises depend on many mining technological factors, most of which are insufficiently taken into account in the analysis and planning of electricity consumption.

Safety Assessment of Brazilian Concrete Bridges Through Reliability Analysis

This paper addresses the need for accurate and objective safety assessments of bridges in Brazil taking into account the increase in traffic load and limited funding for infrastructure. In Brazil, the usual method of ensuring bridge safety involves strengthening based on design codes using deterministic analysis and partial safety factors. This method leads to an increase in the maintenance cost of the bridges. Structural reliability assessment, a higher-tier assessment method, is recommended globally for assessing the safety of existing bridges beyond current deterministic methods. This paper presents a study that evaluates the structural safety of existing road bridges in Brazil using the semi-probabilistic method defined in Brazilian standards and the full probabilistic method. The study selected six case studies of existing reinforced and prestressed concrete bridges to evaluate their structural safety concerning current normative loads. The results suggest that the partial safety factors defined in the Brazilian standards are consistent with international standards. The reliability analysis can guarantee the bridges’ safety, even with increased traffic loads, without additional costs for structural strengthening. Therefore, the paper highlights the importance of promoting reliability analysis in Brazil to ensure the safety of existing bridges and promote cost-effective and objective safety assessments.