Deterministic Model Research Articles

Stochastic modeling for bond deterioration between rebar and concrete due to reinforcement corrosion

Reinforcement corrosion has a significant impact on the bond behavior between rebars and concrete. Accelerated corrosion tests and pullout tests were conducted on 24 concrete cube specimens with embedded rebars to investigate the non-uniformity of corrosion and establish a deterministic model for the bond strength-slip relationship. Then, the probability distribution of the ultimate bond strength for 132 specimens, the peak slip for 79 specimens, and the stochastic process of the ultimate bond strength changing with the corrosion level for 204 specimens from previously published studies were analyzed. By introducing the probability distribution and stochastic process into this deterministic model, a stochastic model is suggested to evaluate the bond deterioration between the rebar and the concrete owing to the reinforcement corrosion. The results showed that: The non-uniformity of reinforcement corrosion was verified since the remaining diameters obeyed an extreme value I distribution. The ultimate bond strength and peak slip obeyed normal distributions and how the ultimate bond strength changed with the corrosion level was a normal stochastic process. The error percentage between the stochastic model and the test results was less than 5 %, indicating that the bond strength can be well predicted when giving a corrosion level.

Optimal dispatching of regional power grid considering vehicle network interaction.

When large-scale electric vehicles are connected to the grid for unordered charging, it will seriously affect the stability and security of the power system. To solve this problem, this paper proposes a regional power network optimization scheduling method considering vehicle network interaction. Initially, based on the user behavior characteristics and charging and discharging characteristics of electric vehicles, a charging and discharging behavior model of electric vehicles was established. Based on the Monte Carlo sampling algorithm, the scheduling upper and lower limits of each scheduling cycle of electric vehicles were described, and the scheduling potential of each scheduling cycle of electric vehicles was obtained. Then, the electricity price is then used as an incentive parameter to guide EV users to charge during periods of low electricity prices and participate in discharge during periods of peak electricity prices. Aiming at the highest economic efficiency, the best consumption effect of new energy and the smoothest demand-side power curve of regional power grid, a three-objective optimal dispatching model was established. In the later stage, uncertainty factors are taken into consideration by introducing the concept of interval numbers, and an interval multi-objective optimization dispatching model is established. The two dispatching models are solved by NSGA-II algorithm and improved NSGA-II algorithm, and the Pareto solution set is obtained. Finally, based on the analytic Hierarchy Process (AHP), the optimal scheduling scheme is determined. The Monte Carlo sampling method is used to simulate the user side charging demand, and the effectiveness of this method is verified. In addition, the results of the interval multi-objective optimization model and the deterministic multi-objective optimization model are compared, and it is proved that the solution results of the interval multi-objective model are more adaptive, practical and robust to the uncertain factors.

A two‐stage adaptive robust model for designing a reliable blood supply chain network with disruption considerations in disaster situations

AbstractWe consider multi‐period blood supply chain network design in disaster situations that involve blood donor groups, permanent and temporary blood collection facilities, blood banks, and hospitals. We use a discrete scenario set to model the uncertain blood supply and demand, and the unforeseeable disruptions in permanent blood collection facilities, blood banks, and road links arising from a disaster, where instead of complete failure, disrupted permanent blood collection facilities and blood blanks may only lose part of their capacities. To design a reliable blood supply network to mitigate the possible disruptions, we present a two‐stage adaptive robust model that integrates the location, inventory, and allocation decisions incorporating a blood sharing strategy, where blood can be delivered from a disrupted/non‐disrupted blood bank to disrupted blood banks to enhance the flexibility of the relief network. For this novel problem, we devise an exact algorithm that integrates column‐and‐constraint generation and Benders decomposition and introduce several non‐trivial acceleration techniques to speed up the solution generation process. We conduct extensive numerical studies on random data sets to evaluate the algorithmic performance. We also conduct a case study in Tehran to demonstrate its real‐life applicability and examine the impacts of key model parameters on the solutions. The numerical results verify the benefits of our model over typical benchmarks, that is, deterministic and stochastic models, and the superiority of our solution algorithm over the CPLEX solver and two well‐known solution approaches, that is, column‐and‐constraint generation and Benders decomposition. Finally, based on the numerical results, we derive managerial insights from the analytical findings.

Deterministic Modeling of the Issue of Dental Caries and Oral Bacterial Growth: A Brief Review

Dental caries is a chronic disease that mostly interferes with oral health worldwide. It is caused by acidic bacteria on the enamel surface, mainly Streptococcus mutans, forming an oral biofilm that can be transmitted among people. The spread behavior and population dynamics of bacteria must be studied to control this disease, which can be approached through mathematical modeling. In this review, we aimed to identify the utilization of compartmental models in studying bacterial behavior. The aim was to explore compartmental model utilization and reveal the research gaps. This study was conducted with the PRISMA guidelines for scoping reviews to identify an existing mathematical model to study the phenomenon. Four databases, Scopus, ScienceDirect, PubMed, and Dimensions, were used to search for related studies. Our results showed that compartmental model utilization for studying bacteria’s role in dental caries is sparse and poorly explained. Moreover, the constructed models have not yet considered more intervention efforts. A study is needed to explore this phenomenon by developing a mathematical model considering some situations. When conducted, it will result in more insights into controlling the spread of bacteria to prevent dental caries.

A direct and analytical method for inverse problems under uncertainty in energy system design: combining inverse simulation and Polynomial Chaos theory

This article introduces and formalizes a novel stochastic method that combines inverse simulation with the theory of generalized Polynomial Chaos (gPC) to solve and study inverse problems under uncertainty in energy system design applications. The method is particularly relevant to design tasks where only a deterministic forward model of a physical system is available, in which a target design quantity is an input to the model that cannot be obtained directly, but can be quantified reversely via the outputs of the model. In this scenario, the proposed method offers an analytical and direct approach to invert such system models. The method puts emphasis on user-friendliness, as it enables its users to conduct the inverse simulation under uncertainty directly in the gPC domain by redefining basic algebra operations for computations. Moreover, the method incorporates an optimization-based approach to integrate supplementary constraints on stochastic quantities. This feature enables the solution of inverse problems bounding the statistical moments of stochastic system variables. The authors exemplify the application of the proposed method with proof-of-concept tests in energy system design, specifically performing uncertainty quantification and sensitivity analysis for a Multi-Energy System (MES). The findings demonstrate the high accuracy of the method as well as clear advantages over conventional sampling-based methods when dealing with a small number of stochastic variables in a system or model. However, the case studies also highlight the current limitations of the proposed method such as slow execution speed due to the optimization-based approach and the challenges associated with, for example, the curse of dimensionality in gPC.

Deterministic modelling of asymptomatic spread and disease stage progression in vaccine preventable infectious diseases

AbstractThis study introduces a deterministic formulation for modelling the asymptotic spread of a vaccine preventable disease as well as the different stages for the progression of the disease. We derive the formula for the associated basic reproduction number. To illustrate the proposed model, we use data from the 2017–2018 diphtheria outbreak in Yemen and fit the parameters of the model. A sensitivity analysis of the basic reproduction number, with respect to the model parameters, show that this number increases with an increase of the transmission rate while this number decreases when vaccination rate increases.

A Hotspot and Mechanism of Enhanced Bottom Intrusion on the Southern New England Shelf

Abstract Understanding the occurrence of the intrusion of open ocean water onto the continental shelf has scientific significance and societal relevance as the intrusion can significantly disrupt the marine ecosystem and fisheries. High-resolution numerical modeling is used to investigate the spatiotemporal occurrence and mechanisms of highly anomalous bottom intrusions on the southern New England shelf. Based on multi-year numerical simulations, this study reveals a hotspot of cross-isobath bottom intensified intrusions at a topographic trough. Examination of multiple events portrays a robust mechanism of locally enhanced bottom intrusions. Persistent upwelling-favorable winds set up an enhanced pressure gradient field at the topographic trough and drive the intrusion a large-distance onshore. Numerical experiments with and without the topographic trough show that the localized pressure gradient results from a combination of the shelf orientation and local bathymetry, the latter being less decisive. Although highly anomalous waters on the shelf relate to wind forcing, correlations between the wind stress anomaly and bottom salinity anomaly at the location of the enhanced intrusion is modest, implying the need to incorporate other environmental factors to develop more deterministic prediction models for subsurface conditions on the shelf. The results have important implications for marine environment and fisheries management.

A framework to analyse the probability of accidental hull girder failure considering advanced corrosion degradation for risk-based ship design

Ship’s hull girder failure could result from maritime accident that can cause human life loss, environmental disaster, and major economic impacts. In risk-based ship design paradigm, accounting for rare phenomena (e.g. ship-ship collision or grounding) is important to provide safe and durable structure. In-service corrosion-induced hull degradation should be considered at the design stage, as it can significantly affect structural strength. The current study presents a novel framework to estimate the probability of ship hull girder failure, accounting for novel corrosion modelling techniques and accidental damage. The associated uncertainties are considered using statistical sampling from evidence-based distributions. A state-of-the-art deterministic model for ultimate strength calculation is applied using Monte Carlo simulation approach, resulting in the probability of hull failure through a reliability assessment. Wave and still-water bending moments are considered random variables. Two case studies of tanker ships with varying sizes are executed to show the applicability of the proposed framework. The results indicate that proper consideration of corrosion is of high importance, as ageing can significantly increase the probability of failure if accidental damage happens. Therefore, whereas future research and model refinement are discussed, the presented framework can serve for risk-based ship design tool and assess existing structures’ safety.

Potential population-level effects of HIV self-test distribution among key populations in Côte d'Ivoire, Mali, and Senegal: a mathematical modelling analysis

During 2019-21, the AutoTest VIH, Libre d'accéder à la connaissance de son Statut (ATLAS) programme distributed around 380 000 HIV self-testing kits to key populations, including female sex workers, men who have sex with men, and their partners, in Côte d'Ivoire, Mali, and Senegal. We aimed to estimate the effects of the ATLAS programme and national scale-up of HIV self-test distribution on HIV diagnosis, HIV treatment coverage, HIV incidence, and HIV-related mortality. We adapted a deterministic compartmental model of HIV transmission in Côte d'Ivoire, parameterised and fitted to country-specific demographic, behavioural, HIV epidemiological, and intervention data in Côte d'Ivoire, Mali, and Senegal separately during 1980-2020. We simulated dynamics of new HIV infections, HIV diagnoses, and HIV-related deaths within scenarios with and without HIV self-test distribution among key populations. Models were separately parameterised and fitted to country-specific sets of epidemiological and intervention outcomes (stratified by sex, risk, age group, and HIV status, if available) over time within a Bayesian framework. We estimated the effects on the absolute increase in the proportion of people with HIV diagnosed at the end of 2021 for the ATLAS-only scenario and at the end of 2028 and 2038 for the HIV self-testing scale-up scenario. We estimated cumulative numbers of additional HIV diagnoses and initiations of antiretroviral therapy and the proportion and absolute numbers of new HIV infections and HIV-related deaths averted during 2019-21 and 2019-28 for the ATLAS-only scenario and during 2019-28 and 2019-38 for the HIV self-testing scale-up scenario. Our model estimated that ATLAS could have led to 700 (90% uncertainty interval [UI] 500-900) additional HIV diagnoses in Côte d'Ivoire, 500 (300-900) in Mali, and 300 (50-700) in Senegal during 2019-21, a 0·4 percentage point (90% UI 0·3-0·5) increase overall by the end of 2021. During 2019-28, ATLAS was estimated to avert 1900 (90% UI 1300-2700) new HIV infections and 600 (400-800) HIV-related deaths across the three countries, of which 38·6% (90% UI 31·8-48·3) of new infections and 70·1% (60·4-77·3) of HIV-related deaths would be among key populations. ATLAS would avert 1·5% (0·8-3·1) of all HIV-related deaths across the three countries during this period. Scaling up HIV self-testing would avert 16·2% (90% UI 10·0-23·1) of all new HIV infections during 2019-28 in Senegal, 5·3% (3·0-8·9) in Mali, and 1·6% (1·0-2·4) in Côte d'Ivoire. HIV self-testing scale-up among key populations was estimated to increase HIV diagnosis by the end of 2028 to 1·3 percentage points (90% UI 0·8-1·9) in Côte d'Ivoire, 10·6 percentage points (5·3-16·8) in Senegal, and 3·6 percentage points (2·0-6·4) in Mali. Scaling up HIV self-test distribution among key populations in western Africa could attenuate disparities in access to HIV testing and reduce infections and deaths among key populations and their partners. Unitaid, Solthis, the UK Medical Research Council Centre for Global Infectious Disease Analysis, the EU European & Developing Countries Clinical Trials Partnership programme, and the Wellcome Trust.

Archaeology, climate change and human adaptation in southern Africa: Evidence from Mapela and Little Mapela, southern Africa

In Africa south of the Zambezi River, archaeologists and other experts have long explored the impact of climate and environmental changes to the development of ancient civilizations during the Iron Age (CE 200–1900). Some of the prevailing thought is however still rooted in environmental deterministic models informed by selected ethnographies, stable isotopes and archaeological evidence. For instance, the drought brought by the medieval Little Ice Age is assumed to have collapsed the civilisation at Mapungubwe in the Shashi-Limpopo valley around 1300 CE. And yet, within the wider region, and in similar ecological settings, upstream (Shashi and Upper Limpopo) and downstream civilisations (Lower Limpopo), persisted and thrived through the same climatic challenges. We draw on African cosmologies, resilience theory and archaeological evidence from Mapela and Little Mapela to spotlight adaptation strategies utilised by their inhabitants to build resilience through time. The main conclusion is that even in cases of climatic extremes, humans responded to opportunities and constraints in context specific ways.

A Comprehensive Review of Radio Signal Propagation Prediction for Terrestrial Wireless Communication Systems

The subject of study known as radio propagation prediction refers to predicting the behaviour and characteristics of radio waves as they propagate through the atmosphere. It is a basic element of all wireless communication systems, including satellite communications, broadcasting and cellular networks. While there is no study covers all the techniques used to predict the radio signal prediction, this study presents a review of the propagation prediction models between 2018-2023 used for terrestrial wireless communication systems; the classic empirical models were briefly explained, followed by the deterministic propagation models that have been developed using ray-tracing with deep and machine learning techniques. Recent studies on an improvement of the computational efficiency and accuracy of propagation prediction models were also reviewed, in addition to an overview of some of the traditional statistical models. Furthermore, some of the new techniques in propagation prediction were described. The results of these studies explain that techniques using ray tracing produce better results than other techniques.

A Comprehensive Review of Radio Signal Propagation Prediction for Terrestrial Wireless Communication Systems

The subject of study known as radio propagation prediction refers to predicting the behaviour and characteristics of radio waves as they propagate through the atmosphere. It is a basic element of all wireless communication systems, including satellite communications, broadcasting and cellular networks. While there is no study covers all the techniques used to predict the radio signal prediction, this study presents a review of the propagation prediction models between 2018-2023 used for terrestrial wireless communication systems; the classic empirical models were briefly explained, followed by the deterministic propagation models that have been developed using ray-tracing with deep and machine learning techniques. Recent studies on an improvement of the computational efficiency and accuracy of propagation prediction models were also reviewed, in addition to an overview of some of the traditional statistical models. Furthermore, some of the new techniques in propagation prediction were described. The results of these studies explain that techniques using ray tracing produce better results than other techniques.

Seasonal variability and stochastic branching process in malaria outbreak probability

Background: Malaria is the world’s most fatal and challenging parasitic disease, caused by the Plasmodium parasite, which is transmitted to humans by the bites of infected female mosquitoes. Bangladesh is the most vulnerable region to spread malaria because of its geographic position. In this paper, we have considered the dynamics of vector-host models and observed the stochastic behavior. This study elaborates on the seasonal variability and calculates the probability of disease outbreaks. Methods: We present a model for malaria disease transmission and develop its corresponding continuous-time Markov chain (CTMC) representation. The proposed vector-host models illustrate the malaria transmission model along with sensitivity analysis. The deterministic model with CTMC curves is depicted to show the randomness in real scenarios. Sequentially, we expand these studies to a time-varying stochastic vector-host model that incorporates seasonal variability. Phase plane analysis is conducted to explore the characteristics of the disease, examine interactions among various compartments, and evaluate the impact of key parameters. The branching process approximation is developed for the corresponding vector-host model to calculate the probability outbreak. Numerous numerical results are accomplished to observe the analytical investigation. Results: Seasonality and contact patterns affect the dynamics of disease outbreaks. The numerical illustration provides that the probability of a disease outbreak depends on the infected host or vector. Additionally, periodic transmission rates have a great influence on the probability outbreak. The basic reproduction number (R0) is derived, which is the main justification for studying the dynamical behavior of epidemic models. Conclusions: Seasonal variability significantly impacts malaria transmission, and the probability of disease outbreaks is influenced by time and the initial number of infected individuals. Moreover, the branching process approximation is applicable when the population size is large enough and the basic reproduction number is less than 1. In the future, such analysis can help decision-makers understand the impact of various parameters and their stochastic behavior in the vector-host model to prevent such types of disease outbreaks.

Interval Assessment Method for Distribution Network Hosting Capacity of Renewable Distributed Generation

The traditional fixed value assessment of the renewable distributed energy hosting capacity of a distribution network cannot accurately and comprehensively reflect the change in hosting capacity; therefore, we propose the interval assessment method for the renewable distributed energy hosting capacity of a distribution network. The renewable distributed energy hosting capacity interval consists of an optimistic upper boundary and a pessimistic lower boundary. First, the optimistic upper bound is described by a deterministic model that takes into account the constraints of safe system operation. Second, the pessimistic lower bound is portrayed by a two-layer robust assessment model that accounts for the DG temporal uncertainty, DG spatial uncertainty, and active distribution network flexible resource dispatch uncertainty. Each pessimistic sub-model was constructed in turn, and then the model was solved by linear simplification using pairwise transformation, as well as McCormick relaxation. Finally, simulations were carried out in the IEEE 135 system, and the results validated the effectiveness and practicality of the proposed method.

Robust Trajectory Planning of Gliding-Guided Projectiles with Weak Maneuverability

Due to constraints in launch platforms and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and state deviation at the control start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Our simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy; compared with parallel MCS, the computation time is reduced by 96.8%. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties (the standard deviations of terminal altitude and lateral deviations are reduced by 23.6% and 35.3%, respectively, compared to deterministic planning) but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

ARIMAX Modelling: Response of Hass Avocado Respiration Rate to Environmental Factors

This research explores how random events influence the respiration rate in Hass avocado beyond deterministic models in order to develop better strategies for extending its shelf life. Understanding these factors can enhance the accuracy of postharvest management strategies. The Autoregressive Integrated Moving Average (ARIMA) model with exogenous variables (ARIMAX) is an alternative stochastic probability model which is capable of modeling complex, externally influenced phenomena such as respiration. This study aimed to elucidate the effect of three exogenous variables, namely temperature, relative humidity, and ambient illumination, on the respiration rate of Hass avocado fruits. Data on the respiration rate and exogenous variables were obtained using sensors coupled to a data acquisition system in a prototype of continuous airflow. The Box–Jenkins methodology was employed to construct the ARIMA models. The temperature, relative humidity, ambient illumination, and respiration rate variables were adjusted to the ARIMA models (3,1,2), ARIMA (1,1,2), ARIMA (1,1,2), and ARIMA (1,1,3), respectively. The ARIMAX (1,1,3) models were obtained from the pre-whitened respiration rate series. The impact detected in the transfer functions indicates increases in the respiration rate of 0.34%, 1.52%, and 0.99% for each unit increase in the temperature, relative humidity, and ambient illumination variables, respectively. In this regard, ARIMAX modeling is reliable for explaining the physiological response of Hass avocado fruits due to external factors. In future research, it is intended to extrapolate this stochastic modeling procedure to measure the effect of dynamic loads on the respiratory metabolism of fruits during transportation, where there is a considerable loss in the quality of fresh products.

A new paradigm for the efficient inclusion of stochasticity in engineering simulations: Time-separated stochastic mechanics

AbstractAs a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also output parameters, e.g., stresses, fluctuate. For the estimation of those fluctuations it is imperative to incoporate randomness into engineering simulations. Unfortunately, incorporating uncertain parameters into the modeling and simulation of inelastic materials is often computationally expensive, as many individual simulations may have to be performed. The promise of the proposed method is simple: using extended material models to include stochasticity reduces the number of needed simulations to one. This single computation is cheap, i.e., it has a comparable numerical effort as a single standard simulation. The extended material models are easily derived from standard deterministic material models and account for the effect of uncertainty by an extended set of deterministic material parameters. The time-dependent and stochastic aspects of the material behavior are separated, such that only the deterministic time-dependent behavior of the extended material model needs to be simulated. The effect of stochasticity is then included during post-processing. The feasibility of this approach is demonstrated for three different and highly non-linear material models: viscous damage, viscous phase transformations and elasto-viscoplasticity. A comparison to the Monte Carlo method showcases that the method is indeed able to provide reliable estimates of the expectation and variance of internal variables and stress at a minimal fraction of the computation cost.

Efficient high‐fidelity deep convolutional generative adversarial network model for received signal strength reconstruction in indoor environments

AbstractWith the rapid development of wireless communication systems, particularly in the era of 5G and the Internet of Things, deploying wireless communication networks in indoor environments has become crucial. Indoor infrastructure deployment necessitates innovative approaches for efficiently and accurately obtaining received signal strength (RSS) maps. However, traditional methods for acquiring RSS maps, such as empirical and deterministic models, are limited by significant inaccuracies and high computational demands. Empirical models often fail to capture the complex dynamics of indoor environments, resulting in deviations from actual signal behaviours. On the other hand, deterministic models, while more accurate, are computationally intensive due to their reliance on detailed physical modelling of wave propagation. This study introduces a machine learning approach based on deep convolutional generative adversarial networks (DCGAN) aimed at reconstructing indoor RSS maps with minimal RSS measurements. By leveraging DCGAN's generative and adversarial training capabilities, the method not only surpasses traditional interpolation methods in efficiency and precision but also offers new possibilities for the rapid deployment and optimization of wireless communication systems in indoor environments.

Pharmaceutical capacity expansion under uncertainty: Framework and models

This work presents a methodology for capacity planning under uncertainty in general multi-stage manufacturing networks. Multiple manufacturing lines are available and the production time on each line must be divided between a set of materials. The methodology generates mixed-integer linear programming models that represent capacity expansions with economy of scale costs functions and production planning details. A deterministic model is solved to create a baseline and the impact of uncertainty is investigated by sensitivity analysis and stochastic programming. The applicability of the methodology is exemplified through two case studies derived from industrial pharmaceutical manufacturing. The methodology identifies bottlenecks that limit supply and, where required, activates, and assigns capacity expansion projects for satisfying demand subject to uncertainty. The methodology determines the best use of existing resources and the location and size of capacity expansions thereby generating a portfolio of recommendations for decision making on integrated planning of capacity and production.

Lyapunov’s stability analysis for first degree polynomial systems, subject to risk - sensitive control

This work presents a novel methodology to verify the stability of first-degree stochastic polynomial systems under a Risk-Sensitive (RS) optimal control using Lyapunov’s stability analysis theory. The so-called Lyapunov’s indirect method is applied to prove its stability when it is combined with the dynamics of Riccati’s gain equation. The proposed methodology guarantees both the exponential stability of deterministic systems and the robustness of stochastic systems. Simulation results demonstrate the robustness, the effectiveness and the feasibility of this proposal.