Different Types Of Uncertainty Research Articles

Assessing uncertainty in building material emissions using scenario-aware Monte Carlo simulation

Global greenhouse gas emissions from the built environment remain high, driving innovative approaches to develop and adopt building materials that can mitigate some of those emissions. However, life-cycle assessment (LCA) practices still lack standardized quantitative uncertainty assessment frameworks, which are urgently needed to robustly assess mitigation efforts. Previous works emphasize the importance of accounting for the three types of uncertainties that may exist within any quantitative assessment: parameter, scenario, and model uncertainty. Herein, we develop a quantitative uncertainty assessment framework that distinguishes between different types of uncertainties and suggest how these uncertainties could be handled systematically through a scenario-aware Monte Carlo simulation (MCS). We demonstrate the framework’s decision-informing power through a case study of two multilevel ordinary Portland cement (OPC) manufacturing scenarios. The MCS utilizes a first-principles-based OPC life-cycle inventory, which mitigates some of the model uncertainty that may exist in other empirical-based cement models. Remaining uncertainties are handled by scenario specification or sampling from developed probability distribution functions. We also suggest a standardized method for fitting distributions to parameter data by enumerating through and implementing distributions based on the Kolmogorov–Smirnov test. The level of detail brought by the high-resolution parameter breakdown of the model allows for developing emission distributions for each process of OPC manufacturing. This approach highlights how specific parameters, along with scenario framing, can impact overall OPC emissions. Another key takeaway includes relating the uncertainty of each process to its contributions to total OPC emissions, which can guide LCA modelers in allocating data collection and refinement efforts to processes with the highest contribution to cumulative uncertainty. Ultimately, the aim of this work is to provide a standardized framework that can provide robust estimates of building material emissions and be readily integrated within any uncertainty assessment.

Variability of Uncertainty in Mental Reconstruction of Danger and Safety

Subjective images of danger and security depend on the context of uncertainty. This article introduces a mental reconstruction of danger and safety for different types of uncertainty. The authors used the methods of associative experiment, subjective ranking, and semantic differential. The empirical data were processed by averaging, ranking, factor analysis, and the Mann-Whitney criterion. The survey involved students from several Russian metropolitan and provincial universities (19–20 y.o.; n = 105; 74 females). Danger demonstrated a less complex mental structure than safety. The mental reconstruction of danger / safety included three types of uncertainty. Temporal uncertainty included period, time, and frequency of danger / safety. Objective uncertainty was connected with the place, environment, and source of danger / safety. Subjective uncertainty covered controllability, scale, and cause of danger / safety. Uncertainty proved more important for danger than for safety. The subjective level of danger grew together with objective uncertainty, especially when the source of danger was unclear, and went down with temporal uncertainty. The subjective level of security increased with temporal and subjective uncertainty and decreased with objective uncertainty. When the subjective significance of danger and safety went up, the differentiation of uncertainty in their assessment became less significant. The study identified the effect of variability of uncertainty on the mental reconstruction made by the subjects of danger / security, as well as identified some understudied areas.

COVID-19 uncertainty index in Japan: Newspaper-based measures and economic activities

This paper measures economic uncertainty induced by the COVID-19 using a newspaper-based approach in Japan and examines its economic impact in the VAR model. We specify two types of uncertainty indices and structural shocks: epidemiological and policy-related uncertainties. The constructed indices can trace well the events related to COVID-19. We then find that stock market variables respond significantly to a policy-related uncertainty shock, while real variables such as mobility and consumption are significantly affected by an epidemiological one. These findings highlight the importance of considering different types of uncertainty to assess the impact of COVID-19 induced uncertainty on economic activity.

Adaptive iterative learning control for high‐order nonlinear systems with different types of uncertainties

AbstractThe present work aims at investigating the adaptive iterative learning control (AILC) design for uncertain high‐order fully actuated nonlinear systems. In order to show the design principles, three types of nonlinear systems are considered, including systems with just parametric uncertainty, systems with both parametric and input distribution uncertainties as well as systems with both parametric uncertainty and an unknown control gain matrix. For different systems, the corresponding AILC schemes are proposed with different techniques in dealing with various system uncertainties, for which the convergence analysis are conducted rigorously based on the composite energy function. The effectiveness of the proposed AILC strategies is verified through numerical simulations.

Communication under Uncertainty and the Role of Founders’ Information Advantage: Evidence from SPAC IPOs

This study develops a novel framework about how a firm’s financing outcome will be shaped by its communication under different types of uncertainty. Whereas prior work has largely focused on uncertainties that arise because of founders having a knowledge advantage over investors, we examine a firm’s communication in situations of more fundamental uncertainty when both founders and investors face knowledge problems. Our framework proposes that in situations where founders have a knowledge advantage over investors (i.e., when there is information asymmetry), firms that reduce uncertainty by sending signals of quality and express less uncertainty in their communications will enjoy better financing outcomes. However, we argue that in situations characterized by high unknowability, and where founders do not have a significant knowledge advantage over investors (i.e., when there is Knightian uncertainty), firms that acknowledge this unknowability by expressing more uncertainty in their communications will have more favorable financing outcomes. Studying the full population of special purpose acquisition companies (SPACs) that sought to complete an initial public offering from the emergence of the sector in 2003–2019, we find support for our predictions. This study expands our understanding of the role of uncertainty in investment decisions, offers deeper insight into how language operates in financial markets, and sheds light on the increasingly popular, but understudied, SPAC vehicle. Funding: Ivana Naumovska received financial support from the INSEAD R&D Committee and the INSEAD Dean’s Annual Fund. Supplemental Material: The online appendix is available at https://doi.org/10.1287/stsc.2022.0043 .

A simple state-of-the-art spectrometer for student labs: Cost-efficient, instructive, and widely applicable

We present a simple, cost-effective, yet instructive spectrometer for use in undergraduate instructional laboratory courses. Deliberate design choices are made to enhance the learning experience provided by the setup, where every component is accessible to students, allowing them to fully understand the function of each individual item. The result is a state-of-the-art spectrometer, built from commercially available components, which balances pedagogical simplicity with the potential for a wide range of applications. Our setup prepares students for future spectroscopy work in research labs. Furthermore, data-taking by means of a CCD camera and the subsequent analysis teach students fundamental computational skills. Within one image, the spectrometer can cover a spectral range of 40 nm and its spectral resolution is about 0.1 nm, limited by the imaging optics. Systematic uncertainties arising from mechanical play of the grating's rotation stage limit the reproducibility of the setup to 0.65 nm. While these parameters can be improved, we decided to maintain the pedagogical and straightforward nature of the presented setup, as any increase in cost or complexity would undermine its educational benefits. Using the spectrometer in an undergraduate instructional laboratory makes possible a variety of valuable experiments, such as calibration measurements, investigation of different types of uncertainties and measurements errors, and historically important measurements (e.g., the Balmer series or solar spectrum). We are convinced that the presented spectrometer will greatly benefit the learning experience of students for many years to come.

Design concept evaluation based on cloud rough model and modified AHP-VIKOR: An application to lithography tool manufacturing process

Design concept evaluation is a wide domain of research as the production process of new product development is mainly based on the evaluations of experts. As different types of uncertainties like vagueness, randomness, and diversity essentially exist in the evaluation information, the manipulation models that deal with just one type of uncertainty are not appropriate for ranking the design alternatives. The integration of multiple approaches into a single mathematical model to create an effective framework is more useful for uncertain information manipulation. This paper presents an innovative group decision-making approach to evaluate design concepts by integrating cloud rough numbers, analytic hierarchy process (AHP) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method to introduce a novel cloud rough AHP-VIKOR model. The concept of cloud rough numbers is utilized by fusing the merits of the cloud model theory and rough approximations in addressing randomness in experts’ judgments and intrapersonal uncertainty for handling consensus inconsistency. Some new modified algebraic operations are introduced to remove the errors in already existing operations of cloud rough numbers. The cloud rough AHP technique is introduced to compute weights of design criteria by computing the cloud rough numbers of linguistic values and their reciprocals. Based on cloud rough values of positive and negative ideals, the individual regret, group utility values and evaluation indices are determined. Using the distance of evaluation indices from minimized cloud rough value, the design alternatives are ranked using different formulae. The significance of the proposed approach is illustrated with a real-world application in lithography tool manufacturing process. The out-performance and reliability of the proposed model is studied by a sensitivity analysis of different parameters in the method, and a comparison analysis with existing approaches.

Uncertainty decomposed: Understanding levels of contingency to enable effective decision-making

Background: Uncertainty is a common challenge in managerial decision-making, especially when it comes to predicting future states, establishing cause-effect relationships, and having knowledge about relevant variables. However, it is difficult to deliberately address different types of uncertainty by applying specific decision-making strategies and hence enable reduction of uncertainty due to overlapping definitions and conflicting operationalization of the uncertainty construct. Purpose: The paper aims to delineate types of uncertainty along their epistemological configurations in terms of specific knowledge contexts to enable choices of suitable strategies for specific decision-making situations. Study design/methodology/approach: A literature review revises and discusses concepts of (un)certainty based on (im)perfect information and objectively/subjectively available assemblages of knowledge. Findings/conclusions: The paper provides a framework that encompasses and differentiates configurations of available information and knowledge applicable to decision-making situations. In order to achieve construct clarity and to free the original concept of uncertainty from conflicting definitions and heterogeneous operationalizations, the umbrella term contingency is introduced. It encompasses all states of (im)perfect information and variations in their epistemological configurations. Finally, the presented epistemological framework delineates levels of contingency along specific qualities of available information. The identified and discussed levels of contingency are certainty, risk, uncertainty in the narrow sense (i.n.s.), complexity, ambiguity/equivocality, and isotropy/radical uncertainty. The delineated levels of contingency help to tailor decision-making situation to specific epistemological configurations and hence may serve as a starting point for concluding and developing appropriate strategies to reduce contingency. Limitations/future research: A holistic understanding how to deal with and solve contingency requires further research focusing on aligning levels of contingency with strategies for decision-making (algorithms, causation, effectuation, bricolage, improvisation, trial & error) by taking types of knowledge (structural, procedural, conceptual) and contextual factors (e.g. time, [origin of] resources) into account.

Bayesian-optimized interpretable surrogate model for seismic demand prediction of urban highway bridges

Urban highway bridges are crucial for regional economic development and population mobility, but they are vulnerable to seismic hazards. Accurately predicting the seismic demands of bridges is essential. Several commonly-used methods for seismic demand estimates, such as cloud analysis, incremental dynamic analysis, and multiple stripe analysis, are computationally expensive and subject to theoretical assumptions and convergence issues, especially for portfolios of bridges. Machine learning techniques can be effective, but their lack of interpretability hinders understanding of the surrogate model's predictions. To address these challenges, this study develops a Bayesian-optimized interpretable ensemble learning surrogate model for predicting and interpreting the critical seismic demands of urban highway bridges.Thousands of continuous prestressed concrete girder bridges with typical geometric configurations in China are generated, and 120 ground motion records with different frequency, waveform, and duration characteristics are chosen. The seismic demand dataset is established based on nonlinear time-history analyses for urban highway bridges, accounting for different types of uncertainties. The surrogate models are developed based on the XGBoost ensemble learning method, with hyperparameters automatically and efficiently determined by Bayesian optimization technique. Compared to the random search and grid search methods, Bayesian optimization is approximately 8 times and 29 times faster, respectively, and it also achieves the highest prediction accuracy. Meanwhile, the relationship of each hyperparameter in the surrogate model is also revealed. The prediction results of the proposed model are compared with other machine learning models. The SHAP algorithm is subsequently used to explain the model predictions regarding the feature importance, global interpretations, and feature dependency analysis. The study quantifies the contribution of each structural feature and seismic intensity measure to the selected critical seismic demand and identifies the interaction effects between different input variables in the prediction.

Interval valued inventory model for deterioration, carbon emissions and selling price dependent demand considering buy now and pay later facility

Uncertainty refers to a lack of precise knowledge or information about a particular event, situation, or outcome. It is an inherent characteristic of many real-world phenomena and is often associated with the presence of risk or ambiguity. Uncertainty can arise due to various factors, such as incomplete information, unpredictability, complexity, or variability of a system or process. In many cases, uncertainty can lead to difficulties in decision-making and pose challenges in planning, forecasting, and managing risks. There are different types of uncertainty, including epistemic uncertainty, which arises from the inherent randomness or variability of a system or process. This study encompasses the inclusion of all inventory parameters as uncertainty parameters, which are expressed in the form of intervals. Furthermore, demand for the product is taken into account in interval form. The conversion of the differential equation into an interval differential equation is carried out in order to account for the variability in demand within a certain interval. The utilisation of the centre-radius technique leads to the derivation of the related optimisation problem under a ‘buy now, pay later’ (BNPL) payment scheme. In order to demonstrate the concept, a numerical case is selected and solved with the MATHEMATICA software and interval order relations. In the end, a comprehensive sensitivity analysis has been conducted to derive insightful conclusions pertaining to this study.

Sensorimotor Uncertainty of Immersive Virtual Reality Environments for People in Pain: Scoping Review.

Decision making and action execution both rely on sensory information, and their primary objective is to minimise uncertainty. Virtual reality (VR) introduces uncertainty due to the imprecision of perceptual information. The concept of "sensorimotor uncertainty" is a pivotal element in the interplay between perception and action within the VR environment. The role of immersive VR in the four stages of motor behaviour decision making in people with pain has been previously discussed. These four processing levels are the basis to understand the uncertainty that a patient experiences when using VR: sensory information, current state, transition rules, and the outcome obtained. This review examines the different types of uncertainty that a patient may experience when they are immersed in a virtual reality environment in a context of pain. Randomised clinical trials, a secondary analysis of randomised clinical trials, and pilot randomised clinical trials related to the scope of Sensorimotor Uncertainty in Immersive Virtual Reality were included after searching. Fifty studies were included in this review. They were divided into four categories regarding the type of uncertainty the intervention created and the stage of the decision-making model. Immersive virtual reality makes it possible to alter sensorimotor uncertainty, but studies of higher methodological quality are needed on this topic, as well as an exploration into the patient profile for pain management using immersive VR.

A Phenology-guided Bayesian-CNN (PB-CNN) framework for soybean yield estimation and uncertainty analysis

Large-scale crop yield estimation is important for understanding the response of agriculture production to environmental forces and management practices, and plays a critical role in insurance designing, trade decision making, and economic planning. The empirical models (e.g., deep learning models) have been increasingly utilized for estimating crop yields with the ability to take into account a range of yield predictors and complex modeling relationships. Yet empirical estimation of crop yields still faces important challenges, particularly in accommodating spatio-temporal crop phenological development patterns as well as tackling the heterogeneity of a diversity of yield predictors. The different types of uncertainties associated with empirical yield estimations have seldom been explored. The objective of this study is to develop a Phenology-guided Bayesian-Convolutional Neural Network (PB-CNN) framework for county-level crop yield estimation and uncertainty quantification, with soybean in the US Corn Belt as a case study. The PB-CNN framework comprises three key components: Phenology Imagery construction, multi-stream Bayesian-CNN modeling, as well as feature importance (i.e., yield predictor and phenological stage) and predictive uncertainty analysis (i.e., aleatoric and epistemic uncertainty). With the innovative integration of critical crop phenological stages in modeling the crop yield response to a heterogeneous set of yield predictors (i.e., satellite-based, heat-related, water-related, and soil predictors) as well as the associated uncertainties, the developed PB-CNN framework outperforms three advanced benchmark models, achieving an average RMSE of 4.622 bu/ac, an average R2 of 0.709, and an average bias of −2.057 bu/ac in estimating the county-level soybean yield of the US Corn Belt in testing years 2014–2018. Among the yield predictor groups, the satellite-based predictor group is the most critical in soybean yield estimation, followed by the water- and heat-related predictor groups. Throughout the growing season, the soybean blooming to dropping leaves phenological stages play a more crucial role in modeling the soybean yield. The soil predictor group as well as the early growing stages can improve the model estimation accuracy yet potentially brings more uncertainties into the yield estimation. The further uncertainty disentanglement indicates that the dominant uncertainty in yield estimation is the aleatoric uncertainty, mainly stemming from the fluctuations and variations inherent in the modeling input observations. The PB-CNN framework largely enhances our understanding of the complex soybean yield response to varying environmental conditions across crop phenological stages as well as associated uncertainties for more sustainable agricultural development.

Chance-Constrained Generic Energy Storage Operations Under Decision-Dependent Uncertainty

Compared with large-scale physical batteries, aggregated and coordinated generic energy storage (GES) resources provide low-cost, but uncertain, flexibility for power grid operations. While GES can be characterized by different types of uncertainty, the literature mostly focuses on decision-independent uncertainties (DIUs), such as exogenous stochastic disturbances caused by weather conditions. Instead, this manuscript focuses on newly-introduced decision-dependent uncertainties (DDUs) and considers an optimal GES dispatch that accounts for uncertain available state-of-charge (SoC) bounds that are affected by incentive signals and discomfort levels. To incorporate DDUs, we present a novel chance-constrained optimization (CCO) approach for the day-ahead economic dispatch of GES units. Two tractable methods are presented to solve the proposed CCO problem with DDUs: (i) a robust reformulation for general but incomplete distributions of DDUs, and (ii) an iterative algorithm for specific and known distributions of DDUs. Furthermore, reliability indices are introduced to verify the applicability of the proposed approach with respect to the reliability of the response of GES units. Simulation-based analysis shows that the proposed methods yield conservative, but credible, GES dispatch strategies and reduced penalty cost by incorporating DDUs in the constraints and leveraging data-driven parameter identification. This results in improved availability and performance of coordinated GES units.

Experimental study on rotational impact dampers

Integrating the benefits of rotational nonlinear energy sinks (NESs) and impact NESs while eliminating the negative effects of impacts, rotational impact dampers (RIDs) are proposed in this study. RIDs consist of multiple eccentric masses that rotate in the same horizontal plane about a common pivot, with impacts occurring between adjacent rotators to facilitate fast and effective energy dissipation. First, the development of the RID system is presented. Subsequently, experiments are conducted on a two-story frame structure under impulse excitation to validate the feasibility of RIDs. The impacts of the RIDs with two, three, and four rotators are identified and their control effectiveness is analyzed. The experimental results demonstrate that the RIDs can effectively attenuate the vibration of the structure, with the number of rotators being the main factor affecting the control capacity. With physical validation provided, this short communication highlights the great potential of RIDs as a viable solution for control problems involving different types of uncertainties.

A survey on uncertainty reasoning and quantification in belief theory and its application to deep learning

An in-depth understanding of uncertainty is the first step to making effective decisions under uncertainty. Machine/deep learning (ML/DL) has been hugely leveraged to solve complex problems involved with processing high-dimensional data. However, reasoning and quantifying different uncertainties to achieve effective decision-making have been much less explored in ML/DL than in other Artificial Intelligence (AI) domains. In particular, belief/evidence theories have been studied in Knowledge representation and reasoning (KRR) since the 1960s to reason and measure uncertainties to enhance decision-making effectiveness. Based on our in-depth literature review, only a few studies have leveraged mature uncertainty research in belief/evidence theories in ML/DL to tackle complex problems under different types of uncertainty. Our present survey paper discusses major belief theories and their core ideas dealing with uncertainty causes and types and quantifying them, along with the discussions of their applicability in ML/DL. Particularly, we discuss three main approaches leveraging belief theories in Deep Neural Networks (DNNs), including Evidential DNNs, Fuzzy DNNs, and Rough DNNs, in terms of their uncertainty causes, types, and quantification methods along with their applicability in diverse problem domains. Through an in-depth understanding of the extensive survey on this topic, we discuss insights, lessons learned, limitations of the current state-of-the-art bridging belief theories and ML/DL, and future research directions. This paper conducts an extensive survey by bridging belief theories and deep learning in reasoning and quantifying uncertainty to help researchers initiate uncertainty and decision-making research.

Waveform Adaptation for Target Classification Using HRRP in a Cognitive Framework

Waveform adaptation is a key-feature for modern radar systems and essential for cognitive radar. In this work we present a concept for the enhancement of the classification performance by using optimised transmit waveforms and a Gaussian template matching high range resolution profile (HRRP)classifier. A straight forward approach is presented, aiming to improve specific parts of the confusion matrix which will be exploited within a cognitive framework. The optimisation includes different types of uncertainties and is designed during a training process to be accessed by a library. Taking different uncertainties into account, the calculation of the expected performance, the optimisation, the range side lobe constraint and the time-domain realisation is explained. A non-linear frequency modulation (NLFM) waveform is used since it provides a compression gain with range resolution and a constant envelope. Based on an electromagnetic simulation the concept is validated for different ground targets and aspect angle uncertainties. The adaptation is compared to a commonly used linear frequency modulation (LFM). The results of the mean performance improvement reached an enhancement between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${8.8}{\%}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${20.9}{\%}$</tex-math></inline-formula> .

The economics of renewable energy portfolio management in solar based microgrids: A comparative study of smart strategies in the market

In this study, an energy-management approach based on digital twin is developed to manage a microgrid (MG) based on the energy generated by renewable sources of solar and wind, diesel generators, energy storage, and a variety of loads consumers in the market. The MG is assumed to participate in the pool market and schedule its controllable sources accordingly as a means of maximizing profits. This paper proposes a risk-limited scenario-driven stochastic programming strategy that uses the conditional value at risk approach for handling different types of uncertainty. Double stochastic optimization levels are used to solve the proposed scheme. The day-ahead market can be optimized at one level by submitting the best bids at hourly intervals based on forecasts. As a second level of optimization, scenario-driven stochastic information has been used for determining the best schedule. Also, shark optimization algorithm is proposed to solve the optimization problem. Aside from being advantageous for MGs and their users, the suggested energy management system likewise takes advantage of the MG's aggregators and non-real power plants. This model is shown to be valid based on the outcomes and would be beneficial for the market owners.

A Bayesian deep-learning framework for assessing the energy flexibility of residential buildings with multicomponent energy systems

This paper addresses the challenge of assessing uncertainty in energy flexibility predictions, which is a significant open question in the energy flexibility assessment field. To address this challenge, a methodology that quantifies the flexibility of multiple thermal and electrical systems is developed using appropriate indicators and considers the different types of uncertainty associated with building energy use. A Bayesian convolutional neural network is developed to capture aleatoric and epistemic uncertainty related to energy conversion device operation and temperature deviations resulting from exploiting building flexibility. The developed prediction models utilise residential occupancy patterns and a sliding window technique and are periodically updated. The energy systems evaluated include a heat pump, a photovoltaic system, and a stationary battery, and use synthetic datasets obtained from a calibrated physics-based model of an all-electric residential building for two occupancy profiles. Simulation results indicate that building flexibility potential predictability is influenced by weather conditions and/or occupant behaviour. Furthermore, the day-ahead and hour-ahead prediction models show excellent performance for both occupancy profiles, achieving coefficients of determination between 0.93 and 0.99. This methodology can enable electricity aggregators to evaluate building portfolios, considering uncertainty and multi-step predictions, to shift electricity demand to off-peak periods or periods of excess onsite renewable electricity generation in an end-user-customised manner.

An analysis of the role of order quantity in supply chains with uncertainties from demand and/or supply

We study the role of order quantity in supply chains when uncertainty exists in demand and/or supply. We consider a supply chain model consisting of one supplier and one buyer. It is widely known that order quantity is a tool used by the buyer to deal with the potential supply shortage or supply surplus due to the uncertainties in supply and/or demand. However, it is unclear how the decision makers use order quantity to hedge against different types of uncertainties. In addition, to comprehensively explore the role of order quantity, we analyze the impact of order quantity on coordinating contract design. In the model with demand uncertainty only, order quantity is a tool applied to hedge against the uncertainty in both of the decentralized system and the centralized system, and the buyer’s incentive for order quantity in the decentralized system is lower than that in the centralized system. To achieve coordination, the buyer’s ordering strategy has to be conservative in both demand and supply, i.e., order quantity is the same as the supply and less than the maximal demand. In the model with supply uncertainty only, the order quantity is used as a tool to hedge against the uncertainty but not in the centralized system. To achieve coordination, the buyer’s ordering strategy has to be conservative in supply but aggressive in demand, i.e., order quantity is less than the maximal supply but higher than the maximal demand. Furthermore, compared to the demand uncertainty, the supply uncertainty makes it more difficult to design a quantity-based coordinating contract. This can be seen from two facts. Finally, in the hybrid model with both uncertainties, the role of the order quantity and the design of the quantity-based coordinating contracts are similar to the model with supply uncertainty only. These results imply that the supply uncertainty seems to have a more significant impact on the application of order quantity than the demand uncertainty.

Analysis under Uncertainty with the Monte Carlo Method Applied to a Bioheat Transfer Problem with Coupled Deep Brain Stimulation Lead

This article deals with an analysis of uncertainties applied to a bioheat transfer problem containing a deep brain stimulation lead. The classic two-dimensional bioheat transfer equation in cylindrical coordinates was considered in the mathematical formulation. The electric potential was solved with a Laplace equation to incorporate the DBS lead effects. Thus, the solution for the electric potential was coupled to the temperature problem, considering an external heat transfer rate. The analysis under uncertainties was performed by the Monte Carlo method considering different types of uncertainties for all parameters of the mathematical model. The uncertainties were chosen according to the information available in the literature in order to analyze the problem more realistically. The solutions showed a significant variation in the temperature profile over time when considering the random variations in the parameters.