Uncertainty Space Research Articles

Egoroff’s theorem and Lusin’s theorem for complex uncertain sequences

Complex uncertain variables are measurable functions from uncertainty spaces to the set of complex numbers and are used to model complex uncertain quantities. In this paper, we investigate Egoroff’s theorem and Lusin’s theorem for complex uncertain sequences. For studying these theorems, we introduce two concepts: strongly order continuous and regular. And as far as we know, our results are new.

Microkinetic Modeling of the Transient CO2 Methanation with DFT‐Based Uncertainties in a Berty Reactor

AbstractThe transient operation of methanation reactors can become desirable when coupled with fluctuating renewable energies in Power‐to‐Gas scenarios, which requires suitable kinetic approaches that can describe the transient catalytic phenomena. A combined experimental and theoretical investigation of the transient CO2 methanation is conducted using concentration forcing to derive a suitable microkinetic model. Methanation experiments are performed with a Ni/SiO2 catalyst in a Berty‐type reactor at industrially relevant conditions. The microkinetics are based on previous work and were automatically constructed for the Ni(111) facet using the Reaction Mechanism Generator. A feasible set of energetic parameters of the microkinetic models was identified in a theory‐constrained optimization procedure within the DFT uncertainty space that can accurately reproduce the experimental results on a first‐principles basis. The microkinetic model unravels that the formation of H2O* and CH3* control the activity and selectivity of Ni(111) under the investigated conditions.

Law of Large Numbers, Central Limit Theorem, and Law of the Iterated Logarithm for Bernoulli Uncertain Sequence

In order to describe human uncertainty more precisely, Baoding Liu established uncertainty theory. Thus far, uncertainty theory has been successfully applied to uncertain finance, uncertain programming, uncertain control, etc. It is well known that the limit theorems represented by law of large numbers (LLN), central limit theorem (CLT), and law of the iterated logarithm (LIL) play a critical role in probability theory. For uncertain variables, basic and important research is also to obtain the relevant limit theorems. However, up to now, there has been no research on these limit theorems for uncertain variables. The main results to emerge from this paper are a strong law of large numbers (SLLN), a weak law of large numbers (WLLN), a CLT, and an LIL for Bernoulli uncertain sequence. For studying these theorems, we first propose an assumption, which can be regarded as a generalization of the duality axiom for uncertain measure in the case that the uncertainty space can be finitely partitioned. Additionally, several new notions such as weakly dependent, Bernoulli uncertain sequence, and continuity from below or continuity from above of uncertain measure are introduced. As far as we know, this is the first study of the LLN, the CLT, and the LIL for uncertain variables. All the theorems proved in this paper can be applied to uncertain variables with symmetric or asymmetric distributions. In particular, the limit of uncertain variables is symmetric in (c) of the third theorem, and the asymptotic distribution of uncertain variables in the fifth theorem is symmetrical.

Heterologous Dimension of the Other Sociality in the Cognitive Space of Uncertainty.

Contemporary society is presented as a model of other sociality demanding extraordinary methods of research in the cognitive space of uncertainty. This article aims at analyzing a heterologous paradigm of postnon-classical social philosophical discourse and how it applies to the socio-philosophical context of modernity by using cognitive and heuristic capabilities of social heterology which explain the uncertainty principle of social cognition in other sociality. The diversity of the other sociality is characterized by structural non-linearity, disequilibrium, rupture, decentralism, and lack of a unified systematic principle. In their research, authors highlighted the two different approaches to analyzing the social structure: the classical ontological and post-non-classical heterologous one. Philosophical and scientific sources of European and Russian traditions were used to suggest new revolutionary post-non-classical methods and social paradigms emphasizing the heterogeneous pattern of contemporary, unexpected and even unpredictable society. Transition to social heterogeneity is attributed to the uncertainty principle in extraordinary processes of social self-development. The authors’ position is that the heterologous dimension of sociality approaches the complete understanding of social life’s contradictions of a modern human not only in a cognitive perspective but also in a practical one to define humanistic social policy.

From optimal to robust climate strategies: expanding integrated assessment model ensembles to manage economic, social, and environmental objectives

Cost-benefit integrated assessment models generate welfare-maximizing mitigation pathways under a set of assumptions to deal with deep uncertainty in future scenarios. These assumptions include socio-economic projections, the magnitude and dynamics of climate impacts on the economy, and physical climate response. As models explore the uncertainty space within the boundaries of their objective functions, they risk providing scenarios which are too narrow and not sufficiently robust. Here, we apply robust and multi-objective decision-making methods to extract relevant information from a large ensemble of optimal emissions-reduction pathways generated by a regionalized cost-benefit integrated assessment model under deterministic welfare optimization. We show that shifting the focus from optimal to robust solutions reduces the uncertainty in mitigation strategies and aligns them toward the Paris goals. Moreover, we analyze the trade-offs between climatic (temperature), social (inequality) and economic (welfare) objectives and illustrate four robust pathways under various decision-making criteria. We show that robust mitigation strategies can lead to regional emission-reduction strategies which are fair. Our results show how to extract more comprehensive climate strategies from available scenario ensembles and that the highest discrepancies at the local level policies are found in the developing and most-impacted regions.

“Fixing” the nuclear waste problem? The new political economy of spent fuel management in the United States

With continued reliance on nuclear energy in the United States, we are increasingly having to contend with the problem of nuclear waste. Growing quantities of spent nuclear fuel, the lack of permanent storage, and an increasing number of decommissioned nuclear reactors are some of the techno-economic and political realities that have thrust US nuclear waste management into a liminal space of uncertainty. Using a qualitative approach combining policy analysis and case studies, we examine this liminality and the consequent emergence of a new political economy of spent fuel management. Our findings indicate a series of regulatory, organizational and spatial ‘fixes’ have recently emerged to capitalize on the liminality of nuclear waste management in the US. These fixes include the US Nuclear Regulatory Commission's Continued Storage Rule, the proposal of private consolidated interim storage facilities, and the reconfiguration of nuclear waste management corporations into vertically integrated nuclear waste assemblages with private equity involvement. Such developments are potentially problematic in that they are inherently contradictory, temporary, and quick ‘fixes’ that do not solve the underlying societal issues, such as distrust in science and lack of democratic governance and energy justice in decision-making, and in many cases they delay permanent solutions. This work contributes to the fields of economic geography, science and technology studies, and nuclear policy studies, by analyzing novel corporate arrangements and developments in the management of spent nuclear fuel in the US. The findings suggest a need to carefully assess policy solutions across contexts, from nuclear waste management to other rapidly evolving energy sectors.

Proceeding From Our Roots in the Dust: An Unfolding Ethics of Care Through the Arts (Étendre nos racines dans la poussière : une éthique des soins qui se déploie à travers les arts)

This theoretical essay invites a reimagining of ethics in art therapy, and a questioning of the reverence of ethical codes and standards in the care professions as universally beneficial. It explores how one may practice care work without replicating systemic violence. I begin exploring these broad quandaries by drawing from partial and situated knowledges (Haraway, 1988). This writing is informed by feminist analyses and theorizations of care ethics, and written from my subject position as a racialized cisgender woman working in mental health services and an art therapy training program in Tkaronto 1 . I begin with a discussion of the discourse of professional ethics and its idealization of masculine rationality and a top-down model of accountability to contemplate why people continue to experience oppressive and unethical treatment within human service systems despite deeply cemented directives to adhere to professional codes of ethics. I argue that it is necessary to center emotions and interdependence in confronting our complicity in oppression. I conclude by contemplating an ethics of foregrounding the arts to hold space for uncertainty, responsibility, and care.

Learning-Based Approach for a Soft Assistive Robotic Arm to Achieve Simultaneous Position and Force Control

Soft robotics have demonstrated great advantages in assisting elderly/disabled people during daily tasks, owing to their highly dexterous motions and safe human-robot interactions. However, simultaneously controlling the position and force of soft robots is still a challenging task due to soft actuators’ nonlinearity, system uncertainty, and high-dimensional control space. Classical control methods are usually based on first-principle/analytical models that are difficult to derive for soft robots without making significant simplifications. To overcome such control challenges, the central concept of this work is to introduce a learning-based data-driven approach. The approach employs a probabilistic model to explicitly capture system nonlinearity and uncertainty. Besides, nonparametric local learning methods are investigated to deal with redundant high-dimensional control space. The approach is applied in a soft robotic arm interacting with a manikin to simulate the bathing task. Experimental results demonstrate that the soft robotic arm could be well controlled to track the desired position and force simultaneously (maximum error of position and force is 6 mm and 0.037 N). Meanwhile, our method outperforms another typical data-driven approach (maximum error of position and force is 10 mm and 0.058 N). The results indicate that our approach is helpful for soft robots because of the physical interactions needed in assistive tasks.

Generalized adaptive partition-based method for two-stage stochastic linear programs: Geometric oracle and analysis

Adaptive Partition-based Methods (APM) are numerical methods that solve, in particular, two-stage stochastic linear problems (2SLP). We say that a partition of the uncertainty space is adapted to the current first stage control xˇ if we can aggregate scenarios while conserving the true value of the expected recourse cost at xˇ. The core idea of APM is to iteratively construct an adapted partition to all past tentative first stage controls. Relying on the normal fan of the dual admissible set, we give a necessary and sufficient condition for a partition to be adapted even for non-finite distribution, and provide a geometric method to obtain an adapted partition. Further, by showing the connection between APM and the L-shaped algorithm, we prove convergence and complexity bounds of the APM methods. The paper presents the fixed recourse case and ends with elements to forgo this assumption.

Some results on statistically convergent triple sequences in an uncertainty space

The concept of statistical convergence plays a very prominent role in the study of sequence spaces. In this treatise, we extend the research on different types of statistical convergence viz., statistical convergence in mean, in measure, in distribution, in almost surely and with respect to uniformly almost surely of complex uncertain triple sequences in a given uncertainty space. We emphasize to focus on characterizing statistical convergence of complex uncertain triple sequence in some extent. Moreover, we initiate the notion of complex uncertain Cauchy triple sequence and establish the interconnection of it with a statistically convergent triple sequence.

A novel heterogeneous preference fusion method with dual interaction influence and dynamic risk spread

Preference fusion is crucial for multi-attribute group decision-making (MAGDM). Heterogeneous preferences and interactions are commonplace situations in real-world MAGDM. Unlike conventional MAGDM fusion methods ignoring interactions or only considering attribute interactions, a novel heterogeneous preference fusion method proposed in this study considers the dual interaction influence of attributes and alternatives, as well as the influence of the dynamic risk spread (IDRS). Specifically, a novel similarity-based three-dimensional determination–uncertainty space method is established to homogenize heterogeneous preferences, avoiding information distortion caused by preference uncertainty loss. The attribute interaction influence is evaluated by constructing an optimization model with ranking maximization. Subsequently, a multi-attribute alternative interaction network and a total interaction measurement model are developed to describe complex interaction relationships and the interaction intensity between alternatives. The susceptible-infected-recovered-susceptible Markov chain model is presented to measure the IDRS. An improved directed weighted degree centrality model based on the IDRS is then established to measure the alternative interaction influence (AII) from a global perspective. Finally, a novel interaction non-additive fusion method is designed to fuse preference more reasonably. A case study of hot dry rock siting and comparative analyses demonstrate the practicality, robustness, and superiority of the proposed method. The results show that the AII and IDRS significantly influence the fusion accuracy and should be considered in MAGDM fusion methods.

On statistically convergent complex uncertain sequences

In this paper, we extend the study of statistical convergence of complex uncertain sequences in a given uncertainty space. We produce the relation between convergence and statistical convergence in an uncertain environment. We also initiate statistically Cauchy complex uncertain sequence to prove that a complex uncertain sequence is statistically convergent if and only if it is statistically Cauchy. We further characterize a statistically convergent complex uncertain sequence via boundedness and density operator.

Evaluation of the government entrepreneurship support by a new dynamic neutrosophic operator based on time degrees

PurposeEntrepreneurship as a development engine has a distinct character in the economic growth of countries. Therefore, governments must support entrepreneurship in order to succeed in the future. The best way to improve the performance of this entrepreneurial advocacy is through efficient measurement methods. For this reason, the purpose of this paper is to propose a new integrated dynamic multi-attribute decision-making (MADM) model based on neutrosophic set (NS) for assessment of the government entrepreneurship support.Design/methodology/approachDue to the nature of entrepreneurship issues, which are multifaceted and full of uncertain, indeterminate and ambiguous dimensions, this measurement requires multi-criteria decision-making methods in spaces of uncertainty and indeterminacy. Also, due to the change in the size of indicators in different periods, researchers need a special type of decision model that can handle the dynamics of indicators. So, in this paper, the authors proposed a dynamic neutrosophic weighted geometric operator to aggregate dynamic neutrosophic information. Furthermore, in view of the deficiencies of current dynamic neutrosophic MADM methods a compromised model based on time degrees was proposed. The principle of time degrees was introduced, and the subjective and objective weighting methods were synthesized based on the proposed aggregated operator and a nonlinear programming problem based on the entropy concept was applied to determine the attribute weights under different time sequence.FindingsThe information of ten countries with the indicators such as connections (C), the country's level of education and experience (EE), cultural aspects (CA), government policies (GP) and funding (F) over four years was gathered and the proposed dynamic MADM model to assess the level of entrepreneurial support for these countries. The findings show that the flexibility of the model based on decision-making thought and we can see that the weights of the criteria have a considerable impact on the final evaluations.Originality/valueIn many decision areas the original decision information is usually collected at different periods. Thus, it is necessary to develop some approaches to deal with these issues. In the government entrepreneurship support problem, the researchers need tools to handle the dynamics of indicators in neutrosophic environments. Given that this issue is very important, nonetheless as far as is known, few studies have been done in this area. Furthermore, in view of the deficiencies of current dynamic neutrosophic MADM making methods a compromised model based on time degrees was proposed. Moreover, the presented neutrosophic aggregation operator is very suitable for aggregating the neutrosophic information collected at different periods. The developed approach can solve the several problems where all pieces of decision information take the form of neutrosophic information collected at different periods.

Real‐time hybrid simulation with multi‐fidelity Co‐Kriging for global response prediction under structural uncertainties

AbstractReal‐time hybrid simulation (RTHS) provides an effective and efficient experimental technique to enable large‐ or full‐scale experiments to account for rate‐dependent behavior in size limited laboratories. Traditional practice of RTHS assumes deterministic substructure properties therefore could not account for structural uncertainties in global response prediction. This study explores the use of Co‐Kriging metamodeling for global response prediction under the presence of structural uncertainties. RTHS in laboratory is used as high‐fidelity (HF) modeling while computational simulation of the prototype structure under investigation is used as low‐fidelity (LF) modeling. Multifidelity modeling is integrated through Co‐Kriging to render accurate response prediction over the entire sample space of structural uncertainties. An entropy‐based adaptive strategy is used to sequentially determine the sampling points for HF RTHS and LF simulation. The proposed multifidelity Co‐Kriging approach is experimentally evaluated through RTHS of a single‐degree‐of‐freedom structure with a self‐centering viscous damper. The Co‐Kriging predicted maximum structural responses are further compared with validation tests. It is demonstrated that the Co‐Kriging can effectively reduce the number of RTHS tests in laboratory and significantly improve the metamodel accuracy for global prediction of structural response under uncertainties. The presented study presents an innovative way to further expand the capacity of RTHS for uncertainty quantification toward seismic hazard mitigation.

Uncertainty Analysis of Inverse Problem of Resistivity Model in Internal Defects Detection of Buildings

Fissure detection in ancient buildings is of vital importance in the evaluation of resistance or remediation in urban areas. Electrical resistivity imaging is an efficient tool to detect fissures or moisture erosion in buildings by highlighting the resistivity contrasts in the inversion models. The traditional results of ERT images give deterministic interpretations of the internal artifact. However, the existence of equivalent models may correspond to different physical realities in engineering cases, to which the traditional ERT model cannot respond. In this paper, through the application of a field test on an ancient wall, it is shown that the segmentation of the equivalent model family is applicable to solve the internal defects detection problem in a probabilistic approach. It is achieved by performing a probabilistic approach to apply the uncertainty analysis. The procedure begins with the reduction in dimensions of the model by spectral decomposition, and the uncertainty space is rebuilt via Particle Swarm Optimization (PSO). By computing the uncertainty space, probabilistic maps are created to demonstrate the electrical anomaly in a simpler structure. The proposed method provides a more accurate approach for the internal defects detection of buildings by considering the possibilities hidden in the equivalent model family of ERT results.

CMAL: Cost-Effective Multi-Label Active Learning by Querying Subexamples

Multi-label active learning (MAL) aims to learn an accurate multi-label classifier by selecting which examples (or example-label pairs) will be annotated and reducing query effort. MAL is a more complicated and expensive process than single-label active learning, due to one example can be associated with a set of non-exclusive labels and the annotator has to scrutinize the whole example and label space to provide correct annotations. Instead of scrutinizing the whole example for annotation, we may just examine some of its subexamples with respect to a label for annotation. In this way, we can not only save the annotation cost but also speedup the annotation process. Given this observation, we introduce CMAL, a two-stage Cost-effective MAL strategy (CMAL) by querying subexamples. CMAL first selects the most informative example-label pairs by leveraging uncertainty, label correlation and label space sparsity. Specifically, the uncertainty of a label to an example can be reduced if its correlated labels already annotated to the example, and its uncertainty can be reduced also if more examples annotated to this label. Next, CMAL greedily queries the most probable positive subexample-label pairs of the selected example-label pair. In addition, we propose rCMAL to account for the representative of examples to more reliably select example-label pairs in the first stage. Extensive experiments on multi-label datasets from diverse domains show that our proposed CMAL and rCMAL can better save the query cost than state-of-the-art MAL methods. The contribution of leveraging label correlation, label sparsity, and representative for saving cost is also confirmed.

MESMER-M: an Earth system model emulator for spatially resolved monthly temperature

Abstract. The degree of trust placed in climate model projections is commensurate with how well their uncertainty can be quantified, particularly at timescales relevant to climate policy makers. On inter-annual to decadal timescales, model projection uncertainty due to natural variability dominates at the local level and is imperative to describing near-term and seasonal climate events but difficult to quantify owing to the computational constraints of producing large ensembles. To this extent, emulators are valuable tools for approximating climate model runs, allowing for the exploration of the uncertainty space surrounding selected climate variables at a substantially reduced computational cost. Most emulators, however, operate at annual to seasonal timescales, leaving out monthly information that may be essential to assessing climate impacts. This study extends the framework of an existing spatially resolved, annual-scale Earth system model (ESM) emulator (MESMER, Beusch et al., 2020) by a monthly downscaling module (MESMER-M), thus providing local monthly temperatures from local yearly temperatures. We first linearly represent the mean response of the monthly temperature cycle to yearly temperatures using a simple harmonic model, thus maintaining month-to-month correlations and capturing changes in intra-annual variability. We then construct a month-specific local variability module which generates spatio-temporally correlated residuals with yearly temperature- and month-dependent skewness incorporated within. The emulator's ability to capture the yearly temperature-induced monthly temperature response and its surrounding uncertainty due to natural variability is demonstrated for 38 different ESMs from the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The emulator is furthermore benchmarked using a simple gradient-boosting-regressor-based model trained on biophysical information. We find that while regional-scale, biophysical feedbacks may induce non-uniformities in the yearly to monthly temperature downscaling relationship, statistical emulation of regional effects shows comparable skill to the more physically informed approach. Thus, MESMER-M is able to statistically generate ESM-like, large initial-condition ensembles of spatially explicit monthly temperature fields, providing monthly temperature probability distributions which are of critical value to impact assessments.

Sustainable power systems operations under renewable energy induced disjunctive uncertainties via machine learning-based robust optimization

For sustainable and reliable power systems operations integrating variable renewable energy, it is essential to incorporate the uncertain intermittent power outputs. A novel robust unit commitment framework with data-driven disjunctive uncertainty sets is proposed for sustainable energy systems with volatile renewable wind power, assisted by machine learning. The approach can flexibly identify the uncertainty space based on renewable power forecast error data with disjunctive structures. Specifically, the uncertainty data are grouped using K-means and density-based spatial clustering of applications with noise (DBSCAN) following the optimal cluster number determined by the Calinski-Harabasz index. Disjunctive uncertainty sets are constructed accordingly as the union of multiple basic uncertainty sets, including conventional box and budget uncertainty sets, and data-driven uncertainty sets using Dirichlet process mixture model, principal component analysis coupled with kernel density estimation, and support vector clustering. Subsequently, the problem is formulated into a two-stage adaptive robust unit commitment model with data-driven disjunctive uncertainty sets and with a multi-level optimization structure. To facilitate the solution process, a tailored decomposition-based optimization algorithm is developed. The effectiveness and scalability of the proposed framework are illustrated with two case studies investigating sustainable operations scheduling based on IEEE 39-bus and 118-bus systems, considering the integration of intermittent renewable energy. Results show that the proposed framework can reduce the price of robustness by 8–48% compared to the conventional “one-set-fits-all” robust optimization approaches. Benchmarking with stochastic programming indicates that the proposed framework can achieve the same or better economic performance for sustainable operations with over 75% less computational time.

From emission scenarios to spatially resolved projections with a chain of computationally efficient emulators: coupling of MAGICC (v7.5.1) and MESMER (v0.8.3)

Abstract. Producing targeted climate information at the local scale, including major sources of climate change projection uncertainty for diverse emissions scenarios, is essential to support climate change mitigation and adaptation efforts. Here, we present the first chain of computationally efficient Earth system model (ESM) emulators that allow for the translation of any greenhouse gas emission pathway into spatially resolved annual mean temperature anomaly field time series, accounting for both forced climate response and natural variability uncertainty at the local scale. By combining the global mean, emissions-driven emulator MAGICC with the spatially resolved emulator MESMER, ESM-specific and constrained probabilistic emulated ensembles can be derived. This emulator chain can hence build on and extend large multi-ESM ensembles such as the ones produced within the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The main extensions are threefold. (i) A more thorough sampling of the forced climate response and the natural variability uncertainty is possible, with millions of emulated realizations being readily created. (ii) The same uncertainty space can be sampled for any emission pathway, which is not the case in CMIP6, where only a limited number of scenarios have been explored and some of the most societally relevant strong mitigation scenarios have been run by only a small number of ESMs. (iii) Other lines of evidence to constrain future projections, including observational constraints, can be introduced, which helps to refine projected ranges beyond the multi-ESM ensembles' estimates. In addition to presenting results from the coupled MAGICC–MESMER emulator chain, we carry out an extensive validation of MESMER, which is trained on and applied to multiple emission pathways for the first time in this study. By coupling MAGICC and MESMER, we pave the way for rapid assessments of any emission pathway's regional climate change consequences and the associated uncertainties.

A critical perspective on uncertainty appraisal and sensitivity analysis in life cycle assessment

AbstractIn this study, we review approaches for uncertainty appraisal in the life cycle assessment literature. We cover the acknowledgment of stochastic and epistemic uncertainty in uncertainty and sensitivity analysis and knowledge quality assessment, respectively. Consistent with previous works, our findings indicate that uncertainty is only appraised in a few studies on life cycle assessment. Most of these contributions cover only one of the phases of life cycle assessment, mainly the life cycle inventory phase. Less attention has been devoted to the phases of goal and scope definition and life cycle impact assessment. Additionally, in most studies, uncertainty analysis and sensitivity analysis have been applied independently, as it is wrongly assumed they cover different uncertainty spaces. We also identify the scope for improvement in the appraisal of epistemic uncertainty and the correct definition of the probability distribution of the uncertain factors. We conclude by highlighting studies in which sensible practices have been adopted, identifying open challenges, and suggesting possible ways forward.