Uncertain Modelling Research Articles

Roughness in Fuzzy Cayley Graphs

Rough set theory is a worth noticing approach for inexact and uncertain system modelling. When rough set theory accompanies with fuzzy set theory, which both are a complementary generalization of set theory, they will be attended by potency in theoretical discussions. In this paper a definition for fuzzy Cayley subsets is put forward as well as fuzzy Cayley graphs of fuzzy subsets on groups inspired from the definition of Cayley graphs. We introduce rough approximation of a Cayley graph with respect to a fuzzy normal subgroup. We introduce the approximation rough fuzzy Cayley graphs and fuzzy rough fuzzy Cayley graphs. The last approximation is the mixture of the other approximations. Some theorems and properties are investigated and proved.

Advancing efficiency and reliability in thermal analysis of laser powder-bed fusion

In laser based powder-bed fusion of metals (PBF-LB/M), parts are fabricated by melting layers of powder using a high-intensity laser beam. During this process, the material is exposed to rapid cooling rates and intense thermal gradients, which are the underlying causes of residual stress formation and development of a unique microstructure in these components. Therefore, understanding the heat transfer phenomenon and reliably representing exposed temperature profiles in simulation frameworks are prerequisites for studying the microstructure and residual stress development during the PBF-LB/M process. This work employs a combination of experimental measurements and model development to study this phenomenon. Thermal properties of Hastelloy X were measured in the as-deposited state and used to setup finite element (FE) thermal simulations of the PBF-LB/M process. In addition, in-situ temperature evolutions near the laser tracks were measured by instrumenting thin-wall structures with K-type thermocouples in a two-stage fabrication process. The gathered data was used to calibrate uncertain modelling parameters, and ultimately, the simulation framework could closely represent the measured temperature histories. To address the high computational cost of FE thermal simulations, an adaptive-local/global multiscale modelling approach was proposed, which substantially reduced computation times without compromising the accuracy of the results. The modelling files and scripts are available in github.

Reliability analysis of uncertain random systems based on uncertain differential equation

Typical failure modes of degradation and shock processes have been applied which are named as soft failures and hard failures, respectively. This paper discusses the reliability of uncertain random systems where randomness is regarded as objective indeterminacy with enough sample data, and uncertainty is referred to epistemic indeterminacy with insufficient sample data. Considering that the combination of internal and external factors, the degradation process is modelled by an uncertain differential equation, and external shocks are driven by an uncertain random renewal process where state variables are uncertain random variables. Chance measure is applied to define the reliability index which is distinguished from traditional reliability assessment methods that utilize probability measure. Three types of reliability models possessed with independent failures are presented, where the general reliability index formulas are provided. The analysis results of Caohai Nature Reserve show that uncertain random modelling method provides an effective approach to system reliability assessment.

Linear uncertain modelling of LIDAR systems for robust wind turbine control design

Light detection and ranging (LIDAR) sensors measure the free wind ahead of the rotor, enabling the use of new feedforward control strategies. However, there exist some sources of error inherent to the measuring process that should be considered during the design of LIDAR-based controllers. Typically, the coherence function is used for that purpose, but it is not compatible with some robust design methodologies. This paper presents an analytic relation between the coherence function and a non-parametric uncertainty model of LIDAR sensors, suitable for the design of controllers via μ-synthesis or Quantitative Feedback Theory. Such a relation is applied to a realistic LIDAR simulator. First, the linear non-parametric uncertainty model is identified using simulation data obtained from the well-known NREL 5 MW wind turbine. Then, it is validated against the coherence model by comparing linear predictions of the simulation outputs.

Stochastic aeroservoelastic analysis of a flapped airfoil

In order to increase the operability range of wings in terms of speed, the suppression of aeroelastic vibrations due to flutter phenomena using a trailing edge flap is analyzed. The aeroelastic modelling of a three degrees of freedom 3DOF airfoil in unsteady incompressible flow with pitch and control surface stiffness non-linearities is studied and an augmented state space representation is used for the time domain analysis of the problem. A V-stack piezoelectric actuator is used to move the trailing edge flap and its dynamic behavior is included in the analyses by means of a finite element model; the actuator input voltage saturation is also taken into account. A heuristic method, named Population Decline Swarm Optimization, is used for the tuning of the filtered PID controller parameters for different velocity values. The optimization algorithm is also used for the tuning of the Simple Adaptive Controller SAC invariant gains. A general uncertain state space modelling of the aero-servo-elastic plant is provided and used first for the open loop stochastic flutter analysis. Then, the stochastic robustness analysis is carried out to verify the robustness to structural, aerodynamic, and actuator parameters uncertainties of the proposed flutter suppression systems and to compare the gain scheduled PID approach with the SAC scheme.

A mixed-integer-linear-logical programming interval-based model for optimal scheduling of isolated microgrids with green hydrogen-based storage considering demand response

Hydrogen produced from renewable sources (green hydrogen) will be recognized as one of the main trends in future decarbonized energy systems. Green hydrogen can be effectively stored from surplus renewable energy to thus reducing dependency of fossil fuels. As it is entirely produced from renewable sources, green hydrogen generation is strongly affected by intermittent behaviour of renewable generators. In this context, proper uncertain modelling becomes essential for adequately management of this energy carrier. This paper deals with this issue, more precisely, a novel optimal scheduling model for robust optimal scheduling of isolated microgrids is developed. The proposal encompasses a green hydrogen-based storage system and various demand-response programs. Logical rules are incorporated into the conventional optimal scheduling tool for modelling green hydrogen production, while uncertain character of weather and demand parameters is added via interval-based formulation and iterative solution procedure. The developed tool allows to perform the scheduling plan under pessimistic or optimistic point of views, depending on the influence assumed by uncertainties in the objective function. A case study serves to validate the model and highlight the paper of green hydrogen-based storage facilities in reducing fossil fuel consumptions and further exploit renewable sources.

A Hybrid Neutrosophic-Grey Analytic Hierarchy Process Method: Decision-Making Modelling in Uncertain Environments

The analytic hierarchy process (AHP) is recognised as one of the most commonly applied methods in the multiple attribute decision-making (MADM) literature. In the AHP, encompassing uncertainty feature necessitates using suitable uncertainty theories, since dealing efficiently with uncertainty in subjective judgements is of great importance in real-world decision-making problems. The neutrosophic set (NS) theory and grey systems are two reliable uncertainty theories which can bring considerable benefits to uncertain decision-making. The aim of this study is to improve uncertain decision-making by incorporating advantages of the NS and grey systems theories with the AHP in investigating sustainability through agility readiness evaluation in large manufacturing plants. This study pioneers a combined neutrosophic-grey AHP (NG-AHP) method for uncertain decision-making modelling. The applicability of the hybrid NG-AHP method is shown in an illustrative real-case study for agility evaluations in the Iranian steel industry. The computational results indicate the effectiveness of the proposed method in adequately capturing uncertainty in the subjective judgements of decision makers. In addition, the results verify the significance of the research in group decision-making under uncertainty. The practical outcome reveals that, to become a more sustainable agile steel producer in the case country, they should first focus on the “organisation management agility” as the most significant criterion in the assessment followed by “manufacturing process agility,” “product design agility,” “integration of information system,” and “partnership formation capability,” respectively.

Identification, Uncertain Modelling, and Robust Control of Embedded Systems

This paper presents a methodology embodying identification procedures, uncertain modeling, and robust control design of embedded multivariable control systems. Concerning the identification, this methodology involved the determination of probabilistic uncertainty bounds for multivariable plants based on the black box or gray box identification. The bounds obtained were used in the derivation of an uncertain model in the form of upper Linear Fractional Transformation (LFT). This model was used in the robust control design implementing μ-synthesis. The problems arising on the different design stages were illustrated by an example presenting the embedded robust control of a two-input two-output analog model. The plant was identified by using black box and gray box identification methods that produced the necessary information to develop the corresponding uncertainty models. Two discrete-time robust controllers relevant to the two types of identification were designed and embedded in the physical system. Simulation results for the embedded closed-loop system and experimental results obtained by using the robust controllers were compared.

Sliding mode control unified with the uncertainty and disturbance estimator for dynamically positioned vessels subjected to uncertainties and unknown disturbances

When considering the characteristics of a dynamic positioning (DP) vessel involving uncertain modelling and unknown disturbances, the vessel control problem becomes a mismatched nonlinear control issue. To resolve this issue, this paper proposes a control method based on the sliding mode control (SMC) and the uncertainty and disturbance estimator (UDE). The total disturbance in the DP vessel is determined using the UDE, whereas the trajectory tracking function of the vessel is achieved via SMC. Moreover, the estimation error in the UDE and the tracking error of the SMC were found to converge based on the Lyapunov theory. The effectiveness of the proposed control strategy was verified via simulations. A comparative study involving the conventional SMC was also conducted, revealing that the proposed SMC unified with the UDE yielded a considerably superior performance.

Antisymmetric cross-correlation of line-intensity maps as a probe of reionization

We present a new estimator for the cross-correlation signal between line intensity maps to probe the Epoch of Reionization. The proposed estimator is the hitherto neglected antisymmetric component of the cross-correlation, under the exchange of line-of-sight positions. We consider the cross-correlation between HI and CO fluctuations, and forecast the improvement in precision on reionization parameters when the antisymmetric contribution is accounted for. As a way to break the degeneracy between astrophysics and cosmology in the intensity mapping power spectrum, we study the ratio between the antisymmetric and symmetric components. While our results depend on the highly uncertain astrophysical modelling, we show that in most standard scenarios including the antisymmetric contribution as a complementary probe can lead to a significant gain in information.

PRO57 CHALLENGES IN COST-EFFECTIVENESS MODELLING AND VALUE ASSESSMENT OF TREATMENTS IN RARE DISEASES

Studies of orphan drugs typically have inferior clinical evidence compared with treatments in common diseases. This can lead to uncertain cost-effectiveness modelling and difficulties for payers to determine whether an orphan treatment provides value for money. This research aims to identify challenges in cost-effectiveness modelling of rare disease treatments within the United Kingdom (UK) and the United States of America (USA) by reviewing National Institute for Health and Care Excellence (NICE) highly specialised technologies (HST) appraisals and Institute for Clinical and Economic Review (ICER) value assessments. NICE HST guidance and ICER assessments were searched without time limitation through January 15, 2020. While all NICE HST appraisals were included in the analysis, ICER assessments were included only if an indication qualified as a rare disease following the definition of the Rare Disease Act of 2002. Submission documents were then screened in a peer-reviewed process. Twelve NICE HST appraisals and three ICER value assessments in various indications were identified. Across all NICE HST appraisals, limited and uncertain clinical data was the most prevalent issue (12/12). Similarly, all ICER value assessments identified showed limited and uncertain clinical data (3/3). Challenges with quality of life (QoL) assessment was the second most common issue in NICE HST appraisals (7/12) and ICER value assessments (1/3). Less common were technical challenges in cost-effectiveness modelling such as capturing all important aspects of a rare disease within the model structure and difficulties with statistical analysis of trial evidence. Despite these challenges, most NICE HST appraisals resulted in a positive guidance recommendation. Cost-effectiveness modelling of rare disease interventions has several challenges such as limited and uncertain trial data, QoL assessment and technical modelling challenges. NICE has given positive guidance recommendation for most orphan treatments to date contingent upon commercial arrangements with manufacturers reflecting the decision uncertainty.

Structural damage identification with uncertain modelling error and measurement noise by clustering based tree seeds algorithm

This paper proposes a novel structural damage identification approach by using the clustering based Tree Seeds Algorithm, termed as C-TSA, taking into account of both the finite element modeling errors and measurement noise. In order to make the standard TSA more powerful and robust, K-means cluster technique is introduced into the standard TSA before starting the seeds search, which is beneficial to enhance the algorithm’s global optimization performance. The objective function based on the modal data is formulated for structural damage identification. Numerical studies on benchmark functions and a 61-bar truss structure are conducted to investigate the accuracy and robustness of the proposed approach. The finite element modelling errors and noises in the measurement data are considered. Experimental verifications on a laboratory steel frame structure model is conducted to further validate the accuracy of the proposed approach. The results from the numerical and experimental studies are compared with those obtained from several latest evolutionary algorithms. The identification results demonstrate that the proposed approach is more competitive and robust for structural damage identification even considering the modelling errors and measurement noises.

Uncertain risk assessment modelling for bus body manufacturing supply chain using AHP and fuzzy AHP

Abstract This paper purposes the uncertain risk management modelling for the bus body manufacturing supply chain which the principle company releases orders to the sub-contractors and suppliers. Automotive industries is familiar with supply chain production because of there are a lot of part to be produced in short time. Bus body manufacturing companies are performed as a supply chain in Thailand. However, uncertain risk can occur when different companies cooperate for making same products and sharing profits. AHP and FAHP methodology is adopted based on the concept of SCOR model in the boundary of risk management including 5 components; Plan, Source, Delivery, Make and Return. The empirical study has studied by the 6 companies.

Regional water resources assessments using an uncertain modelling approach: The example of Swaziland

Study regionThe 5 river basins that flow through or within Swaziland in southern Africa. Study focusA regional water resource assessment using an uncertainty version of the Pitman monthly rainfall-runoff model whose outputs are constrained by six indices of natural hydrological response (mean monthly runoff, mean monthly groundwater recharge, Q10, Q50 and Q90 percentage points of the flow duration curve and% time of zero flows) for each of the 122 sub-basins within the whole of Swaziland. A 2-step approach is adopted where the first step establishes behavioural, but uncertain, model parameter ranges for natural incremental sub-basin hydrological responses, while the second step links all the sub-basin outputs to generate cumulative sub-basin outflows and allows for water use parameters to be included. New hydrological insights for this regionThe analysis of hydrological indices highlights the regional variations in hydrological processes and sub-basin response. The adopted modelling approach provides further insight into all of the uncertainties associated with quantifying the available water resources of Swaziland. The study has provided more insight into the spatial variability of the hydrological response and existing development impacts than was previously available. These new insights should provide an improved basis for future water management in Swaziland.

Backstepping-based model reference adaptive controller for a multi-axial system in the presence of external disturbance and saturated input

This paper presents a backstepping-based model reference adaptive controller for a multi-axial system in the presence of external disturbance and saturated input. The proposed controller synthesizes the backstepping technique and the model reference adaptive control method to construct control inputs for recursive structure and uncertain modelling of the multi-axial system. To cope with the limit of saturated input, an auxiliary system is adopted. A dead-zone modification is introduced to avoid the drift phenomenon of adjusted adaptive parameters. The stability of the proposed controller is proven by Lyapunov’s theory while considering the effect of the auxiliary system and the dead-zone modification in the design stage. The effectiveness and performance of the proposed controller are evaluated by experiment on a transformer winding system.

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

This paper proposes an uncertain modelling and computational method to analyze dynamic responses of rigid-flexible multibody systems (or mechanisms) with random geometry and material properties. Firstly, the deterministic model for the rigid-flexible multibody system is built with the absolute node coordinate formula (ANCF), in which the flexible parts are modeled by using ANCF elements, while the rigid parts are described by ANCF reference nodes (ANCF-RNs). Secondly, uncertainty for the geometry of rigid parts is expressed as uniform random variables, while the uncertainty for the material properties of flexible parts is modeled as a continuous random field, which is further discretized to Gaussian random variables using a series expansion method. Finally, a non-intrusive numerical method is developed to solve the dynamic equations of systems involving both types of random variables, which systematically integrates the deterministic generalized-α solver with Latin Hypercube sampling (LHS) and Polynomial Chaos (PC) expansion. The benchmark slider-crank mechanism is used as a numerical example to demonstrate the characteristics of the proposed method.

Economic Evidence of Pneumococcal Vaccination in Older Adults: Uncertain Modelling or Competitive Tendering?

Diseases caused by Streptococcus pneumonia contribute considerably to morbidity and mortality worldwide [1]. The main types of illness are grouped as bacteremic pneumococcal pneumonia (BPP) and non-bacteremic pneumococcal pneumonia (NBPP), the latter causing less serious manifestations [1, 2]. Pneumococcal vaccination for infants has been widely debated in the last decade following the launch of the new and expensive conjugate vaccines (PCVs); unlike the old and cheap 23-valent polysaccharide vaccine (PPV23), PCV vaccines are immunogenic in children under 2 years of age [3]. Lately, the debate has shifted to the extension of PCV13 (the only PCV approved for adults) to at-risk and older adults instead of PPV23, which is still adopted in many European countries for campaigning on this population target. This hot debate [4, 5] is fuelled by two crucial issues that are still uncertain. First, although PPV23 has been shown to be effective in older adults, the extent and especially the duration of its protection are still doubtful [6, 7]. Second, vaccination of infants with PCVs (unlike with PPV23) provides herd immunity that has an impact on serotype replacement [8] and thus prevents disease in all ages [9], elderly included. Against this background, economic evaluations (EEs) of pneumococcal vaccines for adults published so far have had to rely on many assumptions [4, 10]. Very recently, the CAPiTA (Community-Acquired Pneumonia Immunization Trial in Adults) study (a Dutch clinical trial supported by the manufacturer) [11] showed that PCV13 is efficacious in preventing two thirds of BPP (75 %) and around half the NBPP (45 %) cases in older adults. The Spanish CAPAMIS (Community-Acquired Pneumonia, Acute Myocardial Infarction and Stroke) cohort study [12] (funded by public authorities) confirmed that PPV23 is effective against both BPP (62 %) and NBPP (48 %) in adults C60 years [5], although only for up to 5 years after vaccination. Here we critically review the most recent EEs published in the EU focussed on the elderly, to assess their potential contribution to public decision making and examine whether sponsorship by manufacturers influenced the results, as happened for studies focussed on infants [13].

Uncertain hydrological modelling: application of the Pitman model in the Great Ruaha River basin, Tanzania

Uncertainty analysis has become the standard approach to hydrological modelling, but has yet to be effectively used in practical water resources assessment. This study of the Great Ruaha River basin in Tanzania is based on the use of regional estimates of mean runoff, groundwater recharge and three flow points on flow duration curves (FDCs) to constrain ensemble outputs from the Pitman monthly model using Monte Carlo parameter sampling. The constraint bounds were quantified from gauged data available for 26 sub-basins together with assumptions about the spatial variations in hydrological response using limited physical sub-basin property and climate data. The results are encouraging in that the simulated FDC ranges bracket the observed curves at two gauging stations downstream of many ungauged sub-basins that are important sites for water resources development decision making. Further work is required to refine the constraint bounds, the input parameter sets and climate data and achieve a more robust model of the basin.Editor D. Koutsoyiannis; Guest editor G. Mahé

Design of robust minimum variance controller using type-2 fuzzy set

This paper presents a control strategy for achieving a robust minimum variance controller (MVC) by modelling uncertainty using a type-2 fuzzy set and satisfying H∞ norm specifications. In this paper, an MVC is designed considering three types of structural, parametric and algorithmic uncertainties. Thus, an interval type-2 fuzzy set is utilized. This paper utilizes one method to construct interval type-2 fuzzy set models by the uncertain interval data and model error modelling approach. In addition, a sufficient condition is developed that guarantees the stability and robustness of the controller. The design of a robust generalized MVC by the identified model is presented. Finally, an experimental test is used to clarify the effectiveness of the proposed control scheme. The proposed method (omitting uncertainty of the linear model) considerably decreases output variance from 0.15 to 0.0018.

The dark matter distribution in the spiral NGC 3198 out to 0.22Rvir

We use recent very extended HI kinematics (out to 48 kpc) along with previous H$\alpha$ kinematics of the spiral galaxy NGC 3198 in order to derive its distribution of dark matter (DM). First, we used a chi-square method to model the rotation curve (RC) of this galaxy in terms of different profiles of its DM distribution: the universal rotation curve (URC) mass model (stellar disk $+$ Burkert halo $+$ gaseous disk), the NFW mass model (stellar disk $+$ NFW halo $+$ gaseous disk) and the baryon $\Lambda$CDM mass model (stellar disk $+$ NFW halo modified by baryonic physics $+$ gaseous disk). Second, to derive the DM halo density distribution, we applied a new method that does not require a global and often uncertain mass modelling. While according to the standard method, both URC and NFW mass models can account for the RC, the new method instead leads to a density profile that is sharply disagrees with the dark halo density distribution predicted within the Lambda cold dark matter ($\Lambda$CDM) scenario. We find that the effects of baryonic physics modify the original $\Lambda$CDM halo densities in such a way that the resulting profile is more compatible with the DM density of NGC 3198 derived using our new method. However, at large distances, r $\sim$ 25 kpc, also this modified baryon $\Lambda$CDM halo profile appears to create a tension with the derived DM halo density.