Interval Analysis Research Articles

A study on the solution of interval linear fractional programming problem

Interval linear fractional programming problem (ILFPP) approaches uncertain-ties in real-world systems such as business, manufacturing, finance, and eco-nomics. In this study, we propose solving the interval linear fractional pro-gramming (ILFP) problem using interval arithmetic. Further, to construct the problem, a suitable variable transformation is used to form an equivalent ILP problem, and a new algorithm is depicted to obtain the optimal solution with-out converting the problem into its conventional form. This paper compares the range, solutions, and approaches of ILFP with fuzzy linear fractional pro-gramming (FLFP) in solving real-world optimization problems. The illustrated numerical examples show a better range of interval solutions on practical appli-cations of ILFPs and uncertain parameters.

From physiological complexity to data interactions-A case study of recordings from exercise monitoring.

The popularity of nonlinear analysis has been growing simultaneously with the technology of effort monitoring. Therefore, considering the simple methods of physiological data collection and the approaches from the information domain, we proposed integrating univariate and bivariate analysis for the rest and effort comparison. Two sessions separated by an intensive training program were studied. Nine subjects participated in the first session (S1) and seven in the second session (S2). The protocol included baseline (BAS), exercise, and recovery phase. During all phases, electrocardiogram (ECG) was recorded. For the analysis, we selected corresponding data lengths of BAS and exercise usually lasting less than 5 min. We found the utility of the differences between original data and their surrogates for sample entropy Sdiff and Kullback-Leibler divergence KLDdiff. Sdiff of heart rate variability was negative in BAS and exercise but its sensitivity for phases discrimination was not satisfactory. We studied the bivariate analysis of RR intervals and corresponding QT peaks by Interlayer Mutual Information (IMI) and average edge overlap (AVO) markers. While the IMI parameter decreases in exercise conditions, AVO increased in effort compared to BAS. These findings conclude that researchers should consider a bivariate analysis of extracted RR intervals and corresponding QT datasets, when only ECG is recorded during tests.

Economic Development Drives Massive Global Estuarine Loss in the Anthropocene

AbstractEstuaries have great ecological and economic value and sustain both population and economic growth. Global‐scale analyses suggest that human activities drive estuarine area change but these projections neglect direct human‐estuary interactions and socio‐economic feedbacks. Here, we quantified area changes of 2,396 estuaries in response to recent human impacts (e.g., land reclamation, estuarine dam construction) and economic development between 1984 and 2019, and find that estuarine area shrank by 5,372 km2 whereas upland submergence created 5,015 km2 of estuarine area elsewhere. Approximately 44% (n = 1,046) of today's estuaries have been directly altered through land reclamation, estuarine dam construction, or a combination of both, and ∼250,000 acres (1,027 km2) of estuarine area have been directly converted to urban or agricultural fields. Nearly 90% (923 km2) of land reclamation occurred in Asia linked to recent advances in economic development during the middle‐income stage. Additional historical mapping and 5‐year interval analyses revealed that while human alterations were insignificant during the low‐income stages, estuaries were predominantly altered during their middle‐income stages, where estuarine degradation is a common consequence of economic growth. However, this trend stabilizes in high‐income countries with the adaption of conservation laws and policies. Together, our results indicate that large‐scale estuarine loss can be avoided by preserving estuaries in low‐ and mid‐income countries in the early stages of economic development.

Radial growth response of Pinus Yunnanensis to climate in high mountain forests of northwestern Yunnan, southwestern China

Understanding the relationship between tree growth and environmental conditions is essential to elucidating the impact of global climate change on forest ecosystems. We used the dendrochronology method to examine the growth sensitivity of a typical conifer to climate change in mountain forests of Central Hengduan Mountain. The study involved the establishment of tree ring width chronologies of Pinus yunnanensis in both Haba Snow Mountain (HB) and Yulong Snow Mountain (YL) in northwestern Yunnan, enabling the detection of the relationship between its radial growth and climates, i.e., monthly total precipitation, monthly temperatures (average minimum, mean and maximum) and monthly Palmer Drought Severity Index (PDSI). Response function and redundancy analysis (RDA) were used to identify correlations between climate variables and radial growth, and moving interval analysis was applied to determine the stability of climate-growth relationship. The findings demonstrated that the growth of P. yunnanensis had similar response patterns to climate change at two sites, exhibiting growth synchronization and common signals. Specifically, the radial growth of P. yunnanensis was negatively correlated with May temperature, while temperature in current October significantly promoted radial growth. Precipitation in June was the common climate variable with inverse effects between two sites, with positive impacts on YL and negative impacts on HB. The results of moving interval analysis were consistent with response function and RDA, presenting significant correlations in many years for those climatic variables significantly affecting tree growth. Stability analysis also revealed that the climate-growth relationship could fluctuate over a small range of time scales, induced by an abrupt change in climate. A forecast of strengthen in growth of P. yunnanensis forests was expected, since increases in precipitation and temperature of most months would benefit tree growth, and negative impacts of May temperature would be offset by the increase of precipitation in the corresponding month. These results could provide a basis for developing sustainable strategies of forest management under the climate change.

HyperCube: Implicit Field Representations of Voxelized 3D Models (Student Abstract)

Implicit field representations offer an effective way of generating 3D object shapes. They leverage an implicit decoder (IM-NET) trained to take a 3D point coordinate concatenated with a shape encoding and to output a value indicating whether the point is outside the shape. This approach enables the efficient rendering of visually plausible objects but also has some significant limitations, resulting in a cumbersome training procedure and empty spaces within the rendered mesh. In this paper, we introduce a new HyperCube architecture based on interval arithmetic that enables direct processing of 3D voxels, trained using a hypernetwork paradigm to enforce model convergence. The code is available at https://github.com/mproszewska/hypercube.

Automatic initial value generation procedure for nonlinear process models by interval arithmetic based cutting and splitting

To solve large nonlinear equation systems, we present a hybrid method based on interval arithmetic and real-valued root-finding. The proposed approach includes two new interval arithmetic based methods, the so-called cutting and a special kind of bisection of consistent variable spaces. Applied to three examples from chemical engineering, it is shown that the approach is now able to find all system solutions within a variable space as well as only one process-relevant solution in much less time thanks to the built-in root-finding step. For the latter, a conventional Newton method as well as IPOPT have been examined. The hybrid approach no longer needs a well-estimated initial point to converge to a solution, only rough initial variable bounds are required.

Application of tropical optimization for solving multicriteria problems of pairwise comparisons using log-Chebyshev approximation

We consider a decision-making problem to find absolute ratings of alternatives that are compared in pairs under multiple criteria, subject to constraints in the form of two-sided bounds on ratios between the ratings. Given matrices of pairwise comparisons made according to the criteria, the problem is formulated as the log-Chebyshev approximation of these matrices by a common consistent matrix (a symmetrically reciprocal matrix of unit rank) to minimize the approximation errors for all matrices simultaneously. We rearrange the approximation problem as a constrained multiobjective optimization problem of finding a vector that determines the approximating consistent matrix. The problem is then represented in the framework of tropical algebra, which deals with the theory and applications of idempotent semirings and provides a formal basis for fuzzy and interval arithmetic. We apply methods and results of tropical optimization to develop a new approach for handling the multiobjective optimization problem according to various principles of optimality. New complete solutions in the sense of the max-ordering, lexicographic ordering and lexicographic max-ordering optimality are obtained, which are given in a compact vector form ready for formal analysis and efficient computation. We present numerical examples of solving multicriteria problems of rating four alternatives from pairwise comparisons to illustrate the technique and compare it with others.

An extended moment-based trajectory accuracy reliability analysis method of robot manipulators with random and interval uncertainties

This paper proposes a novel trajectory accuracy reliability analysis method with random and interval variables to evaluate the impact of mixed uncertainties on the motion performance of robot manipulators. To effectively and accurately solve the hybrid reliability model, the interval analysis is first conducted on the positional error model established by differential kinematics, and a maximum positional error searching algorithm is developed based on geometric transformation and cell enumeration. Then, the trajectory accuracy reliability model is reconstructed by the eigen-decomposition technique, which further incorporates the adaptive weight vector-based anisotropic sparse-grid quadrature approach to derive the statistical moments of maximum positional error. Afterward, by matching with the cumulants of the original reliability model, a novel approximation method is proposed based on the Weibull distribution and minimized matching error model to complete the trajectory accuracy reliability analysis. The practicality and advantages of the proposed method are demonstrated by two illustrative examples of 6-degrees-of-freedom robot manipulators. Comparative results affirm that the proposed method outperforms existing state-of-the-art algorithms in terms of accuracy and efficiency for trajectory accuracy reliability analysis encompassing random and interval uncertainties. Overall, the outcomes of this paper contribute significantly to the design and analysis of safety and reliability in moving machinery.

Tri-fuzzy interval arithmetic with deep learning and hybrid statistical approach for analysis and prognosis of cardiovascular disease

Tri-fuzzy interval arithmetic with deep learning and hybrid statistical approach for analysis and prognosis of cardiovascular disease

ANALYSIS OF THE MAGAMP POWER CONVERTER STABILITY TAKING INTO ACCOUNT OF THE INTERVAL UNCERTAINTY OF THE MAGAMP CORES PARAMETERS

To ensure the functioning of radio electronic equipment (RAE), semiconductor power converters (NPEs) are used, which perform the functions of converting and adjusting the parameters of electrical energy. The modern consumer needs NPEs with a rigid set of operational characteristics - ensuring functional parameters in a wide range of changes in all disturbing factors. The existing principles of NPE construction do not always allow such a set of characteristics to be realized. The article analyzes the stability of the pulse voltage stabilizer based on high-frequency magnetic amplifiers, taking into account the technological spread of their core parameters. The circuit of the voltage stabilizer is presented, its operation is described, the principle of operation of the high-frequency magnetic amplifier is disclosed, and its transfer function in the frequency domain is found. The study is based on the use of interval analysis theory. The conducted analysis of the stability of the NPE, taking into account the interval uncertainty of the parameters of the cores of high-frequency magnetic amplifiers, confirmed their performance both with technological dispersion of the parameters of the cores and with a wide range of changes in all disturbing factors, including the parallel operation of voltage stabilizers on a common load.

Risk assessment of water inrush accident during tunnel construction based on FAHP-I-TOPSIS

This study introduces an innovative risk assessment method, namely FAHP-I-TOPSIS, for evaluating water inrush risks during tunnel construction. Its primary objective is to address the challenges posed by various fuzzy and uncertain factors in risk assessment, aiming to enhance the reliability of on-site risk evaluation. The method combines the Fuzzy Analytic Hierarchy Process for weight calculation and the Ideal Solution Similarity Ranking Preference Interval Technique for risk interval computation. Firstly, a comprehensive risk assessment framework is established, categorizing factors influencing tunnel water inrush into geological factors (Ni), construction technology and management (Mi), and the inherent vulnerability of the tunnel itself (Vi). These three indicator layers are further subdivided based on corresponding risk factors. The method is applied to the risk analysis of water inrush in the Shijingshan Tunnel in Zhuhai, analysing the risk weights of 16 influencing factors. It is observed that cracks and fault zones have the most significant impact on the occurrence of the incident. Through a comparison with traditional TOPSIS and VIKOR methods, which calculate a single risk value, the study demonstrates that FAHP-I-TOPSIS effectively integrates various fuzzy and uncertain factors, providing a reasonable level of risk assessment. It enhances adaptability to on-site errors, significantly improving the robustness of water inrush risk assessment during tunnel construction and sustainable management.

Combustion Characteristics of a Hydrogen-Fueled TJI Engine under Knocking Conditions

The use of a two-stage combustion system in a hydrogen-fueled engine is characteristic of modern internal combustion engines. The main problem with hydrogen combustion in such systems is knocking combustion. This paper contains the results of research under knock combustion conditions with a single-cylinder internal combustion engine equipped with a turbulent jet ignition system (TJI). A layout with a passive pre-chamber and a variable value of the excess air ratio range λ = 1.25–2.0 with a constant value of the center of combustion (CoC = 4 deg) after top dead center (TDC) was used. Two indicators of knock combustion were analyzed: maximum oscillation of pressure and the Mahle Knock Index. Analyses were also carried out taking into account the rate of heat release and the amount of heat released. As a result of the investigation, it was found that knock combustion occurs intensively at small values of the air excess ratio. Hydrogen knock combustion disappears for λ = 2.0 and greater. The pressure oscillation index was found to be more applicable, as its limiting value (>1 bar) allows easy diagnosis of knock combustion. The Mahle Knock Index is a quantity that allows interval analysis of the knock. The choice of classes and weighting coefficients requires an iterative operation, as they strictly depend on engine characteristics, load, and knock magnitude.

Computation of prediction intervals for forest aboveground biomass predictions using generalized linear models in a large-extent boreal forest region

Abstract Remotely sensed data have an important application for estimation of forest variables, e.g. height, volume, and aboveground biomass (AGB). The increased use of remotely sensed data implemented along with model-based inference has shown improved efficiency in prediction and mapping of such forest variables. In this study, plot-level airborne laser scanning data and Swedish National Forest Inventory field reference data were used to predict AGB using generalized linear models (GLMs) assuming Gamma and Tweedie distributions for the field observed AGB. The GLMs were selected considering the convenience of not correcting transformation bias as it is required in other regression models with transformed response variable. To overcome the challenge in providing reliable uncertainty estimates for the estimated forest variable map products at individual pixel-scale, we focused on computing 95% prediction intervals (PIs) for Gamma and Tweedie GLMs with a square root link function. The relative uncertainties were computed as the ratio between the half-width of the PIs and the predicted AGBs. The AGB-airborne laser scanning models were developed with root mean square error values of 22.6 Mgha−1 (26%) and 21.7 Mgha−1 (25%), respectively, for the Gamma and Tweedie GLMs. Two methods were applied to compute PIs for the Gamma GLM, one using the R package ‘ciTools’ and another derived through asymptotic theory. It was found that the 95% PIs computed using ‘ciTools’ had the most accurate coverage probability in comparison to the other method. An extended version of these PIs was also utilized for the Tweedie GLMs. The range of PIs associated with the prediction of AGB were narrower for lower predicted AGB values compared with the length of higher predicted AGB values. Comparing the two fitted models, the Gamma GLM showed lower relative uncertainties for the lower range of predicted AGBs, whereas the Tweedie GLM showed lower relative uncertainties for the higher range of predicted AGBs. Overall, the Tweedie GLM provided a better model fit for AGB predictions.

Interval analysis of the small‐signal stability of grid‐connected voltage‐source converter system considering multiparameter uncertainty

AbstractGrid‐connected voltage source converters (VSCs) have been broadly applied in modern power system. However, instability issues may be triggered by the integration of grid‐connected VSCs, jeopardising the operation of the power grid. Conventional stability analysis methods can be utilised to derive system stability margins under nominal conditions. Whereas grid‐connected VSCs inevitably operate under multiparameter uncertainty, which may result in overly optimistic or even incorrect estimations of stability margins, thereby posing potential risks to system operation. To address this issue, an interval small‐signal stability analysis approach is proposed to investigate the system stability under multiparameter uncertainty. First, the interval state‐space model of the grid‐connected VSC system is constructed based on interval symbolic linearisation. Furthermore, the interval eigenvalue decomposition is introduced to calculate the interval eigenvalue distribution of the interval state‐space model. Eventually, the upper bounds of the real part of the dominant interval eigenvalues are utilised for deriving interval stable parameter regions. Results of Monte Carlo analysis and time‐domain simulations of the grid‐connected VSC system are utilised to verify the effectiveness of the proposed interval stability analysis method.

An extension of fuzzy TOPSIS approach using integral values for banking performance evaluation

Banks play a crucial role as financial intermediaries in advancing economies. Increasing market share is a top priority for all banks in today's fiercely competitive market. To achieve this, banks are expected to enhance their efficiency, which boosts their competitive capacity and helps decision-makers identify areas for development. This paper introduces an extended fuzzy TOPSIS approach that incorporates integral values to assess banking performance. Our method includes the averaging and normalization of decision-makers assigned ratings and weights, ensuring a standardized scale for comparison. Subsequently, we create membership functions for the ultimate fuzzy evaluation values of alternatives using interval arithmetic for fuzzy numbers. We employ a novel fuzzy number ranking method based on integral values to streamline the aggregation of fuzzy numbers to defuzzify the weighted ratings. Ultimately, we introduce a closeness coefficient for determining the ranking order of alternatives by computing their distances to both the positive and negative ideal solutions. To illustrate the effectiveness and applicability of our proposed method, we present an application example.

Estimating the coverage measure and the area explored by a line-sweep sensor on the plane

This paper presents a method for determining the area explored by a line-sweep sensor during an area-covering mission in a two-dimensional plane. Accurate knowledge of the explored area is crucial for various applications in robotics, such as mapping, surveillance, and coverage optimization. The proposed method leverages the concept of coverage measure of the environment and its relation to the topological degree in the plane, to estimate the extent of the explored region. In addition, we extend the approach to uncertain coverage measure values using interval analysis. This last contribution allows for a guaranteed characterization of the explored area, essential considering the often critical character of area-covering missions. Finally, this paper also proposes a novel algorithm for computing the topological degree in the 2-dimensional plane, for all the points inside an area of interest, which differs from existing solutions that compute the topological degree for single points. The applicability of the method is evaluated through a real-world experiment.

Association Between Monocyte-to-High-Density Lipoprotein Ratio and Prediabetes: A Cross-Sectional Study in Chinese Population.

The monocyte-to-high-density lipoprotein cholesterol (MHR) ratio has been linked to metabolic disorders. However, there is limited research on the predisposition to MHR and prediabetes. Hence, we conducted a study to investigate the relationship between MHR and the prevalence of prediabetes. In total, 85,293 participants were included in our cross-sectional observational study. Multivariable regression analysis, subgroup analyses, and interaction testing were used to determine the relationship between MHR and prediabetes. To explore the non-linear association of MHR with prediabetes risk, generalized additive model (GAM) and smoothing splines were applied. The threshold effect analysis of MHR on the risk of prediabetes was further employed to identify the turning point. After controlling for covariates, the results indicated that a positive correlation persisted between MHR and prediabetes (odds ratio (OR) =1.64, 95% confidence interval (CI), 1.48-1.82), and subgroup analyses found a more robust correlation between MHR and prediabetes in individuals with lower age, SBP, DBP, TG, TC and higher values of BMI and LDL-C than in their counterparts. Additionally, the correlation between MHR and the risk of prediabetes was found to be non-linear, with a turning point of -0.4 (Log-Likelihood Ratio, P< 0.001). The impact of variables on the two sides of the turning point were 1.94 (1.72, 2.19) and 0.88 (0.69, 1.14). The positive correlation between MHR and the risk of prediabetes in Chinese participants was observed to be non-linear, and MHR ≤ -0.4 was strongly positively correlated with prediabetes risk.

Perceived Participation to Kindergartens, Teachers, and Parents of Physical Education in Xi’an, Shaanxi Province, China

Background and Aim: This study addresses the scarcity of empirical evidence on children's participation in Physical Education (PE) and the perspectives of teachers and parents within the Chinese context. The study aims to determine the level of student engagement in PE and identify factors influencing their participation. It also seeks insights into how teachers and parents view PE's importance in children's well-being. Materials and Methods: Conducted in Xi'an, Shaanxi Province, China, the study involved 201 kindergartens, 200 parents, and 65 teachers. Analytical methods included tables, frequencies, percentages, mean proportion analysis, standard deviation proportion analysis, confidence interval analysis, one-sample z-score test for proportion, two-sample z-score test for proportion, and correlation analysis. The research also led to the development of a guide for creating a kindergarten's physical literacy model. Results: Kindergartens exhibit a moderate perception of PE, with males generally having a higher perception than females. Teachers view PE positively, considering it moderately beneficial for physical and mental development. However, barriers to teaching PE include limited event space, security concerns, venue and equipment issues, weather-related inconveniences, and parents' lack of sports proficiency. Parents have a favorable view of PE, acknowledging its positive impact. Barriers for parents include safety concerns, extracurricular workloads, limited interest in after-school sports, venue limitations, and academic pressures. Kindergartens express enthusiasm for sports like basketball and football, but challenges may reduce physical activity and lead to frustration. Conclusion: The perception of physical education in kindergartens varies among different stakeholders, with gender differences and positive attitudes from teachers and parents. However, numerous barriers, including space limitations and safety concerns, need to be addressed to ensure a more effective and enjoyable PE experience for children in this educational setting.

Atrial fibrillation ablation workflow optimization facilitated by high-power short-duration ablation and high-resolution mapping.

Pulmonary vein isolation (PVI) for catheter ablation of atrial fibrillation (AF) is a time-demanding procedure. High-power short-duration (HPSD) ablation protocols and high-density mapping catheters have recently been introduced to clinical practice. We investigated the impact of high-density mapping and HPSD ablation protocols on procedural timing, efficacy, and safety by comparing different standardized set-ups. Three electrophysiology (EP) laboratory set-ups were analysed: (i) circular catheter for mapping and HPSD ablation with 30/35 W guided by an ablation index (AI); (ii) pentaspline catheter for mapping an HPSD ablation with 50 W guided by an AI; and (iii) pentaspline catheter for mapping and HPSD ablation with 90 W over 4 s using a novel ablation catheter. All patients underwent PVI without additional left atrial ablation strategies. Procedural data and operating intervals in the EP laboratory were systematically analysed. Three hundred seven patients were analysed (30/35 W AI: n = 102, 50 W AI: n = 102, 90 W/4 s: n = 103). Skin-to-skin times [105.3 ± 22.7 (30/35 W AI) vs. 81.4 ± 21.3 (50 W AI) vs. 69.5 ± 12.2 (90 W/4 s) min, P ≤ 0.001] and total laboratory times (132.8 ± 42.1 vs. 107.4 ± 25.7 vs. 95.2 ± 14.0 min, P < 0.001) significantly differed among the study groups. Laboratory interval analysis revealed significant shortening of mapping and ablation times. Arrhythmia-free survival after 12 months was not different among the study groups (log-rank P = 0.96). The integration of high-density mapping and HPSD protocols into an institutional AF ablation process resulted in reduced procedure times without compromising safety or efficacy.

Analisis keterampilan komunikasi peserta didik dalam pembelajaran fisika SMA di Yogyakarta

The purpose of this research is to find out how communication skills are used in physics learning for class X students in Yogyakarta. The research method used in this study is a qualitative descriptive method. The ordinal data for filling out the questionnaire was changed using the successive interval analysis method with the help of Microsoft Excel. Data were analyzed by calculating using the average and standard deviation. The results of data analysis show that students' communication skills in physics learning are in the medium category. There were 3 students with high communication skills category, 26 students with medium communication skills category, and 4 students with low communication skills category. The average score of all indicators is in the category of both oral and written communication skills. Therefore, students' communication skills, both oral and written, still need to be improved