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In this work, the dynamic responses of an uncertain flexible shaft-disk-drum rotor under elastic support and connection are investigated, where uncertain parameters are considered as unknown but bounded interval variables. The energy method is used to derive deterministic analytical model for the flexible shaft-disk-drum rotor, which is validated by modal tests. A non-intrusive interval method based on Chebyshev polynomial approximation is introduced to evaluate the uncertain dynamic response of the flexible shaft-disk-drum rotor system. Comparative studies of Monte Carlo simulation, scanning method and the interval method are conducted to illustrate the validity and accuracy of the approach proposed here. [ABSTRACT FROM AUTHOR]

In order to take uncertain factors of welding process into account, a dissipated energy-based interval fatigue life estimation approach is presented in this paper. The infrared thermography fatigue life tests are conducted on the specimens of butt-welded joints and cruciform welded joints. Then, the dissipated energy-based interval fatigue life prediction model is built, while interval fatigue parameters are determined and interval curve of asymptotic dissipated energy and fatigue life is obtained. The lifetime assessment of cruciform welded joints based on the suggested model is performed, and the predicted results agree well with the experimental data. [ABSTRACT FROM AUTHOR]

Interference fit is often used in rotating machinery to transmit torque and force. The actual interference value is uncertain due to factors such as manufacturing errors and operating conditions, resulting in a gap between the response of the system and theoretical results. Therefore, the interval method is used to study the magnetically suspended dual-rotor system (MSDS) with uncertainty of interference-fit value. Firstly, a theoretical model of the MSDS was established using the finite element method, and the influence mechanism of the interference value on the rotor bending stiffness was derived. Then, the rotor stiffness range was obtained from the uncertain range of interference value. Finally, the dynamic response of the MSDS was studied based on the Chebyshev interval method. The research results indicate that the uncertainty of interference value has an effect on the vibration response of the MSDS. The vibration response of the system is most affected near the first-order bending critical speed, and the effect on rotor response is relatively small in other angular speed regions. The research results can provide a basis for the design of rotor systems. [ABSTRACT FROM AUTHOR]

The purpose of this classroom action research was to improve table tennis candy skills through the use of the interval training method in students of class XI IPA 4 semester 2 SMA Negeri 3 Sukoharjo in the academic year 2021/ 2022. This research is a type of classroom action research, with research subjects being students of class XI IPA 4 semester 2 SMA Negeri 3 Sukoharjo in the academic year 2014/2015. The source of the data came from observations of table tennis training activities through the interval training method. Data collection techniques used observation methods, test formats, questionnaires and point documentation. Data analysis techniques used cycle points consisting of two cycles with steps including planning, evaluation and reflection. Performance indicators include the results of the table tennis skill test using the backboard test and students' interest or motivation in participating in the training program using the interval method. The results showed that the interval training method in the game of table tennis carried out by the researcher showed the results of cycle 1: students' skills were in the moderate category 11 students, 14 students were lacking and 7 students were not very low. Cycle 2 results: showed student skills in the security guard category 13 students, category good 11 students and very good category 8 students. Getting to the point of increasing students' skills in playing table tennis based on class XI IPA 4 semester 2 SMA Negeri 3 Sukorejo in the 2021/ 2022. academic year, this is evident from the results of research conducted in two cycles, namely the results of hitting students right on target that have been determined have increased from the test results cycle I with the results of the test cycle II.

This article discusses a study that introduces an interval method for evaluating Armenia's export dynamics in uncertain economic contexts. The study focuses on export forecasts and interval forecasts to improve accuracy in assessing economic indicators during uncertainty. The analysis shows that the EAEU market offers more favorable export growth compared to the global market during uncertainty, and the interval method significantly improves forecast accuracy. The research highlights the importance of prioritizing trade relations with specific countries and the economic significance of finished product exports. It provides insights into Armenia's export-oriented growth prospects and offers a practical guide for policymakers, emphasizing the importance of modernization, collaboration, and economic competitiveness, particularly in smaller economies. [Extracted from the article]

Hypertension is a frequent diagnosis in power athletes.Aim. To assess the effect of increased muscle oxidative capacity on blood pressure in athletes with arterial hypertension from powersports, heavy weight categories.Material and methods. The study was conducted at the Department of Sports Medicine of the Russian State University of PhysicalCulture, Sports, Youth and Tourism and lasted 180 days. The study involved 65 representatives of strength sports (weightlifting), heavyweight categories with arterial hypertension. Athletes were randomized into two main groups: the HIIT (High Intensity Interval Training,n=23) group, the MICE (Moderate Intensity Continuous Exercise, n=22) group and the RT (Resistance Training, n=20) control group. Thefollowing methods were used to achieve the aim of the study: ergospirometry, muscle tissue oxygenation level measurement, bloodpressure measurement and methods of mathematical statistics. Athletes in the main groups trained for 180 days (3 times per week) ona cycle ergometer using a high-intensity interval and uniform protocol, and participants in the control group trained for 180 days (3times per week) according to their traditional strength protocol.Results. After 180 days of physical rehabilitation, participants of the main groups had increased oxygen consumption at the anaerobicthreshold, decreased thigh muscle oxygenation and increased maximum oxygen consumption, resulting in an average decrease insystolic blood pressure of 11.1 mm Hg and diastolic blood pressure of 11.2 mm Hg in the intervention groups.Conclusion. The physical rehabilitation systems we have developed for power athletes allow us to effectively and safely influence theoxidative capacity of working muscles and blood pressure, but the time spent by athletes on non-specific training activities in the HIITsystem is 38% less.

Interference fit is often used in rotating machinery to transmit torque and force. The actual interference value is uncertain due to factors such as manufacturing errors and operating conditions, resulting in a gap between the response of the system and theoretical results. Therefore, the interval method is used to study the magnetically suspended dual-rotor system (MSDS) with uncertainty of interference-fit value. Firstly, a theoretical model of the MSDS was established using the finite element method, and the influence mechanism of the interference value on the rotor bending stiffness was derived. Then, the rotor stiffness range was obtained from the uncertain range of interference value. Finally, the dynamic response of the MSDS was studied based on the Chebyshev interval method. The research results indicate that the uncertainty of interference value has an effect on the vibration response of the MSDS. The vibration response of the system is most affected near the first-order bending critical speed, and the effect on rotor response is relatively small in other angular speed regions. The research results can provide a basis for the design of rotor systems.

In this study, we derive certain features of a novel fractional derivative of two variables presented lately by Chinchole and Bhadane using a Mittag-Leffler kernel. Initially, It is given how to compute the fuzzy set value function's fractional derivative of the SABC. Hence, it is utilized to show that a solution to a fuzzy fractional differential equation involving the SABC fractional derivative exists and is unique. An example is presented and solved for further illustration. [ABSTRACT FROM AUTHOR]

Statistical equations are widely used to describe the laws of various chemical technological processes. The values of constants and parameters included in these equations are determined by various methods. Methods that can determine the values of equation parameters using a limited amount of experimental data are of particular practical interest. In this manuscript, we propose a method to obtain simplex-interval equations. The proposed approach can be effectively used to control the values of technological process parameters. In this paper, we consider examples of chemical kinetics equation transformations and heterogeneous processes of solid particle dissolution. In addition, we describes mathematical model transformations, including equations for functions of the residence time distribution (RTD) of apparatus particles, the distribution of particles by size, etc. Finally, we apply the proposed approach to an example involving modeling of the calcination of coke in a tubular rotary kiln. [ABSTRACT FROM AUTHOR]

In consideration of uncertainties of material characteristics and its welding and forming process, an interval strain energy density method for predicting fatigue life of dissimilar lightweight metal welded joints was presented in this paper. Firstly, the mechanical performance parameters and fatigue properties of welded joints with parental material aluminum alloy 5083H111 and 5754 were obtained by experimental work. Based on the interval number approach, the interval relationship between the elastic and plastic strain energy density and fatigue life was constructed, including lower and upper interval bounds. Then, a finite element model of the dissimilar lightweight metal cross welded joint was generated to calculate the stress-strain response curve under cyclic loadings through the non-linear finite element analysis. The predicted lifetime and failure location for the cross welded joint based on the interval strain energy density method agreed well with the tested results. [ABSTRACT FROM AUTHOR]

There are various uncertain factors in most practical engineering applications, such as input loads, structural sizes, manufacturing tolerance, and initial and boundary conditions. The interval method and grey number theory are common methods to deal with uncertainty. In this article, the interval truncation method and grey number theory are improved. And a mixed method is proposed to represent the confidence interval of output result based on the improved interval truncation method and improved grey number theory. The proposed methods' feasibility is verified by a stepped bar; the methods are applied to the analysis of aircraft landing gear safety uncertainty. [ABSTRACT FROM AUTHOR]

Titanium alloy Ti6Al4V has the advantages of high specific strength, good heat resistance, and strong corrosion resistance, which is widely used in the manufacturing of aerospace industrial parts. However, in the side milling of titanium alloy, the temperature of the cutting area is high, and the cutting edge position is prone to breakage, which affects the surface quality of the workpiece. In order to reveal the tool damage failure mechanism in the milling process of titanium alloy, firstly, the impact force model when the tool cuts into the workpiece from the empty stroke and the milling force model during milling are established to obtain the cyclic load characteristics and impact effect of the tool. Then, based on the fatigue crack propagation theory and the energy balance equation of sliding crack, the elastic modulus and crack propagation law of tool material under different cutting impacts are analyzed. The interval method is used to recalculate the initial and critical damage value of tool material fracture in the maximum range. Finally, the limit conditions of the edge impact fracture of the end mill are established, and the safe cutting area of tool breakage is redefined. Through the milling test of titanium alloy, the impact damage morphology of tool in different states is redefined. The obtained redefined tool safety area provides a theoretical basis for high-speed and high-efficiency milling of titanium alloy, tool breakage, and tool life. [ABSTRACT FROM AUTHOR]

The innovative Next Generation Subsea Production System (NextGen SPS) concept is a newly proposed petroleum development solution in ultra-deep water areas. The definition of NextGen SPS involves several disciplines, which makes the design process difficult. In this paper, the definition of NextGen SPS is modeled as an uncertain multidisciplinary design optimization (MDO) problem. The deterministic optimization model is formulated, and three concerning disciplines—cost calculation, hydrodynamic analysis and global performance analysis are presented. Surrogate model technique is applied in the latter two disciplines. Collaborative optimization (CO) architecture is utilized to organize the concerning disciplines. A deterministic CO framework with two discipline-level optimizations is proposed firstly. Then the uncertainties of design parameters and surrogate models are incorporated by using interval method, and uncertain CO frameworks with triple loop and double loop optimization structure are established respectively. The optimization results illustrate that, although the deterministic MDO result achieves higher reduction in objective function than the uncertain MDO result, the latter is more reliable than the former. [ABSTRACT FROM AUTHOR]

In this paper there are clarified a few principal concepts that are then being used to explain the process of solving and analysing equations and inequalities with parameter. The process of analysing inequalities is conveyed by including a method of areas which means the intervalmethod expanded to the plane.

This paper deals with the effects of the interval and probability uncertain parameters imposed on the process of unbalance parameters identification from our previous paper (Mao et al. in: Shock Vib 2016:1–9, 2016) in Shock and Vibration. After employing uncertain parameters, we proposed the unbalance parameters identification method, and compared the results with those of previous studies. [ABSTRACT FROM AUTHOR]

In order to improve fuzzy fatigue reliability and make weight reduction of A-type frame in an electric mining dump truck considering multi-source uncertainties from design, manufacturing and use stage, a multi-objectives optimization method based on the interval theory was proposed in this paper. The thickness of four steel plates in welded Atype frame was regarded as certain design variables, while the elastic modulus and density of material was considered as uncertain variables as well as the load at front traction joint. The relationship between optimization objectives and variables was constructed by the response surface method, and was transformed by the interval method. Then, the optimization problem was solved by the non-dominated sorting genetic algorithm, which was found that the fuzzy fatigue reliability reached up to 98.45% at the expense of some weight. [ABSTRACT FROM AUTHOR]

Hypertension is often diagnosed in strength athletes of heavyweight categories. A study was made to assess how high-intensity aerobic work affects the body composition, blood pressure (BP), oxidative capacity, and working muscle hypertrophy and strength in strength athletes with arterial hypertension. Examination and physical rehabilitation were performed in 55 hypertensive heavyweight strength athletes comparable in age, gender, and main clinical manifestations. The athletes were randomized into two groups, a test group (n = 35) and a control group (n = 20). The test-group athletes trained on a bicycle ergometer according to a high-intensity interval protocol 3 times a week for 120 days, and the control-group athletes trained according to their conventional power protocol 3 times a week for 120 days. The study methods included interrogation, physical examination, triplicate BP measurement, bioimpedance analysis with calculation of body composition indices, ergospirometry, measurement of the oxygenation level of muscle tissue, ultrasonographic measurements of the anatomical cross-sectional area (CSA) of the quadriceps femoris, evaluation of the maximal voluntary contraction strength of the quadriceps femoris, and methods of mathematical statistics. After 120 days of training, the athletes of the test group displayed a 72% decrease in oxygenation, an increase in power and working time at the level of maximum oxygen consumption, and an increase in quadriceps femoris CSA. BP decreased significantly in the group: systolic BP (SBP), by 4.7% and diastolic BP (DBP), by 5.6%. The physical rehabilitation protocol developed for strength athletes makes it possible to effectively and safely affect the body composition, hypertrophy, oxidative capacity of working muscles, and BP. [ABSTRACT FROM AUTHOR]

Hypertension is a common diagnosis in power sports athletes. Objective. Evaluate the effect of high-intensity aerobic work on blood pressure, oxidative capacity, hypertrophy and strength of working muscles in power sports athletes. Methods. 55 representatives of power sports (powerlifting), heavy weight categories were involved in the research. Athletes were randomized into two groups: the main group (n = 35) and the control group (n = 20). All athletes were subjected to a comprehensive examination before and after the beginning of the research, including: survey, examination, three-time measurement of blood pressure, bioimpedance analysis and calculations of body composition indices, gas analysis, measurement of the oxygenation level of muscle tissue, ultrasonographic measurements of anatomical cross-sectional area of quadriceps muscle of thigh, estimation of maximum arbitrary power of quadriceps muscle of thigh and methods of mathematical statistics. The athletes of the main group trained 60 days (3 times a week) on a bicycle ergometer according to the high-intensity interval protocol, and the participants of the control group trained 60 days (3 times a week) according to their traditional power protocol. Results. After 60 days of training, there was a decrease in oxygenation by 72 %, an increase in power and working time at the level of maximum oxygen consumption and an increase in the cross-sectional area of quadriceps muscle of thigh in athletes of the main group. Athletes of the main group experienced a significant decrease in arterial blood pressure: systolic arterial pressure by 4.7 %, diastolic arterial pressure by 5.6 %. Conclusion. The physical rehabilitation protocol we developed allows athletes of power sports to effectively and safely influence hypertrophy, as well as the oxidizing abilities of working muscles and arterial blood pressure. [ABSTRACT FROM AUTHOR]

The uncertain parameters of the deviation in link dimensions and joint clearances caused by manufacturing and assembling errors have a strong impact on the degree of accuracy of the industrial robot. Understanding how these uncertain parameters influence the kinematic response of the industrial robot is critical for design. In this paper, the interval method is used for analysing the kinematic response of the industrial robot with uncertain-but-bounded parameters. The interval used for describing the uncertain parameters is estimated by the grayscale theory. The Denavit-Hartenberg (D-H) method is used for establishing the kinematic model of a 6-degree-of-freedom industrial robot. The kinematic response of the industrial robot calculated by the interval method with uncertain parameters is compared with the results obtained by the probabilistic approach. The comparison results show that the upper or lower bound obtained by interval method is far away from the ideal kinematic response than that obtained by the probabilistic approach. That is a true portrayal of the essence of interval method and probabilistic approach. The research contributes to choose the tolerance zone of uncertain parameters, such as the link dimensions and joint clearances, during the design process of industrial robots. [ABSTRACT FROM AUTHOR]

A novel method for load bounds identification for uncertain structures is proposed in the frequency domain. The uncertain parameters are assumed to locate in their intervals and only their bounds rather than their precise information are needed. To quantitatively describe the effect of the interval uncertainty on the load identification in the frequency ranges, the interval extension is then introduced in the frequency response function (FRF)-based least squares approach. Therefore, the load bounds are determined through the summation of the two separate parts including the midpoint part and the perturbed part of the load. The midpoint part is computed by using the Moore–Penrose pseudo-inversion and the perturbed part is transformed into the first derivatives of the midpoint load with respect to the uncertain parameters by applying the truncated total least squares (TTLS). Two numerical examples are investigated to validate that the proposed method is very effective to predict the load bounds for the uncertain structure in frequency domain. [ABSTRACT FROM AUTHOR]