Interval Analysis Method Research Articles

Uncertainty analysis of hypersonic flight dynamics under elastic effects

Abstract In addressing the aerodynamic-elastic coupling issues of hypersonic vehicles, this study delves into the analysis of the elastic deformation of the aircraft based on mechanistic understanding. It employs the Interval Analysis Method based on Polynomial Approximations to conduct uncertainty analysis of the aerodynamic model under elasticity, delineating the range of uncertainty in the aerodynamic model influenced by elastic deformation. The aerodynamic force of the aircraft under elasticity is connected with the rigid body, and then the aerodynamic layout of the aircraft fuselage and control surface after elastic deformation is calculated to study the influence of the elastic effect on the aerodynamic force. The results show that the change caused by uncertainty has a relatively small effect on lift but a relatively large effect on drag and pitching moment.

Dynamic modeling and reliability analysis of the ball bearing rotating accuracy considering the uncertain bearing-shaft interference fit

The rotating accuracy of the rolling bearing is closely related to its precision class and the actual fitting parameters. However, there are few quantitative evaluation models to describe their relationships. In this paper, considering the effect of the uncertain but bounded interference amounts between the bearing inner ring and the shaft, the Chebyshev interval analysis method is utilized and a rotating accuracy dynamic reliability model is presented based on the two degrees of freedom (2-DOF) rotor-ball bearing system. Firstly, the relationships between the bearing radial clearance and bearing-shaft interference amounts are investigated based on the shaft-bearing interference fit model. Thus, in terms of Chebyshev interval analysis method, the 2-DOF rotor-ball bearing system with uncertain bearing-shaft interference amounts is established. Then the rotating accuracy dynamic reliability model of the ball bearing is presented based on the Chebyshev interval theory. The effects of the average values and deviation coefficients of the initial interference amounts on the actual interference amounts, radial clearance and the resultant rotating accuracy dynamic reliability of the ball bearing are analyzed. The results show that the uncertain bearing-shaft interference amounts have a significant effect on the rotating accuracy dynamic reliability of the ball bearing and reasonable design could improve the rotating accuracy of the ball bearing. The results calculated by the present study are compared to the Monte Carlo simulation (MCS), which show the validity of the study.

Interval riccati equation-based and non-probabilistic dynamic reliability-constrained multi-objective optimal vibration control with multi-source uncertainties

Structural vibration control is used to ensure the safety of structures in service and has become an active research area in the past few years. In this study, uncertainties in structural dynamics are considered to propose an interval linear quadratic regulator (LQR) method based on an interval Riccati equation. Multi-objective optimization with non-probabilistic dynamic reliability as a constraint is performed to design an optimal uncertain vibration control system. To alleviate the difficulty of quantifying the probabilistic uncertainty and accurately characterize uncertainty information for small samples, multi-source uncertainties are regarded as interval parameters. The bounds on these uncertainties are determined, and the deterministic and uncertain parts of an interval state-space equation for vibration control are then formulated using an expanded-order matrix and the interval analysis method. Next, the interval perturbation method with a matrix series is used to develop a novel solution method for the linear inhomogeneous time-invariant equation in the interval state-space equation for the vibration control system and is used to accurately predict the interval bounds of the state responses. The conventional LQR method from modern control theory is used to propose a novel optimal control method based on a novel interval Riccati equation using the Lyapunov equation and interval uncertainty propagation. The proposed interval control method can be used to estimate the uncertain bounds of the controlled gain and cost function. A non-probabilistic dynamic reliability model is established to evaluate the reliability index of the system, which can overcome the limitations of the large computational cost of determining the probabilistic reliability. The deterministic controlled cost and uncertain states are considered as two optimization objectives with the proposed reliability constraint. The resulting constrained multi-objective optimal vibration control problem is designed and solved using c-DPEA. A flowchart is presented as a clear overview of the uncertain vibration control method, and the effectiveness of the proposed method is validated using two numerical examples. Different optimal control designs are obtained using different reliability constraints for quantitatively analyzing the safety of the control system.

A method for analyzing wearing uncertainties and enhancing motion transmission smoothness in exoskeletons and its applications for a novel passive knee exoskeleton

It is suggested that exoskeletons may present challenges in terms of wearability due to unexpected human-machine interaction forces, usually caused by wearing uncertainties such as wearing slips, geometric differences in individual knees, and variable-axis knee movements. Additionally, the forces caused by drastic changes in velocity during exoskeleton locomotion may also be a contributing factor. To address these issues, this paper introduces a new passive knee exoskeleton and its human-machine wearing parallel (HMWP) research prototype to compensate and accommodate these uncertainties. Subsequently, a response interval analysis method based on Chebyshev functions is proposed to investigate the effect of uncertainties on the HMWP system's kinematic performance. In order to enhance the motion transmission smoothness, a new kinematic performance evaluation indicator is proposed, which considers solely the exoskeleton-configuration parameters. The response interval analysis method and new indicator are applied together in kinematic dimensional synthesis, resulting in significant improvements in the exoskeleton's kinematic performance. Furthermore, a parameter sensitivity analysis is conducted to facilitate more effective improvements to the exoskeleton's comfort. This research can also be used to improve the wearability of other wearable devices.

Reliability analysis and optimization design of magnetic fluid dynamic seal shell structure under thermal/mechanical load

In order to study the reliability of Magnetic fluid dynamic seal shell structure under thermal/mechanical load, the improving cooling structure, calculating fuzzy fatigue reliability, and collaborative optimization design of fatigue reliability and lightweight are studied in this paper. The temperature model of the shell structure under four temperature conditions is established to analyze the influence of the thermal deformation caused by excessive local temperature. The cooling structure is improved, and the maximum temperature under the maximum temperature condition is reduced by 40.154 °C. For the sake of calculating the reliability of the new shell structure, a strength analysis model under thermal/mechanical load is built, and the fuzzy fatigue reliability function is obtained based on Latin hypercube sampling and the second-order response surface method. Four kinds of reliability are acquired by coding the functional functions and four kinds of membership functions with MATLAB, but all of them are lower than 90 % of the industrial requirements. To improve the reliability of the new shell structure and carry out the anti-fatigue lightweight design at the same time, an approximate model was constructed based on the interval analysis method and second-order response surface method for analysis. The accuracy of the approximate model was verified by re-sampling and finite element analysis. Based on the non-dominated sorting genetic algorithm, the optimal solution is determined. The optimization results show that the stress target value is reduced by 19.3 %, the weight target value is reduced by 3 %, and the fuzzy fatigue reliability reaches 94.65 %, 94.58 %, 93.89 %, and 96.31 % respectively. A new cooling structure of the Magnetic fluid dynamic seal is obtained and the maximum temperature is reduced. Moreover, the reliability of the new shell structure under thermal/mechanical load coupling is improved.

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

Multi-body dynamic evolution sequence-assisted PSO for interval analysis

<p>To enhance the efficiency and accuracy of response analysis in practical multivariable complex engineering problems, we introduced a new interval analysis method—multi-body dynamic evolution sequence-assisted particle swarm optimization (DES-PSO) is introduced in this research. This method optimizes the heterogeneous comprehensive learning particle swarm optimization algorithm (HCLPSO) by incorporating a dynamic evolution sequence (DES), addressing the difficulty of HCLPSO in covering the search space, which makes this method suitable for solving multivariable interval analysis problems. The results of two numerical examples prove that both DES-PSO and HCLPSO can give the accurate upper and lower bounds of the response interval. Compared with HCLPSO, DES-PSO improves the computing speed by about 50%.</p>

EXAMINATION OF EXPERIMENTAL DATA SAMPLES FOR THE PRESENCE OF OUTLIERS: COMPARISON OF METHODS

The task of detecting outliers (misses, abnormalous values, results that stand out sharply, results that have come off) is one of the most relevant, complex and ambiguous in the experimental materialprocessing. Such values are the experiment results, which are abnormally far from other points from a series of parallel observations.
 The source of emissions is often measurement errors. Among these are incorrect recording of the experiment results, possible incorrect coding of data, incorrect conduct of the experiment, etc. Gross errors occur in the event of a sudden change in the conditions of conducting the research, malfunctions in the operation of the equipment, etc.
 At the same time, outliers may indicate an unexpected, extraordinary behavior of the measured value – a yet-to-be-explained property process manifestation. And that's why an analysis using reliable mathematical tools is needed.
 The methods of detecting emissions are diverse and numerous. Parametric tests are more sensitive to the sample size and to the population values probability distribution. Non-parametric tests are more flexible and can be applied if the non-normal distributon of the sample or the sample size is small; such criteria give a better result in asymmetric distributions, because they use the median instead of the mean; they can be applied to ordinal or nominal data, as well as in the situation of an aberrant outlier value.
 Interval analysis methods, in particular interval statistics, are an alternative flexible toolkit for obtaining a more accurate and complete analysis of experimental data in the incomplete information, noise presence, measurement outliers, and the presence of abnormalous and aberrant points.
 A comparison of the results of the application of parametric criteria (-criterion, -criterion, Lvovskyi) and non-parametric criteria (the box-and-whiskers-plot) for detecting emissions, as well as calculation using interval statistics methods, was carried out. One of the outliers was determined by the non-parametric criterion, the -criterion and the procedure for detecting a single outlier using interval methods. Two values are suspicious outliers using the box-whisker rule and the interval statistics recognition algorithm.
 The methods of detecting outliers using interval analysis methods are no less effective than the use of non-parametric tests.

Interval Quadratic Equations: A Review

In this study, we tackle the subject of interval quadratic equations and we aim to accurately determine the root enclosures of quadratic equations, whose coefficients constitute interval variables. This study focuses on interval quadratic equations that contain only one coefficient considered as an interval variable. The four methods reviewed here in order to solve this problem are: (i) the method of classic interval analysis used by Elishakoff and Daphnis, (ii) the direct method based on minimizations and maximizations also used by the same authors, (iii) the method of quantifier elimination used by Ioakimidis, and (iv) the interval parametrization method suggested by Elishakoff and Miglis and again based on minimizations and maximizations. We will also compare the results yielded by all these methods by using the computer algebra system Mathematica for computer evaluations (including quantifier eliminations) in order to conclude which method would be the most efficient way to solve problems relevant to interval quadratic equations.

CTIVA: Censored time interval variable analysis.

Traditionally, datasets with multiple censored time-to-events have not been utilized in multivariate analysis because of their high level of complexity. In this paper, we propose the Censored Time Interval Analysis (CTIVA) method to address this issue. It estimates the joint probability distribution of actual event times in the censored dataset by implementing a statistical probability density estimation technique on the dataset. Based on the acquired event time, CTIVA investigates variables correlated with the interval time of events via statistical tests. The proposed method handles both categorical and continuous variables simultaneously-thus, it is suitable for application on real-world censored time-to-event datasets, which include both categorical and continuous variables. CTIVA outperforms traditional censored time-to-event data handling methods by 5% on simulation data. The average area under the curve (AUC) of the proposed method on the simulation dataset exceeds 0.9 under various conditions. Further, CTIVA yields novel results on National Sample Cohort Demo (NSCD) and proteasome inhibitor bortezomib dataset, a real-world censored time-to-event dataset of medical history of beneficiaries provided by the National Health Insurance Sharing Service (NHISS) and National Center for Biotechnology Information (NCBI). We believe that the development of CTIVA is a milestone in the investigation of variables correlated with interval time of events in presence of censoring.

APPLICATION OF THE SCENARIO APPROACH TO THE ANALYSIS AND CONTROL OF RISKS IN THE OPERATION OF COMPLEX DYNAMIC SYSTEMS UNDER CONDITIONS OF INTERVAL UNCERTAINTY

Introduction. The paper provides a description of the scenario approach to risk control in the operation of complex technical systems under conditions of uncertainty. The scenario is understood as the optimal control action on the system parameters, which allows minimizing the possible costs associated with the implementation of the corresponding risk event.
 The aim of the study is to develop effective risk management methods for the operation of a complex dynamic system under conditions of uncertainty based on a scenario approach that makes it possible to implement the optimal control action on the parameters of an object in the event of a threat of an emergency.
 Materials and methods. The article describes the application of the scenario method to the management of risks that arise during the operation of a complex dynamic system under conditions of interval uncertainty. This approach is based on the application of methods of interval analysis and the theory of situational management.
 The scientific novelty of the implemented approach lies in the use of the interval analysis apparatus, which makes it possible to most correctly take into account the possible errors associated with measuring the values of the system parameters and apply the optimal control actions necessary for correction in the event that the permissible indicators go beyond the operability area.
 Discussion and conclusion. The mathematical model of risk control developed in the course of the study carried out during the process of functioning of a complex technical system under conditions of interval uncertainty based on the scenario approach allows the selection of optimal control actions (scenarios) that allow minimizing possible errors and inaccuracies that arise due to deviation from the calculated nominal values.

A possibility-based solution framework for interval uncertainty-based design optimization

A possibility-based solution framework called the equivalent deterministic method (EDM) is proposed to solve optimization problems with interval uncertainty, which provides an efficient tool for interval uncertainty-based design optimization. First, an interval uncertainty-based design optimization model is established based on the possibility theory and current or reference design from experienced designers. Second, the equivalent deterministic method is proposed to transform the interval optimization problem into a series of interval analyses and deterministic optimizations that are alternately solved, which decouples the double-loop nested optimization into an iterative solving process. The novelties and advantages of the proposed method lie in two aspects. First, the shift scalar is deducted in the objective function and constraints in the possibility degree space, rather than the uncertain design variables and parameters, through which the violated constraints rapidly move toward the flexible region and the design points are optimized progressively. Second, interval analysis methods that calculate the interval responses and possibility, rather than the maximum and minimum points, can be integrated into the proposed method, which enhances the application scope for the existing interval optimization methods. Finally, a mathematical example and two engineering applications are utilized to demonstrate the performance of accuracy and efficiency.

Uncertain optimal attitude control for space power satellite based on interval Riccati equation with non-probabilistic time-dependent reliability

Considering the multi-source uncertainties and disturbances in the attitude dynamics of space power satellite (SPS), an interval dynamic model of SPS is proposed based on the non-probabilistic theory, which is controlled by a novel uncertainty-based linear–quadratic regulator (LQR) method with time-dependent reliability. Based on the interval analysis method, an interval time-varying attitude dynamic model of SPS for sun-pointing is established considering the uncertain inertia and initial states as unknown-but-bounded parameters. Feedforward and feedback controllers are designed to offset the disturbance and control attitude, respectively. An interval Riccati equation-based optimal control method is proposed to develop a novel uncertainty-based LQR method. Non-probabilistic time-dependent reliability is constituted based on the interval process and first passage theory to assess attitude states. An uncertain multi-objective optimization of attitude control with reliability constraints is proposed to realize the uncertain LQR method. Verified by a numerical example of SPS, the proposed method takes only 0.6‰∼0.8‰ time consumption of 10,000 Monte Carlo simulations while maintaining a certain accuracy.

An interval uncertainty optimization algorithm based on radial basis function network differentiation

A new interval uncertainty optimization algorithm is proposed to replace two-layer nested optimization, owing to the low efficiency of the latter. The radial basis function network is established to obtain the first-order differential, which is difficult to achieve in practical engineering problems. The results obtained by this network differential method are verified by a mathematical example. The network differential method is combined with the interval perturbation method to compute the bounds of uncertain objective functions and constraints, and the subinterval method is introduced to address the large level of uncertainty. The example of a compression spring shows the feasibility of this interval analysis method. The interval uncertain optimization problem is transformed into a deterministic one through the interval order relationship and probability model, and solved using the genetic algorithm or non-dominated sorting genetic algorithm-II. A numerical example and electromagnetic buffer model demonstrate the accuracy, efficiency and practicability of this new method.

Robust optimization for functional multiresponse in 3D printing process

Computer models are commonly used to simulate the functional relationships between inputs and outputs for quality design in 3D printing. However, the high-dimensional outputs of functional multiresponse make it challenging to develop the simulation model and perform robust optimization. This paper proposes a novel optimization method with an additive multiresponse Gaussian process model for dealing with functional multiresponse optimization problems. First, an additive covariance function is constructed to capture the correlation of the temporal inputs. Second, the Markov Chain Monte Carlo sampling technique is adopted to determine the simulation model and quantify the uncertainty. Finally, the optimization model is constructed by integrating the quality loss function and interval analysis method, and the Bayesian optimization algorithm is used to obtain the optimal solution. A numerical simulation example and a 3D printing case study are used to illustrate the effectiveness of the proposed method. The comparison results show that the responses of the proposed method are closer to the targets than the current ones, and all fall within the specified interval.

A novel dynamic load identification approach for multi-source uncertain structures based on the set-theoretical wavelet transform and layered noise reduction

This paper presents a dynamic load identification method based on wavelet decomposition. This method can identify multiple types of dynamic loads. Firstly, the parametric matrix is simplified to a diagonal matrix requiring the number of modal truncations by taking advantage of the orthogonality of the principal mode shapes and the mass, stiffness and damping matrices. By using the excellent characteristics of the wavelet space, such as the integrity of the wavelet space and the multi-resolution analysis, the generalized matrix of each parameter is transformed into the wavelet transform, which can effectively express the response history with the wavelet coefficients, further improve the computational efficiency, reduce the singularity of the inverse matrix, and enhance the anti-noise property of load recognition. In order to get closer to the practical engineering application, the interval analysis method of Taylor series expansion is proposed, and the propagation analysis of uncertain variables is carried out. Finally, the wavelet semi-soft threshold method is used to filter the signal to improve the accuracy of load recognition. The applicability of the proposed method is verified by numerical examples and simulation test cases.

Calculation of harrington function (desirability function) values under interval determination of its arguments

Purpose of work. Development of proposals for desirability function calculation by interval arithmetic method. Obtained results. A connection was shown between multiple-criterial (vector) optimization problem and calculation of Harrington function (desirability function) values. Generalized desirability function was shown to be treated as a multiplicative convolution of partial desirabilities. Using golden section properties, a connection was discerned between hierarchy analysis methods and calculation of desirability function values. In this case the distribution of probable desirability function values among intervals determined in accordance with golden mean rule does coincide with values obtained by expert method. Application of golden proportion enables increasing the number of intervals; thus, it may prove convenient in improvement of Harrington function sensitivity. Conclusions. For partial desirability function in its explicit form such geometric characteristics were determined as values of tangent, curvature of curve and center of curvature coordinates. For a necessary averaged desirability system obtaining process control, such characteristics were determined in general and explicit form as partial desirability elasticity, generalized desirability elasticity relative to partial desirability, generalized desirability elasticity relative to a variable that has physical sense and respective dimension depending on particular subject area and affects partial desirability value. To determine the boundary value of one partial desirability being substituted for another partial desirability, the rate of substitution function and boundary rate of substitution elasticity function were established. Due to errors emerging in determination of desirability function values application of interval analysis methods was proposed. Application of interval numbers as presented in hyperbolic form was shown for calcutaion of partial and generalized desirability, A partial power series sum was determined relative to a variable presented in hyperbolic form. Suggestions. The method of calculation of Harrington function (desirability function) values at interval determination of arguments was shown to be eventually used in development of specifications and preliminary design of complicated engineering аnd organizational systems.

One approach to drawing implicit 2D curves using interval analysis and Runge Method type.

One approach to drawing implicit 2D curves using interval analysis and Runge Method type.

A credible interval analysis method for uncertain structures under nonprobabilistic framework

In this paper, a novel credible structural interval analysis method is proposed. Traditionally, nonprobabilistic uncertainties are modeled as interval or convex models, and no description of their credibility is given. Based on credible nonprobability uncertainty theory, the credible interval and ellipsoid are quantified to model irrelevant and relevant uncertain structural parameters. An efficient adaptive kriging (EAK) method is developed to solve the interval dynamic responses of structures with credible intervals and ellipsoids. In contrast to existing propagation methods, the proposed EAK method shares the samples of different time steps to improve the computational efficiency. A numerical example and two engineering applications are used to show the validity, accuracy and efficiency of the proposed method. Comparisons show that the proposed method can effectively calculate interval dynamic responses with credibility and is competitive when addressing nonlinear or coupled structural systems.

Monotonicity-Based Interval Analysis Methods of Half-Wave Wall Radomes With Thickness and Permittivity Errors

The complex relation between permittivity and transmission coefficients has been a great obstacle to the interval-based tolerance analysis of radomes. This work presents two monotonicity-based methods (global/local) to facilitate precise interval analysis (IA) of half-wave-wall radomes with thickness and permittivity errors. The global monotonicity method reveals that the key parameters of radome transmission coefficients decrease monotonously with permittivity under a loose constraint in the form of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert $ </tex-math></inline-formula> tan(x) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert \le \text {x}$ </tex-math></inline-formula> , which makes the IA of permittivity errors as simple/accurate as thickness errors. The local monotonicity method, with no premises and less accuracy, treats the two correlative parts of the key parameters independently and can be a potential supplement to the global one. Results of spherical radomes and tangent ogival radomes indicate that the monotonicity-based methods can well improve the IA precision, and the global monotonicity method applies to general cases.