Interval Analysis Theory Research Articles

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.

New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings (FNVMs) because fuzzy theory depends upon the unit interval that make a significant contribution to overcoming the issues that arise in the theory of interval analysis and fuzzy number theory. In this paper, the new class of p-convexity over up and down (UD) fuzzy relation has been introduced which is known as UD-p-convex fuzzy number-valued mappings (UD-p-convex FNVMs). We offer a thorough analysis of Hermite–Hadamard-type inequalities for FNVMs that are UD-p-convex using the fuzzy Aumann integral. Some previous results from the literature are expanded upon and broadly applied in our study. Additionally, we offer precise justifications for the key theorems that Kunt and İşcan first deduced in their article titled “Hermite–Hadamard–Fejer type inequalities for p-convex functions”. Some new and classical exceptional cases are also discussed. Finally, we illustrate our findings with well-defined examples.

Certain Novel Fractional Integral Inequalities via Fuzzy Interval Valued Functions

Fuzzy-interval valued functions (FIVFs) are the generalization of interval valued and real valued functions, which have a great contribution to resolve the problems arising in the theory of interval analysis. In this article, we elaborate the convexities and pre-invexities in aspects of FIVFs and investigate the existence of fuzzy fractional integral operators (FFIOs) having a generalized Bessel–Maitland function as their kernel. Using the class of convexities and pre-invexities FIVFs, we prove some Hermite–Hadamard (H-H) and trapezoid-type inequalities by the implementation of FFIOs. Additionally, we obtain other well known inequalities having significant behavior in the field of fuzzy interval analysis.

The Inventory Control Problem for a Supply Chain With a Mixed Type of Demand Uncertainty

This paper is concerned with a dynamic inventory control system described by a network model where the nodes are warehouses and the arcs represent production and distribution activities. We assume that an uncertain demand may take any value in an assigned interval and we allow that the system is disturbed by noise inputs. These assumptions yield a model with a mix of interval and stochastic demand uncertainties. We use the method of model predictive control to derive the control strategy. To deal with interval uncertainty we use the interval analysis tools and act according to the interval analysis theory. The developed results are illustrated using a numerical example.

Interval uncertainty analysis of vibration response of hydroelectric generating unit based on Chebyshev polynomial

The uncertainty of the hydroelectric generating unit (HGU) is unavoidable in practical engineering. However, up to now, the research about influences of the uncertain parameters on the system responses is still very scarce, especially in the case that the probability distribution of the uncertain parameter is not clear. So, this paper will aim to study the influence of interval uncertain parameters on the vibration response characteristics of HGU. Firstly, a nonlinear mathematical model of rotor-shaft-bearing system of the HGU is established under the action of interval uncertain parameters. Then, based on Chebyshev polynomial and interval analysis theory, three feasible analysis methods of interval uncertainty for the HGU are proposed, which are also compared with the brute-force Monte Carlo Simulation (MCS) method. And it is proved the proposed Chebyshev-MCS method has higher accuracy and lower cost obtaining the vibration response boundary of the HGU. Next, using Chebyshev-MCS method, the uncertain response characteristics of the system under single parameter, multiple parameters and shock excitation are further analyzed, respectively. Meanwhile, the upper and lower boundaries of the vibration response under different degrees of uncertainty and rotational speeds are obtained. Besides, the coupling effects of several uncertain parameters on the vibration response under the rated rotational speed condition are also presented. And the influence of uncertain parameters on the transient characteristics of the system under shock excitation is also gotten. More importantly, the proposed method and obtained conclusions are helpful to the manufacture, installation, operation of the HGU.

Theoretical Lower Bounds on the Performance of the First-Order Differential Microphone Arrays With Sensor Imperfections

The first-order differential microphone arrays (DMAs) offer the appealing properties such as compact size, and frequency-invariant response, and thus have found a wide range of applications. However, they are known to be sensitive to sensor imperfections, i.e., microphone gain errors, phase errors and self-noise. In this paper, we study the analysis and design of the first-order DMAs in the presence of sensor imperfections. Particularly, the theoretical lower bounds on the performance of the first-order DMAs with sensor imperfections are derived in closed form by using the theory of interval analysis, including the lower bounds on directivity factor (DF) and front-to-back ratio (FBR), which are two essential performance measures in DMAs design. Unlike the existing related works, we have considered a more general and realistic scenario when all the above-mentioned three kinds of sensor imperfections coexist. Based on the derived performance lower bounds, a method is presented to design the first-order DMA with its performance exceeding the worst-case optimum performance. Moreover, an analysis is presented, which takes into account the sensor imperfections in the design of the first-order DMAs so the optimum worst-case performance is guaranteed. Extensive simulation results are also shown to demonstrate the effectiveness of our theoretical findings.

A Novel Joint TDOA/FDOA Passive Localization Scheme Using Interval Intersection Algorithm

Due to the large measurement error in the practical non-cooperative scene, the passive localization algorithms based on traditional numerical calculation using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) often have no solution, i.e., the estimated result cannot meet the localization background knowledge. In this context, this paper intends to introduce interval analysis theory into joint FDOA/TDOA-based localization algorithm. The proposed algorithm uses the dichotomy algorithm to fuse the interval measurement of TDOA and FDOA for estimating the velocity and position of a moving target. The estimation results are given in the form of an interval. The estimated interval must contain the true values of the position and velocity of the radiation target, and the size of the interval reflects the confidence of the estimation. The point estimation of the position and the velocity of the target is given by the midpoint of the estimation interval. Simulation analysis shows the efficacy of the algorithm.

Calculation Method of Permanent Deformation of Asphalt Mixture Based on Interval Number.

There are great uncertainties in road design parameters, and the traditional point numerical calculation results cannot reflect the complexity of the actual project well. Additionally, the calculation method of road design theory based on interval analysis is more difficult in the use of uncertain design parameters. In order to simplify the calculation process of the interval parameters in the road design theory, the asphalt pavement design is taken as the analysis object, and the permanent deformation of the asphalt mixture is simplified by combining the interval analysis theory. Considering the uncertainty of the design parameters, the data with boundaries but uncertain size are expressed in intervals, and then the interval calculation formula for the permanent deformation of the asphalt mixture is derived, and the interval results are obtained. In order to avoid the dependence of interval calculation on the computer code, according to the interval calculation rule, the interval calculation method with the upper and lower end point values as point operations is proposed. In order to overcome the contradiction between interval expansion results and engineering applications, by splitting the multi-interval variable formulas, the interval variable weights are reasonably given, and the synthesis of each single interval result realizes a simplified calculation based on interval variable weight assignment. The analysis results show that the interval calculation method based on the point operation rule is accurate and reliable, and the simplified method based on the interval variable weight assignment is effective and feasible. The simplified interval calculation method proposed in this paper provides a reference for the interval application of road design theory.

Interval Inspired Approach Based on Temporal Sequence Constraints to Place Recognition

Place recognition is an essential task in many robotics applications. Recognizing if the robot is crossing an already visited place may be used to improve its localization and map estimation. A place recognition strategy must be as accurate as possible, despite the challenges related to environment dynamicity. It should avoid generating false positives since even a few erroneous matches may be enough to cause the degradation of the Simultaneous Localization and Mapping (SLAM) process. We propose a novel approach for place recognition inspired by interval analysis theory. Our approach models the known world as a set of intervals based on the robot’s observations. The search to determine whether the current robot location is new or known begins as the robot explores its surroundings. Our approach has three main steps. First, it selects a set of nearest neighbors based on the similarity between the current robot observation and the intervals composing the known world. In the second step, our approach uses temporal constraints to select one element of the set. And finally, the third step is to sweep the selected interval looking for the query best match. We evaluate our proposal by dealing with visual place recognition using only image information and demonstrate its effectiveness using some challenging public datasets.

Economic quality design under model uncertainty in micro-drilling manufacturing process

Integrated parameter design and tolerance design (IPTD) is an effective way to improve product quality and reduce manufacturing cost in micro-manufacturing processes. However, the current modeling techniques rarely analyze the influence of model uncertainty on the optimal machining parameters. It may not obtain the robust optimal machining parameters due to model uncertainty. This paper proposes a novel economically integrated design method which considers the correlations among quality characteristics, the variability of manufacturing process, and uncertainty in the model predictions. First, a new rework and scrap cost functions are established via Monte Carlo simulation. Meanwhile, an integrative expected quality loss function is constructed based on interval analysis theory for quantifying model uncertainty. Second, to make the proposed method closer to the practical micro-manufacturing problem, we consider the trade-offs among cost, time, and success rate in the modeling process. Finally, a total cost model is proposed to take into account the quality loss, tolerance cost, unit manufacturing cost, and scrap cost. The effectiveness of the proposed modeling method is verified by a laser beam micro-drilling manufacturing. The results illustrate that the proposed method can achieve better robustness property and economically than the traditional method that does not consider model uncertainty.

Fatigue cracking checking of cement stabilized macadam based on measurement uncertainty and interval analysis

The discreteness of fatigue test results of inorganic bonded stabilized materials is very voluminous. In this study, the fatigue crack checking process of cement stabilized macadam is analyzed by using measurement uncertainty and interval analysis theory in order to improve the efficiency of fatigue test data. Firstly, the measurement uncertainty of the bending strength and fatigue life of cement stabilized macadam is evaluated based on the measurement uncertainty theory. Secondly, the regression analysis of the fatigue life interval of different stress ratio conditions is realized, following which the regression model of the fatigue life interval of cement stabilized macadam is derived. Finally, the calculation model of fatigue cracking life interval is deduced, and the fatigue cracking life interval of cement stabilized macadam is then obtained by interval algorithm. Meanwhile an evaluation method of interval comparison results is proposed in order to undertake a comparative analysis of the fatigue cracking life interval of cement stabilized macadam. According to the findings, the non-uniformity of the specimen is determined as the root cause of the large discreteness of fatigue test results. A fatigue interval model with 95% guarantee rate can be obtained based on the regression analysis method of fatigue life interval, which is proved to be effective in improving the efficiency of fatigue test data. There is a case of interval expansion in calculating the equation of fatigue cracking life interval. It is verified that the extended interval result has engineering applicability. Therefore, it can be surmised that the interval result comparison method proposed in this paper can achieve both quantitative and qualitative evaluation, which is particularly suitable for the engineering field of interval analysis.

Application of discrete‐time Bayesian network on reliability analysis of uncertain system with common cause failure

AbstractWith the increasing complexity of engineering systems, reliability analysis and evaluation of systems with traditional methods can't meet practical engineering requirements. Based on limited experimental conditions, lack of data, complex structure models, insufficient cognitive abilities, and many other issues, people have to consider many uncertain factors in system reliability research. Besides, common cause failure (CCF) has become an important factor of system failure. In this paper, a discrete‐time Bayesian network (DTBN) associated with an eight‐rotor unmanned aerial vehicle (UAV) system is presented to discuss above problems. In this approach, the system is assumed as a two‐state system. After that, interval analysis theory is employed to deal with uncertainty. We consider the four sets of auxiliary propellers in the auxiliary power group as a 3/8 voting system, and β factor model is used to process CCF in the auxiliary power group. The proposed methods prove the validity of proposing interval analysis theory to solve uncertain problems and it is necessary to consider reducing or avoiding CCFs in system.

Thermo-electro-mechanical vibration analysis of nonlocal piezoelectric nanoplates involving material uncertainties

This study aims to detect the influence of material uncertainties on the free vibration of nonlocal piezoelectric nanoplates under thermo-electro-mechanical loadings. The size-dependent governing equations are derived based on the nonlocal theory and Hamilton’s principle, and Navier method is used for the solution. Considering inadequate experimental data, uncertain-but-bounded parameters are used to quantify the uncertain nanomaterial properties. Based on the interval analysis theory, a novel hull iterative algorithm (HIA) is proposed to evaluate the thermo-electro-mechanical vibration behavior of piezoelectric nanoplates. The presented method is compared with Monte Carlo method and sensitivity based interval analysis method, and well agreements are achieved. A sensitivity analysis is performed to identify the most dominant uncertain parameters. Using the HIA, parametric studies are carried out to explore the combined effects of material uncertainties and temperature change, external electric voltage, biaxial force as well as nonlocal parameter on the natural frequency of piezoelectric nanoplates.

Parameters identification of a cannon counter-recoil mechanism based on PSO and interval analysis theory

In this paper, two methods based on PSO algorithm and interval sequence conversion model or interval analysis theory are proposed to identify two kinds of uncertain parameters of a cannon counter-recoil mechanism during the manual recoil and forward moving process. Before identifying, some test data were obtained during the manual recoil process. Then, the uncertain parameters were described by interval number and a mathematical model about recoil process of a cannon was built. Taking the similarity degree of time-series data as an optimization objective function, Particle Swarm Optimization (PSO) algorithm was used to solve the deterministic optimization problem which was transformed by interval sequence conversion model, and the parameter identification of recuperator in the manual recoil process of a cannon was achieved. On this basis, combining PSO algorithm and Krawczyk algorithm of interval analysis theory, the uncertain parameters of recoil brake were identified. Finally, the results of identification proved that the above-mentioned two methods had a relatively high identification accuracy.

Standardization of Fatigue Characteristics of Cement-Treated Aggregate Base Materials under Different Stress States

In this study, to decrease the evaluation uncertainty of the fatigue characteristics of cement-treated aggregate base materials under different test conditions, unconfined compressive, indirect tensile, flexural tensile strength tests and fatigue tests of these base materials with different cement content and at different curing times were carried out. The Weibull distribution was employed to analyze fatigue test results. The standardization model of fatigue characteristics for cement-treated aggregate base materials under different stress states was established. Based on the interval analysis theory, the fatigue characteristic model under different stress states was established using interval parameters. Results revealed that the curing time and cement content considerably affect the strength and fatigue characteristics of cement-treated aggregate base materials, and with increasing cement content and curing time, the fatigue resistance of cement-treated aggregate base materials can be improved. Clear differences between the fitting parameters a and b of the S-N fatigue equation of cement-treated aggregate base materials under different stress states were observed, which can be eliminated by using the analysis method based on the Weibull distribution and the standardization model, and a unified expression for the cement-treated aggregate base materials under different test conditions was realized. A Standardization model of fatigue characteristics based on the interval analysis new method could solve several problems such as inadequate sampling representation, low precision, and insufficient stability of test equipment; thus, the errors caused by materials, structures, the environment, and loads can be reduced, making the fatigue life interval more reasonable and scientific compared to the point numerical fatigue life. Regression parameters a and be were in intervals [9.0, 10.6] and [9.9, 11.3], respectively, and parameters a and b were similar, which improve the test accuracy and reduce the data error.

Nonlinear free vibration analysis of defective FG nanobeams embedded in elastic medium

Defects in atomic structure can deteriorate the mechanical properties of nanomaterials, which is crucial to the potential application in nano electromechanical systems. This work studies the effect of the material defects on nonlinear vibration behavior of embedded functionally graded (FG) nanobeams. Employing the nonlocal strain gradient theory, the size-dependent governing equations accounting for the geometric nonlinearity and elastic medium are derived and the analytical solution for nonlinear frequency is presented. To quantify the material defects, the concept of defect degree is freshly introduced and then the defective FG nanobeam model is developed. Two methods, i.e., sensitivity based interval analysis method and iterative algorithm based interval analysis method, are proposed to solve this model in the framework of interval analysis theory. After model verification, the detailed parametric investigations are carried out to understand the combined effects of the material defects and size-dependent parameter, elastic medium as well as power-law index on the vibration frequency of FG nanobeam. Numerical results validate some significant conclusions which will offer guidance in the design of nanodevices.

Optimal Economic Life Interval Evaluation Method of Transformers

This paper proposed a method of optimal economic life interval evaluation of transformer, thus providing scientific support for power system planning and reconstruction. First, obtaining the transformer failure rate by using Levenberg-Marquardt based least squares algorithm on the consumption that transformer failure mode meets three-parameters Weibull distribution. Second, calculating operation cost and failure cost of transformer during its life cycle on the basis of transformer failure rate. Then, acquiring the optimal economic life interval of transformer through life cycle minimal average annual cost based on the theory of interval analysis. Finally, the proposed method is proved to be effective by applying to some real transformers.

基于区间分析理论的摩擦补偿研究

基于区间分析理论的摩擦补偿研究

Combined Parametric and Worst Case Circuit Analysis via Taylor Models

This paper proposes a novel paradigm to generate a parameterized model of the response of linear circuits with the inclusion of worst case bounds. The methodology leverages the so-called Taylor models and represents parameter-dependent responses in terms of a multivariate Taylor polynomial, in conjunction with an interval remainder accounting for the approximation error. The Taylor model representation is propagated from input parameters to circuit responses through a suitable redefinition of the basic operations, such as addition, multiplication or matrix inversion, that are involved in the circuit solution. Specifically, the remainder is propagated in a conservative way based on the theory of interval analysis. While the polynomial part provides an accurate, analytical and parametric representation of the response as a function of the selected design parameters, the complementary information on the remainder error yields a conservative, yet tight, estimation of the worst case bounds. Specific and novel solutions are proposed to implement complex-valued matrix operations and to overcome well-known issues in the state-of-the-art Taylor model theory, like the determination of the upper and lower bound of the multivariate polynomial part. The proposed framework is applied to the frequency-domain analysis of linear circuits. An in-depth discussion of the fundamental theory is complemented by a selection of relevant examples aimed at illustrating the technique and demonstrating its feasibility and strength.

Influence of the Parameterization in the Interval Solution of Elastic Beams

We are going to analyze the interval solution of an elastic beam under uncertain boundary conditions. Boundary conditions are defined as rotational springs presenting interval stiffness. Developments occur according to the interval analysis theory, which is affected, at the same time, by the overestimation of interval limits (also known as overbounding, because of the propagation of the uncertainty in the model). We suggest a method which aims to reduce such an overestimation in the uncertain solution. This method consists in a reparameterization of the closed form Euler-Bernoulli solution and set intersection.