Subinterval Method Research Articles

Comparison of Various Ranking Methods with Pareto Distribution Methods in Imprecise Data

The Pareto distribution has seen wide application in many different fields recently. Nowadays, the data we collect may be imprecise and contain uncertainties. This means that the values we gather cannot necessarily be considered a single, definitive value. In this paper, it is explored how various estimation methods like the method of moments, maximum likelihood estimation, and least squares estimation are used to determine the parameters of a Pareto distribution when the data is fuzzy or uncertain in nature. When making decisions, ranking methods are often heavily relied upon. For this reason, the application of several different ranking techniques to triangular fuzzy numbers (TFNs) is considered. The ranking methods for TFNs are found to tend to produce estimated parameters that are quite similar or even identical. The estimating parameters of a Pareto distribution can be solved for when dealing with fuzziness by the use of ranking methods such as alpha-cut, Yeager’s method, sub-interval method, Pascal method, magnitude method, and centroid method on the TFNs. By comparing the results of these various ranking techniques, an analysis is conducted to whether the estimated parameters of the Pareto distribution are consistent across the different ranking methods for TFNs get the uniqueness of the solution or differ. The decision making done by among the various ranking techniques, which method preferable for future comparison with extended of new ranking techniques. The conclusion is that the simulation results match up well with actual application data, serving as a good example for explaining this overall strategy.

ENHANCING UNDERWATER IMAGE QUALITY THROUGH ADAPTIVE COLOR CORRECTION AND MULTI-SCALE HISTOGRAM EQUALIZATION

Due to the selective attenuation of light in water, underwater images are poorly visible and pose significant challenges in visual activities. The structural and statistical properties of different areas of degraded underwater images are damaged to different levels, resulting in an overall uneven drift of object representation and further degrading the image quality. In order to solve these problems, we introduce a method for enhancing underwater images through multi-bin histogram perspective equalization under to solve the problems caused by underwater images. We estimate the degree of feature variation in each image region by extracting the statistical features of the image and using this information to control feature enhancement to achieve adaptive feature enhancement, thereby improving the visual effect of degraded images. We first design a vibration model that exploits the difference between data elements and regular elements to improve the color correction performance of the linear transformation-based sub-interval method. In addition, a multiple threshold selection method was developed that adaptively selects a set of thresholds for interval division. Finally, a multi-bin sub-histogram equalization method is presented, which performs histogram equalization in each sub-histogram to improve image contrast. Underwater imaging experiments in various scenarios show that our method significantly outperforms many state-of-the-art methods in terms of quality and quantity. INDEX TERMS: Multiple intervals, multi-scale fusion (MF), sub histogram equalization (SHE), underwater image.

An interval perturbation method for singular value decomposition (SVD) with unknown-but-bounded (UBB) parameters

The singular value decomposition (SVD) is a crucial method with successful practical applications. However, the quantification of uncertainties in SVD perturbation is challenging. To address this issue, this study introduces an interval perturbation method for SVD with unknown-but-bounded (UBB) parameters. Unlike probabilistic approaches that require statistical data on uncertain parameters, this method only necessitates the bounds of uncertain parameters. By using non-probabilistic theory, the proposed method can provide accurate and fast estimation of singular values and vectors. The paper provides a detailed derivation process for obtaining the interval bounds of singular values and vectors using the interval perturbation method. The subinterval method is applied to improve the estimation precision. The effectiveness of the proposed method is demonstrated through four numerical examples and an application example. The robustness of the proposed method is verified by various levels of uncertainties, different cases of subintervals, different matrix scales, close singular values, rectangular matrices, and small but nonzero singular values. The proposed method can be used in engineering numerical calculation inverse problem fields that require SVD with small uncertainties, including dynamic identification, image processing, and signal processing. Therefore, the superiority of the proposed method in accurately and quickly estimating singular values and vectors with uncertainties can be applied in the aforementioned research fields.

A bivariate subinterval method for dynamic analysis of mechanical systems with interval uncertain parameters

Dynamic analysis involving interval uncertainties can provide accurate reference to performance evaluation and reliability optimization. However, methodologies for dynamic problems under high dimensional interval uncertainties in mechanical systems need further exploration and development. To this end, this paper proposes a bivariate subinterval method (BSM) to handle interval dynamic problems, in which multiple uncertain parameters with small uncertainty levels in mechanical systems are involved. The BSM is developed by combining the subinterval technique and the bivariate decomposition of response functions expanded by the second-order Taylor series. Additionally, the subinterval-division-based bivariate subinterval method (SBSM) is developed to obtain a tight bound for the dynamic analysis of mechanical systems considering interval parameters with large uncertainty levels. To verify the efficiency and accuracy of the developed methods, numerical examples and engineering applications with consideration of interval uncertainties are employed and discussed. Results show that compared with the existing bivariate Chebyshev method, the BSM presents a better tradeoff between the accuracy of results and computational cost, which is more suitable to interval dynamic problems for the analysis of mechanical systems with uncertainties of high dimensions and small uncertainty levels. Furthermore, the SBSM can obtain a tight bound of dynamic responses for the interval dynamic problems with uncertain parameters of low dimensions and large uncertainty levels in mechanical systems.

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.

Uncertainty Analysis of Accident Vehicle Speed Based on Tire Marks

Accidents without video information often cannot obtain trace information accurately, and it is difficult to accurately select parameters when using the tire marks formula, resulting in inaccurate results calculated during research and analysis. To obtain more authentic and reliable analysis results and improve the reliability and authority of accident identification and treatment, it is necessary to reflect the measurement error into the conclusion of calculation and analysis more completely and reliably, to ensure that the true value of the calculation result is within the calculation range of theoretical error. Therefore, through the Monte Carlo method and Subinterval method, the uncertainty analysis of the accident speed is carried out, and the accident vehicle speed is restored more accurately, which is conducive to the accident handling personnel to judge and analyze the accident speed.

A novel interval dynamic reliability computation approach for the risk evaluation of vibration active control systems based on PID controllers

PID control is widely used in vibration control systems. However, there are various uncertainties present in practical engineering, and the PID parameters obtained from a deterministic system may fail. Thus, reliability estimation is necessary to solve this problem. To avoid the disadvantages of traditional probabilistic methods, a non-probability based method to calculate time-dependent reliability is introduced to estimate the safety of a vibration active control system of based on PID controller performance. Next, the subinterval method is used to calculate a closed-loop response with large uncertainties and the first-passage theory is utilized to calculate the time-dependent reliability. Finally, one discrete mass-spring-damper system is analyzed for comparison with the collocation method and two panel structures (an elastic panel and a solar panel) are reliability evaluated to show the effects of the number of PID controllers and the displacement constraints.

An interval uncertain optimization method using back-propagation neural network differentiation

An interval uncertain optimization method is proposed for engineering uncertain optimization problems. The first-order derivative information may be unavailable in practical engineering systems. To overcome this drawback, the method to calculate the first-order partial derivatives with a back-propagation neural network is investigated, and a numerical example is presented to demonstrate its fine precision. In the optimization process, the back-propagation neural network and its first-order derivatives are introduced into the interval perturbation method and combined with the subinterval method, the extrema of the uncertain objective function and uncertain constraints can be approximated without much computational cost. Thus the most challenging problem in current interval optimization, namely low optimization efficiency caused by nested optimization can be solved to a certain extent. A two-bar structure system is adopted to validate its fine precision and high computational efficiency in interval bounds estimation. Based on the interval order relation and interval possibility degree model, an interval uncertain optimization model can be transformed into a deterministic optimization model, and be solved by some auxiliary optimization algorithm. A numerical example and an engineering application have indicated that this method is efficient for uncertain optimization problems.

An interval uncertainty analysis method for structural response bounds using feedforward neural network differentiation

This paper proposes a new interval uncertainty analysis method for structural response bounds with uncertain‑but-bounded parameters by using feedforward neural network (FNN) differentiation. The information of partial derivative may be unavailable analytically for some complicated engineering problems. To overcome this drawback, the FNNs of real structural responses with respect to structure parameters are first constructed in this work. The first-order and second-order partial derivative formulas of FNN are derived via the backward chain rule of partial differentiation, thus the partial derivatives could be determined directly. Especially, the influences of structures of multilayer FNNs on the accuracy of the first-order and second-order partial derivatives are analyzed. A numerical example shows that an FNN with the appropriate structure parameters is capable of approximating the first-order and second-order partial derivatives of an arbitrary function. Based on the parameter perturbation method using these partial derivatives, the extrema of the FNN can be approximated without requiring much computational time. Moreover, the subinterval method is introduced to obtain more accurate and reliable results of structural response with relatively large interval uncertain parameters. Three specific examples, a cantilever tube, a Belleville spring, and a rigid-flexible coupling dynamic model, are employed to show the effectiveness and feasibility of the proposed interval uncertainty analysis method compared with other methods.

A subinterval decomposition analysis method for uncertain structures with large uncertainty parameters

A simple and efficient subinterval decomposition analysis method is proposed to evaluate the lower and upper bounds of structural responses with large uncertain parameters. The proposed method decomposes the original structural system with multi-dimensional interval parameters into multiple one-dimensional subsystems. Every subsystem has only one interval parameter and the other interval parameters are substituted by their midpoint values. By dividing the interval parameter of each subsystem into several subintervals with small uncertainty, the lower and upper bounds of the system are approximately calculated by only a few subinterval combinational analyses instead of all possible combinations of subintervals. Finally, the accuracy and efficiency of the proposed method compared with the first-order Taylor method, Chebyshev interval method and traditional subinterval method are verified by several numerical examples and applications.

On a possible error of type II in statistical evaluation of pseudo-random number generators

In an earlier paper, cf. [7], the first author developed methods for evaluation of pseudo-random number generators based on ideas of computer simulation. More precisely, pseudo-random numbers of the tested generator are used to model certain distributions which can be compared with theoretical ones or with distributions modeled by means of well-known canonical generators. But this method can fail if essentially different generators produce simulations that cannot be distinguished by means of simple statistical tests developed in [7]. In the present paper two critical types of distributions, named geometric and arthmetic, are constructed that illustrate the circumstances above. Also it is shown how the subinterval method derived from the tests in [7] can serve to detect the described critical types of distributions. Additional aspects of old and new methods are shortly discussed.