scholarly journals NON-LINEARITY SYSTEM RECTIFICATION USING MATHEMATICAL APPROXIMATION TECHNIQUE

2020 ◽  
Author(s):  
Souvik Roy ◽  
Rajesh De
Keyword(s):  
Approximation Technique ◽  
Mathematical Approximation

The minimum zone fitting and error evaluation for the logarithmic curve based on geometry optimization approximation algorithm

2019 ◽  
Vol 41 (15) ◽  
pp. 4380-4386
Author(s):  
Tu Xianping ◽  
Lei Xianqing ◽  
Ma Wensuo ◽  
Wang Xiaoyi ◽  
Hu Luqing ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Evaluation Method ◽  
Geometry Optimization ◽  
Reference Points ◽  
Approximation Technique ◽  
Error Evaluation ◽  
Iterative Approximation ◽  
Logarithmic Curve ◽  
Normal Distance ◽  
Minimum Zone

The minimum zone fitting and error evaluation for the logarithmic curve has important applications. Based on geometry optimization approximation algorithm whilst considering geometric characteristics of logarithmic curves, a new fitting and error evaluation method for the logarithmic curve is presented. To this end, two feature points, to serve as reference, are chosen either from those located on the least squares logarithmic curve or from amongst measurement points. Four auxiliary points surrounding each of the two reference points are then arranged to resemble vertices of a square. Subsequently, based on these auxiliary points, a series of auxiliary logarithmic curves (16 curves) are constructed, and the normal distance and corresponding range of values between each measurement point and all auxiliary logarithmic curves are calculated. Finally, by means of an iterative approximation technique consisting of comparing, evaluating, and changing reference points; determining new auxiliary points; and constructing corresponding auxiliary logarithmic curves, minimum zone fitting and evaluation of logarithmic curve profile errors are implemented. The example results show that the logarithmic curve can be fitted, and its profile error can be evaluated effectively and precisely using the presented method.

scholarly journals Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models

2021 ◽  
Author(s):  
Alessandro Barbiero ◽  
Asmerilda Hitaj
Keyword(s):  
Order Approximation ◽  
Linear Optimization ◽  
Closed Form Solution ◽  
Random Variables ◽  
Discrete Distribution ◽  
Computation Time ◽  
Form Solution ◽  
Engineering Problem ◽  
Approximation Technique ◽  
Reliability Parameter

AbstractIn many management science or economic applications, it is common to represent the key uncertain inputs as continuous random variables. However, when analytic techniques fail to provide a closed-form solution to a problem or when one needs to reduce the computational load, it is often necessary to resort to some problem-specific approximation technique or approximate each given continuous probability distribution by a discrete distribution. Many discretization methods have been proposed so far; in this work, we revise the most popular techniques, highlighting their strengths and weaknesses, and empirically investigate their performance through a comparative study applied to a well-known engineering problem, formulated as a stress–strength model, with the aim of weighting up their feasibility and accuracy in recovering the value of the reliability parameter, also with reference to the number of discrete points. The results overall reward a recently introduced method as the best performer, which derives the discrete approximation as the numerical solution of a constrained non-linear optimization, preserving the first two moments of the original distribution. This method provides more accurate results than an ad-hoc first-order approximation technique. However, it is the most computationally demanding as well and the computation time can get even larger than that required by Monte Carlo approximation if the number of discrete points exceeds a certain threshold.

Treatment of Pediatric Sternotomy Wound Complications: A Minimally Invasive Approach

2021 ◽  
Author(s):  
Taehee Jo ◽  
Joon Hur ◽  
Eun Key Kim
Keyword(s):  
Negative Pressure Wound Therapy ◽  
Wound Dehiscence ◽  
Surgical Debridement ◽  
Wound Complications ◽  
Approximation Technique ◽  
Invasive Approach ◽  
Nonsurgical Management ◽  
Single Use ◽  
Sternal Wound Infections ◽  
Deep Sternal Wound Infections

Abstract Background Pediatric sternal wound complications (SWCs) include sterile wound dehiscence (SWD) and superficial/deep sternal wound infections (SSWI/DSWI), and are generally managed by repetitive debridement and surgical wound approximation. Here, we report a novel nonsurgical management strategy of pediatric sternotomy wound complications, using serial noninvasive wound approximation technique combined with single-use negative pressure wound therapy (PICO) device. Methods Nine children with SWCs were managed by serial approximation with adhesive skin tapes and serial PICO device application. Thorough surgical debridement or surgical approximations were not performed. Results Three patients were clinically diagnosed as SWD, two patients as SSWI, and four patients as DSWI. None of the wounds demonstrated apparent mediastinitis or bone destructions. PICO device was applied at 16.1 days (range: 6–26 days) postoperatively, together with serial wound approximation by skin tapes. The average duration of PICO use was 16.9 days (range: 11–29 days) and the wound approximation was achieved in all patients. None of the patients underwent aggressive surgical debridement or invasive surgical approximation by sutures. Conclusion We report our successful management of selected pediatric SWCs, using serial noninvasive wound approximation technique combined with PICO device.

scholarly journals Bearing Anomaly Recognition Using an Intelligent Digital Twin Integrated with Machine Learning

2021 ◽  
Vol 11 (10) ◽  
pp. 4602
Author(s):  
Farzin Piltan ◽  
Jong-Myon Kim
Keyword(s):  
Machine Learning ◽  
Variable Structure ◽  
Vibration Signal ◽  
Crack Size ◽  
Approximation Technique ◽  
Digital Twin ◽  
Average Accuracy ◽  
Machine Learning Approach ◽  
The Impact ◽  
Signal Approximation

In this study, the application of an intelligent digital twin integrated with machine learning for bearing anomaly detection and crack size identification will be observed. The intelligent digital twin has two main sections: signal approximation and intelligent signal estimation. The mathematical vibration bearing signal approximation is integrated with machine learning-based signal approximation to approximate the bearing vibration signal in normal conditions. After that, the combination of the Kalman filter, high-order variable structure technique, and adaptive neural-fuzzy technique is integrated with the proposed signal approximation technique to design an intelligent digital twin. Next, the residual signals will be generated using the proposed intelligent digital twin and the original RAW signals. The machine learning approach will be integrated with the proposed intelligent digital twin for the classification of the bearing anomaly and crack sizes. The Case Western Reserve University bearing dataset is used to test the impact of the proposed scheme. Regarding the experimental results, the average accuracy for the bearing fault pattern recognition and crack size identification will be, respectively, 99.5% and 99.6%.

A METHOD FOR THE DIRECT INTERPRETATION OF ELECTRICAL SOUNDINGS MADE OVER A FAULT OR DIKE

Geophysics ◽  
1973 ◽  
Vol 38 (4) ◽  
pp. 762-770 ◽  
Author(s):  
Terry Lee ◽  
Ronald Green
Keyword(s):  
Bessel Functions ◽  
Direct Analysis ◽  
Hankel Transform ◽  
Approximation Technique ◽  
Polarization Data ◽  
Resistivity Data ◽  
Vertical Fault ◽  
Direct Interpretation ◽  
Electrical Soundings ◽  
Infinite Integral

The potential function for a point electrode in the vicinity of a vertical fault or dike may be expressed as an infinite integral involving Bessel functions. Beginning with such an expression, two methods are presented for the direct analysis of resistivity data measured both normal and parallel to dikes or faults. The first method is based on the asymptotic expansion of the Hankel transform of the field data and is suitable for surveys done parallel to the strike of the dike or fault. The second method is based on a successive approximation technique which starts from an initial approximate solution and iterates until a solution with prescribed accuracy is found. Both methods are suitable for programming on a digital computer and some illustrative numerical results are presented. These examples show the limitations of the methods. In addition, the application of resistivity data to the interpretation of induced‐polarization data is pointed out.

PIECEWISE AFFINE SYSTEM MODELING AND CONTROL OF PWM CONVERTERS

2007 ◽  
Vol 16 (01) ◽  
pp. 113-128 ◽  
Author(s):  
FARZAD TAHAMI ◽  
BEHROOZ MOLAEI
Keyword(s):  
High Performance ◽  
Piecewise Linear ◽  
System Modeling ◽  
Synthesis Method ◽  
Operating Point ◽  
Approximation Technique ◽  
Piecewise Affine ◽  
Pwm Converters ◽  
Linear Controller ◽  
Wide Range

The averaged switch modeling approach is a powerful method for representing the behavior of a wide variety of converters through equivalent circuits. The model is not linear and it is common to perform a small signal linearization about an operating point and design a linear controller. Models obtained with such method involve considerable approximation and produce results that are limited for high performance controller designs. In this paper a piecewise affine approximation technique is introduced for modeling PWM converters. This model is much more precise in predicting the dynamic response of averaged nonlinear model comparing the linear model. This paper also presents a piecewise linear controller synthesis method for PWM converters described by the proposed PWA model. The proposed controller is very efficient and effective. The design method is well suited for converters having a wide range of variation about their operating point. A simulation example on buck-boost converter is presented to demonstrate the performance of the proposed method for modeling the dynamics of the converter and designing the appropriate controller.

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