scholarly journals What Can Students Learn While Solving Colebrook’s Flow Friction Equation?

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 114 ◽  
Author(s):  
Dejan Brkić ◽  
Pavel Praks
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Iterative Methods ◽  
Special Functions ◽  
Floating Point ◽  
Numerical Examples ◽  
Flow Friction ◽  
Newton Raphson ◽  
The Difference ◽  
Fixed Point Iterative Method

Even a relatively simple equation such as Colebrook’s offers a lot of possibilities to students to increase their computational skills. The Colebrook’s equation is implicit in the flow friction factor and, therefore, it needs to be solved iteratively or using explicit approximations, which need to be developed using different approaches. Various procedures can be used for iterative methods, such as single the fixed-point iterative method, Newton–Raphson, and other types of multi-point iterative methods, iterative methods in a combination with Padé polynomials, special functions such as Lambert W, artificial intelligence such as neural networks, etc. In addition, to develop explicit approximations or to improve their accuracy, regression analysis, genetic algorithms, and curve fitting techniques can be used too. In this learning numerical exercise, a few numerical examples will be shown along with the explanation of the estimated pedagogical impact for university students. Students can see what the difference is between the classical vs. floating-point algebra used in computers.

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 130 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ = ζ ( R e , ε * , λ ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton–Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three- or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma–Guha–Gupta, Sharma–Sharma, Sharma–Arora, Džunić–Petković–Petković; Bi–Ren–Wu, Chun–Neta based on Kung–Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

scholarly journals Prediksi Pemakaian Listrik Kelompok Tarif Menggunakan Jaringan Syaraf Tiruan dan ARIMA

2013 ◽  
Vol 7 (2) ◽  
pp. 189
Author(s):  
Silviani E Rumagit ◽  
Azhari SN
Keyword(s):  
Neural Network ◽  
Artificial Intelligence ◽  
Neural Networks ◽  
Statistical Method ◽  
Moving Average ◽  
Electric Energy ◽  
Backpropagation Neural Network ◽  
The Difference ◽  
The Government ◽  
Increasing Demand

AbstrakLatar Belakang penelitian ini dibuat dimana semakin meningkatnya kebutuhan listrik di setiap kelompok tarif. Yang dimaksud dengan kelompok tarif dalam penelitian ini adalah kelompok tarif sosial, kelompok tarif rumah tangga, kelompok tarif bisnis, kelompok tarif industri dan kelompok tarif pemerintah. Prediksi merupakan kebutuhan penting bagi penyedia tenaga listrik dalam mengambil keputusan berkaitan dengan ketersediaan energi listik. Dalam melakukan prediksi dapat dilakukan dengan metode statistik maupun kecerdasan buatan.            ARIMA merupakan salah satu metode statistik yang banyak digunakan untuk prediksi dimana ARIMA mengikuti model autoregressive (AR) moving average (MA). Syarat dari ARIMA adalah data harus stasioner, data yang tidak stasioner harus distasionerkan dengan differencing. Selain metode statistik, prediksi juga dapat dilakukan dengan teknik kecerdasan buatan, dimana dalam penelitian ini jaringan syaraf tiruan backpropagation dipilih untuk melakukan prediksi. Dari hasil pengujian yang dilakukan selisih MSE ARIMA, JST dan penggabungan ARIMA, jaringan syaraf tiruan tidak berbeda secara signifikan. Kata Kunci— ARIMA, jaringan syaraf tiruan, kelompok tarif.  AbstractBackground this research was made where the increasing demand for electricity in each group. The meaning this group is social, the household, business, industry groups and the government fare. Prediction is an important requirement for electricity providers in making decisions related to the availability of electric energy. In doing predictions can be made by statistical methods and artificial intelligence.            ARIMA is a statistical method that is widely used to predict where the ARIMA modeled autoregressive (AR) moving average (MA). Terms of ARIMA is the data must be stationary, the data is not stationary should be stationary  use differencing. In addition to the statistical method, predictions can also be done by artificial intelligence techniques, which in this study selected Backpropagation neural network to predict. From the results of tests made the difference in MSE ARIMA, ANN and merging ARIMA, artificial neural networks are not significantly different. Keyword—ARIMA, neural network, tarif groups

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation – Numerical Validation

2018 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation ζ is implicitly given in respect to the unknown flow friction factor λ ;  λ=ζ(Re,ε*,λ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. Common approach to solve it is through the Newton-Raphson iterative procedure or through the fixed-point iterative procedure. Both requires in some case even eight iterations. On the other hand numerous more powerful iterative methods such as three-or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require in worst case only two iterations to reach final solution. The recommended representatives are Sharma-Guha-Gupta, Sharma-Sharma, Sharma-Arora, Džunić-Petković-Petković; Bi-Ren-Wu, Chun-Neta based on Kung-Traub, Neta, and Jain method based on Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

scholarly journals Influence of the Depth of the Convolutional Neural Networks on an Artificial Intelligence Model for Diagnosis of Orthognathic Surgery

2021 ◽  
Vol 11 (5) ◽  
pp. 356
Author(s):  
Ye-Hyun Kim ◽  
Jae-Bong Park ◽  
Min-Seok Chang ◽  
Jae-Jun Ryu ◽  
Won Hee Lim ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Orthognathic Surgery ◽  
Area Under The Curve ◽  
Network Models ◽  
Neural Network Models ◽  
Test Set ◽  
The Neural Networks ◽  
The Difference ◽  
Average Success Rate

The aim of this study was to investigate the relationship between image patterns in cephalometric radiographs and the diagnosis of orthognathic surgery and propose a method to improve the accuracy of predictive models according to the depth of the neural networks. The study included 640 and 320 patients requiring non-surgical and surgical orthodontic treatments, respectively. The data of 150 patients were exclusively classified as a test set. The data of the remaining 810 patients were split into five groups and a five-fold cross-validation was performed. The convolutional neural network models used were ResNet-18, 34, 50, and 101. The number in the model name represents the difference in the depth of the blocks that constitute the model. The accuracy, sensitivity, and specificity of each model were estimated and compared. The average success rate in the test set for the ResNet-18, 34, 50, and 101 was 93.80%, 93.60%, 91.13%, and 91.33%, respectively. In screening, ResNet-18 had the best performance with an area under the curve of 0.979, followed by ResNets-34, 50, and 101 at 0.974, 0.945, and 0.944, respectively. This study suggests the required characteristics of the structure of an artificial intelligence model for decision-making based on medical images.

scholarly journals Compression of Convolutional Neural Network for Natural Language Processing

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Krzysztof Wróbel ◽  
Michał Karwatowski ◽  
Maciej Wielgosz ◽  
Marcin Pietroń ◽  
Kazimierz Wiatr
Keyword(s):  
Neural Network ◽  
Artificial Intelligence ◽  
Neural Networks ◽  
Natural Language Processing ◽  
Natural Language ◽  
Language Processing ◽  
Original Model ◽  
Floating Point ◽  
Memory Footprint ◽  
Classification Tasks

Convolutional Neural Networks (CNNs) were created for image classification tasks. Quickly, they were applied to other domains, including Natural Language Processing (NLP). Nowadays, the solutions based on artificial intelligence appear on mobile devices and in embedded systems, which places constraints on, among others, the memory and power consumption. Due to CNNs memory and computing requirements, to map them to hardware they need to be compressed.This paper presents the results of compression of the efficient CNNs for sentiment analysis. The main steps involve pruning and quantization. The process of mapping the compressed network to FPGA and the results of this implementation are described. The conducted simulations showed that 5-bit width is enough to ensure no drop in accuracy when compared to the floating point version of the network. Additionally, the memory footprint was significantly reduced (between 85% and 93% comparing to the original model).

scholarly journals Note on the Reliability of Biological vs. Artificial Neural Networks

2021 ◽  
Vol 12 ◽  
Author(s):  
Ruedi Stoop
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Key Features ◽  
Artificial Neural ◽  
The Difference

Various types of neural networks are currently widely used in diverse technical applications, not least because neural networks are known to be able to “generalize.” The latter property raises expectations that they should be able to handle unexpected situations with similar success than humans. Using fundamental examples, we show that in situations for which they have not been trained, artificial approaches tend to run into substantial problems, which highlights a deficit in comparisons to human abilities. For this problem–which seems to have obtained little attention so far–we provide a first analysis, based on simple examples, which exhibits some key features responsible for the difference between human and artificial intelligence.

scholarly journals Suitability for coding of the Colebrook’s flow friction relation expressed by symbolic regression approximations of the Wright-ω function

2020 ◽  
Vol 1 (1) ◽  
pp. 174-179
Author(s):  
Pavel Praks ◽  
◽  
Dejan Brkić ◽  
Keyword(s):  
Artificial Intelligence ◽  
Asymptotic Expansion ◽  
Pipe Flow ◽  
Numerical Experiments ◽  
Special Functions ◽  
Symbolic Regression ◽  
Lambert W Function ◽  
Flow Friction ◽  
Classical Formulation ◽  
Speed And Accuracy

This article analyses a form of the empirical Colebrook’s pipe flow friction equation given originally by the Lambert W-function and recently also by the Wright ω-function. These special functions are used to explicitly express the unknown flow friction factor of the Colebrook equation, which is in its classical formulation given implicitly. Explicit approximations of the Colebrook equation based on approximations of the Wright ω-function given by an asymptotic expansion and symbolic regression were analyzed in respect of speed and accuracy. Numerical experiments on 8 million Sobol’s quasi-Monte points clearly show that also both approaches lead to approximately the same complexity in terms of speed of execution in computers. However, the relative error of the developed symbolic regression-based approximations is reduced significantly, in comparison with the classical basic asymptotic expansion. These numerical results indicate promising results of artificial intelligence (symbolic regression) for developing fast and accurate explicit approximations.

Using neural networks and artificial intelligence as a modern method of glaucoma diagnosis

2020 ◽  
pp. 27-28
Author(s):  
A.B. Movsisyan ◽  
◽  
A.V. Kuroyedov ◽  
G.A. Ostapenko ◽  
S.V. Podvigin ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Modern Method ◽  
Glaucoma Diagnosis

Актуальность. Определяется увеличением заболеваемости глаукомой во всем мире как одной из основных причин снижения зрения и поздней постановкой диагноза при имеющихся выраженных изменений со стороны органа зрения. Цель. Повысить эффективность диагностики глаукомы на основании оценки диска зрительного нерва и перипапиллярной сетчатки нейросетью и искусственным интеллектом. Материал и методы. Для обучения нейронной сети были выделены четыре диагноза: первый – «норма», второй – начальная глаукома, третий – развитая стадия глаукомы, четвертый – глаукома далеко зашедшей стадии. Классификация производилась на основе снимков глазного дна: область диска зрительного нерва и перипапиллярной сетчатки. В результате классификации входные данные разбивались на два класса «норма» и «глаукома». Для целей обучения и оценки качества обучения, множество данных было разбито на два подмножества: тренировочное и тестовое. В тренировочное подмножество были включены 8193 снимка с глаукомными изменениями диска зрительного нерва и «норма» (пациенты без глаукомы). Стадии заболевания были верифицированы согласно действующей классификации первичной открытоугольной глаукомы 3 (тремя) экспертами со стажем работы от 5 до 25 лет. В тестовое подмножество были включены 407 снимков, из них 199 – «норма», 208 – с начальной, развитой и далекозашедшей стадиями глаукомы. Для решения задачи классификации на «норма»/«глаукома» была выбрана архитектура нейронной сети, состоящая из пяти сверточных слоев. Результаты. Чувствительность тестирования дисков зрительных нервов с помощью нейронной сети составила 0,91, специфичность – 0,93. Анализ полученных результатов работы показал эффективность разработанной нейронной сети и ее преимущество перед имеющимися методами диагностики глаукомы. Выводы. Использование нейросетей и искусственного интеллекта является современным, эффективным и перспективным методом диагностики глаукомы.

Encapsulation and the C++ class

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Program Design ◽  
Internal Representation ◽  
Floating Point ◽  
Complex Class ◽  
Numerical Examples ◽  
Important Notion ◽  
Standard Library

Built-in datatypes and C++ classes are introduced in this chapter, and discussed in relation to the important notion of encapsulation, which refers to the separation between the internal representation of the datatype and the operations to which it responds. Encapsulation later becomes an important consideration in the design of custom C++ classes that programmers develop themselves. It is illustrated with built-in floating-point datatypes float and double and with the complex class from the C++ standard library. While a sophisticated programmer is aware of the internal representation of data and its resulting limitations, encapsulation allows one to consider these as details and frees one to think at a higher level of program design. Some simple numerical examples are discussed in the text and in the exercises.

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