Application of Bayesian Inference to Milling Force Modeling

This paper describes the application of Bayesian inference to the identification of force coefficients in milling. Mechanistic cutting force coefficients have been traditionally determined by performing a linear regression to the mean force values measured over a range of feed per tooth values. This linear regression method, however, yields a deterministic result for each coefficient and requires testing at several feed per tooth values to obtain a high level of confidence in the regression analysis. Bayesian inference, on the other hand, provides a systematic and formal way of updating beliefs when new information is available while incorporating uncertainty. In this work, mean force data is used to update the prior probability distributions (initial beliefs) of force coefficients using the Metropolis-Hastings (MH) algorithm Markov chain Monte Carlo (MCMC) approach. Experiments are performed at different radial depths of cut to determine the corresponding force coefficients using both methods and the results are compared.

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Overview of Bayesian Statistics

Evaluation Review ◽

10.1177/0193841x19895623 ◽

2020 ◽

pp. 0193841X1989562

Author(s):

David Rindskopf

Keyword(s):

Bayesian Inference ◽

Bayesian Statistics ◽

Statistical Modeling ◽

Probability Distributions ◽

Bayes Theorem ◽

Special Issue ◽

Popular Approach ◽

New Information ◽

Basic Concepts ◽

Phd Program

Bayesian statistics is becoming a popular approach to handling complex statistical modeling. This special issue of Evaluation Review features several Bayesian contributions. In this overview, I present the basics of Bayesian inference. Bayesian statistics is based on the principle that parameters have a distribution of beliefs about them that behave exactly like probability distributions. We can use Bayes’ Theorem to update our beliefs about values of the parameters as new information becomes available. Even better, we can make statements that frequentists do not, such as “the probability that an effect is larger than 0 is .93,” and can interpret 95% (e.g.) intervals as people naturally want, that there is a 95% probability that the parameter is in that interval. I illustrate the basic concepts of Bayesian statistics through a simple example of predicting admissions to a PhD program.

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Rainfall Prediction in South-Eastern Part of Bangladesh by Linear Regression Method

International Journal of Emerging Research in Management and Technology ◽

10.23956/ijermt.v6i6.255 ◽

2018 ◽

Vol 6 (6) ◽

pp. 119

Author(s):

Mohammad Shohidul Islam ◽

Sultana Easmin Siddika ◽

S M Injamamul Haque Masum

Keyword(s):

Linear Regression ◽

Correlation Coefficients ◽

Rain Gauge ◽

Regression Method ◽

Linear Regression Method ◽

Climate Data ◽

Rainfall Forecasting ◽

Statistical Parameters ◽

Time Duration ◽

Rainfall Prediction

Rainfall forecasting is very challenging task for the meteorologists. Over the last few decades, several models have been utilized, attempting the successful analysing and forecasting of rainfall. Recorded climate data can play an important role in this regard. Long-time duration of recorded data can be able to provide better advancement of rainfall forecasting. This paper presents the utilization of statistical techniques, particularly linear regression method for modelling the rainfall prediction over Bangladesh. The rainfall data for a period of 11 years was obtained from Bangladesh Meteorological department (BMD), Dhaka i.e. that was surface-based rain gauge rainfall which was acquired from 08 weather stations over Bangladesh for the years of 2001-2011. The monthly and yearly rainfall was determined. In order to assess the accuracy of it some statistical parameters such as average, meridian, correlation coefficients and standard deviation were determined for all stations. The model prediction of rainfall was compared with true rainfall which was collected from rain gauge of different stations and it was found that the model rainfall prediction has given good results.

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An alternative model of the vibronic coupling in octahedral complexes

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19881134 ◽

1988 ◽

Vol 53 (6) ◽

pp. 1134-1140

Author(s):

Martin Breza ◽

Peter Pelikán

Keyword(s):

Linear Regression ◽

Alternative Model ◽

Potential Surface ◽

Analytical Formula ◽

Coupling Model ◽

Regression Method ◽

Vibronic Coupling ◽

Linear Regression Method ◽

Active Systems ◽

Jahn Teller

It is suggested that for some transition metal hexahalo complexes, the Eg-(a1g + eg) vibronic coupling model is better suited than the classical T2g-(a1g + eg) model. For the former, alternative model, the potential constants in the analytical formula are evaluated from the numerical map of the adiabatic potential surface by using the linear regression method. The numerical values for 29 hexahalo complexes of the 1st row transition metals are obtained by the CNDO/2 method. Some interesting trends of parameters of such Jahn-Teller-active systems are disclosed.

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Prediction Models for Truck Accidents at Freeway Ramps in Washington State Using Regression and Artificial Intelligence Techniques

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/1635-04 ◽

1998 ◽

Vol 1635 (1) ◽

pp. 30-36 ◽

Cited By ~ 9

Author(s):

Wael H. Awad ◽

Bruce N. Janson

Keyword(s):

Artificial Intelligence ◽

Neural Networks ◽

Linear Regression ◽

Prediction Models ◽

Washington State ◽

Training Data ◽

Coefficient Of Determination ◽

Training Process ◽

Truck Accidents ◽

High Level

Three different modeling approaches were applied to explain truck accidents at interchanges in Washington State during a 27-month period. Three models were developed for each ramp type including linear regression, neural networks, and a hybrid system using fuzzy logic and neural networks. The study showed that linear regression was able to predict accident frequencies that fell within one standard deviation from the overall mean of the dependent variable. However, the coefficient of determination was very low in all cases. The other two artificial intelligence (AI) approaches showed a high level of performance in identifying different patterns of accidents in the training data and presented a better fit when compared to the regression model. However, the ability of these AI models to predict test data that were not included in the training process showed unsatisfactory results.

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The Accuracy Assessment of Weapon System Using Grey Linear Regression Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.268-270.1809 ◽

2012 ◽

Vol 268-270 ◽

pp. 1809-1813

Author(s):

Dai Yu Zhang ◽

Bao Wei Song ◽

Zhou Quan Zhu

Keyword(s):

Linear Regression ◽

Fuzzy Theory ◽

Accuracy Assessment ◽

Regression Method ◽

Small Sample ◽

Easy Access ◽

Linear Regression Method ◽

Grey Theory ◽

Weapon System ◽

Complex Engineering

The accuracy assessment of weapon system is always a complex engineering. How to make the most of the information given in only a few tests and obtain reasonable estimate is always a problem. Based on the fuzzy theory and grey theory, a grey linear regression method is presented. From the numerical example, we can see that this method provides an easy access to deal with data in small sample case and may have potential use in the analysis of weapon performance.

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Demineralization Depth Using QLF and a Novel Image Processing Software

International Journal of Dentistry ◽

10.1155/2010/958264 ◽

2010 ◽

Vol 2010 ◽

pp. 1-7 ◽

Cited By ~ 8

Author(s):

Jun Wu ◽

Zachary R. Donly ◽

Kevin J. Donly ◽

Steven Hackmyer

Keyword(s):

Image Processing ◽

Linear Regression ◽

Polarized Light ◽

Region Of Interest ◽

Linear Regression Method ◽

Percent Loss ◽

Significant Linear Correlation ◽

Processing Software ◽

Image Processing Software ◽

Imagej Software

Quantitative Light-Induced fluorescence (QLF) has been widely used to detect tooth demineralization indicated by fluorescence loss with respect to surrounding sound enamel. The correlation between fluorescence loss and demineralization depth is not fully understood. The purpose of this project was to study this correlation to estimate demineralization depth. Extracted teeth were collected. Artificial caries-like lesions were created and imaged with QLF. Novel image processing software was developed to measure the largest percent of fluorescence loss in the region of interest. All teeth were then sectioned and imaged by polarized light microscopy. The largest depth of demineralization was measured by NIH ImageJ software. The statistical linear regression method was applied to analyze these data. The linear regression model wasY=0.32X+0.17, whereXwas the percent loss of fluorescence andYwas the depth of demineralization. The correlation coefficient was 0.9696. The two-tailed t-test for coefficient was 7.93, indicating theP-value=.0014. TheFtest for the entire model was 62.86, which shows theP-value=.0013. The results indicated statistically significant linear correlation between the percent loss of fluorescence and depth of the enamel demineralization.

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Perancangan Aplikasi Prediksi Jumlah Pendaftar Siswa Baru Dengan Metode Regresi Linier (Studi Kasus: SMA RK Deli Murni Bandar Baru)

Jurnal Nasional Komputasi dan Teknologi Informasi (JNKTI) ◽

10.32672/jnkti.v3i3.2520 ◽

2020 ◽

Vol 3 (3) ◽

pp. 330-334

Author(s):

Novita Ria Lase ◽

Fristi Riandari

Keyword(s):

Linear Regression ◽

Regression Method ◽

Point Of View ◽

Computational Techniques ◽

Linear Regression Method ◽

Simple Linear Regression ◽

Tuition Fees ◽

Use Of Data ◽

New Students ◽

New Student

The problem of the SMA RK Deli Murni Bandar Baru school is to predict how many facilities that need to be provided for new students such as chairs, tables and others. This study discusses the prediction of the number of new student registrants at SMA RK Deli Murni Bandar Baru based on the amount of tuition fees using a simple linear regression method. From a commercial point of view, the use of data mining can be used to handle the explosion of data volumes, using computational techniques can be used to produce information needed which is an asset that can increase the competitiveness of an institution. Prediction is almost the same as classification and estimation, except that in the prediction the value of the results will be in the future. This system can be used to predict the number of applicants in the following year to help the school. The advantage is that this simple linear regression method is very simple so that it is easy to calculate and use. Saves the time needed to solve problems, especially those that are very complex.

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Effect of Air Fraction on Force Coefficients in Oscillatory Flow

10.1115/omae2021-61122 ◽

2021 ◽

Author(s):

Malene Hovgaard Vested ◽

Erik Damgaard Christensen

Keyword(s):

High Speed ◽

Offshore Structures ◽

Air Injection ◽

Wave Loads ◽

Morison Equation ◽

Force Coefficients ◽

Air Content ◽

Set Up ◽

High Level ◽

Spilling Breakers

Abstract The forces on marine and offshore structures are often affected by spilling breakers. The spilling breaker is characterized by a roller of mixed air and water with a forward speed approximately equal to the wave celerity. This high speed in the top of the wave has the potential to induce high wave loads on upper parts of the structures. This study analyzed the effect of the air content on the forces. The analyses used the Morison equation to examine the effect of the percentage of air on the forces. An experimental set-up was developed to include the injection of air into an otherwise calm water body. The air-injection did introduce a high level a turbulence. It was possible to assess the amount of air content in the water for different amounts of air-injection. In the mixture of air and water the force on an oscillating square cylinder was measured for different levels of air-content, — also in the case without air. The measurements indicated that force coefficients for clear water could be use in the Morison equation as long as the density for water was replaced by the density for the mixture of air and water.

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