Directionally Independent Failure Prediction of End-Milling Tools by Tracking Increasing Chaotic Noise at the Machining Frequencies Due to Wear

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Christopher A. Suprock ◽  
John T. Roth
Keyword(s):  
Discrete Cosine Transform ◽  
End Milling ◽  
Dimensional Space ◽  
Data Sets ◽  
Cosine Transform ◽  
Modal Reduction ◽  
Milling Operations ◽  
Higher Dimensional ◽  
System Energy ◽  
Fourier Type

Accurate on-line forecasting of a tool’s condition during end-milling operations is advantageous to the functionality and reliability of automated industrial processes. The ability to disengage the tool prior to catastrophic failure reduces manufacturing costs, excessive machine deterioration, and personnel hazards. Rapid computational feedback describing the system’s state is critical for realizing a practical failure forecasting model. To this end, spectral analysis by fast Fourier type algorithms allows a rapid computational response. The research described herein explores the development of nontraditional real fast Fourier transform (discrete cosine transform) based algorithms performed in unique higher-dimensional states of observed data sets. Moreover, the developed Fourier algorithm quantifies chaotic noise rather than relying on the more traditional observation of system energy. By increasing the vector dimensionality of the discrete cosine transform, the respective linear transform basis more effectively cross correlates the transform data into fewer (more significant) transform coefficients. Thus, a single vector in orthogonally higher-dimensional space is observed instead of multiple orthogonal vectors in single-dimensional space. More specifically, a novel modal reduction technique is utilized to track trends measured from triaxial force dynamometer signals. This transformation effectively achieves both modal reduction and directional independence by observing the chaotic noise instead of system energy. Algorithm output trends from six end-milling life tests are tracked from both linear and pocketing maneuvers in order to demonstrate the technique’s capabilities. In all six tests, the algorithm predicts impending tool failure with sufficient time for tool removal.

Directionally Independent Failure Prediction of End Mill Cutting Tools: An Investigation of Noise Reduction Using Higher Dimensional Real Fourier Analysis

2006 ◽  
Author(s):  
Christopher A. Suprock ◽  
John T. Roth
Keyword(s):  
Noise Reduction ◽  
End Milling ◽  
Dimensional Space ◽  
Cutting Tools ◽  
Milling Operations ◽  
Higher Dimensional ◽  
Life Tests ◽  
On Line ◽  
System Energy ◽  
Fourier Type

Accurate on-line forecasting of a tool's condition during end-milling operations is advantageous to the functionality and reliability of automated industrial processes. The ability to disengage the tool prior to catastrophic failure reduces manufacturing costs, excessive machine deterioration, and personnel hazards. Rapid computational feedback describing the system's state is critical for realizing a practical failure forecasting model. To this end, spectral analysis by fast Fourier type algorithms allows a rapid computational response. The research described herein explores the development of nontraditional real FFT (Discrete Cosine Transform) based algorithms performed in unique higher-dimensional states of observed datasets. The developed Fourier algorithm is novel since it quantifies chaotic noise rather than relying on the more traditional observation of system energy. By increasing the vector dimensionality of the DCT, the respective linear transform basis will more effectively cross-correlate the transform data into fewer (more significant) transform coefficients. Thus, a single vector in orthogonally higher-dimensional space is observed instead of multiple orthogonal vectors in single-dimensional space. More specifically, a novel noise reduction technique is utilized to track trends measured from tri-axial force dynamometer signals. This transformation effectively achieves both system noise reduction and directional independence by observing the chaotic noise instead of system energy. Algorithm output trends from six end-milling life-tests are tracked from both linear and pocketing maneuvers in order to demonstrate the technique's capabilities. In all six tests, the algorithm predicts impending tool failure with sufficient time for tool removal.

Directionally Independent Failure Prediction of End-Milling Tools During Pocketing Maneuvers

2007 ◽  
Vol 129 (4) ◽  
pp. 770-779 ◽  
Author(s):  
Christopher A. Suprock ◽  
Joseph J. Piazza ◽  
John T. Roth
Keyword(s):  
Discrete Cosine Transform ◽  
End Milling ◽  
Cutting Tools ◽  
Primary Component ◽  
Operating Conditions ◽  
Frequency Method ◽  
Cosine Transform ◽  
Impending Fracture ◽  
Triaxial Dynamometer ◽  
Acceleration Signals

Tracking the health of cutting tools under typical wear conditions is advantageous to the speed and efficiency of manufacturing processes. Existing techniques monitor tool performance through analyzing force or acceleration signals whereby prognoses are made from a single sensor type. This work proposes to enhance the spectral output of autoregressive (AR) models by combining triaxial accelerometer and triaxial dynamometer signals. Through parallel processing of force and acceleration signals using single six degree of freedom modeling, greater spectral resolution is achieved. Two entirely independent methods of tracking the tool wear are developed and contrasted. First, using the discrete cosine transform, primary component analysis will be applied to the spectral output of each AR auto and cross spectrum (Method 1). Each discrete cosine transform of the six-dimensional spectral data is analyzed to determine the magnitude of the critical (primary) variance energy component of the respective spectrum. The eigenvalues of these selected spectral energies are then observed for trends toward failure. The second method involves monitoring the eigenvalues of the spectral matrices centered at the toothpass frequency (Method 2). The results of the two methodologies are compared. Through the use of the eigenvalue method, it is shown that, for straight and pocketing maneuvers, both methods successfully track the condition of the tool using statistical thresholding. The techniques developed in this work are shown to be robust by multiple life tests conducted on different machine platforms with different operating conditions. Both techniques successfully identify impending fracture or meltdown due to wear, providing sufficient time to remove the tools before failure is realized.

Directionally Independent Failure Prediction of End-Milling Tools During Pocketing Maneuvers

2006 ◽  
Author(s):  
Christopher A. Suprock ◽  
Jospeh J. Piazza ◽  
John T. Roth
Keyword(s):  
Discrete Cosine Transform ◽  
End Milling ◽  
Cutting Tools ◽  
Primary Component ◽  
Frequency Method ◽  
Cosine Transform ◽  
Eigenvalue Method ◽  
Tool Performance ◽  
Six Degree Of Freedom ◽  
Acceleration Signals

Tracking the health of cutting tools under typical wear conditions is advantageous to the speed and efficiency of manufacturing processes. Existing techniques monitor tool performance through analyzing force or acceleration signals whereby prognoses are made from a single sensor type. However, this work proposes to enhance the spectral output of autoregressive models by combining tri-axial accelerometer and tri-axial dynamometer signals. Through parallel processing of force and acceleration signals using single six degree of freedom modeling, greater spectral resolution is achieved. Two entirely independent methods of tracking the tool wear are developed and contrasted. First, using the discrete cosine transform, primary component analysis will be applied to the spectral output of each AR auto and cross spectrum (Method 1). Each discrete cosine transform of the 6 dimensional spectral data is analyzed to determine the magnitude of the critical (primary) variance energy component of the respective spectrum. The eigenvalues of these selected spectral energies are then observed for trends towards failure. The second method involves monitoring the eigenvalues of the spectral matrices centered at the toothpass frequency (Method 2). The results of the two methodologies are compared. Through the use of the eigenvalue method, it is shown that, for straight and pocketing maneuvers, both methods successfully track the condition of the tool using statistical thresholding.

LWT-DCT based Image Watermarking Scheme using Normalized SVD

2020 ◽  
Vol 13 ◽  
Author(s):  
Rahul Dixit ◽  
Amita Nandal ◽  
Arvind Dhaka ◽  
Vardan Agarwal ◽  
Yohan Varghese
Keyword(s):  
Wavelet Transform ◽  
Singular Value Decomposition ◽  
Discrete Cosine Transform ◽  
Image Watermarking ◽  
Singular Value ◽  
Cover Image ◽  
Lifting Wavelet Transform ◽  
Cosine Transform ◽  
Lifting Wavelet ◽  
Value Decomposition

Background: Nowadays information security is one of the biggest issues of social networks. The multimedia data can be tampered with, and the attackers can then claim its ownership. Image watermarking is a technique that is used for copyright protection and authentication of multimedia. Objective: We aim to create a new and more robust image watermarking technique to prevent illegal copying, editing and distribution of media. Method : The watermarking technique proposed in this paper is non-blind and employs Lifting Wavelet Transform on the cover image to decompose the image into four coefficient matrices. Then Discrete Cosine Transform is applied which separates a selected coefficient matrix into different frequencies and later Singular Value Decomposition is applied. Singular Value Decomposition is also applied to the watermarking image and it is added to the singular matrix of the cover image which is then normalized followed by the inverse Singular Value Decomposition, inverse Discrete Cosine Transform and inverse Lifting Wavelet Transform respectively to obtain an embedded image. Normalization is proposed as an alternative to the traditional scaling factor. Results: Our technique is tested against attacks like rotation, resizing, cropping, noise addition and filtering. The performance comparison is evaluated based on Peak Signal to Noise Ratio, Structural Similarity Index Measure, and Normalized Cross-Correlation. Conclusion: The experimental results prove that the proposed method performs better than other state-of-the-art techniques and can be used to protect multimedia ownership.

Celestial Tapestry

2020 ◽  
Author(s):  
Nicholas Mee
Keyword(s):  
Mathematics Curriculum ◽  
Dimensional Space ◽  
Golden Section ◽  
Single Point ◽  
Historical Context ◽  
Computer Art ◽  
Lightning Strike ◽  
Secret Message ◽  
Axiomatic Method ◽  
Higher Dimensional

Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.

Fast odd discrete cosine transform algorithms

1990 ◽  
Vol 26 (8) ◽  
pp. 503
Author(s):  
S.C. Chan ◽  
K.L. Ho
Keyword(s):  
Discrete Cosine Transform ◽  
Cosine Transform
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