scholarly journals A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Franz Konstantin Fuss
Keyword(s):  
Time Series ◽  
Time Derivative ◽  
Fractal Dimensions ◽  
Human Movement ◽  
Robust Algorithm ◽  
Practical Applications ◽  
Linear Effect ◽  
Scaling Methods ◽  
The Difference ◽  
Nowhere Differentiable Functions

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal’s time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

Characteristic Lengths and Distances: Fast and Robust Features for Nonlinear Time Series

2012 ◽  
Author(s):  
Son Hai Nguyen ◽  
David Chelidze
Keyword(s):  
Time Series ◽  
Vector Fields ◽  
Fractal Dimensions ◽  
Large Data ◽  
Practical Applications ◽  
Force Microscopy ◽  
Birkhoff Ergodic Theorem ◽  
Long Time ◽  
Computational Resources ◽  
Simple Features

Estimation of most of the metrics used to characterize dynamical systems’ output require fairly long time series (e.g., Lyapunov Exponents, Fractal Dimensions), or substantial computational resources (e.g., phase space warping metrics, sensitivity vector fields). In many practical applications, when there is abundance of data (e.g., in Atomic Force Microscopy) fast and simple features are needed, and when there is sparsity of data (e.g., in many Structural Health Monitoring situations) robust features are needed. Here, we propose a new class of features based on Birkhoff Ergodic Theorem, which are fast to calculate and do not require large data or computational resources. Applications of these metrics, in conjunction with the smooth orthogonal decomposition, to identifying underlying processes causing nonstationarity both in simulations and actual experiments are demonstrated.

EVALUASI PROYEKSI DEMAND BARANG DAN PENUMPANG PELABUHAN DI PROVINSI MALUKU

2019 ◽  
Vol 19 (2) ◽  
pp. 101-110
Author(s):  
Adrian Firdaus ◽  
M. Dwi Yoga Sutanto ◽  
Rajin Sihombing ◽  
M. Weldy Hermawan
Keyword(s):  
Time Series ◽  
Projection Method ◽  
Development Plan ◽  
Master Plan ◽  
Port Development ◽  
Loading And Unloading ◽  
The Difference ◽  
Existing Data

Abstract Every port in Indonesia must have a Port Master Plan that contains an integrated port development plan. This study discusses one important aspect in the preparation of the Port Master Plan, namely the projected movement of goods and passengers, which can be used as a reference in determining the need for facilities at each stage of port development. The case study was conducted at a port located in a district in Maluku Province and aims to evaluate the analysis of projected demand for goods and passengers occurring at the port. The projection method used is time series and econometric projection. The projection results are then compared with the existing data in 2018. The results of this study show that the econometric projection gives adequate results in predicting loading and unloading activities as well as the number of passenger arrival and departure in 2018. This is indicated by the difference in the percentage of projection results towards the existing data, which is smaller than 10%. Whereas for loading and unloading activities, time series projections with logarithmic trends give better results than econometric projections. Keywords: port, port master plan, port development, unloading activities  Abstrak Setiap pelabuhan di Indonesia harus memiliki sebuah Rencana Induk Pelabuhan yang memuat rencana pengem-bangan pelabuhan secara terpadu. Studi ini membahas salah satu aspek penting dalam penyusunan Rencana Induk Pelabuhan, yaitu proyeksi pergerakan barang dan penumpang, yang dapat dipakai sebagai acuan dalam penentuan kebutuhan fasilitas di setiap tahap pengembangan pelabuhan. Studi kasus dilakukan pada sebuah pelabuhan yang terletak di sebuah kabupaten di Provinsi Maluku dan bertujuan untuk melakukan evaluasi ter-hadap analisis proyeksi demand barang dan penumpang yang terjadi di pelabuhan tersebut. Metode proyeksi yang dipakai adalah proyeksi deret waktu dan ekonometrik. Hasil proyeksi selanjutnya dibandingkan dengan data eksisting tahun 2018. Hasil studi ini menunjukkan bahwa proyeksi ekonometrik memberikan hasil yang cukup baik dalam memprediksi aktivitas bongkar barang serta jumlah penumpang naik dan turun di tahun 2018. Hal ini diindikasikan dengan selisih persentase hasil proyeksi terhadap data eksisting yang lebih kecil dari 10%. Sedangkan untuk aktivitas muat barang, proyeksi deret waktu dengan tren logaritmik memberikan hasil yang lebih baik daripada proyeksi ekonometrik. Kata-kata kunci: pelabuhan, rencana induk pelabuhan, pengembangan pelauhan, aktivitas bongkar barang

Optimization Study to Develop Once-a-day Controlled Release Formulation of Metoclopramide with Predictable Design Space

1970 ◽  
Vol 1 (1) ◽  
pp. 71-76
Author(s):  
Rajesh Dubey ◽  
Udaya K. Chowdary ◽  
Venkateswarlu V.
Keyword(s):  
Controlled Release ◽  
Drug Release ◽  
Design Space ◽  
Release Kinetics ◽  
Release Profile ◽  
Release Formulation ◽  
Linear Effect ◽  
Controlled Release Formulation ◽  
The Difference ◽  
Face Centered

A controlled release formulation of metoclopramide was developed using a combination of hypromellose (HPMC) and hydrogenated castor oil (HCO). Developed formulations released the drug over 20 hr with release kinetics following Higuchi model. Compared to HCO, HPMC showed significantly higher influence in controlling the drug release at initial as well as later phase. The difference in the influence can be explained by the different swelling and erosion behaviour of the polymers. Effect of the polymers on release was optimized using a face-centered central composite design to generate a predictable design space. Statistical analysis of the drug release at various levels indicated a linear effect of the polymers’ levels on the drug release. The release profile of formulations containing the polymer levels at extremes of their ranges in design space was found to be similar to the predicted release profile

scholarly journals A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 436
Author(s):  
Ruirui Zhao ◽  
Minxia Luo ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Distance Measures ◽  
Numerical Comparison ◽  
Mathematical Tool ◽  
Practical Applications ◽  
Fuzzy Point ◽  
Point Operator ◽  
The Difference ◽  
Picture Fuzzy Sets

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

279 WACSAW: A Statistical and Individually Adaptive Method to Determine Sleep and Wakefulness from Activity

SLEEP ◽  
2021 ◽  
Vol 44 (Supplement_2) ◽  
pp. A111-A112
Author(s):  
Austin Vandegriffe ◽  
V A Samaranayake ◽  
Matthew Thimgan
Keyword(s):  
Time Series ◽  
Optimal Transport ◽  
Activity Patterns ◽  
Adaptive Method ◽  
Wasserstein Distance ◽  
Activity Data ◽  
Commercial Grade ◽  
Movement Data ◽  
The Difference ◽  
Levene Test

Abstract Introduction Technological innovations have broadened the type and amount of activity data that can be captured in the home and under normal living conditions. Yet, converting naturalistic activity patterns into sleep and wakefulness states has remained a challenge. Despite the successes of current algorithms, they do not fill all actigraphy needs. We have developed a novel statistical approach to determine sleep and wakefulness times, called the Wasserstein Algorithm for Classifying Sleep and Wakefulness (WACSAW), and validated the algorithm in a small cohort of healthy participants. Methods WACSAW functional routines: 1) Conversion of the triaxial movement data into a univariate time series; 2) Construction of a Wasserstein weighted sum (WSS) time series by measuring the Wasserstein distance between equidistant distributions of movement data before and after the time-point of interest; 3) Segmenting the time series by identifying changepoints based on the behavior of the WSS series; 4) Merging segments deemed similar by the Levene test; 5) Comparing segments by optimal transport methodology to determine the difference from a flat, invariant distribution at zero. The resulting histogram can be used to determine sleep and wakefulness parameters around a threshold determined for each individual based on histogram properties. To validate the algorithm, participants wore the GENEActiv and a commercial grade actigraphy watch for 48 hours. The accuracy of WACSAW was compared to a detailed activity log and benchmarked against the results of the output from commercial wrist actigraph. Results WACSAW performed with an average accuracy, sensitivity, and specificity of >95% compared to detailed activity logs in 10 healthy-sleeping individuals of mixed sexes and ages. We then compared WACSAW’s performance against a common wrist-worn, commercial sleep monitor. WACSAW outperformed the commercial grade system in each participant compared to activity logs and the variability between subjects was cut substantially. Conclusion The performance of WACSAW demonstrates good results in a small test cohort. In addition, WACSAW is 1) open-source, 2) individually adaptive, 3) indicates individual reliability, 4) based on the activity data stream, and 5) requires little human intervention. WACSAW is worthy of validating against polysomnography and in patients with sleep disorders to determine its overall effectiveness. Support (if any):

Multiscale Mutual Mode Entropy Based Coupling Analysis of Alpha Rhythm Electroencephalogram

2014 ◽  
Vol 574 ◽  
pp. 718-722
Author(s):  
Ning Ji ◽  
Jun Tan ◽  
An Shan Pei ◽  
Jia Fei Dai ◽  
Jun Wang
Keyword(s):  
Time Series ◽  
Clinical Evaluation ◽  
Brain Function ◽  
Alpha Rhythm ◽  
Physiological Status ◽  
Noise Resistance ◽  
Middle Aged ◽  
Coupling Analysis ◽  
Scale Change ◽  
The Difference

This paper presents the Multiscale Mutual Mode Entropy algorithm to quantify the coupling degree between two alpha rhythm EEG time series which are simultaneously acquired. The results show that in the process of scale change, the young and middle-aged differ from each other in terms of the coupling degree of alpha rhythm EEG and the difference grow clear gradually. So the Multiscale Mutual Mode Entropy can be used to analyze the coupling information of time series under different physiological status, and it also has good noise resistance. Besides, as an indicator of measuring brain function, in the future it can also come to the aid of clinical evaluation of brain function.

Data Fusion of Total Solar Irradiance Composite Time Series Using 40 years of Satellite Measurements: First Results 

2021 ◽  
Author(s):  
Jean-Philippe Montillet ◽  
Wolfgang Finsterle ◽  
Werner Schmutz ◽  
Margit Haberreiter ◽  
Rok Sikonja
Keyword(s):  
Time Series ◽  
Data Fusion ◽  
Solar Irradiance ◽  
Total Solar Irradiance ◽  
Maunder Minimum ◽  
The Sun ◽  
Climate Reconstructions ◽  
The Earth ◽  
First Results ◽  
The Difference

<p><span>Since the late 70’s, successive satellite missions have been monitoring the sun’s activity, recording total solar irradiance observations. These measurements are important to estimate the Earth’s energy imbalance, </span><span>i.e. the difference of energy absorbed and emitted by our planet. Climate modelers need the solar forcing time series in their models in order to study the influence of the Sun on the Earth’s climate. With this amount of TSI data, solar irradiance reconstruction models  can be better validated which can also improve studies looking at past climate reconstructions (e.g., Maunder minimum). V</span><span>arious algorithms have been proposed in the last decade to merge the various TSI measurements over the 40 years of recording period. We have developed a new statistical algorithm based on data fusion.  The stochastic noise processes of the measurements are modeled via a dual kernel including white and coloured noise.  We show our first results and compare it with previous releases (PMOD,ACRIM, ... ). </span></p>

scholarly journals Tunable Adhesion of a Bio-Inspired Micropillar Arrayed Surface Actuated by a Magnetic Field

2018 ◽  
Vol 86 (1) ◽  
Author(s):  
Xingji Li ◽  
Zhilong Peng ◽  
Yazheng Yang ◽  
Shaohua Chen
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Magnetic Particles ◽  
Rotation Angle ◽  
Adhesion Force ◽  
Practical Applications ◽  
Section Shape ◽  
Theoretical Predictions ◽  
Large Elastic Deformation ◽  
The Difference

Bio-inspired functional surfaces attract many research interests due to the promising applications. In this paper, tunable adhesion of a bio-inspired micropillar arrayed surface actuated by a magnetic field is investigated theoretically in order to disclose the mechanical mechanism of changeable adhesion and the influencing factors. Each polydimethylsiloxane (PDMS) micropillar reinforced by uniformly distributed magnetic particles is assumed to be a cantilever beam. The beam's large elastic deformation is obtained under an externally magnetic field. Specially, the rotation angle of the pillar's end is predicted, which shows an essential effect on the changeable adhesion of the micropillar arrayed surface. The larger the strength of the applied magnetic field, the larger the rotation angle of the pillar's end will be, yielding a decreasing adhesion force of the micropillar arrayed surface. The difference of adhesion force tuned by the applied magnetic field can be a few orders of magnitude, which leads to controllable adhesion of such a micropillar arrayed surface. Influences of each pillar's cross section shape, size, intervals between neighboring pillars, and the distribution pattern on the adhesion force are further analyzed. The theoretical predictions are qualitatively well consistent with the experimental measurements. The present theoretical results should be helpful not only for the understanding of mechanical mechanism of tunable adhesion of micropillar arrayed surface under a magnetic field but also for further precise and optimal design of such an adhesion-controllable bio-inspired surface in future practical applications.

Failure time prognosis in manufacturing process using multi-dislocated time series convolutional neural network

2020 ◽  
pp. 095440892097414
Author(s):  
Bohao Li ◽  
Liping Zhao ◽  
Yiyong Yao
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Convolutional Neural Network ◽  
Manufacturing Process ◽  
Failure Time ◽  
Great Difficulty ◽  
Milling Process ◽  
Machining Process ◽  
Massive Data ◽  
The Difference

Failure time prognosis in manufacturing process plays a crucial role in guaranteeing manufacturing safety and reducing maintenance loss. However, most current prognosis methods face great difficulty when handling massive data collected from manufacturing process. Convolutional neural network (CNN) provides an effective way to extract features with massive data. Due to the difference between images and multisensory signals, CNN is not suitable for machining process. Inspired by the idea of CNN, a novel prognosis framework is proposed based on the characteristics of multisensory signals, which is called multi-dislocated time series convolutional neural network (MDTSCNN). The proposed MDTSCNN is composed of multi-dislocate layer, convolutional layer, pooling layer and fully connected layer. By adding a multi-dislocate layer, this model can learn the relationship between different signals and different intervals in periodic multisensory signals. The effectiveness of proposed method is validated by a milling process. Compared to other prognosis method, the proposed MDTSCNN shows enhanced performances in prediction accuracy.

Sign in / Sign up

Export Citation Format

Share Document