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Comparing the direct normal form and multiple scales methods through frequency detuning.

ABSTRACT: Approximate analytical methods, such as the multiple scales (MS) and direct normal form (DNF) techniques, have been used extensively for investigating nonlinear mechanical structures, due to their ability to offer insight into the system dynamics. A comparison of their accuracy has not previously been undertaken, so is addressed in this paper. This is achieved by computing the backbone curves of two systems: the single-degree-of-freedom Duffing oscillator and a non-symmetric, two-degree-of-freedom oscillator. The DNF method includes an inherent detuning, which can be physically interpreted as a series expansion about the natural frequencies of the underlying linear system and has previously been shown to increase its accuracy. In contrast, there is no such inbuilt detuning for MS, although one may be, and usually is, included. This paper investigates the use of the DNF detuning as the chosen detuning in the MS method as a way of equating the two techniques, demonstrating that the two can be made to give identical results up to ?2 order. For the examples considered here, the resulting predictions are more accurate than those provided by the standard MS technique. Wolfram Mathematica scripts implementing these methods have been provided to be used in conjunction with this paper to illustrate their practicality.

SUBMITTER: Elliott AJ

PROVIDER: S-EPMC6404644 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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Comparing the direct normal form and multiple scales methods through frequency detuning.

Elliott A J AJ Cammarano A A Neild S A SA Hill T L TL Wagg D J DJ

Nonlinear dynamics 20180914 4

Approximate analytical methods, such as the multiple scales (MS) and direct normal form (DNF) techniques, have been used extensively for investigating nonlinear mechanical structures, due to their ability to offer insight into the system dynamics. A comparison of their accuracy has not previously been undertaken, so is addressed in this paper. This is achieved by computing the backbone curves of two systems: the single-degree-of-freedom Duffing oscillator and a non-symmetric, two-degree-of-freed ...[more]

PMID: 30930539

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Project description:BACKGROUND:Heparin is one of the most commonly used medications in intensive care units. In clinical practice, the use of a weight-based heparin dosing nomogram is standard practice for the treatment of thrombosis. Recently, machine learning techniques have dramatically improved the ability of computers to provide clinical decision support and have allowed for the possibility of computer generated, algorithm-based heparin dosing recommendations. OBJECTIVE:The objective of this study was to predict the effects of heparin treatment using machine learning methods to optimize heparin dosing in intensive care units based on the predictions. Patient state predictions were based upon activated partial thromboplastin time in 3 different ranges: subtherapeutic, normal therapeutic, and supratherapeutic, respectively. METHODS:Retrospective data from 2 intensive care unit research databases (Multiparameter Intelligent Monitoring in Intensive Care III, MIMIC-III; e-Intensive Care Unit Collaborative Research Database, eICU) were used for the analysis. Candidate machine learning models (random forest, support vector machine, adaptive boosting, extreme gradient boosting, and shallow neural network) were compared in 3 patient groups to evaluate the classification performance for predicting the subtherapeutic, normal therapeutic, and supratherapeutic patient states. The model results were evaluated using precision, recall, F1 score, and accuracy. RESULTS:Data from the MIMIC-III database (n=2789 patients) and from the eICU database (n=575 patients) were used. In 3-class classification, the shallow neural network algorithm performed the best (F1 scores of 87.26%, 85.98%, and 87.55% for data set 1, 2, and 3, respectively). The shallow neural network algorithm achieved the highest F1 scores within the patient therapeutic state groups: subtherapeutic (data set 1: 79.35%; data set 2: 83.67%; data set 3: 83.33%), normal therapeutic (data set 1: 93.15%; data set 2: 87.76%; data set 3: 84.62%), and supratherapeutic (data set 1: 88.00%; data set 2: 86.54%; data set 3: 95.45%) therapeutic ranges, respectively. CONCLUSIONS:The most appropriate model for predicting the effects of heparin treatment was found by comparing multiple machine learning models and can be used to further guide optimal heparin dosing. Using multicenter intensive care unit data, our study demonstrates the feasibility of predicting the outcomes of heparin treatment using data-driven methods, and thus, how machine learning-based models can be used to optimize and personalize heparin dosing to improve patient safety. Manual analysis and validation suggested that the model outperformed standard practice heparin treatment dosing.

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Comparing the direct normal form and multiple scales methods through frequency detuning.

Publications

Comparing the direct normal form and multiple scales methods through frequency detuning.

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