scholarly journals Neural networks and dynamical system techniques for volcanic tremor analysis

1996 ◽  
Vol 39 (2) ◽  
Author(s):  
R. Carniel
Keyword(s):  
Dynamical System ◽  
State Space ◽  
Structural Changes ◽  
Volcanic Tremor ◽  
Lag Time ◽  
State Variables ◽  
Stromboli Volcano ◽  
Structural Configuration ◽  
Experimental Time Series ◽  
Tremor Analysis

A volcano can be seen as a dynamical system, the number of state variables being its dimension N. The state is usually confined on a manifold with a lower dimension f, manifold which is characteristic of a persistent «structural configuration». A change in this manifold may be a hint that something is happening to the dynamics of the volcano, possibly leading to a paroxysmal phase. In this work the original state space of the volcano dynamical system is substituted by a pseudo state space reconstructed by the method of time-delayed coordinates, with suitably chosen lag time and embedding dimension, from experimental time series of seismic activity, i.e. volcanic tremor recorded at Stromboli volcano. The monitoring is done by a neural network which first learns the dynamics of the persistent tremor and then tries to detect structural changes in its behaviour.

Design of Reduced Order State Space Controllers With Adaptive Limiting Functions for Industrial Twin Shaft Gas Turbines

2006 ◽  
Author(s):  
Markus Beukenberg ◽  
Michael Brodmann ◽  
Hans Weibel ◽  
Detlef Mu¨ller ◽  
Alexander Schwarzin
Keyword(s):  
Nonlinear System ◽  
State Space ◽  
Gas Turbines ◽  
Structural Changes ◽  
Pole Placement ◽  
State Variables ◽  
Reduced Order ◽  
Quality Of Control ◽  
Full State ◽  
Order State

The designs of model-based state space controllers for industrial twin shaft gas turbines, presented at last year’s conference [1], were enhanced by a limiting function for selected state variables. In order to avoid the disadvantages of common controller concepts involving abrupt structural changes, the limitation was realised by a parameter-variant state space controller. To reduce the sensitivity of the full state space controller to parameter changes, a reduced order controller was developed, taking into account only the dominant state variables of the system. As in previously presented designs, a PI state space controller was designed for the reduced system using the pole placement method. Subsequently, this reduced controller was adapted to the original nonlinear system. With appropriate pole placements for the reduced order state space controller, a high quality of control, comparable to the behaviour of a full state space controller, can be obtained. The resulting controller also shows a reduced sensitivity to variations of the feedback parameters. The intended state variable limitation of the original nonlinear system to defined thresholds has been achieved by applying floating functions between different controller parameter sets.

Structural changes of volcanic tremor at Stromboli volcano

2008 ◽  
Vol 171 (1-2) ◽  
pp. 103-117 ◽  
Author(s):  
Francesca Fattori Speranza ◽  
Roberto Carniel
Keyword(s):  
Structural Changes ◽  
Volcanic Tremor ◽  
Stromboli Volcano

scholarly journals On choosing state variables for piecewise-smooth dynamical system simulations

2018 ◽  
Vol 95 (2) ◽  
pp. 1165-1188 ◽  
Author(s):  
Jin-Song Pei ◽  
Joseph P. Wright ◽  
François Gay-Balmaz ◽  
James L. Beck ◽  
Michael D. Todd
Keyword(s):  
Dynamical System ◽  
Piecewise Smooth ◽  
State Variables ◽  
Smooth Dynamical System

scholarly journals Spectral precursors of paroxysmal phases of Stromboli

1996 ◽  
Vol 39 (2) ◽  
Author(s):  
R. Carniel ◽  
F. Iacop
Keyword(s):  
Continuous Monitoring ◽  
Energy Content ◽  
Volcanic Tremor ◽  
Energy Concentration ◽  
Stromboli Volcano ◽  
Stable States ◽  
Spectral Content ◽  
Abrupt Changes ◽  
Intense Activity ◽  
Dangerous Activity

In this work we investigate the characteristics of the seismicity at Stromboli volcano during more than two years, i.e. from 11 May 1992 to 21 August 1994. The three paroxysmal phases of 1993 mark significant changes in the Strombolian activity; nevertheless, these are not the only ones observed. In fact, the energy content, both in terms of volcanic tremor and of number of events drops to very low values after the periods of intense activity, accompanied by a change in the spectral content of the tremor. However, equally abrupt changes in the frequency content, not accompanied by evident intensity variations, can be observed some weeks after the end of the crises. The volcano seems therefore to behave like a dynamical system with many «quite stable » states with abrupt transitions between them. An interesting observation is the appearance of an energy concentration in the spectral sectors below 3 Hz before more violent eruptive episodes; although the duration of such a phenomenon is variable, it has to be investigated as a possible precursor of potentially dangerous activity of the volcano. A continuous monitoring of the spectral content of volcanic tremor on Stromboli is confirmed to be an essential tool in order to understand the behaviour of Stromboli volcano and to try to forecast its paroxysmal phases.

Derived Nodes Approach for Improving Accuracy of Machining Stability Prediction

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Le Cao ◽  
Xiao-Ming Zhang ◽  
Tao Huang ◽  
Han Ding
Keyword(s):  
State Space ◽  
Polynomial Interpolation ◽  
Recursive Estimation ◽  
Machining Process ◽  
Stability Prediction ◽  
State Variables ◽  
Piecewise Polynomials ◽  
Discrete Equations ◽  
Runge Phenomenon ◽  
The Stability

Machining process dynamics can be described by state-space delayed differential equations (DDEs). To numerically predict the process stability, diverse piecewise polynomial interpolation is often utilized to discretize the continuous DDEs into a set of linear discrete equations. The accuracy of discrete approximation of the DDEs generally depends on how to deal with the piecewise polynomials. However, the improvement of the stability prediction accuracy cannot be always guaranteed by higher-order polynomials due to the Runge phenomenon. In this study, the piecewise polynomials with derivative-continuous at joint nodes are taken into consideration. We develop a recursive estimation of derived nodes for interpolation approximation of the state variables, so as to improve the discretization accuracy of the DDEs. Two different temporal discretization methods, i.e., second-order full-discretization and state-space temporal finite methods, are taken as demonstrations to illustrate the effectiveness of applying the proposed approach for accuracy improvement. Numerical simulations prove that the proposed approach brings a great improvement on the accuracy of the stability lobes, as well as the rate of convergence, compared to the previous recorded ones with the same order of interpolation polynomials.

scholarly journals Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 300 ◽  
Author(s):  
Artur Karimov ◽  
Erivelton G. Nepomuceno ◽  
Aleksandra Tutueva ◽  
Denis Butusov
Keyword(s):  
Dynamical System ◽  
Nonlinear Systems ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Data Series ◽  
Lorenz Attractor ◽  
State Variables ◽  
Laurent Polynomials ◽  
Actual Problem ◽  
Partially Observed

The identification of partially observed continuous nonlinear systems from noisy and incomplete data series is an actual problem in many branches of science, for example, biology, chemistry, physics, and others. Two stages are needed to reconstruct a partially observed dynamical system. First, one should reconstruct the entire phase space to restore unobserved state variables. For this purpose, the integration or differentiation of the observed data series can be performed. Then, a fast-algebraic method can be used to obtain a nonlinear system in the form of a polynomial dynamical system. In this paper, we extend the algebraic method proposed by Kera and Hasegawa to Laurent polynomials which contain negative powers of variables, unlike ordinary polynomials. We provide a theoretical basis and experimental evidence that the integration of a data series can give more accurate results than the widely used differentiation. With this technique, we reconstruct Lorenz attractor from a one-dimensional data series and B. Muthuswamy’s circuit equations from a three-dimensional data series.

Statistical analyses and characteristics of volcanic tremor on Stromboli Volcano (Italy)

1998 ◽  
Vol 60 (2) ◽  
pp. 75-88 ◽  
Author(s):  
S. Falsaperla ◽  
H. Langer ◽  
S. Spampinato
Keyword(s):  
Volcanic Tremor ◽  
Statistical Analyses ◽  
Stromboli Volcano

scholarly journals A Stochastic and State Space Model for Tumour Growth and Applications

2009 ◽  
Vol 10 (2) ◽  
pp. 117-138 ◽  
Author(s):  
Wai-Yuan Tan ◽  
Weiming Ke ◽  
G. Webb
Keyword(s):  
State Space ◽  
Stochastic System ◽  
Tumour Growth ◽  
Deterministic Model ◽  
State Space Model ◽  
Tumour Cells ◽  
The State ◽  
System Model ◽  
State Variables ◽  
Space Model

We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.

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