scholarly journals Parameter estimation for energy balance models with memory

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140349 ◽  
Author(s):  
Lionel Roques ◽  
Mickaël D. Chekroun ◽  
Michel Cristofol ◽  
Samuel Soubeyrand ◽  
Michael Ghil
Keyword(s):  
Parameter Estimation ◽  
Energy Balance ◽  
Statistical Model ◽  
Ice Cores ◽  
Temperature Measurements ◽  
Age Dating ◽  
Observation Process ◽  
Wide Range ◽  
Energy Balance Models ◽  
With Memory

We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations with integral memory terms. First, we show that a space-dependent parameter can be determined uniquely everywhere in the PDE's domain of definition D , using only temperature information in a small subdomain E ⊂ D . This result is valid only when the data correspond to exact measurements of the temperature. We propose a method for estimating a model parameter of the EBMM using more realistic, error-contaminated temperature data derived, for example, from ice cores or marine-sediment cores. Our approach is based on a so-called mechanistic-statistical model that combines a deterministic EBMM with a statistical model of the observation process. Estimating a parameter in this setting is especially challenging, because the observation process induces a strong loss of information. Aside from the noise contained in past temperature measurements, an additional error is induced by the age-dating method, whose accuracy tends to decrease with a sample's remoteness in time. Using a Bayesian approach, we show that obtaining an accurate parameter estimate is still possible in certain cases.

scholarly journals Optical whispering-gallery mode barcodes for high-precision and wide-range temperature measurements

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Jie Liao ◽  
Lan Yang
Keyword(s):  
High Precision ◽  
Dynamic Range ◽  
Single Mode ◽  
Whispering Gallery Mode ◽  
Temperature Measurements ◽  
Laser Source ◽  
Multiple Modes ◽  
Whispering Gallery ◽  
Wide Range ◽  
Thermal Sensing

AbstractTemperature is one of the most fundamental physical properties to characterize various physical, chemical, and biological processes. Even a slight change in temperature could have an impact on the status or dynamics of a system. Thus, there is a great need for high-precision and large-dynamic-range temperature measurements. Conventional temperature sensors encounter difficulties in high-precision thermal sensing on the submicron scale. Recently, optical whispering-gallery mode (WGM) sensors have shown promise for many sensing applications, such as thermal sensing, magnetic detection, and biosensing. However, despite their superior sensitivity, the conventional sensing method for WGM resonators relies on tracking the changes in a single mode, which limits the dynamic range constrained by the laser source that has to be fine-tuned in a timely manner to follow the selected mode during the measurement. Moreover, we cannot derive the actual temperature from the spectrum directly but rather derive a relative temperature change. Here, we demonstrate an optical WGM barcode technique involving simultaneous monitoring of the patterns of multiple modes that can provide a direct temperature readout from the spectrum. The measurement relies on the patterns of multiple modes in the WGM spectrum instead of the changes of a particular mode. It can provide us with more information than the single-mode spectrum, such as the precise measurement of actual temperatures. Leveraging the high sensitivity of WGMs and eliminating the need to monitor particular modes, this work lays the foundation for developing a high-performance temperature sensor with not only superior sensitivity but also a broad dynamic range.

scholarly journals A Modified NM-PSO Method for Parameter Estimation Problems of Models

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
An Liu ◽  
Erwie Zahara ◽  
Ming-Ta Yang
Keyword(s):  
Genetic Algorithm ◽  
Parameter Estimation ◽  
Particle Swarm Optimization ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Wide Range ◽  
Estimation Problems

Ordinary differential equations usefully describe the behavior of a wide range of dynamic physical systems. The particle swarm optimization (PSO) method has been considered an effective tool for solving the engineering optimization problems for ordinary differential equations. This paper proposes a modified hybrid Nelder-Mead simplex search and particle swarm optimization (M-NM-PSO) method for solving parameter estimation problems. The M-NM-PSO method improves the efficiency of the PSO method and the conventional NM-PSO method by rapid convergence and better objective function value. Studies are made for three well-known cases, and the solutions of the M-NM-PSO method are compared with those by other methods published in the literature. The results demonstrate that the proposed M-NM-PSO method yields better estimation results than those obtained by the genetic algorithm, the modified genetic algorithm (real-coded GA (RCGA)), the conventional particle swarm optimization (PSO) method, and the conventional NM-PSO method.

Acoustic Energy Balance During the Onset, Growth and Saturation of Thermoacoustic Instabilities

2020 ◽  
Author(s):  
R. Gaudron ◽  
D. Yang ◽  
A. S. Morgans
Keyword(s):  
Energy Balance ◽  
Network Models ◽  
Acoustic Energy ◽  
Dimensionless Numbers ◽  
Weakly Nonlinear ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Wide Range ◽  
Acoustic Absorption Coefficient ◽  
Flame Describing Function

Abstract Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh’s criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Δ and the cycle-to-cycle acoustic energy ratio λ, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles, 2) the acoustic energy transfers occurring at the combustor’s boundaries and 3) the sources and sinks of acoustic energy located within the combustor. The acoustic energy balance of the well-documented Palies burner is then analyzed during the onset, growth and saturation of thermoacoustic instabilities using this new methodology. It is demonstrated that this new approach allows a deeper understanding of the physical mechanisms at play. For instance, it is possible to determine when the flame acts as an acoustic energy source or sink, where acoustic damping is generated, and if acoustic energy is transmitted through the boundaries of the burner.

Improvements in the Design and Operation of a Suction Pyrometer

1981 ◽  
Vol 14 (8) ◽  
pp. 301-305 ◽  
Author(s):  
M. S. Wojtan ◽  
K. A. G. Jones
Keyword(s):  
Temperature Measurements ◽  
Gas Temperature ◽  
Wide Range ◽  
Specific Project

There is a need to make reliable gas temperature measurements in combustion research. Conventional suction pyrometers and the associated methods of estimating their error do not always give satisfactory results. A new suction pyrometer has been developed to meet the requirements of a specific project at the Coal Research Establishment of the NCB. The unit incorporates a means of estimating directly the error in the pyrometer reading at the time the gas temperature is measured. The pyrometer has been used to measure gas temperatures in a wide range of environments. The results demonstrate the advantages of using the new pyrometer.

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (3) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive scheme Xn = pXn-1 + ∊n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (03) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊ n } such that the sequence of random variables {X n } generated by the linear, additive first-order autoregressive scheme X n = pXn-1 + ∊ n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

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