scholarly journals Detection of Model Uncertainty in the Dynamic Linear-Elastic Model of Vibrations in a Truss

2021 ◽  
pp. 281-295
Author(s):  
Alexander Matei ◽  
Stefan Ulbrich
Keyword(s):  
Model Uncertainty ◽  
Optimization Problem ◽  
Dynamic Models ◽  
Hypothesis Test ◽  
Model Parameters ◽  
Data Sets ◽  
State Variables ◽  
Linear Elastic ◽  
Validation Procedure ◽  
The Time Domain

AbstractDynamic processes have always been of profound interest for scientists and engineers alike. Often, the mathematical models used to describe and predict time-variant phenomena are uncertain in the sense that governing relations between model parameters, state variables and the time domain are incomplete. In this paper we adopt a recently proposed algorithm for the detection of model uncertainty and apply it to dynamic models. This algorithm combines parameter estimation, optimum experimental design and classical hypothesis testing within a probabilistic frequentist framework. The best setup of an experiment is defined by optimal sensor positions and optimal input configurations which both are the solution of a PDE-constrained optimization problem. The data collected by this optimized experiment then leads to variance-minimal parameter estimates. We develop efficient adjoint-based methods to solve this optimization problem with SQP-type solvers. The crucial test which a model has to pass is conducted over the claimed true values of the model parameters which are estimated from pairwise distinct data sets. For this hypothesis test, we divide the data into k equally-sized parts and follow a k-fold cross-validation procedure. We demonstrate the usefulness of our approach in simulated experiments with a vibrating linear-elastic truss.

Study on the Dynamic Models of Systems Biology from the View of Engineering

2012 ◽  
Vol 220-223 ◽  
pp. 952-957
Author(s):  
Chen Liu ◽  
Xiao Yan Liu
Keyword(s):  
Mathematical Model ◽  
Systems Biology ◽  
Dynamic Process ◽  
Biological System ◽  
Dynamic Models ◽  
Model Parameters ◽  
State Variables ◽  
Biochemical Pathway ◽  
The Right ◽  
The Mathematical Model

From the view of engineering, based on expatiating the features of systems biology, the paper discusses the workflows and the research emphasis of systems biology. It also explains how to model and analyze the dynamic process of signal transmitting network for a biological system by an example. Based on the complexity and uncertainty of the mathematical model, the right methods are chosen to realize the effective estimation of state variables and model parameters for the biochemical pathway.

scholarly journals Magnetically Nonlinear Dynamic Models of Synchronous Machines and Experimental Methods for Determining their Parameters

Energies ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 3519 ◽  
Author(s):  
Štumberger ◽  
Štumberger ◽  
Marčič
Keyword(s):  
Reference Frame ◽  
Permanent Magnets ◽  
Dynamic Models ◽  
Nonlinear Behavior ◽  
Experimental Methods ◽  
Iron Core ◽  
Model Parameters ◽  
Permanent Magnet Machines ◽  
State Variables ◽  
End Effects

This paper deals with rotary and linear synchronous reluctance machines and synchronous permanent magnet machines. It proposes a general method appropriate for determining the two-axis dynamic models of these machines, where the effects of slotting, mutual interaction between the slots and permanent magnets, saturation, cross-saturation, and—in the case of linear machines—the end effects, are considered. The iron core is considered to be conservative, without any losses. The proposed method contains two steps. In the first step, the dynamic model state variables are selected. They are required to determine the model structure in an arbitrarily chosen reference frame. In the second step, the model parameters, described as state variable dependent functions, are determined. In this way, the magnetically nonlinear behavior of the machine is accounted for. The relations among the Fourier coefficients of flux linkages and electromagnetic torque/thrust are presented for the models written in dq reference frame. The paper presents some of the experimental methods appropriate for determining parameters of the discussed dynamic models, which is supported by experimental results.

scholarly journals EKF-Based Parameter Identification of Multi-Rotor Unmanned Aerial VehiclesModels

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4174 ◽  
Author(s):  
Rodrigo Munguía ◽  
Sarquis Urzua ◽  
Antoni Grau
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Dynamic Models ◽  
Model Parameters ◽  
State Variables ◽  
Test Bed ◽  
Estimation Process ◽  
Observability Analysis ◽  
Aerial Vehicles ◽  
Aerial Vehicle

This work presents a method for estimating the model parameters of multi-rotor unmanned aerial vehicles by means of an extended Kalman filter. Different from test-bed based identification methods, the proposed approach estimates all the model parameters of a multi-rotor aerial vehicle, using a single online estimation process that integrates measurements that can be obtained directly from onboard sensors commonly available in this kind of UAV. In order to develop the proposed method, the observability property of the system is investigated by means of a nonlinear observability analysis. First, the dynamic models of three classes of multi-rotor aerial vehicles are presented. Then, in order to carry out the observability analysis, the state vector is augmented by considering the parameters to be identified as state variables with zero dynamics. From the analysis, the sets of measurements from which the model parameters can be estimated are derived. Furthermore, the necessary conditions that must be satisfied in order to obtain the observability results are given. An extensive set of computer simulations is carried out in order to validate the proposed method. According to the simulation results, it is feasible to estimate all the model parameters of a multi-rotor aerial vehicle in a single estimation process by means of an extended Kalman filter that is updated with measurements obtained directly from the onboard sensors. Furthermore, in order to better validate the proposed method, the model parameters of a custom-built quadrotor were estimated from actual flight log data. The experimental results show that the proposed method is suitable to be practically applied.

scholarly journals Regularized full-waveform inversion with automated salt flooding

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R569-R582 ◽  
Author(s):  
Mahesh Kalita ◽  
Vladimir Kazei ◽  
Yunseok Choi ◽  
Tariq Alkhalifah
Keyword(s):  
Optimization Problem ◽  
Waveform Inversion ◽  
Dominant Frequency ◽  
Model Parameters ◽  
Constant Density ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Low Frequencies ◽  
Full Waveform

Full-waveform inversion (FWI) attempts to resolve an ill-posed nonlinear optimization problem to retrieve the unknown subsurface model parameters from seismic data. In general, FWI fails to obtain an adequate representation of models with large high-velocity structures over a wide region, such as salt bodies and the sediments beneath them, in the absence of low frequencies in the recorded seismic signal, due to nonlinearity and nonuniqueness. We alleviate the ill posedness of FWI associated with data sets affected by salt bodies using model regularization. We have split the optimization problem into two parts: First, we minimize the data misfit and the total variation in the model, seeking to achieve an inverted model with sharp interfaces; and second, we minimize sharp velocity drops with depth in the model. Unlike conventional industrial salt flooding, our technique requires minimal human intervention and no information about the top of the salt. Those features are demonstrated on data sets of the BP 2004 and Sigsbee2A models, synthesized from a Ricker wavelet of dominant frequency 5.5 Hz and minimum frequency 3 Hz. We initiate the inversion process with a simple model in which the velocity increases linearly with depth. The model is well-retrieved when the same constant density acoustic code is used to simulate the observed data, which is still one of the most common FWI tests. Moreover, our technique allows us to reconstruct a reasonable depiction of the salt structure from the data synthesized independently with the BP 2004 model with variable density. In the Sigsbee2A model, we manage to even capture some of the fine layering beneath the salt. In addition, we evaluate the versatility of our method on a field data set from the Gulf of Mexico.

Multiple data parameter identification for nonlinear conceptual models

1997 ◽  
Vol 36 (5) ◽  
pp. 61-68 ◽  
Author(s):  
Hermann Eberl ◽  
Amar Khelil ◽  
Peter Wilderer
Keyword(s):  
Optimization Problem ◽  
Conceptual Models ◽  
Reference Data ◽  
Transport Model ◽  
Calibration Method ◽  
Data Sets ◽  
Multiple Data ◽  
Marquardt Algorithm ◽  
Multicriteria Optimization Problem ◽  
Higher Order Differential Equations

A numerical method for the identification of parameters of nonlinear higher order differential equations is presented, which is based on the Levenberg-Marquardt algorithm. The estimation of the parameters can be performed by using several reference data sets simultaneously. This leads to a multicriteria optimization problem, which will be treated by using the Pareto optimality concept. In this paper, the emphasis is put on the presentation of the calibration method. As an example identification of the parameters of a nonlinear hydrological transport model for urban runoff is included, but the method can be applied to other problems as well.

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

Model of the influence of Internet finance on monetary policy based on gibbs sampling and vector autoregression

2020 ◽  
pp. 1-11
Author(s):  
Hui Wang ◽  
Huang Shiwang
Keyword(s):  
Monetary Policy ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
Estimation Method ◽  
Financial Supervision ◽  
Var Model ◽  
Model Parameters ◽  
State Variables ◽  
Frequency Data ◽  
Internet Finance

The various parts of the traditional financial supervision and management system can no longer meet the current needs, and further improvement is urgently needed. In this paper, the low-frequency data is regarded as the missing of the high-frequency data, and the mixed frequency VAR model is adopted. In order to overcome the problems caused by too many parameters of the VAR model, this paper adopts the Bayesian estimation method based on the Minnesota prior to obtain the posterior distribution of each parameter of the VAR model. Moreover, this paper uses methods based on Kalman filtering and Kalman smoothing to obtain the posterior distribution of latent state variables. Then, according to the posterior distribution of the VAR model parameters and the posterior distribution of the latent state variables, this paper uses the Gibbs sampling method to obtain the mixed Bayes vector autoregressive model and the estimation of the state variables. Finally, this article studies the influence of Internet finance on monetary policy with examples. The research results show that the method proposed in this article has a certain effect.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

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