Identify Model Parameters Research Articles

Adjoint- and Hybrid-Based Hessians for Optimization Problems in System Identification

An adjoint sensitivity-based approach to determine the gradient and Hessian of cost functions for system identification of dynamical systems is presented. The motivation is the development of a computationally efficient approach relative to the direct differentiation (DD) technique and which overcomes the challenges of the step-size selection in finite difference (FD) approaches. An optimization framework is used to determine the parameters of a dynamical system which minimizes a summation of a scalar cost function evaluated at the discrete measurement instants. The discrete time measurements result in discontinuities in the Lagrange multipliers. Two approaches labeled as the Adjoint and the Hybrid are developed for the calculation of the gradient and Hessian for gradient-based optimization algorithms. The proposed approach is illustrated on the Lorenz 63 model where part of the initial conditions and model parameters are estimated using synthetic data. Examples of identifying model parameters of light curves of type 1a supernovae and a two-tank dynamic model using publicly available data are also included.

Fermentation of Saccharomyces cerevisiae – Combining kinetic modeling and optimization techniques points out avenues to effective process design

A combined experimental/theoretical approach is presented, for improving the predictability of Saccharomyces cerevisiae fermentations. In particular, a mathematical model was developed explicitly taking into account the main mechanisms of the fermentation process, allowing for continuous computation of key process variables, including the biomass concentration and the respiratory quotient (RQ). For model calibration and experimental validation, batch and fed-batch fermentations were carried out. Comparison of the model-predicted biomass concentrations and RQ developments with the corresponding experimentally recorded values shows a remarkably good agreement for both batch and fed-batch processes, confirming the adequacy of the model. Furthermore, sensitivity studies were performed, in order to identify model parameters whose variations have significant effects on the model predictions: our model responds with significant sensitivity to the variations of only six parameters. These studies provide a valuable basis for model reduction, as also demonstrated in this paper. Finally, optimization-based parametric studies demonstrate how our model can be utilized for improving the efficiency of Saccharomyces cerevisiae fermentations.

Model-Based Lithium-Ion Battery Resistance Estimation From Electric Vehicle Operating Data

State-of-health estimates of batteries are essential for onboard electric vehicles in order to provide safe, reliable, and cost-effective battery operation. This paper suggests a method to estimate the 10-s discharge resistance, which is an established battery figure of merit from laboratory testing, without performing the laboratory test. Instead, a state-of-health estimate of batteries is obtained using data directly from their operational use, e.g., onboard electric vehicles. It is shown that simple dynamical battery models, based on a current input and a voltage output, with model parameters dependent on temperature and state of charge, can be derived using AutoRegressive with eXogenous input models, whose order can be adjusted to describe the complex battery behavior. Then, the 10-s discharge resistance can be conveniently computed from the identified model parameters. Moreover, the uncertainty of the estimated resistance values is provided by the method. The suggested method is validated with usage data from emulated electric vehicle operation of an automotive lithium-ion battery cell. The resistance values are estimated accurately for a state-of-charge and temperature range spanning typical electric vehicle operating conditions. The identification of the model parameters and the resistance computation are very fast, rendering the method suitable for onboard application.

System identification of a low-order heat transfer model for shape memory alloy wires

Shape memory alloys exhibit a strong thermomechanical coupling. This coupling has been modeled extensively using energy-based constitutive models. Equally as important in the dynamics of shape memory alloy–based systems is the heat transfer behavior. The literature is comprehensive on parameter identification for constitutive models but is lacking in a complete resource for identification of the parameters for the heat transfer behavior. In this article, the parameters for a low-order differential equation heat transfer model are determined through experimental system identification. This is completed with two objectives in mind: keeping the order of the model low and accurately modeling the response within an acceptable tolerance. A comparison of identified model parameters to nominal values shows similar magnitudes in all parameters with exception to a significant difference in the heat transfer coefficient. For all parameters, it is shown that a methodical system identification is necessary to develop an accurate predictive model. This article details a clear method to identify the parameters of the low-order heat transfer model.

Turbidity Current Dynamics: 1. Model Formulation and Identification of Flow Equilibrium Conditions Resulting From Flow Stripping and Overspill

This study expands the widely used one‐dimensional, four‐equation model for turbidity currents to account for mass, momentum, and energy sinks associated with flow stripping and overspill processes acting upon the turbidity current suspension cloud. The suspension cloud is defined as any portion of the flow extending above the channel levees. The expanded model allows steady turbidity currents to evolve to a uniform, or equilibrium, state where mass, momentum, and energy gained through sediment and clear‐water entrainment processes are balanced by the mass, momentum, and energy lost to flow stripping and overspill. We perform a sensitivity analysis of the expanded model to assess how changes in channel (e.g., slope, channel height, width, bed friction, and radius of curvature) and flow (e.g., sediment grain size, suspension cloud concentration, and turbulence) properties affect the equilibrium flow conditions. By varying the model inputs from half to double their base case values, we find that the equilibrium values can change by up to a factor of 2. We find that the equilibrium conditions, including the flow Richardson number, were generally most sensitive to changes in slope, channel height, grain size, and suspension cloud concentration. Additionally, we identify model parameter space where Richardson subcritical equilibrium flow is possible. The fact that turbidity currents can attain equilibrium, and particularly subcritical equilibrium, might help elucidate the long turbidity current runout distances on low slopes inferred from extensive submarine channel levee systems.

Estimating the frequency of indolent breast cancer in screening trials.

Cancer screening can detect cancer that would not have been detected in a patient's lifetime without screening. Standard methods for analyzing screening data do not explicitly account for the possibility that a fraction of tumors may remain latent indefinitely. We extend these methods by representing cancers as a mixture of those that progress to symptoms (progressive) and those that remain latent (indolent). Given sensitivity of the screening test, we derive likelihood expressions to simultaneously estimate (1) the rate of onset of preclinical cancer, (2) the average preclinical duration of progressive cancers, and (3) the fraction of preclinical cancers that are indolent. Simulations demonstrate satisfactory performance of the estimation approach to identify model parameters subject to precise specifications of input parameters and adequate numbers of interval cancers. In application to four breast cancer screening trials, the estimated indolent fraction among preclinical cancers varies between 2% and 35% when assuming 80% test sensitivity and varying specifications for the earliest time that participants could plausibly have developed cancer. We conclude that standard methods for analyzing screening data can be extended to allow some indolent cancers, but accurate estimation depends on correctly specifying key inputs that may be difficult to determine precisely in practice.

МАТЕМАТИЧЕСКИЕ МОДЕЛИ НЕЛИНЕЙНОЙ ВЯЗКОУПРУГОСТИ С ОПЕРАТОРАМИ ДРОБНОГО ИНТЕГРО-ДИФФЕРЕНЦИРОВАНИЯ

Based on the method of structural modelling and the Boltzmann-Volterra hypothesis of the hereditary elasticity deformable solid, the article considers linear and nonlinear fractional analogues of classical rheological models, such as Newton (the so-called model of Scott Blair), Voigt, Maxwell, Kelvin and Zener using the tool of fractional integro-differentiation of Riemann Liouville. The classes of nonlinear mathematical models are distinguished, for which the solution of the creep problem can be obtained explicitly in terms of known special functions. A technique for identifying the parameters of the proposed mathematical models is developed on the basis of known experimental data on uniaxial stretching of samples at different and constant load levels. In the presence of explicit solutions to the creep problem, the parameters of mathematical models are determined from the solution of the problem of approximating the experimental values of deformation using the method of least squares with subsequent refinement by the coordinate-wise descent method at all time points for all stress values in a series of experiments. For nonlinear mathematical models of viscoelastic deformation, which do not allow to find the solution of the creep problem in an explicit form, a method for determining the model parameters based on the coordinate-wise descent method with inversion at each step to the numerical solution of the defining integral equation has been developed. The method of identifying model parameters with operators of fractional integro-differentiation is realized on the example of creep of polyvinylchloride plastic compound. The values of the parameters for all the models studied are given, their adequacy to the experimental data is checked, and errors in the deviation of the calculated data from the experimental values are analyzed. As an example, a comparative analysis of the relative error in approximating the experimental creep curves by theoretical deformation values is made in the framework of a linear, nonlinear integrable and nonlinear nonintegrable fractional analog of the Kelvin model. The article oulines the appropriateness of using the viscoelastic deformation models with the operators of fractional integro-differentiation, based on the comparison of calculations of the considered models with the calculations of the viscoelasticity models having integral operators of integro-differentiation.

Estimating Semi-Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity

This paper proposes a new semi-parametric identification and estimation approach to multinomial choice models in a panel data setting with individual fixed effects. Our approach is based on cyclic monotonicity, which is a defining feature of the random utility framework underlying multinomial choice models. From the cyclic monotonicity property, we derive identifying inequalities without requiring any shape restrictions for the distribution of the random utility shocks. These inequalities point identify model parameters under straightforward assumptions on the covariates. We propose a consistent estimator based on these inequalities.

Self-Tuning Distributed Fusion Filter for Multi-Sensor Systems Subject to Unknown Model Parameters and Missing Measurement Rates

A self-tuning fusion estimation problem is addressed for multi-sensor (MS) linear discrete-time stochastic systems subject to unknown model parameters (UMPs) and missing measurement rates. The phenomena of missing measurements for different sensors are described by random variable sequences obeying Bernoulli distributions. The UMPs and missing measurement rates are identified online by the recursive extended least squares (RELS) algorithms and correlation functions, respectively. A distributed fusion identifier for UMPs is presented by using matrix-weighted fusion estimation (MWFE) algorithm in the linear unbiased minimum variance sense. Furthermore, the corresponding self-tuning state estimation algorithms are obtained by substituting the identified model parameters and missing measurement rates into the local optimal filters, cross-covariance matrices (CCMs), and distribution optimal fusion filter. Finally, the convergence of the presented algorithms is analyzed. A numerical example shows the effectiveness of the presented algorithms.

Vibration Characteristics of Heavy‐Duty CNC Machine Tool‐Foundation Systems

Vibration characteristics of heavy CNC machine tools are directly affected by their foundations. To analyze vibrations of heavy CNC machine tools caused by internal and external loads, a system dynamics model of a rigid‐flexible coupled heavy‐duty CNC machine tool‐foundation system was established based on the multibody transfer matrix method. Since joint surfaces can seriously affect the accuracy of system mechanics models, the substructure synthesis method was first used to establish a dynamic model of the joint surface. The frequency response function was then used to identify model parameters. Moreover, to improve the accuracy of parameter identification of the joint surface, a residual frequency compensation function was used to reconstruct the frequency response function. Finally, the multibody system model was implemented by combining surface elements. To verify the system dynamics model, an experimental model of the heavy‐duty machine‐foundation system was built, taking into consideration joint surface factors, and the theoretical model was validated by comparing theoretical, simulation, and experimental results. Using the theoretical model, the influence of different forms of concrete foundations, materials, and soil properties on the vibration characteristics of heavy‐duty CNC machine tools was analyzed, thus providing a theoretical basis for optimizing and improving CNC machine tools.

A new state-of-health estimation method for lithium-ion batteries through the intrinsic relationship between ohmic internal resistance and capacity

For secure and reliable operation of lithium-ion batteries in electric vehicles, diagnosis of the battery degradation is essential. This can be achieved by monitoring the increase of the internal resistance of the battery cells over the whole lifetime of the battery. In this paper, a method to estimate state of health (SoH) is presented through the established linear relationship between ohmic internal resistance and capacity fade. Firstly, the Thevenin model and the recursive least squares (RLS) algorithm are applied to simulate battery dynamic characteristics and identify model parameters, respectively. Secondly, based on the established linear relationship between ohmic internal resistance and capacity fade, both ohmic internal resistances at the start and the end of the battery’s lifetime are estimated by only two random discharge cycles at different aging stages. Finally, an online SoH estimator is formulated and applied to estimate the SoH of a battery’s remaining cycles. In addition, a series of experiments were carried out based on dynamic loading to verify the proposed method. The SoH estimates indicate that the evaluated maximum SoH errors are within ±4%. The proposed SoH estimation method is consistent with the measurement data of the battery and shows good results with very low computational effort.

Data‐driven simulation of metastatic processes within brain tissue

AbstractThe modelling of biological processes like the metastasation of lung cancer in brain tissue requires the inclusion of the major processes at the metastasis site as well as to identify model parameters from experiments. In this regard, experimental data from proliferation, malnutrition and drug experiments are embedded into a continuum‐mechanical metastases model. Successfully implemented, such models can serve as prototype tools to estimate the metastases growth and response to therapeutic applications. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Complex Models of Sequence Evolution Require Accurate Estimators as Exemplified with the Invariable Site Plus Gamma Model.

The invariable site plus n}{}Gamma model (In}{}+Gamma) is widely used to model rate heterogeneity among alignment sites in maximum likelihood and Bayesian phylogenetic analyses. The proof that the In}{}+ continuous n}{}Gamma model is identifiable (model parameters can be inferred correctly given enough data) has increased the creditability of its application to phylogeny reconstruction. However, most phylogenetic software implement the In}{}+ discrete n}{}Gamma model, whose identifiability is likely but unproven. How well the parameters of the In}{}+ discrete n}{}Gamma model are estimated is still disputed. Especially the correlation between the fraction of invariable sites and the fractions of sites with a slow evolutionary rate is discussed as being problematic. We show that optimization heuristics as implemented in frequently used phylogenetic software (PhyML, RAxML, IQ-TREE, and MrBayes) cannot always reliably estimate the shape parameter, the proportion of invariable sites, and the tree length. Here, we propose an improved optimization heuristic that accurately estimates the three parameters. While research efforts mainly focus on tree search methods, our results signify the equal importance of verifying and developing effective estimation methods for complex models of sequence evolution.

Preference Discovery and Experimentation

I provide axiomatic foundations for a model of taste uncertainty with endogenous learning through consumption. In this setting, uncertainty is over an unobservable, subjective state space. Preference over lottery-menu pairs is sufficient to identify the state space and the learning process. In this model, the agent is viewed as if he learns the utility of an object upon its consumption. This information is used to improve choice from the follow-on menu. This implies a trade-off between consumption value and information leading to experimentation. I provide a behavioral definition of experimentation. While the literature focuses on identifying subjective states through a demand for flexibility, I show that experimentation also (partially) identifies taste uncertainty. Furthermore, only choice data on a small set of binary menus (analogous to financial options) is required to uniquely identify model parameters. An application of the model shows that the compromise effect can often be understood as rational experimentation.

Coordinated state‐estimation method for air‐conditioning loads to provide primary frequency regulation service

The penetration of large-scale renewable generation leads to a shortage of primary frequency regulation resources as well as increasing regulation demand. By exploiting the thermal capacity of buildings, the authors achieve linear power–frequency characteristics comparable to turbine droop control via clustering a number of air-conditioning units (ACs) to participate in primary frequency regulation without affecting indoor comfort. Due to the bandwidth limitations and latency in communication, the real-time centralised control method face great challenges. This study proposes a two-level coordinated state-estimation method to reduce the coordination burden, in which a central coordinator and local controller for each AC are involved. The central coordinator periodically gathers the working state of every AC and estimated thermal parameters individually, then broadcasts this identified model parameters – the coordination information – to each local controller. Resorting to a state-estimation method considering the coordinated information and local measurements, local controller determines whether to toggle the state of local AC to realise a fast frequency response. Simulation results show that the approach can effectively manage a large number of ACs with heterogeneous parameters to provide a primary frequency regulation service without inducing a rebound effect.

System identification and robust position control for electro-hydraulic servo system using hybrid model predictive control

This paper examined system identification using grey-box model estimation and position-tracking control for an electro-hydraulic servo system (EHSS) using hybrid controller composed of proportional-integral control (PIC) and model predictive control (MPC). The nonlinear EHSS model is represented by differential equations. We identify model parameters and verify their accuracy against experimental data in MATLAB to evaluate the validity of this mathematical model. To guarantee improved performance of EHSS and precision of cylinder position, we propose a hybrid controller composed of PIC and MPC. The controller is designed using the Control Design and Simulation module in the Laboratory Virtual Instrumentation Engineering Workbench (LabVIEW). A LabVIEW-based experimental rig is developed to apply the proposed controller in real time. Then, the validity and performance superiority of the hybrid controller were confirmed by comparing them with the MPC and PIC results. Results of real-life experiments show improved robustness and dynamic and static properties of EHSS.

An On-Board Calibration Scheme for Map-Based Combustion Phase Control of Spark-Ignition Engines

To improve the transient-state combustion phase control performance and adapt to the shift of engine dynamics, this paper presents an on-board calibration scheme to control the combustion phase of spark-ignition (SI) engines. First, taking a crank angle of 50% of the mass fraction burnt (CA50) as the combustion phase indicator, the relationship between CA50 and SA is studied, and the influences of two other important factors, engine speed and load, are regarded, as the parameters need calibration or update. Second, a bilinear interpolation algorithm is employed to depict the polynomial influence function of speed and load on CA50, which is also used for the CA50 control later. Then, the on-board calibration issue is converted to a parameters identification problem, and a stochastic gradient descent algorithm is utilized to identify model parameters by iterative updates, which reduces computational complexity and the use of memory space for the embedded control system. Finally, the proposed strategy is verified on a gasoline SI engine and is applied to the combustion phase control in the feedforward channel, which can significantly improve the performance at a transient-state operating condition.

Estimation of basic reproduction number of the Middle East respiratory syndrome coronavirus (MERS-CoV) during the outbreak in South Korea, 2015

BackgroundIn South Korea, an outbreak of Middle East respiratory syndrome (MERS) occurred in 2015. It was the second largest MERS outbreak. As a result of the outbreak in South Korea, 186 infections were reported, and 36 patients died. At least 16,693 people were isolated with suspicious symptoms. This paper estimates the basic reproduction number of the MERS coronavirus (CoV), using data on the spread of MERS in South Korea.MethodsThe basic reproduction number of an epidemic is defined as the average number of secondary cases that an infected subject produces over its infectious period in a susceptible and uninfected population. To estimate the basic reproduction number of the MERS-CoV, we employ data from the 2015 South Korea MERS outbreak and the susceptible-infected-removed (SIR) model, a mathematical model that uses a set of ordinary differential equations (ODEs).ResultsWe fit the model to the epidemic data of the South Korea outbreak minimizing the sum of the squared errors to identify model parameters. Also we derive the basic reproductive number as the terms of the parameters of the SIR model. Then we determine the basic reproduction number of the MERS-CoV in South Korea in 2015 as 8.0977. It is worth comparing with the basic reproductive number of the 2014 Ebola outbreak in West Africa including Guinea, Sierra Leone, and Liberia, which had values of 1.5–2.5.ConclusionsThere was no intervention to control the infection in the early phase of the outbreak, thus the data used here provide the best conditions to evaluate the epidemic characteristics of MERS, such as the basic reproduction number. An evaluation of basic reproduction number using epidemic data could be problematic if there are stochastic fluctuations in the early phase of the outbreak, or if the report is not accurate and there is bias in the data. Such problems are not relevant to this study because the data used here were precisely reported and verified by Korea Hospital Association.

Study on driver model for hybrid truck based on driving simulator experimental results

In this paper, a proposed car-following driver model taking into account some features of both the compensatory and anticipatory model representing the human pedal operation has been verified by driving simulator experiments with several real drivers. The comparison between computer simulations performed by determined model parameters with the experimental results confirm the correctness of this mathematical driver model and identified model parameters. Then the driver model is joined to a hybrid vehicle dynamics model and the moderate car following maneuver simulations with various driver parameters are conducted to investigate influences of driver parameters on vehicle dynamics response and fuel economy. Finally, major driver parameters involved in the longitudinal control of drivers are clarified.

Identification of Bouc-Wen hysteretic parameters based on enhanced response sensitivity approach

This paper aims to identify parameters of Bouc-Wen hysteretic model using time-domain measured data. It follows a general inverse identification procedure, that is, identifying model parameters is treated as an optimization problem with the nonlinear least squares objective function. Then, the enhanced response sensitivity approach, which has been shown convergent and proper for such kind of problems, is adopted to solve the optimization problem. Numerical tests are undertaken to verify the proposed identification approach.