Single-rate Model Research Articles

Design of LQ regulators with prescribed degree of stability for dual-rate systems based on reinforcement learning

This paper considers dual-rate systems, where the output is measured at a relatively slow rate while the control signal is adjusted at a faster rate. The output sampling time is an integer multiple of the input sampling time. The paper examines dual-rate inferential control systems, which consist of a fast model, a slow model, and a switch. Missing output samples are estimated using the fast single-rate model. The single-rate control algorithm is then implemented at the fast-sampling rate. The fast-sampling discrete-time model is derived from the plant’s continuous-time model using the first-order hold (FOH) element. A discrete LQ regulator is proposed for this plant model, with a prescribed degree of stability (all closed-loop eigenvalues are within the range 0 < λ < 1 in magnitude). The matrix gain is calculated offline, and an online method for calculating the regulator gain is provided. The regulator gain is calculated using policy iteration, specifically Hewer’s algorithm. Finally, it is demonstrated that the presented inferential control system remains effective in the presence of multiplicative unmodeled dynamics. The main contributions of the paper are: (i) Designing the LQ regulator with a prescribed degree of stability using reinforcement learning (RL) (generalized policy iteration); and (ii) Considering the robust stability of the inferential control system in the presence of multiplicative unmodeled dynamics using the lifting technique.

Indirect taxation on VAT consumption. A possible study of alternative tax rate models in Portugal

The adoption of a single VAT rate system in the EU is a complex and controversial issue, since the current model includes several differentiated rates and is intended to reflect sectoral needs and ensure greater fairness in the taxation of consumption. This study aims to analyse which of the general consumption tax models (differentiated rates or a single rate) is more efficient in terms of revenue collection. The study uses official statistics available on the official website of the Tax and Customs Authority for the period 1996–2022. VAT revenue is measured by applying the formula of the EU’s common VAT model with the necessary adaptations to the flat rate model. Quantitative methods are applied to verify which of the tax models is more efficient in terms of collection. For this purpose, two scenarios were defined (17% and 21%). The results suggest that the estimated revenues for the proposed flat rate models are higher than the amounts actually collected through the differentiated rates. They also suggest that the 21% flat rate is preferable to the 17% rate, although the latter has the capacity to maintain current revenue levels and increase the amount collected compared to the current system. The conclusions suggest that the single VAT rate model is technically more preferable and notably more efficient than the current common consumption tax model adopted by the European Union. The study concludes that the refusal to adopt the single-rate model is not due to technical reasons but to political ones.

Multiloop Multirate Continuous-Discrete Drone Stabilization System: An Equivalent Single-Rate Model

The article discusses the UAV lateral motion stabilization system, as a MIMO multiloop multirate continuous-discrete system, specified in the form of an input–output model in the domain of discrete Laplace transform or in the form of a structural diagram. Approaches to the construction of equivalent T and NT single-rate models for MIMO multiloop multirate continuous-discrete systems are considered. Here, T is the largest common divisor of the sampling periods of the system, N is a natural number that is the smallest common multiple of the numbers characterizing the sampling periods of the system. The resulting impulse representations of the outputs of equivalent models are in the form of rational functions. The basis for the construction of these models is a matrix of sampling densities—a structural invariant of sampling chains. An example of the construction of the indicated matrix and an equivalent single-rate model are given. Obtaining equivalent single-rate models for MIMO multiloop multirate systems allows us to extend the methods of research and synthesis of MIMO continuous and continuous-discrete systems to a common theoretical base—the theory of polynomials and rational functions, which are typical elements of the description of these classes of systems.

Single versus dual-rate learning when exposed to Coriolis forces during reaching movements.

When we reach for an object during a passive whole body rotation, a tangential Coriolis force is generated on the arm. Yet, within a few trials, the brain adapts to this force so it does not disrupt the reach. Is this adaptation governed by a single-rate or dual-rate learning process? Here, guided by state-space modeling, we studied human reach adaptation in a fully-enclosed rotating room. After 90 pre-rotation reaches (baseline), participants were trained to make 240 to-and-fro reaches while the room rotated at 10 rpm (block A), then performed 6 reaches under opposite room rotation (block B), and subsequently made 100 post-rotation reaches (washout). A control group performed the same paradigm, but without the reaches during rotation block B. Single-rate and dual-rate models can be best dissociated if there would be full un-learning of compensation A during block B, but minimal learning of B. From the perspective of a dual-rate model, the un-learning observed in block B would mainly be caused by the faster state, such that the washout reaches would show retention effects of the slower state, called spontaneous recovery. Alternatively, following a single-rate model, the same state would govern the learning in block A and un-learning in block B, such that the washout reaches mimic the baseline reaches. Our results do not provide clear signs of spontaneous recovery in the washout reaches. Model fits further show that a single-rate process outperformed a dual-rate process. We suggest that a single-rate process underlies Coriolis force reach adaptation, perhaps because these forces relate to familiar body dynamics and are assigned to an internal cause.

Restructuring the European VAT tax system: advantages and disadvantages of the adoption of a single-rate model - a study based on the Portuguese case

The common VAT system adopted by EU member states comprises a set of various rates, which differentiate the goods and services subject to this tax. However, from a technical and management point of view, it would be preferable to adopt a single tax rate as it reduces distortions and facilitates tax compliance and management. This research seeks to analyse the benefits and disadvantages of adopting a single VAT as a means of simplifying the European VAT model. It takes Portugal as a case study. The main objective of this research is to contribute to the academic debate around the theme of the single rate of VAT versus differentiated rates, through the achievement of a series of analyses and statistical tests to revenues and percentages of GDP that they correspond, in the three scenarios considered in the study: differentiated rates, single rate of 17% and single rate of 21%.In the empirical part, hypotheses were developed, the effects on tax revenue of a differential collection system were analyzed and compared to a possible single rate regime on consumption to verify which one would be more efficient. data comparison permits to verify that the estimated revenue of the single rate of VAT is higher than the values ​​obtained by the system of differentiated rates, in any of the proposed models (17% or 21%). The results of this research are valid for all countries that adopt VAT or general tax transactions.

A MEMS Nonlinear Dynamic Approach for Neural Computing

This paper presents a novel concept for a micro-electro-mechanical-system (MEMS) neural computing unit based on the neuron rate model theory that is the basis of the dynamic field theory; a qualitative neuron approach to model cognition and human behavior, and the continuous time recurrent neural networks (CTRNNs); a class of artificial neural network. The concept utilizes the nonlinear dynamics of MEMS resonators, specifically, bi-stability and hysteresis, to simulate the detection and memory of a single rate model neuron. We introduce bi-stability into a straight microbeam by actuating the microbeam with an AC voltage at a frequency near its electric circuit resonance, which also significantly amplifies the applied voltage and introduces electromechanical coupling. Moreover, the memory and detection processes have been demonstrated using a MEMS arch beam by utilizing snap-through instability. Finally, we demonstrate electrical coupling between multiple artificial MEMS neurons to produce the selection process. Single degree of freedom models and initial preliminary experimental data are presented to qualitatively compare the dynamics of bi-stable MEMS to that of a rate model neuron. [2017-0316]

Prediction of the Ash Deposition Characteristics of Blended Coals in a 500 MWe Tangentially Fired Boiler

A computational simulation was performed to predict ash deposition in an industrial scale coal-fired boiler. The single-rate model and the improved nth order model were employed for devolatilization and char reaction with the model constants obtained from PC Coal LAB.(1) Ash particles were deposited on the wall by inertial impaction with the capture efficiency in terms of the estimated viscosity. The models for char combustion and ash deposition were implemented as new user defined functions in ANSYS-FLUENT.(2) The results showed that the deposition of blended coals was in good agreement with measurements under the influence of the surrounding flow field in a pilot scale furnace. The same combustion and ash deposition models were applied to the 500 MWe tangentially fired boiler burning blended coals. Ash deposition results for the boiler showed the same tendency as the measured data in terms of the wall fouling resistance. A larger deposition was predicted at the heat exchangers for sub-bituminous coal than for bituminous coal. However, there was no significant influence of the coal types in the furnace region. A parametric investigation was performed on ash deposition with respect to injection location and tilt angle of the burners. Deposition in the ash hopper was affected by the injection location but not by the coal types. The results showed a maximum ash deposition at the heat exchanger section for sub-bituminous coal from the lower burner set. Ash deposition increased in the ash hopper for the downward tilt angle of burners, whereas the maximum deposition occurred at the heat exchangers for the upward tilt angle.

Automatic Parallelization of Multirate Block Diagrams of Control Systems on Multicore Platforms

This article addresses the problem of parallelizing model block diagrams for real-time embedded applications on multicore architectures. We describe a Mixed Integer Linear Programming formulation for finding a feasible mapping of the blocks to different CPU cores. For single-rate models, we use an objective function that minimizes the overall worst-case execution time. We introduce a set of heuristics to solve the problem for large models in a reasonable time. For multirate models, we solve the feasibility problem for finding a valid mapping. We study the scalability and efficiency of our approach with synthetic benchmarks and an engine controller from Toyota.

Ability of Single-Rate Models to Predict Solute Distribution Coefficients in Systems with Heterogeneous Sorption Kinetics

Several sorption nonequilibrium models have been developed to gain a better understanding of solute transport in porous media, among which are those that assume a single-rate behavior. In this study, two commonly used single-rate models were fitted to computer-simulated breakthrough data from hypothetical column experiments in which multirate sorption kinetics exist at the pore scale. The objective was to determine how the sorption distribution coefficient (K) predicted using these models depends on the conditions under which the data were obtained. Simulated cases covered a range of experimental conditions and involved compounds with different sorption characteristics and different degrees of sorption rate heterogeneity. Results revealed that, for a system with a multirate sorption behavior, the true K value is under-predicted if the parameter estimation is determined by curve fitting a single-rate model. The extent of deviation between the fitted and true K increases with the decrease in residence time and increase in sorption rate heterogeneity. Functional relationships were developed between the relative reduction in K and solute residence time. Analysis using the relationships developed suggests that a major potential cause of the previously reported discrepancy between batch- and column-determined K could be attributed to the use of single-rate models for parameter prediction.

Numerical Study of Pulverized Coal MILD Combustion in a Self-Recuperative Furnace

A numerical study of pulverized coal combustion under Moderate or Intense Low oxygen Dilution (MILD) combustion conditions is presented in a parallel jet self-recuperative MILD combustion furnace. The Reynolds-Averaged Navier–Stokes equations, in a three-dimensional axisymmetric furnace domain, were solved using the Eddy Dissipation Concept model for the turbulence–chemistry interaction. The main aim of this study is to understand the influence of devolatilization models on the prediction accuracy of pulverized coal combustion under MILD combustion conditions. In particular, three devolatilization models are analyzed: a conventional single-rate model, a two-competing-rates model, and an advanced chemical percolation devolatilization (CPD) model based upon structural networks of the coal with a global kinetics mechanism. In addition, a new simplified numerical model is developed for Australian black and/or hard coal and optimized for the MILD combustion conditions. The modeling cases are validated with the experimental results of MILD combustion of high volatile Australian brown coal from Kingston using N2 as a carrier gas and low volatile Australian black coal from the Bowen basin using CO2 as a carrier gas in a MILD combustion furnace. From the comparison, the advanced CPD devolatilization model with a three-step global kinetic mechanism gives, as expected, the best agreement with the experimental measurements for the Kingston brown coal case, while all the models tested provide similar results for the Bowen basin black coal case. The heterogeneous reactions on the char burnout rate for pulverized coal combustion under MILD combustion conditions are presented and discussed. The characteristics of three NO formation mechanisms, namely, thermal-NO, prompt-NO, and fuel-NO, together with the NO reduction mechanism, named NO-reburning, are evaluated using the postprocessing modeling approach. The results reveal that the sum of contributions from the thermal-NO and prompt-NO routes only accounts for less than 3.8% to the total NO emissions, while the fuel-NO route dominates the NO emissions under MILD combustion conditions. It is also found that the total NO emission is reduced by up to 47% for the brown coal case and up to 39% for the black coal case via the reburning mechanisms.

Identification of Dual-Rate Sampled Hammerstein Systems with a Piecewise-Linear Nonlinearity Using the Key Variable Separation Technique

The identification difficulties for a dual-rate Hammerstein system lie in two aspects. First, the identification model of the system contains the products of the parameters of the nonlinear block and the linear block, and a standard least squares method cannot be directly applied to the model; second, the traditional single-rate discrete-time Hammerstein model cannot be used as the identification model for the dual-rate sampled system. In order to solve these problems, by combining the polynomial transformation technique with the key variable separation technique, this paper converts the Hammerstein system into a dual-rate linear regression model about all parameters (linear-in-parameter model) and proposes a recursive least squares algorithm to estimate the parameters of the dual-rate system. The simulation results verify the effectiveness of the proposed algorithm.

Modeling solute transport affected by heterogeneous sorption kinetics using single-rate nonequilibrium approaches

Single-rate transport models are commonly used for interpreting sorption-related mass transfer in porous media, often with the intention of approximating the kinetics of the sorption process. Among the most commonly used single-rate models are the two-site first-order (TSFO) and the two-site radial diffusion (TSRD) models. We fitted the parameters of the TSFO and TSRD models to simulated breakthrough data of hypothetical column experiments in which sorption rates were described by a γ-distributed sorption sites (GS) model. Our objective was to determine the conditions under which the assumption of a single-rate sorption parameter will be applicable to systems with heterogeneous sorption rates. We were further interested in knowing in what manner the fitted single-rate nonequilibrium model parameters depend upon the conditions under which the data were obtained. The considered hypothetical cases covered a range of experimental conditions and involved compounds with different sorption characteristics. The study revealed that the goodness of fit of the single rate models in simulating the transport of solutes exhibiting heterogeneous sorption rates is affected by solute residence time and pulse injection duration. Compared to the TSFO model, the TSRD model generally results in better prediction of solute transport affected by heterogeneous sorption kinetics. In addition, for such systems, the nonequilibrium parameters fitted using the TSFO model and their counterparts in the TSRD model are highly correlated. Moreover, an increase in the fitted mass transfer timescale of each of the single-rate models is coupled with an increase in the associated fraction of instantaneous sorption sites. A strong correlation was found between the time of the experiment and the product of the fitted characteristic time for mass transfer, pulse duration, and solute residence time. The correlation explains many of the variations in the mass transfer timescale encountered when single-rate sorption approaches were utilized to model solute transport in previous miscible displacement studies.

Determining the evolutionary history of gene families

Recent large-scale studies of individuals within a population have demonstrated that there is widespread variation in copy number in many gene families. In addition, there is increasing evidence that the variation in gene copy number can give rise to substantial phenotypic effects. In some cases, these variations have been shown to be adaptive. These observations show that a full understanding of the evolution of biological function requires an understanding of gene gain and gene loss. Accurate, robust evolutionary models of gain and loss events are, therefore, required. We have developed weighted parsimony and maximum likelihood methods for inferring gain and loss events. To test these methods, we have used Markov models of gain and loss to simulate data with known properties. We examine three models: a simple birth-death model, a single rate model and a birth-death innovation model with parameters estimated from Drosophila genome data. We find that for all simulations maximum likelihood-based methods are very accurate for reconstructing the number of duplication events on the phylogenetic tree, and that maximum likelihood and weighted parsimony have similar accuracy for reconstructing the ancestral state. Our implementations are robust to different model parameters and provide accurate inferences of ancestral states and the number of gain and loss events. For ancestral reconstruction, we recommend weighted parsimony because it has similar accuracy to maximum likelihood, but is much faster. For inferring the number of individual gene loss or gain events, maximum likelihood is noticeably more accurate, albeit at greater computational cost. www.bioinf.manchester.ac.uk/dupliphy simon.lovell@manchester.ac.uk; simon.whelan@manchester.ac.uk Supplementary data are available at Bioinformatics online.

Modelling rate distributions using character compatibility: implications for morphological evolution among fossil invertebrates

Rate distributions are important considerations when testing hypotheses about morphological evolution or phylogeny. They also have implications about general processes underlying character evolution. Molecular systematists often assume that rates are Poisson processes with gamma distributions. However, morphological change is the product of multiple probabilistic processes and should theoretically be affected by hierarchical integration of characters. Both factors predict lognormal rate distributions. Here, a simple inverse modelling approach assesses the best single-rate, gamma and lognormal models given observed character compatibility for 115 invertebrate groups. Tests reject the single-rate model for nearly all cases. Moreover, the lognormal outperforms the gamma for character change rates and (especially) state derivation rates. The latter in particular is consistent with integration affecting morphological character evolution.

CodonTest: Modeling Amino Acid Substitution Preferences in Coding Sequences

Codon models of evolution have facilitated the interpretation of selective forces operating on genomes. These models, however, assume a single rate of non-synonymous substitution irrespective of the nature of amino acids being exchanged. Recent developments have shown that models which allow for amino acid pairs to have independent rates of substitution offer improved fit over single rate models. However, these approaches have been limited by the necessity for large alignments in their estimation. An alternative approach is to assume that substitution rates between amino acid pairs can be subdivided into rate classes, dependent on the information content of the alignment. However, given the combinatorially large number of such models, an efficient model search strategy is needed. Here we develop a Genetic Algorithm (GA) method for the estimation of such models. A GA is used to assign amino acid substitution pairs to a series of rate classes, where is estimated from the alignment. Other parameters of the phylogenetic Markov model, including substitution rates, character frequencies and branch lengths are estimated using standard maximum likelihood optimization procedures. We apply the GA to empirical alignments and show improved model fit over existing models of codon evolution. Our results suggest that current models are poor approximations of protein evolution and thus gene and organism specific multi-rate models that incorporate amino acid substitution biases are preferred. We further anticipate that the clustering of amino acid substitution rates into classes will be biologically informative, such that genes with similar functions exhibit similar clustering, and hence this clustering will be useful for the evolutionary fingerprinting of genes.

Benchmarking Multi-Rate Codon Models

The single rate codon model of non-synonymous substitution is ubiquitous in phylogenetic modeling. Indeed, the use of a non-synonymous to synonymous substitution rate ratio parameter has facilitated the interpretation of selection pressure on genomes. Although the single rate model has achieved wide acceptance, we argue that the assumption of a single rate of non-synonymous substitution is biologically unreasonable, given observed differences in substitution rates evident from empirical amino acid models. Some have attempted to incorporate amino acid substitution biases into models of codon evolution and have shown improved model performance versus the single rate model. Here, we show that the single rate model of non-synonymous substitution is easily outperformed by a model with multiple non-synonymous rate classes, yet in which amino acid substitution pairs are assigned randomly to these classes. We argue that, since the single rate model is so easy to improve upon, new codon models should not be validated entirely on the basis of improved model fit over this model. Rather, we should strive to both improve on the single rate model and to approximate the general time-reversible model of codon substitution, with as few parameters as possible, so as to reduce model over-fitting. We hint at how this can be achieved with a Genetic Algorithm approach in which rate classes are assigned on the basis of sequence information content.

Effect of turbulence and devolatilization models on coal gasification simulation in an entrained-flow gasifier

Numerical simulations of the oxygen-blown coal gasification process inside a generic entrained-flow gasifier are carried out. The Eulerian–Lagrangian approach is applied to solve the Navier–Stokes equations and the particle dynamics. Seven species transport equations are solved with three heterogeneous global reactions and two homogeneous reactions. Finite rates are used for the heterogeneous solid-to-gas reactions. Both finite rate and eddy-dissipation combustion models are calculated for each homogeneous gas-to-gas reaction, and the smaller of the two rates is used. Four different devolatilization models are employed and compared. The Kobayashi model produces slower devolatilization rate than the other models. The constant rate model produces the fastest devolatilization rate. The single rate model and the chemical percolation model produce moderate and consistent devolatilization rate. Slower devolatilization rate produces higher exit gas temperature and higher CO and CO 2 mass fractions, but lower H 2 and heating value, and hence, achieves lower gasification efficiency. Combustion of volatiles is modeled with two-stage global reactions with an intermediate stage via benzene. Turbulence models significantly affect the simulated results. Among five turbulence models employed, the standard k– ε and the RSM models give consistent results. The time scale for employing stochastic time tracking of particles also affects simulated result. Caution has to be exerted to select the appropriate time constant value. Smaller particles have a higher surface/volume ratio and react faster than larger particles. However, large particles possessing higher inertia could impinge on the opposing jet and change the thermal-flow filed and the reaction rates.

A Two-Stage Method for Identification of Dual-Rate Systems with Fast Input and Very Slow Output

A dual-rate system with fast input and very slow output is very common in the chemical process industry. To identify its original fast single-rate model based on the output error method, a two-stage method combining techniques for dealing with initialization and local minimum problems is proposed in this paper. In its first stage, a finite impulse response (FIR) model is developed directly from the original dual-rate sampled data using the combined least-squares criterion and Newton−Raphson (N−R) method. In the second stage, a single-and-fast-rate output error model is developed on the basis of the original fast input signal and the derived slow rate model output. Besides the simulation examples, the method is also applied to develop a composition observer for an industrial distillation column.

Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems

A continuous-time system cannot be recovered solely from its uniformly sampled discrete-time model through the zero-order hold discretization or step-invariant transformation, but our studies indicate that it can be recovered uniquely from its non-uniformly sampled discrete-time model. In this paper, we discuss some related issues of non-uniformly sampled systems, including model derivation, controllability and observability, computation of single-rate models with different sampling periods, reconstruction of continuous-time systems, and parameter identification of non-uniformly sampled discrete-time systems. A numerical example is also given for illustration.

Generalized Yule-walker and two-stage identification algorithms for dual-rate systems

In this paper, two approaches are developed for directly identifying single-rate models of dual-rate stochastic systems in which the input updating frequency is an integer multiple of the output sampling frequency. The first is the generalized Yule-Walker algorithm and the second is a two-stage algorithm based on the correlation technique. The basic idea is to directly identify the parameters of underlying single-rate models instead of the lifted models of dual-rate systems from the dual-rate input-output data, assuming that the measurement data are stationary and ergodic. An example is given.