Tuning Constants Research Articles

Empirical tests of performance of some M – estimators

Abstract The paper presents an empirical comparison of performance of three well known M - estimators (i.e. Huber, Tukey and Hampel’s M - estimators) and also some new ones. The new M - estimators were motivated by weighting functions applied in orthogonal polynomials theory, kernel density estimation as well as one derived from Wigner semicircle probability distribution. M - estimators were used to detect outlying observations in contaminated datasets. Calculations were performed using iteratively reweighted least-squares (IRLS). Since the residual variance (used in covariance matrices construction) is not a robust measure of scale the tests employed also robust measures i.e. interquartile range and normalized median absolute deviation. The methods were tested on a simple leveling network in a large number of variants showing bad and good sides of M - estimation. The new M - estimators have been equipped with theoretical tuning constants to obtain 95% efficiency with respect to the standard normal distribution. The need for data - dependent tuning constants rather than those established theoretically is also pointed out.

Evaluation of three current methods for including the mean stress effect in fatigue crack growth rate prediction

AbstractThe fatigue crack growth rates curves of engineering materials depend on two parameters. In addition to the dependence on the classical stress intensity factor (SIF) range ΔK, there is a dependence on the mean load (or mean SIF), mainly in the near‐threshold region. The present paper provides some useful suggestions and good practices for using three of the current available methods to reduce this second dependence through the use of tuning constants. The methods considered here are the Elber, Walker and Vasudevan (or unified approach). For each approach, multiple regression analyses are performed on experimental data from the literature, and the correlations in two and three dimensions are graphically analyzed. Numerical examples of crack growth analysis for cracks growing under nominal stresses of constant amplitude in single‐edge and notch/hole geometries are performed, assuming an identical material component to that of the available experimental data. The resulting curves of crack size versus number of cycles (a versus N) are then compared. All three models gave approximately the same (a versus N) curves in both geometries. Differences between the behaviors of the (a versus N) curves in both geometries are highlighted, and the reasons for these particular behaviors are discussed.

Stator resistance estimator for direct torque control of permanent magnet synchronous motor drive systems using multi-resolution analysis wavelet

This paper presents an innovative technique for stator resistance estimation of direct torque control permanent magnet synchronous motor based on multi-resolution analysis wavelet PI controller. The online stator resistance estimation employed adjusts precisely the stator resistance value relatively to the evolution of the stator current estimation error gradient to avoid the drive instability and ensure the tracking of the actual value of the stator resistance. The multi-resolution wavelet PI controller implemented for the three level wavelet decomposition is computationally far simpler as compared to the multi-resolution technique with separate computations for high and low pass filtering at each level of decomposition. Also it is prominent by less number of tuning constants and less tuning effort as compared to a standard multi-resolution wavelet controller. The simulation results show that the proposed method can reduce the torque ripple and current ripple, superior to track the actual value of the stator resistance for different operating conditions.

Steady Modeling of a Turbocharger Turbine for Automotive Engines

Nowadays the turbocharging technique is playing a fundamental role in improving automotive engine performance and reducing fuel consumption and the exhaust emissions, in spark-ignition and compression ignition engines, as well. To this end, one-dimensional (1D) modeling is usually employed to compute the engine-turbocharger matching, to select the boost level in different operating conditions, and to estimate the low-end torque level and the transient response. However, 1D modeling of a turbocharged engine requires the availability of the turbine and compressor characteristic maps. This leads to some typical drawbacks: (1)Performance maps of the turbocharger device are usually limited to a reduced number of rotational speeds, pressure ratios, and mass flow rates because of turbine/compressor matching limits; (2) as a consequence of previous issue, unphysical extrapolation of maps' data is commonly required; and (3) heat transfer conditions may strongly differ between test bench measurements and actual operation, where turbocharger is coupled to an internal combustion engine. To overcome the above problems, in the present paper a numerical procedure is introduced: It solves 1D steady flow equations inside the turbine components with the aim of accurately reproducing the experimentally derived characteristic maps. The steady procedure describes the main phenomena and losses arising within the stationary and rotating channels constituting the turbine. It is utilized to directly compute the related steady maps, starting from the specification of a reduced set of geometrical data. An optimization process is employed to identify a number of tuning constants included in the various loss correlations. The procedure is applied to the simulation of five different turbines: three waste-gated turbines, a twin-entry turbine, and a variable geometry turbine. The numerical results show good agreement with the experimentally derived maps for all the tested devices. The model is, hence, used to evaluate the turbine performance in the whole operating domain.

Design of non-parametric process-specific optimal tuning rules for PID control of flow loops

The problem of designing optimal process-specific rules for non-parametric tuning is undertaken in the paper. It is shown that producing non-parametric process-specific optimal tuning rules for PID controllers leads to the problem that can be characterized as optimization under uncertainty. This happens due to the fact that tuning rules, unlike tuning constants, are produced not for a particular process or plant model but for a set of models from a certain domain. The novelty of the proposed approach is that the problem of obtaining optimal tuning rules for a flow process is formulated and solved as a problem of optimization of an integral performance criterion parametrized through values that define the domain of available process models. The considered non-parametric tuning assumes the use of the modified relay feedback test (MRFT) recently proposed in the literature. It allows one to tune the PID controller satisfying the requirements to gain or phase margins that is achieved through coordinated selection of tuning rules and test parameters. This approach constitutes a holistic approach to tuning. In the present paper, optimal tuning rules coupled with MRFT, for flow loops, are proposed. Final results are presented in the form of tables containing coefficients of optimal tuning rules for the PI controller, obtained for a number of specified gain margins. The produced non-parametric tuning rules well agree with the practice of loop tuning.

Computing highly accurate confidence limits from discrete data using importance sampling

For discrete data, frequentist confidence limits based on a normal approximation to standard likelihood based pivotal quantities can perform poorly, even for quite large sample sizes. To construct exact limits requires the probability of a suitable tail set as a function of the unknown parameters. In this paper, importance sampling is used to estimate this surface and hence the confidence limits. The technology is simple and straightforward to implement. Unlike the recent methodology of Garthwaite and Jones (in J. Comput. Graph. Stat. 18, 184–200, 2009), the new method allows for nuisance parameters; is an order of magnitude more efficient than the Robbins-Monro bound; does not require any simulation phases or tuning constants; gives a straightforward simulation standard error for the target limit; includes a simple diagnostic for simulation breakdown.

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This article focuses on the developed procedure of determining the degree of impact damage honeycomb panels. It is proposed to use the robust regression method due to the fact that the nondestructive testing method of low-velocity impact, as with any measurement, may have excess errors distributed by any law results. A robust method is based on M-estimates and an Huber iterative procedure. The difficulty in the implementation of the developed procedure is the choice of tuning constants and weighting function. The procedure was modified for estimating the parameters of the regression model by analyzing the sources of scientific and experimental calculations. The resulting equation of the linear regression was more robust and resistant to errors than regression dependence, calculated by the method of least squares. This procedure can be adapted to different types of data obtained in the diagnosis of any objects without significant changes in the structure of the software. The research results can be applied in the diagnosis of honeycomb panels of composite materials during the production or pre-flight preparation of aircraft

Validation of analytical expressions for turbulent burning velocity in stagnating and freely propagating turbulent premixed flames

A general expression is derived for the turbulent burning velocity, ST, from the continuum form of the c¯ transport equation and shown to be valid in all turbulent premixed combustion regimes. It involves the inverse length scale, 1/Lw, for which new analytical relationships are proposed in the laminar flamelet and the distributed reaction regime. They are combined to give new predictive relationships for the ST in the two limiting regimes and extended to be applicable in the intermediate regime as well. They involve flamelet thickness, mean curvature, molecular and turbulent diffusivities at the leading edge without any tuning constants. The proposed relationships are shown to be consistent with measurements in literature at varying pressures, laminar flame speeds, turbulent intensities and mixture compositions. Convincing agreement is achieved for ST and 1/Lw for different turbulence and laminar flame properties of stagnating compressible flames and in parametric study with respect to turbulent intensity, laminar flamelet thickness and integral length scale for freely propagating incompressible flames. There is no gravity and the Lewis number is assumed unity for simplification.

Bounding endogenous regressor coefficients using moment inequalities and generalized instruments

The main approach to deal with regressor endogeneity is instrumental variable estimator (IVE), where an instrumental variable (IV) m is required to be uncorrelated to the regression model error term u (COR(m,u)=0) and correlated to the endogenous regressor. If COR(m,u)≠0 is likely, then m gets discarded. But even when COR(m,u)≠0, often one has a good idea on the sign of COR(m,u). This article shows how to make use of the sign information on COR(m,u) to obtain an one‐sided bound on the endogenous regressor coefficient, calling m a ‘generalized instrument’ or ‘generalized instrumental variable (GIV)’. If there are two GIV's m1 and m2, then a two‐sided bound or an improved one‐sided bound can be obtained. Our approach is simple, needing only IVE; no non‐parametrics, nor any ‘tuning constants’. Specifically, the usual IVE is carried out, and the only necessary modification is that the estimate for the endogenous regressor coefficient is interpreted as a lower/upper bound depending on the prior notion on the sign of COR(m,u) and some estimable moment. A real data application is done to Korean household data with two or more children to illustrate our approach for the issue of child quantity–quality trade‐off.

Control of TAME reactive distillation using Non-Dominated Sorting Genetic Algorithm-II

The control system performs poor in characteristics and even it becomes unstable, if improper values of the controller tuning constants are used. So it becomes necessary to tune the controller parameters to achieve good control performance with the proper choice of tuning constants. Many control problems involve simultaneous optimization of multiple variables that competing with each other. In this paper, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) has been successfully applied to optimization of dynamic state of t-amyl-methyl-ether (TAME) reactive distillation process. This paper presents the tuning of Proportional–Integral–Derivative (PID) controllers by minimizing of two objective functions (overshoot and Integral of Absolute Error (IAE)) through the NSGA-II. Results show that genetic algorithm is more suitable method for optimal control of the TAME reactive distillation columns than traditional methods such as Tyreus–Luyben.

Optimal control of amine plant using non-dominated sorting genetic algorithm-II

Many control problems involve simultaneous optimization of multiple variables that competing with each other (such as Integral of Absolute Error (IAE), Overshoot, Undershoot, Response time, and etc). On the other hand, the control system performs poor in characteristics and even it becomes unstable, if improper values of the controller tuning constants are used. So it becomes necessary to tune the controller parameters to achieve good control performance with the proper choice of tuning constants. An optimal control of Amine Plant is studied in this paper utilizing the multiobjective genetic algorithm concept in conjunction of Proportional–Integral–Derivative (PID) controller. This paper presents the tuning of PID controllers by minimizing two objective functions (Overshoot and IAE) through the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II). Numerical results show that NSGA-II based tuning method has excellent ability in optimal control of Amine Plant.

Robust Value at Risk Prediction: Appendix

This appendix extends simulation and empirical results reported in Mancini and Trojani (2010). It discusses the choice of the robustness tuning constants; describes the unconditional, independence and conditional coverage tests for VaR forecast evaluation; provides additional Monte Carlo simulation results on GARCH model estimation and VaR prediction; extends the empirical analysis on backtesting. Notation is the same as in Mancini and Trojani (2010).

A comparison of design and model selection methods for supersaturated experiments

Various design and model selection methods are available for supersaturated designs having more factors than runs but little research is available on their comparison and evaluation. Simulated experiments are used to evaluate the use of E ( s 2 ) -optimal and Bayesian D -optimal designs and to compare three analysis strategies representing regression, shrinkage and a novel model-averaging procedure. Suggestions are made for choosing the values of the tuning constants for each approach. Findings include that (i) the preferred analysis is via shrinkage; (ii) designs with similar numbers of runs and factors can be effective for a considerable number of active effects of only moderate size; and (iii) unbalanced designs can perform well. Some comments are made on the performance of the design and analysis methods when effect sparsity does not hold.

Large eddy simulation of sediment transport in open-channel flow

Large Eddy Simulation (LES) is used to investigate the 3D-transport of sediment suspension in an open channel flow at a Reynolds number based on the frictional velocity.An Eulerian model was employed to represent the fluid and the sediment phases. The subgrid-scale fluid stresses were modeled with the Smagorinsky model, whereas subgrid-scale sediment fluxes were based on a gradient approach. To avoid tuning constants, a dynamic procedure was applied. A two-way coupling between sediment and fluid improved the computational description of sediment transport. Sediment concentration profiles and the statistics of sediment fluxes are presented and compared with the Rouse profile and the RANS solution. The results obtained agree well with the theory and with measurements. The LES results also indicate that the assumption of a constant Schmidt number, as is mostly assumed in RANS simulations is erroneous.

Dynamic simulation and operation of a high pressure ethylene-vinyl acetate (EVA) copolymerization autoclave reactor

Polyethylene (PE) is one of the most widely used polymers in chemical industry. In all the PE processes, low density polyethylene (LDPE) process is generally considered as the most profitable segment of the polyethylene business worldwide. There are two basic processes used for the manufacturing of LDPE: autoclave and tubular reactor, where autoclave reactor is often used to produce high-value specialty-type grades including ethylene-vinyl acetate (EVA) copolymer. Depending on different grades of the product, reactor zone temperatures in this autoclave process can be in the range 150–230 °C and pressure in the range of 1500–2000 kg/cm 2. In this paper, dynamic simulation of an industrial EVA copolymerization reactor will be established. Industrial operating condition data of seven product grades with melt index ranging from ones to over four hundred will be used as fitted data to obtain the key kinetic parameters in the model. The predicted outputs of melt index, vinyl acetate wt.% in polymer, and polymer production rate will be compared to plant data. This dynamic model was used in determining the controller tuning constants of the three important zone temperature control loops of the autoclave reactor and was also used for comparative study of various operating policies during grade transition.

Accurate prediction of the rate of heat release in a modern direct injection diesel engine

An accurate model for the heat release rate in a modern direct injection (DI) diesel engine is newly evolved from the known mixing controlled combustion model. The combustion rate could be precisely described by relating the mixing rate to the turbulent energy created at the exit of the nozzle as a function of the injection velocity and by considering the dissipation of energy in free air and along the wall. The complete absence of tuning constants distinguishes the model from the other zero-dimensional or pseudomultidimensional models, at the same time retaining the simplicity. Successful prediction of the history of heat release in engines widely varying in bores, rated speeds and types of aspirations, at all operating conditions, validated the model.

Breakdown points of Cauchy regression-scale estimators

The lower bounds for the explosion and implosion breakdown points of the simultaneous Cauchy M-estimator (Cauchy MLE) of the regression and scale parameters are derived. For appropriate tuning constants, the breakdown point attains the maximum possible value.

Robust Adaptive PID Controller Tuning for Unmeasured Load Rejection

Abstract A simple and direct algebraic method of calculating PID tuning constants for unmeasured load rejection based on a linear differential-equation process model (including time delay) is presented. Methods are discussed for experimentally identifying the process model from an open-loop doublet-pulse response and for robustly updating the process model from a closed-loop oscillatory response to an unmeasured load disturbance. These methods are combined to provide field-proven self-adaptive PID gain scheduling.

Tuning Proportional−Integral Controllers for Processes with Both Inverse Response and Deadtime

Many tuning methods have been proposed over the last half-century. Most apply to deadtime/lag processes, but several have studied either integrating processes or inverse response processes. Very few have explored processes in which both deadtime and inverse responses occur. This type of response is observed in adiabatic tubular reactors when reactor outlet temperature Tout is the controlled variable and reactor inlet temperature Tin is the manipulated variable. Typically the control structure uses a cascade arrangement in which the secondary loop uses furnace heat input or heat-exchanger bypassing to control Tin. This paper addresses the problem of controlling processes that exhibit both inverse response and deadtime. The Ziegler−Nichols tuning method recommended in the literature is shown to give poor performance at both small and large values of deadtime and positive-zero time constant. A new tuning method is proposed in which the PI tuning constants are presented as functions of the positive zero τz and the deadtime D. Results are given in the form of easy-to-use tuning charts.

Design and Simulation of an Entry Edge Guide Control System for Tandem Cold Mills

A new entry edge guide control system for cold mills was designed using a dual-mode control system. One control loop regulated the cylinder pressure to prevent machine damage due to pressure surge while the other loop provided edge guide position control. The target control level was ±1.59 mm accuracy for a maximum operating strip speed of 530 mpm with coil sidewall location variations of ±12.5 mm/sec. A mathematical model was developed to simulate the dynamic behavior of the control system using the state space design method. The control system features two PID controllers, two hydraulic proportional valves, and a digital edge sensor. The PID tuning constants and the hydraulic proportional valves were specified by simulation results considering system response and signal noise. Data from 35 coils was used to investigate control performance. The results show that the average standard error is entirely acceptable. The majority of the coils are expected to have tracking errors less than the required accuracy.