Nonlinear Regression Method Research Articles

Dimensionless data-driven model for optimizing hole cleaning efficiency in daily drilling operations

Poor cuttings transport in deviated wells limit drill rate, induce excessive torque and drag, or in severe cases result in a stuck pipe. This paper presents a generalized data-driven model that utilizes statistical techniques for optimizing hole cleaning efficiency under different drilling conditions in deviated and extended reach wells. For this purpose, the model is constructed based on three approaches including extensive experiments conducted in our flow loop of 5-m horizontal length (4.5in. × 2in.), a validated Computational Fluid Dynamics (CFD) model was developed, and experimental data were collected from the literature to develop a reliable predictive tool that can estimate cuttings concentration in deviated wells. The developed model utilized a non-linear regression method, and was trained with 75% of the gathered data and validated with the remaining 25% to ensure the capability of the proposed model for accurate estimation of cuttings accumulation under different conditions. Unique dimensionless parameters were developed to shift the model results from lab-scale to field-scale applications.Findings revealed that the developed model provides promising results in estimating cuttings accumulation in deviated wells (20–90° from vertical). Predicted points lay in between 30% error margin in most cases, and the relation between estimated and measured cuttings accumulation has an adjusted R2 = 0.9. The proposed model outperforms the Duan, and Song models and introduces new dimensionless parameters to characterize hole cleaning efficiency during daily operations. The developed model proves to be a robust tool for simulating cuttings transport in real-time, monitoring cuttings accumulation, improving drilling efficiency, and avoiding Non-Productive Time (NPT) related to hole cleaning issues.

Prediction model for maximum shear displacement of pipe joints with preexisting defects based on finite element–multiple nonlinear regression method

AbstractUnder the coupling effect of the defects inside and around pipes, the shear displacement of the joints of old concrete pipes fallen into disrepair usually shows an accelerated deterioration trend, and its excessive value can lead to structural damage or fluid leakage. Therefore, developing a prediction model for the maximum shear displacement of concrete drainage pipe joints with preexisting defects is of crucial significance. To this end, this work selects internal corrosion and erosion voids as the typical defects inside and around old pipes, establishes 300 sets of three‐dimensional fine finite element (FE) models of the concrete drainage pipes with corrosion and void, and verifies the reliability of the developed FE model by the full‐scale tests. Based on the verified FE data, a prediction model is successfully proposed for the assessment of the maximum shear displacement of the concrete drainage pipe joints with corrosion and void defects. Moreover, parameter sensitivity analysis is carried out to reveal their relative contribution to the maximum shear displacement of pipe joints. The results show that the model proposed herein has the ability to accurately predict the maximum shear displacement of the pipe joints. The maximum and minimum relative error between the value predicted by the proposed model and the one computed by the FE model is also 12.4% and 4.8% respectively. Moreover, the traffic load with a contribution of 28.7% has the greatest impact on the maximum shear displacement of pipe joints.

Convergence of Levenberg-Marquardt Estimates of Nonlinear Parameters in EIS Analysis of Coated Aluminum Panels

Equivalent circuit models are frequently employed to analyze electrochemical impedance spectroscopy (EIS) data. However, aside from some simple cases in which the equivalent circuit element parameters can be estimated directly from a plot of the data, the parameters for each of the equivalent circuit elements must often be estimated through the implementation of a nonlinear least-squares regression method. One frequently-used approach is the powerful Levenberg-Marquardt algorithm. This algorithm functions as a damped least-squares method that performs an interpolation between the steepest-descent and the Gauss-Newton methods for estimating nonlinear parameters. However, there are several challenges to using a Levenberg-Marquardt algorithm to model EIS data. The nonlinear nature of the impedance equations along with the difference in the magnitude of the parameter values can result in the algorithm failing to converge to a local minimum in the parameter space. This convergence challenge can be seen in determining equivalent circuit values for undamaged coating systems that have a high pore resistance, a small capacitance, as well as contributions from the underlying metal substrate. A Levenberg-Marquardt algorithm, along with a heuristic approach to use the raw data to improve the initial parameter estimates, is implemented that provides an improved approach for nonlinear regression fits of equivalent circuit models. A comparison of three equivalent circuit models fits, with residuals, for a two-layer coating system on an aluminum substrate is shown in the attached figure.Figure caption: Plot of EIS data (+ symbols) from a cured coating system prior to any environmental exposures compared with 3 equivalent circuit model fits (solid lines). The model fits were obtained using an NRL-developed Levenberg-Marquardt nonlinear regression fitting routine.The Department of Defense Strategic Environmental Research and Development Program (SERDP) sponsored this project under work unit 5399. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Office of Naval Research, the U.S. Navy, the Department of Defense, or the U.S. government. Figure 1

Degradation identification and prognostics of proton exchange membrane fuel cell under dynamic load

Proton exchange membrane (PEM) fuel cell has seen its recent increasing deployment in both automotive and stationary applications. However, the unsatisfied durability of the fuel cell has barriered in the way of its successful commercialization. Recent research on prognostics and predictive maintenance has demonstrated its effectiveness in predicting the system failure and improving the durability of the PEM fuel cell. This paper contributes to developing a degradation identification method for the PEM fuel cell operating under dynamic load. A degradation indicator is proposed based on the polarization model and the nonlinear regression method is applied to extract the degradation feature by segmenting the voltage measurement. To perform prognostics, a machine learning method based on a multi-step echo state network is developed, in which a sliding window is used to recursively reformulate the input sequence with predicted values in the prediction phase. The length of the sliding window is optimized by a genetic algorithm. The proposed method is verified on the experimental PEM fuel cell degradation data and improves the prediction performance on both accuracy and computation speed when comparing with other prognostics methods.

Azo Dye Adsorption onto Cobalt Oxide: Isotherm, Kinetics, and Error Analysis Studies

The current study focused on utilizing cobalt oxide to eliminate hazardous Eriochrome Black T (EBT) dye. The impact of pH (2, 4, 7, 8, and 10) and temperature (45, 50, and 55 °C) was examined for EBT removal. The results show that the maximum sorption occurred at pH = 2 and that the removal percentage increased with increasing temperature. Five non-linear regression methods were used to predict the best isotherm and kinetic models. A coefficient of non-determination, K2, was very helpful for selecting the RMSD function as a preferable error function among the five methods. Isothermal models to illustrate equilibrium sorption information, the Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich models were used. The results showed that the Langmuir model (R2 = 0.99) was the most favorable, indicating monolayer sorption of EBT occurred. The kinetics models were analyzed using pseudo-first-order and pseudo-second-order whereas the sorption information was well described by the pseudo-second-order model (R2 = 0.99). The results of the thermodynamic study appeared that the adsorption of EBT was endothermic, feasible, spontaneous, and physical adsorption.

Predicting adulteration of grated Parmigiano Reggiano cheese with Ricotta using electrophoresis, multivariate nonlinear regression and computational intelligence methods

Urea polyacrylamide gel electrophoresis combined with statistical methods was used to detect the addition of Ricotta to grated Parmigiano Reggiano cheese. The adulterated samples were prepared by adding grated Ricotta to grated Parmigiano Reggiano cheese in six different ratios. The logistic regression and rank correlation performed worse than the naïve Bayes classifier at identifying samples of grated Parmigiano Reggiano containing more than 20% Ricotta in terms of area under the receiver operating characteristic curve and classification accuracy. This work can be considered a pilot study to investigate the potential of machine‐learning methods to predict the authenticity of Parmigiano Reggiano cheese.

Infiltration and Some Physical Properties of soil

The research aims to study the effect of some physical properties of the soil as soil components of sand, silt, and clay, as well as bulk density, and the initial soil moisture, on both cumulative infiltration depth, infiltration rate, and basic infiltration rate.Depending on data of 31 laboratory infiltration tests represented by 516 values ​​for cumulative infiltration depth and cumulative infiltration time, including a wide range of change in soil physical properties. Using the statistical program (SPSS), and by applying the nonlinear regression method, the best empirical equation has been derived to estimate the cumulative infiltration depth, with a determination coefficient of 0.975, as a function of some physical properties of soil and in the form of Kostakov's equation to include estimation of basic infiltration rate.

Deep Learning for Rapid Analysis of Spectroscopic Ellipsometry Data

High‐throughput experimental approaches to rapidly develop new materials require high‐throughput data analysis methods to match. Spectroscopic ellipsometry is a powerful method of optical properties characterization, but for unknown materials and/or layer structures the data analysis using traditional methods of nonlinear regression is too slow for autonomous, closed‐loop, high‐throughput experimentation. Herein, three methods (termed spectral, piecewise, and pointwise) of spectroscopic ellipsometry data analysis based on deep learning are introduced and studied. After initial training, the incremental time for inferring optical properties can be a thousand times faster than traditional methods. Results for multilayer sample structures with optically isotropic materials are presented, appropriate for high‐throughput studies of thin films of phase‐change materials such as GeSbTe (GST) alloys. Results for studies on highly birefringent layered materials are also presented, exemplified by the transition metal dichalcogenide MoS2. How the materials under test and the experimental objectives may guide the choice of analysis methods are discussed. The utility of our approach is demonstrated by analyzing data measured on a composition spread of GeSbTe phase‐change alloys containing 177 distinct compositions, and identifying the composition with optimal phase‐change figure of merit in only 1.4 s of analysis time.

A comprehensive study on the effective thermal conductivity of random hybrid polymer composites

Polymer composites have a wide range of applications in frontier science and technology, such as flexible electronic packaging and thermally actuated soft robotics. However, most of the theoretical and numerical researches on the thermal properties of polymer composites have been focusing on the composites with homogenous mono-fillers. In this paper, a comprehensive study on the effective thermal conductivity of the composites containing both particulate and fibrous fillers is performed through experimental, numerical and theoretical approaches. Firstly, the PDMS composites with aluminum nitride particles and/or multiwalled carbon nanotubes are prepared. Then, a series of random digital models are constructed by the simulated annealing method and monte carlo method to characterize the microstructure of such composites. And then, the lattice Boltzmann method is used to calculate the effective thermal conductivity of the random microstructure. The present numerical results are fully verified by experiments. Finally, a phenomenological prediction model is developed by the nonlinear regression method based on the systematic numerical simulations. To show the versatility of the present model, an interesting experiment on thermal management materials is designed and performed. By virtue of this model, quantitatively controlling the temperature of electronic devices may be fulfilled.

Structural Design Optimization and Prestress Simulation of the Laminate-Containment Launcher

The laminate-containment launcher is a high-efficiency electromagnetic railgun launcher (EMRL), which uses a laminate structure to reduce eddy current loss. However, the research on the design optimization of the laminate-containment launcher with prestress and mass as the goal is rarely mentioned. In this article, some key parameters of the laminate-containment launcher—the magnitude of interference $s$ , the axial thickness of the steel laminate $t_{s}$ and insulation laminate $t_{i}$ , the thickness of inner glass fiber $r_{g}$ , and the radial thickness of the laminate $r_{l}$ —are studied. On this basis, the influence of the five parameters on the hoop stress of the rail is fitted as a function by using the multiple nonlinear regression method. Then, the maximum hoop stress $f_{\mathrm {1max}}$ and the maximum hoop stress difference $f_{\mathrm {2max}}$ of the rail are calculated by using a nonlinear programming algorithm. Finally, the maximum hoop stress $f_{\mathrm {1max}}$ , the maximum hoop stress difference $f_{\mathrm {2max}}$ , and the maximum mass $f_{\mathrm {3max}}$ are taken as the reference values, and the optimal solution of the multiobjective function is obtained by using the weighted nonlinear programming algorithm. The results can be described as follows: the hoop stress of the rail changes linearly with the increase of the magnitude of interference, while the hoop stress changes approximately quadratic with the change of other parameters. Through the optimization of nonlinear programming algorithm with weighted form, the optimal design under different weighted values is obtained, which has a small error compared with the calculation results of ANSYS. The important characteristic that the hoop stress of the laminate-containment launcher presents wavy variation along the axial direction is obtained by numerical simulation. These results can provide theoretical guidance for the structural design of the laminate-containment launcher.

Optimizing the Control System of Clinker Cooling: Process Modeling and Controller Tuning

This paper aims to present efficient efforts to optimize the proportional-integral-differential (PID) controller of clinker cooling in grate coolers, which have a fixed grate and at least two moving ones. The process model contains three transfer functions between the speed of the moving grate and the pressures of the static and moving grates. The developed software achieves the identification of the model parameters using industrial data and by implementing non-linear regression methods. The design of the PID controller follows a loop-shaping technique, imposing as a constraint the maximum sensitivity, Ms, of the open-loop transfer function and providing a set of PIDs that satisfy a range of Ms. A simulator determines the optimal PID sets among those calculated at the design step using the integral of absolute error (IAE) as a performance criterion. The combination of a robustness constraint with a performance criterion, Ms and IAE respectively, leads to an area of controllers with Ms belonging to the range of 1.2 to 1.35. The IAE is between 4.2% and 4.8%, depending on the set-point value. PID sets located near the middle of this area can be chosen and implemented in the cooler’s routine operation.

Nonisothermal Crystallization Kinetics: Studying the Validity of Different Johnson–Mehl–Avrami–Erofeev–Kolmogorov (JMAEK) Based Equations

The Johnson–Mehl–Avrami–Erofeev–Kolmogorov (JMAEK) equation modifications proposed by Jeziorny, by Atiqullah and by Ruitenberg and Woldt were applied on the nonisothermal crystallization data of Poly(ethylene 2,5-furandicarboxylate)/2.5 wt. % Carbon Nanotubes (PEF/2.5 CNTs) nanocomposite. The classic JMAEK equation and the JMAEK model using the multivariate nonlinear regression method were also used to evaluate the cold crystallization's kinetic parameters of PEF/2.5 CNTs. Differential Scanning Calorimetry (DSC) measurements were carried out at heating rates of 1, 2.5, 5, 10 and 15 K/min. The effective activation energy (Eα) of the process was calculated using the isoconversional method of Vyazovkin. The Eα values indicate a nonlinear Arrhenian behavior and a complex process. The multivariate nonlinear regression method suggested a consecutive two-mechanism reaction model described by the JMAEK equation for both mechanisms. This method provided better fitting results of the experimental data for all the heating rates simultaneously and kinetic parameters' values within the limits of physical meaning. In any case, Jeziorny's modification of the JMAEK model was the most inadequate since the extracted Avrami exponents exceed in value those with a physical meaning.

A neural network model for free-falling condensation heat transfer in the presence of non-condensable gases

Condensation heat transfer has been widely studied for various applications such as power generation, water desalination, data centers, chemical and pharmaceutical syntheses, heating and air conditioning systems, and especially, the passive containment cooling system (PCCS) in nuclear power plants. The PCCS is designed to reduce the risk resulting from a loss of AC power or compounding human error. In a hypothetical accident situation, one of the main safety systems, the PCCS, condenses water vapor with gravity-driven force to remove the heat from the containment vessel. Although the condensation heat transfer in the presence of non-condensable gases for predicting the heat transfer performance of the PCCS has been successfully investigated, there is still no generalized model or correlation available. In this work, we focused on the development of universal models for predicting the heat transfer coefficients of free-fall condensation heat transfer on the external surfaces of vertical tubes in the presence of non-condensable gases. For this, we created a consolidated database covering a broad range of geometric values and operating conditions, including tube hydraulic diameter Dh = 10–41.2 mm, tube length L = 0.3–3.5 m, total pressure Ptot = 0.15–2.0 MPa, wall subcooling temperature ΔTsub = 5–71 K, average condensation heat transfer coefficients of 90 ≤ ͞h ≤ 19,400 W/m2K, and Reynolds numbers of the film of 8 ≤ Refilm ≤ 7160. We analyzed the influence of varying the geometric and operational parameter values by using this database. Conventional machine learning techniques such as nonlinear regression and multilayer perceptron (MLP) neural network methods were adopted to predict the condensation heat transfer rate based on the consolidated database. Moreover, the prediction accuracies of the condensation heat transfer rates of the proposed prediction models and 12 relevant correlations were compared by using the consolidated database. The proposed nonlinear regression model exhibited good prediction accuracy with a mean absolute error (MAE) of 12.7 % for average ͞h, which is much lower than those achieved by previously proposed relevant correlations. In addition, the MLP neural network model showed excellent prediction accuracy with an MAE of 4.2 % for the consolidated database.

Stochastic Tree Ensembles for Regularized Nonlinear Regression

This article develops a novel stochastic tree ensemble method for nonlinear regression, referred to as accelerated Bayesian additive regression trees, or XBART. By combining regularization and stochastic search strategies from Bayesian modeling with computationally efficient techniques from recursive partitioning algorithms, XBART attains state-of-the-art performance at prediction and function estimation. Simulation studies demonstrate that XBART provides accurate point-wise estimates of the mean function and does so faster than popular alternatives, such as BART, XGBoost, and neural networks (using Keras) on a variety of test functions. Additionally, it is demonstrated that using XBART to initialize the standard BART MCMC algorithm considerably improves credible interval coverage and reduces total run-time. Finally, two basic theoretical results are established: the single tree version of the model is asymptotically consistent and the Markov chain produced by the ensemble version of the algorithm has a unique stationary distribution.

Catalytic Ozonation of Toluene over Acidic Surface Transformed Natural Zeolite: A Dual-Site Reaction Mechanism and Kinetic Approach

Volatile organic compounds (VOCs) are responsible for damage to health due to their carcinogenic effects. Catalytic ozonation using zeolite appears as a valuable process to eliminate VOCs from industrial emissions at room temperature. For full-scale application of this new abatement technology, an intrinsic reaction rate equation is needed for an effective process design and scale-up. Results obtained here provide a mechanistic approach during the initial stage of catalytic ozonation of toluene using an acidic surface transformed natural zeolite. In particular, the contribution of Lewis and Brønsted acid sites on the surface reaction mechanism and overall kinetic rate are identified through experimental data. The least-squares non-linear regression method allows the rate-determining step to be established, following a Langmuir–Hinshelwood surface reaction approximation. Experimental evidence suggest that ozone is adsorbed and decomposed at Lewis acid sites, forming active atomic oxygen that leads to the oxidation of adsorbed toluene at Brønsted acid sites.

Isotherms for adsorption of boron onto new fibrous adsorbent containing glycidol ligands: linear and nonlinear regression methods

The most appropriate way to design and evaluate an adsorption system performance is by having an idea of the equilibrium relationship, which is also known as adsorption isotherms. The adsorption isotherms provide information on how pollutants such as boron are interacting with adsorbent materials. A novel glycidol-containing adsorbent for selective boron removal was synthesised by radiation-induced grafting of N-vinylformamide (NVF) onto non-woven polyethylene/polypropylene (PE/PP) fiber, followed by hydrolysis and chemical treatment. The adsorbent equilibrium behaviour was investigated using the Langmuir, Freundlich, and Redlich-Peterson isotherms. Comparison of linear and non-linear regression methods was used to determine the most suitable isotherm that best describes the boron adsorption by the new adsorbent. The non-linear method is a better way of obtaining isotherm parameters. The best-fitting isotherm was found to be the Redlich-Peterson (R2 > 0.99) and Langmuir isotherms (R2 = 0.99).

Poly(ε-caprolactone) electrospun nanofibers decorated with copper hexacyanoferrate as an ion exchanger for effective cesium ion removal

ABSTRACT In this study, poly(ε-caprolactone) electrospun nanofibers-copper hexacyanoferrate composite ion exchanger (PCL nanofibers–CuHCF) was prepared and used for the cesium ion removal from aqueous solution. The properties and morphology of the synthesized ion exchanger were characterized by Fourier-transform infrared spectroscopy (FTIR), scanning electron microscope (SEM), Brunauer–Emmett–Teller (BET) surface area analysis, X-ray diffraction analysis (XRD), and thermogravimetric analysis (TGA). The cesium ion removal experiments showed that the obtained PCL nanofibers–CuHCF composite exhibited excellent performance for the removal of cesium ions. The influences of several variables such as temperature, pH, and contact time were evaluated in batch experiments. The thermodynamic study indicated a spontaneous and endothermic ion-exchange process. The adsorption isotherm and kinetics of the PCL nanofibers–CuHCF composite were evaluated using the non-linear regression method, indicating monolayer chemisorption of the Langmuir type. The maximum sorption capacities by applying the Langmuir equation were 178.7 mg/g, which is much higher than those of previous reports of some metal-hexacyanoferrates-based composites. PCL nanofibers–CuHCF composite ion exchanger showed excellent selectivity for Cs+ in the presence of competing cations, mainly because of the excellent features of CuHCF.

Catalytic pyrolysis of mechanically non-recyclable waste plastics mixture: Kinetics and pyrolysis in laboratory-scale reactor

Post-consumer waste plastics that cannot be mechanically recycled represent a concerning environmental issue. According to the latest available data for Europe, as much as 25% of collected post-consumer waste plastics are landfilled, 43% is energy recovered, and 32% is recycled. One possible way of recovering non-recyclable plastics is pyrolysis, which is considered environmentally friendly technology for obtaining fuel or chemicals from plastic waste. To tackle the challenge of recovering non-recyclable plastics via pyrolysis, it is necessary to determine their actual composition. Visual separation of collected non-recyclable plastics was performed, and Fourier-transform infrared spectroscopy was used to confirm the accuracy of visual separation. A significant amount of plastics labelled as “other” was found. Since the composition of “other” waste plastics has not been sufficiently investigated, relatively few studies on their pyrolysis have been conducted. Therefore, they were characterised and added to the mixture with other found polymer types of non-recyclable plastics. Thermogravimetric analysis was conducted to determine thermochemical behaviour and kinetic parameters required for laboratory pyrolysis investigation. Kinetic analysis was conducted using the Friedman isoconversional model-free method and non-linear multivariate regression method. The goal of this paper was to analyse the kinetics, determine the product yield and characteristics of the pyrolysis process of non-recyclable plastics over zeolite catalysts. It was found how the decomposition of non-recyclable plastics occurs in two decomposition steps. The activation energy of non-recyclable plastics was 144 kJ/mol in the first stage of decomposition and 262 kJ/mol in the second stage of decomposition. It decreased by 34% and 6.5% after fresh fluid catalytic cracking catalyst was added and 41% and 18.3% with iron-modified Zeolite Socony Mobil-5 catalyst. The yield of condensate was 55% (wax) for the original sample, and it decreased to 50% (wax and oil) and 27% (mostly oil) with fresh fluid catalytic cracking and iron modified Zeolite Socony Mobil-5 catalysts. Processes with catalysts promoted the formation of olefins and aromatic compounds in pyrolytic oil. All pyrolysis products had a high value of higher heating value ranging from 39 MJ/kg to 43 MJ/kg showing good potential for further energy use.

Buckling of composite cylindrical shells with ovality and thickness variation subjected to hydrostatic pressure

The initial geometric imperfection is one of the primary factors affecting the buckling behaviors of composite cylindrical shells under hydrostatic pressure. In this study, ovality and thickness variations as two representative types of the geometric imperfections are considered. After measuring the geometric imperfections, a typical carbon fiber reinforced polymers (CFRP) cylindrical shell is tested to obtain the buckling pressure. The buckling behaviors of the shell sample are analyzed in combination with the strain responses. By using the nonlinear numerical analysis, the buckling shapes of the CFRP cylinder shells with different combinations of ovality and thickness variation are firstly discussed. The rules of influence of such imperfections on the buckling pressure are then obtained by nonlinear regression method. Finally, an empirical formula is proposed to predict the buckling pressure of the composite cylinder shells, and the calculated results from the formula are in good agreement with the numerical results.

COMPARISON OF METHODS FOR CONTROLLED THERMAL DEFORMATIONS IN MACHINE TOOLS

Progress in improving the accuracy of metal-cutting machines is inextricably linked and driven by deeper knowledge gained through the study of thermal processes and effects occurring in machines, which can be used to manage them. This led to the dominance of temperature errors in the balance of machine accuracy, the share of which changed from 20-30% to 70% during the period from 1950 to 2020, which is determined by the absolute value of the achievable machine accuracy. Types and forms of compensation methods were formed (1990-2020), which were based on the use of linear and nonlinear regression or correlation methods. Performing experiments can establish the functional relationship between the measured temperature in the machine nodes and the amount of displacement. With good repeatability and stable reproducibility of the result, an equation expresses this functional relationship. Applying this equation to a program, a control device compensates the thermal deformations. However, in all cases, it is necessary to determine the number and location of temperature measurements on the machine, determining the compensation accuracy. The proposed sensorless model is based on a thermal behavior model and does not require temperature measurements. A method is presented and justified for estimating the number of temperature measurement locations based on thermophysical analysis by applying the finite element method in comparison with the analytical method in order to achieve the required compensation accuracy. For several machine tool types, a comparison is given regarding the control method of the TCP spindle displacement without sensors and with temperature sensors. The limits of their rational use are presented.