Error Minimization Technique Research Articles

A regression method for estimating Gini index by decile

Based on the three-parametric Lorenz curve proposed by Kakwani (1980), this paper builds a multiple linear regression model to estimate the parameters by the weighted least square method named the regression method. Using the Lorenz curve, the Gini index and its variance are then calculated. Compared to the error minimization technique, the regression method has a better performance in estimating the Gini index using Kakwani (1980)’s Lorenz curve and a dataset of sixteen economies from the United Nation University-World Income Inequality Database (UNU-WIID). The results also suggest that the regression method has an advantage when estimating the Gini index and fitting the income shares by decile for the medium and higher inequality economies. We find that the three-parametric Lorenz curve has a better performance than the double-parametric Lorenz curve, and the double-parametric Lorenz curve is superior to the single-parametric Lorenz curve, judged by the RMSE of the actual Gini index and the estimated ones.

AI and semantic ontology for personalized activity eCoaching in healthy lifestyle recommendations: a meta-heuristic approach

BackgroundAutomated coaches (eCoach) can help people lead a healthy lifestyle (e.g., reduction of sedentary bouts) with continuous health status monitoring and personalized recommendation generation with artificial intelligence (AI). Semantic ontology can play a crucial role in knowledge representation, data integration, and information retrieval.MethodsThis study proposes a semantic ontology model to annotate the AI predictions, forecasting outcomes, and personal preferences to conceptualize a personalized recommendation generation model with a hybrid approach. This study considers a mixed activity projection method that takes individual activity insights from the univariate time-series prediction and ensemble multi-class classification approaches. We have introduced a way to improve the prediction result with a residual error minimization (REM) technique and make it meaningful in recommendation presentation with a Naïve-based interval prediction approach. We have integrated the activity prediction results in an ontology for semantic interpretation. A SPARQL query protocol and RDF Query Language (SPARQL) have generated personalized recommendations in an understandable format. Moreover, we have evaluated the performance of the time-series prediction and classification models against standard metrics on both imbalanced and balanced public PMData and private MOX2-5 activity datasets. We have used Adaptive Synthetic (ADASYN) to generate synthetic data from the minority classes to avoid bias. The activity datasets were collected from healthy adults (n = 16 for public datasets; n = 15 for private datasets). The standard ensemble algorithms have been used to investigate the possibility of classifying daily physical activity levels into the following activity classes: sedentary (0), low active (1), active (2), highly active (3), and rigorous active (4). The daily step count, low physical activity (LPA), medium physical activity (MPA), and vigorous physical activity (VPA) serve as input for the classification models. Subsequently, we re-verify the classifiers on the private MOX2-5 dataset. The performance of the ontology has been assessed with reasoning and SPARQL query execution time. Additionally, we have verified our ontology for effective recommendation generation.ResultsWe have tested several standard AI algorithms and selected the best-performing model with optimized configuration for our use case by empirical testing. We have found that the autoregression model with the REM method outperforms the autoregression model without the REM method for both datasets. Gradient Boost (GB) classifier outperforms other classifiers with a mean accuracy score of 98.00%, and 99.00% for imbalanced PMData and MOX2-5 datasets, respectively, and 98.30%, and 99.80% for balanced PMData and MOX2-5 datasets, respectively. Hermit reasoner performs better than other ontology reasoners under defined settings. Our proposed algorithm shows a direction to combine the AI prediction forecasting results in an ontology to generate personalized activity recommendations in eCoaching.ConclusionThe proposed method combining step-prediction, activity-level classification techniques, and personal preference information with semantic rules is an asset for generating personalized recommendations.

Model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

AbstractJoint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells, batteries, and supercapacitors. To increase the reliability of time–frequency analysis, a theoretical correlation between frequency‐domain stationary analysis and time‐domain transient analysis is urgently required. The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional‐order models to integer‐order models and from high‐ to low‐order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process. The following work has been carried out: (i) the model‐reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique, respectively; (ii) the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis; (iii) the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured; and (iv) the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium‐ion batteries, supercapacitors, and solid oxide fuel cells. In turn, the numerical validation has demonstrated the powerful function of the joint time–frequency analysis. The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time‐domain transient analysis and frequency‐domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.

A novel adaptive class weight adjustment‐based multiclass segmentation error minimization technique for COVID‐19 X‐ray image analysis

AbstractCoronavirus outbreaks during the last couple of years created a huge health disaster for human lives. Diagnosis of COVID‐19 infections is, thus, very important for the medical practitioners. For a quick detection, analysis of the COVID‐19 chest X‐ray images is inevitable. Therefore, there is a strong need for the development of a multiclass segmentation method for the purpose. Earlier techniques used for multiclass segmentation of images are mostly based on entropy measurements. Nonetheless, entropy methods are not efficient when the gray‐level distribution of the image is nonuniform. To address this problem, a novel adaptive class weight adjustment‐based multiclass segmentation error minimization technique for COVID‐19 chest X‐ray image analysis is investigated. Theoretical investigations on the first‐hand objective functions are presented. The results on both the biclass and multiclass segmentation of medical images are enlightened. The key to our success is the adjustment of the pixel counts of different classes adaptively to reduce the error of segmentation. The COVID‐19 chest X‐ray images are taken from the Kaggle Radiography database for the experiments. The proposed method is compared with the state‐of‐the‐art methods based on Tsallis, Kapur's, Masi, and Rényi entropy. The well‐known segmentation metrics are used for an empirical analysis. Our method achieved a performance increase of around 8.03% in the case of PSNR values, 3.01% for FSIM, and 4.16% for SSIM. The proposed technique would be useful for extracting dots from micro‐array images of DNA sequences and multiclass segmentation of the biomedical images such as MRI, CT, and PET.

Information and sensing beamforming optimization for multi-user multi-target MIMO ISAC systems

Integrated sensing and communication (ISAC) has been envisioned as a key enabler in the next-generation wireless networks. In this paper, we consider the joint information and sensing beamforming design in a multi-user and multi-target multi-input multi-output ISAC system, where a transmit BS and a sensing BS collaborate to sense targets, and the transmit BS sends information streams to communication users at the same time. To optimize the sensing performance and guarantee the communication throughput, we formulate a joint beamforming design problem to minimize the trace of the weighted Cramer–Rao bound of target parameters subject to the sum-rate constraint. The problem is challenging to solve due to the intricate non-convex objective function and constraints. We firstly exploit the weighted mean square error minimization (WMMSE) and semidefinite relaxation (SDR) techniques to devise a WMMSE–SDR algorithm that can achieve a KKT point of the problem. The SDR can be shown to be tight for a subproblem in the WMMSE–SDR algorithm, which implies zero duality for the subproblem. Based on this property and fractional programming techniques, we further reformulate the beamforming problem as a min–max form with simple constraints which then can be efficiently solved by first-order min–max optimization algorithms. Finally, the proposed algorithms are evaluated extensively in simulations. Numerical results show that both proposed algorithms can achieve promising performance in sensing and communication, and the low-complexity algorithm has a significantly reduced computation time.

A Multivector-Based Model Predictive Current Control of PMSM Drive With Enhanced Torque and Flux Response

Model predictive current control (MPCC) is a modern current control technique with the provision to include multivariable objectives and nonlinearities. In this article, a multivector-based MPCC is proposed for the speed control of a two-level voltage source inverter (VSI) fed permanent magnet synchronous motor (PMSM) drive, to improve the steady-state (SS) torque and flux response. The multivector operation is obtained using an extended control set (ECS) that utilizes two adjacent-active voltage-space vectors (VSVs) with an appropriate distribution coefficient. However, the augmentation of the control set (CS) catalyzes an undesirable increase in the computational burden. To address this limitation, a lookup table-based VSV preselection scheme based on stator current error is employed. The VSV grouping is based on the gradient of stator current error and effectively replicates the control scheme with all ECS-VSVs. Subsequently, the amplitude of the selected optimum ECS-VSV is optimized using an average error minimization technique. The optimum duration of the ECS-VSV is determined without employing space vector modulation (SVM). Hence, the complexity of the proposed scheme is minimized, and the SS torque and flux performance are enhanced without compromising the dynamic performance of the drive. The effectiveness of the proposed scheme is verified by conducting comprehensive comparisons with conventional MPCC and recently published literature.

Using Computer Vision for Monitoring the Quality of 3D-Printed Concrete Structures

Concrete 3D printing has the potential to reduce material and process waste in construction. Thus, it contributes to making the construction industry more sustainable through the use of digital-fabrication technologies. While concrete 3D printing is attractive due to its potential to realize complex designs, practical challenges include an increased chance of defects and deformities. Quality assessment of 3D-printed elements is essential for large-scale implementation. Workability of concrete is known to decrease with printing time and it impacts extrudability. It is usually visible in 3D-printed elements, with the lower layers having a smooth finish, while the top layers have cracks and discontinuities. A computer-vision-based quality assessment method is proposed in this paper using a two-bin Linear Binary Pattern textural analysis. Information entropy is used as the metric for measuring the texture variation within each layer and its changes over the layers are studied. A higher entropy value is found for layers having deformities. Finally, through the error-minimization technique, a threshold entropy value is calculated and, using this, the printed layers can be assessed and corrective actions taken. This paper contributes to developing a non-intrusive quality assessment technique for concrete 3D-printed elements.

Numerical computation of the effective thermal conductivity of two-phase composite materials by digital image analysis

We consider the numerical determination of the effective thermal conductivity of 2D, two-phase composite materials, whose microstructural geometries are described by digital images. More specifically, key microstructural data pertaining to the spatial distribution and volume fractions of the constituent phases in the material are extracted, along with the shapes of the interphase boundaries, using computer vision techniques. For inclusions of simple shapes (polygons, circles, ellipses), the extracted interphase boundary data is easily obtained and can be exploited immediately (e.g. polygonal vertices) or can be fitted with smooth curves, using least square error minimization techniques in order to reconstruct parametric representations in the case of circular or elliptical boundaries. For more intricate microstructure geometries characterized by clustered or agglomerated intersecting inclusions, piecewise cubic spline functions are adopted to obtain a least-square fitting of the interphase boundaries. The effective thermal conductivities are then calculated based on a boundary integral formulation defined over the reconstructed inclusion boundaries. They are expressed in terms of power series expansions of a conductivity contrast parameter of the constituent phases in the material. To accelerate the convergence of these expansions, nonlinear transformations (known as Padé Approximants) are used to yield rational approximations of the effective thermal conductivity tensor. Tests conducted on a variety of 2D, two-phase microstructures yielded accurate results over a wide range of microstructure image resolution, regardless of the contrast parameters of the constituent phases, thus, validating the efficacy and robustness of the proposed scheme.

ICEBEAR‐3D: A Low Elevation Imaging Radar Using a Non‐Uniform Coplanar Receiver Array for E Region Observations

AbstractThe Ionospheric Continuous‐wave E region Bistatic Experimental Auroral Radar (ICEBEAR) has been reconfigured using a phase error minimization and stochastic antenna location perturbation technique. The resulting 45‐baseline sparse non‐uniform coplanar T‐shaped array, ICEBEAR‐3D, is used for aperture synthesis radar imaging of low elevation targets. The reconfigured receiver antenna array now has a field of view ±45° azimuth and 0°–45° elevation at 0.1° angular resolution. Within this field of view no aliasing occurs. Radar targets are imaged using the Suppressed Spherical Wave Harmonic Transform (Suppressed‐SWHT) technique. This imaging method uses precalculated constant coefficient matrices to solve the integral transform from visibility to brightness through direct matrix multiplication. The method then suppresses image artefacts (dirty beam) due to undersampling by combining brightness maps of differing harmonic order. Measuring elevation angles of targets at low elevations with radar interferometers has been a long standing problem. ICEBEAR‐3D elucidates the underlying misinterpretations of the conventional geometry for vertical interferometry especially for low elevation angles. The proper phase reference vertical interferometry geometry is given which allows radar interferometers to unambiguously measure elevation angles from zenith to horizon without special calibration. The receiver antenna array reconfiguration, Suppressed‐SWHT imaging technique, and proper geometry for vertical interferometry are validated by showing agreement of the meteor trail altitude distribution with numerous data sets from other radars.

Reverse physically motivated frameworks for investigation of strain energy function in rubber-like elasticity

This paper introduces three innovative frameworks to obtain the strain energy function for rubber-like materials through an inverse approach. To this end, we inspire from the statistical background of physically motivated models to represent the strain energy function in terms of variables that correspond to the kinetics of a polymeric chain. We employ the micro-sphere concept to cast different structure-based models with unknown core functions or kernels and reveal them directly from experimental data. Accordingly, we use the basis spline (B-Spline) curve to represent these core functions and derive the macroscopic stress tensor based on the unknown control points associated with the B-Spline curves. Following this, we define a loss function to tie experimental data to these unknown control points, followed by a least-square error minimization technique that ultimately leads to a linear system of equations. In this way, we circumvent the nonlinear optimization in current structure-based models used for material parameter fitting that comes with the solution’s uncertainty. We also minimize simplifying hypotheses and bypass the unnecessary assumptions that have been influenced the accuracy of physical-based methods. Furthermore, one can integrate these functions with a high accuracy scheme over the micro-sphere, resulting in an integration-free model with competitive computational complexity to closed-form models. Finally, we validate the robustness of each framework in a challenging benchmark for three different polymeric materials. Considering the same dataset for the calibration of all models( which is uniaxial, pure shear, and equi-biaxial tests), the proposed frameworks outperform other well-known physical-based models in the literature in this challenging benchmark to the best of our knowledge ( we also show that the same performance is attainable by using only uniaxial and equi-biaxial tests ). Moreover, in the case of a limited dataset, we show that it is possible to apply prior knowledge regarding a material into one of the frameworks (RFN) to enhance the accuracy of predictions.

A seismic fragility model accounting for torsional irregularity in low‐rise non‐ductile RC moment‐resisting frames

AbstractBuildings characterized by torsional irregularity are notorious for their vulnerability to earthquakes. However, most fragility/vulnerability models used for regional seismic risk assessment fail to distinguish between buildings with torsionally balanced and unbalanced configurations. The present study aims to develop a seismic fragility model sensitive to torsional irregularity for low‐rise non‐ductile RC moment frame buildings. To this end, a numerical investigation centred on 13 three‐storied plan‐asymmetric models, each characterized by a distinct combination of normalized stiffness eccentricity, torsional radius to mass radius of gyration ratio and normalized strength eccentricity, is presented. Using high‐dimensional model representation (HDMR), a metamodel for the maximum inter‐storey drift under bi‐directional seismic action is calibrated, considering average spectral acceleration and the above trio of torsional irregularity descriptors (TIDs) as the predictor variables. Carrying out numerical simulations on limit state functions formulated using the above demand model and appropriate capacity thresholds, the seismic fragility is estimated. The parameters of a lognormal fragility function compatible with the above estimates are determined using the method of maximum likelihood. A strong correlation is observed between the TIDs and the fragility function parameters. This reinforces the importance of accounting for all three TIDs while rating the seismic fragility of a building. Using least‐square error minimization technique, a functional relationship is established between the fragility model parameters and the TIDs. The framework described herein provides a simple, yet rational means to develop the next generation of seismic fragility models accounting for one of the most critical factors governing seismic behaviour––‘torsional irregularity’.

A simple method for estimating the Lorenz curve

Given many popular functional forms for the Lorenz curve do not have a closed-form expression for the Gini index and no study has utilized the observed Gini index to estimate parameter(s) associated with the corresponding parametric functional form, a simple method for estimating the Lorenz curve is introduced. It utilizes three indicators, namely, the Gini index and the income shares of the bottom and the top in order to calculate the values of parameters associated with the specified functional form which has a closed-form expression for the Gini index. No error minimization technique is required in order to estimate the Lorenz curve. The data on the Gini index and the income shares of four countries that have a different level of income inequality, economic, sociological, and regional backgrounds from the United Nations University-World Income Inequality Database are used to illustrate how the simple method works. The overall results indicate that the estimated Lorenz curves fit the actual observations practically well. This simple method could be useful in the situation where the availability of data on income distribution is low. However, if more data on income distribution are available, this study shows that the specified functional form could be used to directly estimate the Lorenz curve. Moreover, the estimated values of the Gini index calculated based on the specified functional form are virtually identical to their actual observations.

An indirect approach for online identification of continuous time‐delay systems

AbstractThis article proposed an online identification technique, also known as a real‐time recursive identification technique for continuous time‐delay systems. The proposed approach is based on online output‐error modeling of unknown continuous time‐delay models, indirectly from discrete time‐delay models. The developed indirect formulation is employed to propose three online identification algorithms using least square, instrument variable, and prediction error minimization techniques. The proposed algorithms utilize auxiliary models and fixed or optimal filtering of input/output data samples to obtain unbiased fixed as well as time‐varying parameter estimates. An estimated error variance‐based stochastic approach is also incorporated to improve the parameter estimates. Extensive simulation experiments are conducted to validate the proposed algorithms' performance. Some useful guidelines are suggested to achieve improved identification accuracy, convergence consistency, and robustness in the presence of the measurement noise and modeling uncertainties. A real practical application for online identification of a heating system is also demonstrated.

A water cycle-based error minimization technique in predicting the bearing capacity of shallow foundation

Selecting the appropriate training technique is a significant step in utilizing intelligent approaches. It becomes even more important when it comes to critical problems like analyzing the bearing capacity of foundations. This study investigates the feasibility of a capable metaheuristic algorithm, called the water cycle algorithm (WCA), for training a multi-layer perceptron (MLP). The WCA-MLP is applied to a large finite element dataset to predict the settlement. The results of this model are compared with electromagnetic field optimization (EFO) and shuffled complex evolution (SCE) benchmarks. With reference to the obtained Pearson correlation factors (larger than 0.88 in all stages), all employed models are suitable for the mentioned objective. Moreover, it was observed that the training error of the WCA was 5.84 and 3.89% smaller than the EFO and SCE, respectively. Likewise, the accuracy of the WCA-MLP was 1.85 and 2.04% larger in the testing phase. Also, a predictive equation is finally elicited for practical applications in compatible circumstances.

Retracted] A Novel Optimal Robotized Parking System Using Advanced Wireless Sensor Network

This article addresses the importance of parking system which makes the movement of moving vehicles to be unrestricted thus providing integration between hominid classification and sensing systems. If two distinct systems are combined, then all the vehicles can monitor the parking space, and they can directly move towards the destination end within short span of time. In addition for this type of establishment, rapidity of transportation vehicles is calculated with error minimization technique where all technical hitches will be avoided by sustaining the user constraints. Further, to solve the designed user constraints, a nonlinear optimization which is termed as machine learning algorithm is introduced for avoiding high loss during packet transmission technique, and percentage of efficiency is analyzed using simulated results with network simulator (NS2). Moreover, from simulated results, it is substantiated that the projected method on automatic parking of vehicles provides high efficient operation, and even cost of installation is reduced.

The Eventual Decline of Empirical Law and Economics.

This Article suggests the necessity of a co-evolutionary process among empirical and theoretical advances in law and economics. Empirical work alone is suggestive, but should not be taken too seriously. The weaknesses in empirical work are a kind of virus that begins with over-statements and misapprehensions, and then spreads as more scholars copy the mistakes and engage in empirial work as a means of entry into the field. Empiricism will become suspect as its current assumptions are questioned, and as replication failures reveal its weaknesses. Empirical work looks very different when underlying distributions are not easily probed with regressions but are understood as reflecting power-laws, or as simply random. Once inconvenient distributions are acknowledged, the key question is why observations might be distributed in this fashion. This is likely to be a task for theorists as law and economics enters its next phase. The focus here is on three weaknesses of empirical work. First, much of the empirical work in law and economics is driven by models that rely on error minimization techniques, and these techniques are unreliable when errors are surprisingly and unevenly distributed (that is, when they suffer from heteroscedasticity). Second, it is likely that when empiricists connect data with a model, the process is flawed because there might be a hidden transition to a second distribution. Discovering multiple distributions is likely to require theoretical work. These and other problems are exacerbated by the likelihood that conclusions are based on the tail end of data sets, inasmuch as scholarly journals only bring to light statistically significant results. Finally, empirical work in law and economics suffers from the absence of sizeable data sets. Without such sets it is difficult to test conclusions and to escape the omni-present challenge of omitted variables. Reversal paradoxes are another serious problem, and especially so in the absence of large data sets. The larger and more optimistic claim is that data and theory can and must work together. Empirical work has come to play a critical role in law and economics, and its methods have improved over time. It has become apparent that data can suggest theories, and theories can be tested, to a degree, with data. But some theoretical insights are so convincing that data testing, though comforting, may be unnecessary – and testing may, in any event, be tainted by the spread of the theory. It is likely that the surge of empirical work in law and economics will be pushed back unless there is renewed attention to theory.

Accurate method for PV solar cells and modules parameters extraction using I–V curves

The main contribution of this paper is proposing a new approach for retrieving the five parameters of the single diode equivalent model (SDM) of photovoltaic cells/modules including the series and shunt resistances. The least square method is used as an error minimization technique for fitting the non-linear transcendental model equation of the solar panel to the measured I–V characteristics. Newton Raphson method is applied to solve the system of five non-linear equations which represent the error of each parameter. Initial guess values are calculated with an optimised algorithm depending on information extracted from the same measured data. MATLAB programming script was used in all implementation steps. This approach is useful for a wide variety of applications where the five SDM parameters have to be determined from the measured curves, particularly, for self-fabricated cells/modules or in case of no available datasheet. One of the strengths of this method is the higher level of accuracy because of the absence of mathematical simplifications and physical assumptions. The method was validated on different types of PV devices, including a crystalline silicon cell, a polycrystalline module, and an amorphous module by using measurement data obtained at a wide range of solar irradiance conditions and temperatures.

Fractional modeling of blood ethanol concentration system with real data application.

In this study, a physical system called the blood ethanol concentration model has been investigated in its fractional (non-integer) order version. The three most commonly used fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu fractional derivative in the Caputo sense-ABC and the Caputo-Fabrizio-CF) kernels have been used to fractionalize the model, whereas during the process of fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations.

Benthic coverage and bottom topography of coral reef environment over Pirotan reef, Gulf of Kachchh region, India

Remote sensing measurements in coral reef environments commonly confront the problem of overlying atmosphere and modification of spectral signal due to water column over the bottom substrates. In order to correct these problems, hyperspectral observations offer an advantage over multispectral observations. Airborne hyperspectral remote sensing data from Airborne Visible Infrared Imaging Spectrometer- Next Generation (AVIRIS-NG) sensor was acquired during low tidal condition on 14 February 2016 at Pirotan reef, Gulf of Kachchh region, India. The objective of this study is to map benthic coverage and bottom topography over Pirotan reef. The methodology involved atmospheric correction, simultaneous retrieval of water parameters, bathymetry, water column correction and mapping. Atmospheric correction was performed by removing path radiance and aerosol contribution and dividing by atmospheric transmittance and incoming solar irradiance to obtain remote sensing reflectance. Model derived error minimization technique was used for simultaneous retrieval of water parameters and bathymetry. Derived water parameters were used to account for water column attenuation and retrieve concomitant true bottom signature.

Performance-Based Linearization Approach for Modeling Induction Motor Drive Loads in Dynamic Simulation

This paper describes a technique to model a vector-controlled induction motor drive in large-scale phasor-level dynamic simulation programs. The performance-based load model is implemented by obtaining the linearized power-voltage and power-frequency transfer functions from test data or from detailed electro-magnetic transient simulation used as a surrogate for test data. Voltage and frequency modulations are performed to obtain the amplitude and phase responses of the detailed vector-controlled drive model for a range of discrete frequencies. The prediction error minimization technique is utilized to generate best-fit analytical transfer function expressions. The electrical interface of the performance-based drive load model is developed to interact with the external system in positive-sequence dynamic simulation programs. The drive model is used to investigate the relative damping effects of drive-connected and direct-connected motors on system voltage and frequency oscillations.