Integral Error Research Articles

Space-filling designs on Riemannian manifolds

This paper proposes a new approach to generating space-filling designs over Riemannian manifolds by using a Hilbert curve. Different from ordinary Euclidean spaces, a novel transformation is constructed to link the uniform distribution over a Riemannian manifold and that over its parameter space. Using this transformation, the uniformity of the design points in the sense of Riemannian volume measure can be guaranteed by the intrinsic measure preserving property of the Hilbert curve. It is proved that these generated designs are not only asymptotically optimal under minimax and maximin distance criteria, but also perform well in minimizing the Wasserstein distance from the target distribution and controlling the estimation error in numerical integration. Furthermore, an efficient algorithm is developed for numerical generation of these space-filling designs. The advantages of the new approach are verified through numerical simulations.

Tracking performance and power quality enhancement of DFIG based wind turbine using robust integral terminal sliding mode control

The aim of this work is to develop a robust Integral Terminal Sliding Mode Control (ITSMC) strategy for a Doubly Fed Induction Generator (DFIG) wind turbine (WT) operating in challenging conditions. This controller is designed to manage the system's rotor side converter (RSC) and grid side converter (GSC), ensuring maximum power production, improved power quality, and accurate tracking of system state variables, even in the face of fluctuating wind conditions, parameter uncertainties, and external disturbances. The stability of the proposed controller is assured using the Lyapunov theory. The performance of ITSMC is compared with that of the conventional sliding mode controller (SMC) and backstepping controller through simulation tests, using the integral absolute error (IAE) as a performance metric. The results highlight the superiority of ITSMC, demonstrating its ability to precisely track reference values, eliminate static errors, and minimize chattering. ITSMC consistently achieves the lowest IAE for all tracked state variables and across all test scenarios. A comparative study analyzing the Total Harmonic Distortion (THD) of the proposed controller versus SMC, the backstepping controller, and other similar works in the literature shows a marked improvement in the THD of stator and filter currents by at least 24.53 % and 7.96 %, respectively. These findings underscore the controller's capability to enhance the power quality delivered to the grid.

Dynamic Modeling and Control Strategy Optimization of a Volkswagen Crafter Hybrid Electrified Powertrain

This article studies the transformation and assembly process of the Volkswagen (VW) Crafter from conventional to hybrid vehicle of the department of vehicles engineering, University of Debrecen, and uses a computer-aided simulation (CAS) to design the vehicle based on the real measurement data (hardware-in-the-loop, HIL method) obtained from an online CAN bus data measurement platform using MATLAB/Simulink/Simscape and LabVIEW software. The conventional vehicle powered by a 6-speed manual transmission and a 4-stroke, 2.0 Turbocharged Direct Injection Common Rail (TDI CR) Diesel engine and the transformed hybrid electrified powertrain are designed to compare performance. A novel methodology is introduced using Netcan plus 110 devices for the CAN bus analysis of the vehicle’s hybrid version. The acquired raw CAN data is analyzed using LabVIEW and decoded with the help of the database (DBC) file into physical values. A classical proportional integral derivative (PID) controller is utilized in the hybrid powertrain system to manage the vehicle consumption and CO2 emissions. However, the intricate nonlinearities and other external environments could make its performance unsatisfactory. This study develops the energy management strategies (EMSs) on the basis of enhanced proportional integral derivative-based genetic algorithm (GA-PID), and compares with proportional integral-based particle swarm optimization (PSO-PI) and fractional order proportional integral derivative (FOPID) controllers, regulating the vehicle speed, allocating optimal torque and speed to the motor and engine and reducing the fuel and energy consumption and the CO2 emissions. The integral time absolute error (ITAE) is proposed as a fitness function for the optimization. The GA-PID demonstrates superior performance, achieving energy efficiency of 90%, extending the battery pack range from 128.75 km to 185.3281 km and reducing the emissions to 74.79 gCO2/km. It outperforms the PSO-PI and FOPID strategies by consuming less battery and motor energy and achieving higher system efficiency.

A Novel Spotted Hyena Optimizer for the Estimation of Equivalent Circuit Model Parameters in Li-Ion Batteries

Li-ion batteries possess significant advantages like large energy density, fast recharge, and high reliability; hence, they are widely adopted in electric vehicles, portable electronics, and military and aerospace applications. Albeit having their merits, accurate battery modeling is subjected to problems like prior information on internal chemical reactions, complexity in problem formulation, a large number of unknown parameters, and the need for extensive experimentation. Hence, this article presents a reliable Spotted Hyena Optimizer (SHO) to determine the equivalent circuit parameters of lithium-ion (Li-ion) batteries. The methodology of the SHO is derived from the living and hunting tactics of spotted hyenas, and it is efficiently applied to solve the battery parameter estimation problem. Nine unknown battery model parameters of a Samsung INR 18650-25R are determined using this method. The model parameters estimated are endorsed for five different datasets with various discharge current values. Further, the effect of parameter range and its selection is also emphasized. Secondly, for validation, various performance metrics such as Integral Squared Error, mean best, mean worst, and Standard Deviation are evaluated to authenticate the superiority of the proposed parameter extraction. From the computed results, the SHO algorithm is able to explore the search area up to 89% in the case of larger search ranges. The chosen model and range of the SHO precisely predict the behavior of the proposed Li-ion battery, and the results are in accordance with the catalog data.

Design and implementation of Golden Eagle optimized cascaded PI and LQR controller for PFC SEPIC converter in EV charging

This research article focuses on designing and implementing a single ended primary inductor converter (SEPIC) for an AC-DC converter, followed by an electric vehicle (EV) charger. It improves the high-power factor at the AC supply with minimum harmonic distortion. The Golden Eagle optimization techniques are adapted to optimize the tuning of Proportional-Integral (PI) and Linear Quadratic Regulator (LQR) controller parameters for better converter performance. The optimization is designed based on the eagle knowledge of hunting methods at various angles of spiral trajectories in capturing the animal. The SEPIC converter is designed and derived from the state space model by state space averaging, and the reduced model is obtained through the moment matching method to reduce computational complexity. The Golden Eagle Optimize the parameters of KP and KI of the PI controller and weighing matrix Q of the linear quadratic controller. The fitness function of the proposed optimization is the sum of the Integral Absolute error (IAE) and Integral Square error (ISE). The proposed optimization is implemented using MATLAB/SIMULINK software, and the simulation outcomes demonstrate an improved settling time, fast recovery against input and output variations, Total Harmonic Distortion (THD) of 1.75 %, and enhanced stability.

Adaptive integration of history variables in constrained mixture models for organ-scale growth and remodeling.

In the last decades, many computational models have been developed to predict soft tissue growth and remodeling (G&R). The constrained mixture theory describes fundamental mechanobiological processes in soft tissue G&R and has been widely adopted in cardiovascular models of G&R. However, even after two decades of work, large organ-scale models are rare, mainly due to high computational costs (model evaluation and memory consumption), especially in long-range simulations. We propose two strategies to adaptively integrate history variables in constrained mixture models to enable large organ-scale simulations of G&R. Both strategies exploit that the influence of deposited tissue on the current mixture decreases over time through degradation. One strategy is independent of external loading, allowing the estimation of the computational resources ahead of the simulation. The other adapts the history snapshots based on the local mechanobiological environment so that the additional integration errors can be controlled and kept negligibly small, even in G&R scenarios with severe perturbations. We analyze the adaptively integrated constrained mixture model on a tissue patch for a parameter study and show the performance under different G&R scenarios. To confirm that adaptive strategies enable large organ-scale examples, we show simulations of different hypertension conditions with a real-world example of a biventricular heart discretized with a finite element mesh. In our example, adaptive integrations sped up simulations by a factor of three and reduced memory requirements to one-sixth. The reduction of the computational costs gets even more pronounced for simulations over longer periods. Adaptive integration of the history variables allows studying more finely resolved models and longer G&R periods while computational costs are drastically reduced and largely constant in time.

Anti Wind‐Up and Robust Data‐Driven Model‐Free Adaptive Control for MIMO Nonlinear Discrete‐Time Systems

ABSTRACTThis article addresses a solution to one of the main challenges of online data‐driven control (DDC) methods: reducing the sensitivity of the model‐free adaptive control (MFAC) method to initial conditions and control parameters with the new control cost function and added the output error rate and integral along with a new anti‐wind up strategy for multi‐input multi‐output (MIMO) systems. The parameters introduced to the new control law have been validated using the boundary‐input boundary‐output (BIBO) approach to design and converge the controller. The simulation findings on a nonlinear auto‐regressive moving average model with exogenous inputs (NARMAX) system with triangular control input demonstrate that the proposed control rule will outperform to prototype MFAC. Furthermore, to analyze the sensitivity of the controller to the initial conditions and the uncertainties of the control parameters, 30 Monte Carlo simulations were performed with random initial conditions in the presence of disturbance in the control input, and output noise, and the results were compared with the prototype MFAC and conventional PID controller using standard criteria such as integral time absolute error, standard deviation, steady‐state error, and mean maximum error, which shows a noticeable superiority of proposed controller relative to the prototype MFAC.

A Quasi-Isotropic Probe for High-Power Microwave Field Measurement.

In the paper, a new design of a quasi-isotropic antenna for high-power electromagnetic (EM) field measurement is presented, along with its investigation into suitability. The measuring probe is intended for assessing pulsed microwaves, which cannot be measured by available meters due to the high value of electric field strength and short pulse duration. The measurement of such a strong field is required according to guidelines for protecting people against microwave fields, especially those emitted by radars. The proposed probe is based on the concept of dipole-diode detection. To enable high-power measurement, the receiving antenna is electrically "small," allowing diode detection within the diode square-law characteristics range. Additionally, the shortened dipole length minimizes the spatial integration error, which can be significant in the case of microwave measurement. To obtain the desired antenna polarization, a new dipole geometry was proposed. Fulfilling the requirement of measuring all incident EM field polarizations, the receiving antenna was based on three dipoles arranged within a specific "magic" angular arrangement, ensuring a suitable quasi-isotropic radiation pattern. The proposed probe can operate in a frequency range from 1 GHz to 12 GHz.

Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules.

We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm, in which the multiplication of Ĥ-k to the reference wave function is replaced by the Fourier transformed multiplication of e-iλĤ, as a function of the integration parameters and the iteration power k for various systems, including H2, LiH, BeH2 and the notorious H4 molecule at square geometry. We further consider the possibility of employing the Gaussian-quadrature rule as an alternate integration method and compared it to the results employing trapezoidal integration. The Q-Inv algorithm is compared to the inverse iteration method using the Ĥ-1 inverse (I-Iter) and the exact inverse by lower-upper decomposition. Energy values are evaluated as the expectation values of the Hamiltonian. Results suggest that the Q-Inv method provides lower energy results than the I-Iter method up to a certain k, after which the energy increases due to errors in the numerical integration that are dependent on the integration interval. A combined Gaussian-quadrature and trapezoidal integration method proved to be more effective at reaching convergence while decreasing the number of operations. For systems like H4, in which the Q-Inv cannot reach the expected error threshold, we propose a combination of Q-Inv and I-Iter methods to further decrease the error with k at lower computational cost. Finally, we summarize the recommended procedure when treating unknown systems.

Integrated error modeling for abrasive waterjet cutting at various nozzle tilt angle

The research investigates the specific impact of high-pressure abrasive waterjet (AWJ) on the cutting accuracy of circular trajectories. The coupling relationship between the kerf taper and the jet lag of the cutting front profiles is analyzed. Thus, an integrated error model for abrasive waterjet cutting of circular trajectories is innovatively established, which can predict the deformation of the circular arc trajectory not only at right angles but also at tilt angles. Cutting experiments at vertical angles were conducted, with a maximum prediction accuracy of 2.41%. Besides, arc trajectories with different diameters were conducted with a prediction accuracy of 2.26%. In order to reduce the deformation error of arc trajectories, compensation experiments for nozzle tilt ranging from 76° to 94° were carried out. The experimental results showed that when the nozzle was tilted in the direction opposite to the traverse speed up to half of the maximum deviation angle at the jet outlet point, the maximum deformation of arc trajectories was 1.218 mm, which was reduced by 0.532 mm compared to the case of vertical incidence, and the cylindricity increased by 31.74%. This adjustment can meet the precision requirements for cutting thick materials with abrasive waterjet.

Golden eagle optimized fractional-order PI controller design for a PFC SEPIC converter in EV charging

The power factor correction converter is the function of the front-end converter, followed by the DC–DC converter of the electric vehicle charger. It improves the power factor and regulates the output voltage and current. This research article proposes the Golden Eagle optimization for fractional order PI (FOPI) controller for Single Ended Primary Inductor Converter (SEPIC) power factor correction. The Golden eagle optimization is based on its knowledge of hunting tactics at various degrees of spiral trajectories to catch the prey. The FOPI controller has a broad range of controller parameters that provide better control and performance of the converter. The tuning of the parameters of the FOPI controller is optimized in Golden Eagle Optimization, and the Integral Absolute error with Integral Square error is used for the objective function. The optimized parameters of FOPI compare with the conventional PI controller performance. The SEPIC converter is designed and derived from the state space model by state space averaging, and the reduced model is obtained through the moment matching method. This system is tested under MATLAB/SIMULINK, and simulation results show improved settling time, fast dynamic response, reduction of inrush current, less harmonic distortion, and stability.

A fourth-order kernel for improving numerical accuracy and stability in Eulerian SPH for fluids and total Lagrangian SPH for solids

The error of smoothed particle hydrodynamics (SPH) using a kernel for particle-based approximation mainly arises from smoothing and integration errors. The choice of the kernel significantly impacts numerical accuracy, stability and computational efficiency. Currently, the most popular kernels, such as B-spline, truncated Gaussian (for compact support), and Wendland kernels, have 2nd-order smoothing errors, and the Wendland kernel has become mainstream in the SPH community due to its stability and accuracy. Since the particle distribution after relaxation can achieve fast convergence of integration error with respect to support radius, it is logical to choose kernels with higher-order smoothing error to improve the numerical accuracy. In this paper, the error of the 4th-order Laguerre-Wendland kernel proposed by Litvinov et al. [1] is revisited, and another 4th-order truncated Laguerre-Gauss kernel is further analyzed and considered to replace the widely used Wendland kernel. The proposed kernel has the following three properties: One is that it avoids the pair-instability problem during the relaxation process, unlike the original truncated Gaussian kernel, and achieves much less relaxation residue than the Wendland and Laguerre-Wendland kernels; One is the truncated compact support size is the same as the non-truncated one of the Wendland kernel, which leads to both kernels' comparably computational efficiency; Another is that the truncation error of this kernel is much less than that of the Wendland kernel. Furthermore, a comprehensive set of 2D and 3D benchmark cases on Eulerian SPH for fluid dynamics and total Lagrangian SPH for solid dynamics validate the considerably improved numerical accuracy of the truncated Laguerre-Gauss kernel without introducing extra computational effort.

A parameter-free particle relaxation technique for smoothed particle hydrodynamics

In this paper, we present a parameter-free particle relaxation technique to improve the accuracy and stability of smoothed particle hydrodynamics (SPH). Instead of imposing a background pressure, particles are regularized following the criteria of 0th-order consistency, i.e., the gradient of a constant to be zero. Specifically, the modifications of particles' position are solved by a gradient decent method according to the error between zero value and the gradient of a constant. This modification decreases the integration error and leads a more uniform particles distribution. A set of challenging benchmarks including lid-driven cavity flow, Taylor-Green vortex, FSI (fluid-solid interaction) problem, 2D (two-dimensional) dam-break case, and water exit of a cylinder are investigated to validate the effectiveness of the present technique for addressing the well-known tensile instability and particle clumping problems. Finally, the study of 3D (three-dimensional) dam-break against an obstacle demonstrates the stability and versatility of the present method.

Comparison of the Performance of Type-1 and Interval Type-2 Fuzzy PI Controllers for Liquid Level Control in a Coupled Tank System

In this study, liquid level control in a coupled tank system is realized with PI controllers whose parameters are adapted using fuzzy logic approximation methods. Type-1 fuzzy PI control, interval type-2 fuzzy PI control and classical PI+Feedforward control methods are applied to the tank system in real time for different reference liquid levels. The performances of the controllers are compared in terms of system response parameters such as rise time, settling time and overshoot percentage. In addition, the performance evaluation of the controllers over a certain period of time is also compared by calculating integral-based concepts that express error performance metrics such as integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE) and integral time absolute error (ITAE). The obtained results show that the type-2 fuzzy PI controller shows the best performance, followed by type-1 fuzzy PI control and classical PI+FF controller, respectively.

Integrated error modeling and evaluation of the effect for the Wolter-I grazing incidence focusing mirror imaging quality

The imaging quality determines the performance of the Wolter-I grazing incidence focusing mirror. When the design parameters are specified, the factors affecting the imaging quality are mainly machining and assembly errors; finding the error sources and evaluating the main errors are critical fundamental issues to achieve process optimization and control and improve imaging quality. This paper constructs a model of surface distribution error based on Nurbs surface reconstruction by non-contact measurement. It proposes an integrated error modeling method based on the surface distribution error model, taking into account the typical assembly errors such as decenter error, defocus error, and tilt error formed during the assembly process. First, the theoretical modeling and analysis of imaging quality based on ideal surface shape are carried out, and the sensitivity analysis of each error is carried out by using the Monte Carlo ray tracing method; then, an integrated optical simulation model containing assembly errors based on the surface distribution error is established, and the imaging quality of the focused spot is evaluated; finally, the experimental validation is carried out. The results of the experiment and the integrated optical simulation model show overall consistency, where the decenter error and defocus error have less influence, and the tilt error has the greatest impact, with the 10′ tilt error causing a decrease in the angular resolution of the focused spot of about 50″. The method can provide effective modeling and computational approaches to support the optimization of the precision assembly process and quality control of the Wolter-I grazing incidence focusing mirror.

Isles of regularity in a sea of chaos amid the gravitational three-body problem

Context. The three-body problem (3BP) poses a longstanding challenge in physics and celestial mechanics. Despite the impossibility of obtaining general analytical solutions, statistical theories have been developed based on the ergodic principle. This assumption is justified by chaos, which is expected to fully mix the accessible phase space of the 3BP. Aims. This study probes the presence of regular (i.e. non-chaotic) trajectories within the 3BP and assesses their impact on statistical escape theories. Methods. Using three-body simulations performed with the accurate, regularized code TSUNAMI, we established criteria for identifying regular trajectories and analysed their impact on statistical outcomes. Results. Our analysis reveals that regular trajectories occupy a significant fraction of the phase space, ranging from 28% to 84% depending on the initial setup, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. Integration errors manifest as numerical chaos, artificially enhancing the mixing of the phase space and affecting the reliability of individual simulations, yet preserving the statistical correctness of an ensemble of realizations. Conclusions. Our findings underscore the challenges in applying statistical escape theories to astrophysical problems, as they may bias results by excluding the outcome of regular trajectories. This is particularly important in the context of formation scenarios of gravitational wave mergers, where biased estimates of binary eccentricity can significantly impact estimates of coalescence efficiency and detectable eccentricity.

Four-wheel steering vehicle trajectory tracking control based on PSO optimized MPC

In order to address the difficulty induced by controller parameter uncertainty in trajectory tracking control of four-wheel steering vehicles(4WS), a trajectory tracking control method for unmanned vehicles based on particle swarm optimization (PSO) is proposed to improve the robustness of the controller. The approach involves the use of model predictive control (MPC) for implementing trajectory tracking control for the unmanned vehicle. Iterative optimization is conducted by utilizing the integral time absolute error (ITAE) as the objective function, which involves multiplying the time integral of lateral deviation and yaw rate deviation. This process ultimately determines the optimized MPC weight matrix parameters. Co-simulation using CarSim/Simulink reveals a remarkable reduction of 46.1% in the maximum longitudinal error, and the optimization proves effective across various vehicle speed conditions. Experimental results validate the effectiveness of the proposed control strategy, with the 4WS control strategy yielding a maximum longitudinal error of 0.28 meters, affirming that the overall controller design successfully accomplishes its intended objectives.

A new hybrid learning control system for robots based on spiking neural networks

This paper presents a new hybrid learning and control method that can tune their parameters based on reinforcement learning. In the new proposed method, nonlinear controllers are considered multi-input multi-output functions and then the functions are replaced with SNNs with reinforcement learning algorithms. Dopamine-modulated spike-timing-dependent plasticity (STDP) is used for reinforcement learning and manipulating the synaptic weights between the input and output of neuronal groups (for parameter adjustment). Details of the method are presented and some case studies are done on nonlinear controllers such as Fractional Order PID (FOPID) and Feedback Linearization. The structure and the dynamic equations for learning are presented, and the proposed algorithm is tested on robots and results are compared with other works. Moreover, to demonstrate the effectiveness of SNNFOPID, we conducted rigorous testing on a variety of systems including a two-wheel mobile robot, a double inverted pendulum, and a four-link manipulator robot. The results revealed impressively low errors of 0.01 m, 0.03 rad, and 0.03 rad for each system, respectively. The method is tested on another controller named Feedback Linearization, which provides acceptable results. Results show that the new method has better performance in terms of Integral Absolute Error (IAE) and is highly useful in hardware implementation due to its low energy consumption, high speed, and accuracy. The duration necessary for achieving full and stable proficiency in the control of various robotic systems using SNNFOPD, and SNNFL on an Asus Core i5 system within Simulink’s Simscape environment is as follows:– Two-link robot manipulator with SNNFOPID: 19.85656 hours– Two-link robot manipulator with SNNFL: 0.45828 hours– Double inverted pendulum with SNNFOPID: 3.455 hours– Mobile robot with SNNFOPID: 3.71948 hours– Four-link robot manipulator with SNNFOPID: 16.6789 hours.This method can be generalized to other controllers and systems like robots.

Enhancing Load Frequency Control of Interconnected Power System Using Hybrid PSO-AHA Optimizer

The integration of nonconventional energy sources such as solar, wind, and fuel cells into electrical power networks introduces significant challenges in maintaining frequency stability and consistent tie-line power flows. These fluctuations can adversely affect the quality and reliability of power supplied to consumers. This paper addresses this issue by proposing a Proportional–Integral–Derivative (PID) controller optimized through a hybrid Particle Swarm Optimization–Artificial Hummingbird Algorithm (PSO-AHA) approach. The PID controller is tuned using the Integral Time Absolute Error (ITAE) as a fitness function to enhance control performance. The PSO-AHA-PID controller’s effectiveness is evaluated in two networks: a two-area thermal tie-line interconnected power system (IPS) and a one-area multi-source power network incorporating thermal, solar, wind, and fuel cell sources. Comparative analyses under various operational conditions, including parameter variations and load changes, demonstrate the superior performance of the PSO-AHA-PID controller over the conventional PSO-PID controller. Statistical results indicate that in the one-area multi-source network, the PSO-AHA-PID controller achieves a 76.6% reduction in overshoot, an 88.9% reduction in undershoot, and a 97.5% reduction in settling time compared to the PSO-PID controller. In the dual-area system, the PSO-AHA-PID controller reduces the overshoot by 75.2%, reduces the undershoot by 85.7%, and improves the fall time by 71.6%. These improvements provide a robust and reliable solution for enhancing the stability of interconnected power systems in the presence of diverse and variable energy sources.

All-Analytic Statistical Modeling of Constellations in (Optical) Transmission Systems Driven by High-Speed Electronic Digital to Analog Converters Part I: DAC Mismatch Statistics, Metrics, Symmetries, Error Vector Magnitude

This two-part work develops a comprehensive toolbox for the statistical characterization of nonlinear distortions of DAC-generated signal constellations to be transmitted over communication links, be they electronic (wireline, wireless) or photonic, Mach–Zehnder modulator (MZM)-based optical interconnects in particular. The all-analytic toolbox developed here delivers closed-form expressions for the second-order statistics (means, variances) of all relevant constellation metrics of the DACs’ building blocks and of DAC-driven MZM-based optical transmitters, all the way to the slicer in the optical receivers over a linear channel with coherent detection. The key impairment targeted by the model is the random current mismatch of the ASIC devices implementing the DAC drivers. In particular the (skew-)centrosymmetry of the DAC metrics is formally derived and explored. A key applicative insight is that the conventional INL/DNL (Integral NonLinearity/Differential NonLinearity) constellation metrics, widely adopted in the electronic devices and circuits community, are not quite useful in the context of communication systems, since these metrics are ill-suited to predict communication link statistical performance. To rectify this deficiency of existing electronic DAC metrics, we introduce modified variants of the INL|DNL, namely the integral error vector (IEV) and the differential error vector (DEV) constellation metrics. The new IEV|DEV represent straightforward predictors of relevant communication-minded metrics: error vector magnitude (EVM) treated here in Part I, and Symbol/Bit Error-Rates (SER, BER) treated in the upcoming Part II of this paper.