Improve Control Performance Research Articles

Dynamic neural network switching for active noise control of nonlinear systems

Advancements in digital technologies have allowed for the development of increasingly complex active noise and vibration control solutions, with a wide range of applications. Such control systems are commonly designed using linear digital filters which cannot fully capture the dynamics of nonlinear systems. To overcome this, it has previously been shown that replacing linear controllers with neural networks (NNs) can improve control performance in the presence of nonlinearities in both the system plant and primary path. Inferring the outputs of NN controllers can, however, be computationally expensive, limiting the practicality and real-time performance of such control systems. It has been demonstrated previously that, with nonlinearity in the primary path, the range of nonlinearity over which a single NN controller can achieve significant levels of control is limited by the size of the NN. In this paper, a method of dynamically switching between multiple smaller NN controllers is presented. In a simple time-discrete simulation, the performance and computational cost of this approach is compared to that of individual fixed NN controllers, demonstrating improved computational efficiency and performance over a range of nonlinearity as the system disturbance changes over time.

Functionally Adaptive Myosite Selection Using High-Density sEMG for Upper Limb Myoelectric Prostheses.

Our study defines a novel electrode placement method called Functionally Adaptive Myosite Selection (FAMS), as a tool for rapid and effective electrode placement during prosthesis fitting. We demonstrate a method for determining electrode placement that is adaptable towards individual patient anatomy and desired functional outcomes, agnostic to the type of classification model used, and provides insight into expected classifier performance without training multiple models. FAMS relies on a separability metric to rapidly predict classifier performance during prosthesis fitting. The results show a predictable relationship between the FAMS metric and classifier accuracy (3.45%SE), allowing estimation of control performance with any given set of electrodes. Electrode configurations selected using the FAMS metric show improved control performance ( ) for target electrode counts compared to established methods when using an ANN classifier, and equivalent performance ( R2 ≥ .96) to previous top-performing methods on an LDA classifier, with faster convergence ( ). We used the FAMS method to determine electrode placement for two amputee subjects by using the heuristic to search through possible sets, and checking for saturation in performance vs electrode count. The resulting configurations that averaged 95.8% of the highest possible classification performance using a mean 25 number of electrodes (19.5% of the available sites). FAMS can be used to rapidly approximate the tradeoffs between increased electrode count and classifier performance, a useful tool during prosthesis fitting.

Application of Multivariate Reinforcement Learning Engine in Optimizing the Power Generation Process of Domestic Waste Incineration

Garbage incineration is an ideal method for the harmless and resource-oriented treatment of urban domestic waste. However, current domestic waste incineration power plants often face challenges related to maintaining consistent steam production and high operational costs. This article capitalizes on the technical advantages of big data artificial intelligence, optimizing the power generation process of domestic waste incineration as the entry point, and adopts four main engine modules of Alibaba Cloud reinforcement learning algorithm engine, operating parameter prediction engine, anomaly recognition engine, and video visual recognition algorithm engine. The reinforcement learning algorithm extracts the operational parameters of each incinerator to obtain a control benchmark. Through the operating parameter prediction algorithm, prediction models for drum pressure, primary steam flow, NOx, SO2, and HCl are constructed to achieve short-term prediction of operational parameters, ultimately improving control performance. The anomaly recognition algorithm develops a thickness identification model for the material layer in the drying section, allowing for rapid and effective assessment of feed material thickness to ensure uniformity control. Meanwhile, the visual recognition algorithm identifies flame images and assesses the combustion status and location of the combustion fire line within the furnace. This real-time understanding of furnace flame combustion conditions guides adjustments to the grate and air volume. Integrating AI technology into the waste incineration sector empowers the environmental protection industry with the potential to leverage big data. This development holds practical significance in optimizing the harmless and resource-oriented treatment of urban domestic waste, reducing operational costs, and increasing efficiency.

Isokinetic thigh muscles strength in semi-professional athletics: A one season prospective cohort study

IntroductionContinuous evaluations of athletes, including strength testing, can help control performance improvement or facilitate the restoration of normality after an injury. The aim of the present study was to prospectively determine the peak torque (PT), angle at which PT is achieved, and functional ratios of flexors and extensors thigh muscles during one season. Material and methodsThirty semi-professional male athletes competing in long jumping (n = 10), javelin throwing (n = 10), and sprinting (n = 10) participated. PT was evaluated in relation to limb length; the angle at which PT was achieved was obtained from the force-curve displayed in the isokinetic dynamometer; functional ratios were calculated by dividing concentric hamstring strength by eccentric quadriceps strength (flexor ratio) or vice-versa for the extensor ratio. Assessment was performed at 60º/s and 300º/s. ResultsSignificant variations were seen for both extensor and flexor PTs at different stages of the season, with moderate to large effect sizes observed (effect size (d) = 0.49–0.93). Functional ratios and the angle at which peak torque was achieved remained stable throughout the season. ConclusionsThigh muscle strength is unstable throughout a track and field season, coaches or medical staff should consider these findings when programming training sessions or rehabilitating an athlete.

Active disturbance rejection control: an application to continuous microalgae photobioreactors

AbstractBACKGROUNDMathematical modelling is a widely employed approach for investigating the growth behaviour of microalgae. As a result, the development of model‐based controllers to regulate process variables has garnered increasing attention. However, despite the significant efforts invested in this area, control performance can be adversely affected by unmodelled dynamics and disturbances.RESULTSTwo active disturbance rejection controllers (ADRC) were designed to enable robust tracking of biomass concentration in continuous microalgae photobioreactors, with reduced reliance on the mathematical model of the system. The controllers were tuned to achieve a nonovershoot response and minimize settling time based on the culture's characteristics. Simulations were performed using optimal setpoints specific to each model. The results showcased a maximum output signal deviation of ±2.2%, ±7.8% and ± 7.62% for the Dunaliella tertiolecta, Isochrysis affinis galbana and Chlorella vulgaris models, respectively, regardless of the presence of simulated disturbances.CONCLUSIONSThe findings of this study significantly contribute to the advancement of the field of sustainable microalgae production. By introducing less dependent model‐based controllers, this research enhances the feasibility of implementing robust control strategies. These controllers require only knowledge of the equation system's order and the control gain function, simplifying the design process. This approach effectively addresses control performance degradation arising from unmodelled dynamics and disturbances. The ability to maintain desired process variables through ADRC controllers not only ensures improved control performance, but also supports the cultivation of specific microalgal species, when an accurate model is not available, thus promoting the overall progress and viability of microalgae biomass production. © 2023 Society of Chemical Industry.

Learning from output‐feedback control of sampled‐data systems in normal form

AbstractThis paper investigates the learning and control problem of sampled‐data systems with only output measurements. A unified approach is presented by integrating the sampled‐data observer and deterministic learning. First, an adaptive radial basis function network (RBFN) learning controller with a sampled‐data observer is designed to track a recurrent reference model. Along the trajectory estimated by the observer, it is proven that the RBFN weights can exponentially converge to their ideal values with the satisfaction of a persistent excitation (PE) condition and the closed‐loop dynamics can be accurately learned during the output‐feedback process. Second, by using the learning results, a knowledge‐based output‐feedback controller is developed to improve the tracking performance. Further research shows that choosing appropriate parameters for the observer and RBFN can guarantee learning and control performance. The significance of the proposed approach is that the closed‐loop dynamics of the output‐feedback process can be accurately learned and further utilized to improve control performance. Simulation studies indicate the effectiveness and advantages of the learning control approach.

A novel approach to performance improvement of a VAWT using plasma actuators

The numerous advantages of Vertical-Axis Wind Turbines (VAWTs) have made them suitable for urban areas compared to other types of wind turbines; however, the occurrence of phenomena such as vortices and flow separation around the blades which have adverse effects on the turbine performance, indicates the necessity of using control methods to improve the behavior of the flow around the blades. This study numerically examines the effect of different installation positions and activation timing of plasma actuators and presents new strategies for flow control and turbine performance improvement. The model presented by Shyy et al. was used for the numerical modeling of the plasma actuator. The results showed that applying actuators in ten different positions from 10% to 90% of the airfoil chord length on the outer and inner edges of the blades, can lead to an increase in the turbine production power; however, the high-power consumption of the actuator clarifies the necessity of reducing the actuator activity time to smaller azimuthal intervals. The results revealed that applying the actuators under the optimal combined strategy in a 90° interval, increases the turbine power coefficient by 29.2%, while it leads to the lowest power consumption of the actuator.

Modeling of battery energy storage systems for AGC performance analysis in wind power systems

Battery energy storage system (BESS) is being widely integrated with wind power systems to provide various ancillary services including automatic generation control (AGC) performance improvement. For AGC performance studies, it is crucial to accurately describe BESS’s power regulation behavior and provide a correct state of charge (SOC). In addition, BESS model is required to maintain a sufficiently high simulation speed, since it usually is involved in hour- or day-scale simulations. Different from existing models, this paper develops a new BESS model which considers DC-AC converter control, DC link circuit and switching loss, thus providing an accurate power regulation behavior. In addition, it also considers the nonlinear relationship between open-circuit voltage and SOC of battery so that it provides a correct SOC. As a whole, the BESS is simplified as a controlled current source with fundamental frequency (50/60 Hz) and described by algebraic phasor equations to reduce computational burden. This makes the proposed model capable of finishing hour- or day-scale simulations within a few minutes. Time-domain simulations are used to validate and compare the simulation accuracy with the classical first-order transfer function model and electromagnetic model. Based on the proposed model, this paper also introduces and verifies a new BESS-based strategy to improve the AGC performance of wind farms.

Multi-agent deep meta-reinforcement learning-based active fault tolerant gas supply management system for proton exchange membrane fuel cells

The output performance of proton exchange membrane fuel cells (PEMFCs) is highly susceptible to the influence of various parameters, which in turn are affected by PEMFC failures. A data-driven active fault-tolerant control (DD-AFTC) method is proposed to achieve the stable control of a PEMFC in the event of a fault. In addition, this proposed method combines meta-reinforcement learning with multiagent reinforcement learning to offer a distributed multiagent deep meta-deterministic policy gradient (DMA-DMDPG) algorithm, which provides the agents with independent multitask cooperative learning capabilities, thus ensuring excellent robustness. This algorithm consists of a meta-learner and a base learner. The base learner equates the hydrogen controller and the oxygen controller as independent decision-making agents. At the same time, the meta-learner is responsible for identifying PEMFC faults and selecting the appropriate joint policy according to each specific PEMFC failure. Experimental validation for a 75 kW PEMFC illustrates that DD-AFTC can improve control performance in terms of output voltage and oxygen excess rate (OER) under fault-induced conditions.

L1 Adaptive Control Based on Dynamic Inversion for Morphing Aircraft

Morphing aircraft are able to keep optimal performance in diverse flight conditions. However, the change in geometry always leads to challenges in the design of flight controllers. In this paper, a new method for designing a flight controller for variable-sweep morphing aircraft is presented—dynamic inversion combined with L1 adaptive control. Firstly, the dynamics of the vehicle is analyzed and a six degrees of freedom (6DOF) nonlinear dynamics model based on multibody dynamics theory is established. Secondly, nonlinear dynamic inversion (NDI) and incremental nonlinear dynamic inversion (INDI) are then employed to realize decoupling control. Thirdly, linear quadratic regulator (LQR) technique and L1 adaptive control are adopted to design the adaptive controller in order to improve robustness to uncertainties and ensure the control accuracy. Finally, extensive simulation experiments are performed, wherein the demonstrated results indicate that the proposed method overcomes the drawbacks of conventional methods and realizes an improvement in control performance.

Trajectory control of a hydraulic system using intelligent control approach based on adaptive prediction model

Electro-hydraulic actuators (EHAs) have become a preferred alternative to traditional hydraulic actuators with valve control systems due to their numerous advantages, making them an ideal choice for applications requiring high-precision force or position control. However, the highly complex nonlinear nature of EHAs makes modelling and controlling them a challenging task. To address this challenge, a new position control approach has been proposed for an EHA system using a combination of a feedforward online-tuning PID (FOPID) controller and an adaptive grey predictor (AGP), known as the feedforward online-tuning adaptive grey predictor (FOAGP). The FOPID controller is constructed based on PID controller and fuzzy logic algorithm to control the EHA system towards referred trajectory, while an updating rule that consists of robust checking terms optimizes its parameters online to minimize control error. The AGP predictor is an important aspect of the proposed approach. It consists of a self-tuning step size mechanism, which estimates the performance of the plant to tune the parameters of the controller and create an additive control signal that is used to counteract environment noises and perturbations. This approach significantly improves control performance by reducing the effect of disturbances and sensor noises on the system. The FOAGP approach was tested in simulation to investigate its effectiveness. The results showed that the proposed approach outperformed other existing control methods, with a higher accuracy and better control performance. One of the significant advantages of the FOAGP approach is its ability to learn and adapt to changing system dynamics. The learning mechanism used in the FOPID controller allows the system to optimize its parameters online, which is especially useful in systems with varying operating conditions. The AGP predictor also continuously adjusts its parameters to accurately estimate the system output, making it an effective tool for controlling EHAs. The proposed approach offers a significant improvement in control performance, making it a better alternative to traditional control methods. This approach can be applied to various EHA systems, including those used in aerospace, automobile, and robotic applications, among others.

Investigation on application and running characteristics of permanent magnet synchronous motor used in lifting system of deep well drilling rig

Most geological drilling rigs using asynchronous motor with gear box as the drive device of drawworks have problems of instability at low speed, complex mechanism, and lots maintenance work. This paper proposes an application of permanent magnet synchronous motor (PMSM) used in drawworks. Firstly, running characteristics of PMSM in steady state are analyzed and calculated theoretically, and mathematical models of motor’s power, torque, and power loss are given. Secondly, vector control principle of PMSM is analyzed and introduced, and maximum torque/current control method is finally decided as the basis for the design of control system. Thirdly, running parameters of PMSM in three stages (lowering drill string, constant speed/pressure drilling, and lifting drill string) of each test point were measured, and the curves of key parameters of PMSM are given. Finally, it is concluded that drawworks with PMSMs can not only improve control performance, reduce power consumption, and save energy, but also omit the gearbox, which makes structure of lifting system more compact and reduce lots maintenance work. The research work of this paper lays a foundation for the popularization and application of PMSM in the industry of deep well drilling rig.

Bandwidth-Aware Event-Triggered Load Frequency Control For Power Systems Under Time-Varying Delays

Networked Load frequency control (LFC) inevitably subjects to constrained bandwidth and time delays. However, the network traffic essentially varies from time to time and then the bandwidth status may be only busy during some specific peak periods but idle during others. This paper proposes a bandwidth-aware event-triggered load frequency control (ETLFC) scheme for multi-area power systems under time-varying delays by incorporating bandwidth-aware adaptive regulation scheme into decentralized ETLFC scheme. Different from existing time-delay ETLFC model, a model of aperiodic sampled-data system with time delay is constructed for the ETLFC scheme to obtain less conservative stability and co-design conditions based on looped Lyapunov functional. The regulation scheme is designed to adaptively adjust the threshold parameter of the ETLFC scheme based on variable bandwidth status and system output change in order to lessen communication burden while ensuring desired control performance. For fixed output change, a better bandwidth status generates a smaller threshold parameter to raise the triggering frequency in order to utilize available communication resources to improve control performance rather than unilaterally reduce data transmissions in the existing research. Case studies are undertaken by an IEEE 39-bus test system to show the effectiveness and advantages of the proposed scheme.

Harmonic Analysis of Sliding-Mode-Controlled Buck Converters Imposed by Unmodeled Dynamics of Hall Sensor

DC–DC buck converters have become prominent components for energy optimization in power systems, and how to improve control performances is a challenging issue to be addressed. In this paper, we aim to investigate the harmonic problem of sliding mode (SM) controlled buck converters imposed by the often-ignored unmodeled dynamics of the Hall sensor. The unified mathematical model of the whole system is established by combining the SM controller, the buck converter, and the Hall sensor, where the signal loss in the transmission process of the whole closed-loop control system is considered. Based on the Lyapunov stability theorem, the SM controller is designed to guarantee system stability, as well as to deduce the stable working areas and the tuned controller parameters. Furthermore, we introduce the descriptive function (DF) approach to investigate the influence of the unmodeled dynamics of the Hall sensor on the system harmonics in the frequency domain, which can deduce the relationship between the amplitude-frequency characteristics of the output signal and the Hall sensor. Simulations and experiments validate this paper.

Simultaneous multistep transformer architecture for model predictive control

Transformer neural networks have revolutionized natural language processing by effectively addressing the vanishing gradient problem. This study focuses on applying Transformer models to time-series forecasting and customizing them for a simultaneous multistep-ahead prediction model in surrogate model predictive control (MPC). The proposed method showcases improved control performance and computational efficiency compared to LSTM-based MPC and one-step-ahead prediction models using both LSTM and Transformer networks. The study introduces three key contributions: (1) a new MPC system based on a Transformer time-series architecture, (2) a training method enabling multistep-ahead prediction for time-series machine learning models, and (3) validation of the enhanced time performance of multistep-ahead Transformer MPC compared to one-step-ahead LSTM networks. Case studies demonstrate a significant fifteen-fold improvement in computational speed compared to one-step-ahead LSTM, although this improvement may vary depending on MPC factors like the lookback window and prediction horizon.

TiO2@g-C3N4/SiO2 with superior visible-light degradation of formaldehyde for indoor humidity control coatings

Indoor air quality is a critical concern in people's daily life due to the adverse effects of formaldehyde and humidity on human health. The development of multifunctional indoor coatings which can photodegrade formaldehyde and regulate humidity is desirable. In this study, we use a simple route to synthesize a heterostructure photocatalyst (denoted as TiO2@g-C3N4/SiO2-x%) via combining TiO2, graphitic carbon nitride (g-C3N4), and enhancement silica fume (SiO2). The results indicate that the prepared TiO2@g-C3N4/SiO2-12% photocatalyst is capable of degrading formaldehyde with a removal efficiency of 83.5%, which is higher than those of pure TiO2 (10.8%) and g-C3N4 (67.8%) after 3 h of visible-light irradiation. The above findings may be attributed to the enhanced visible light absorption and the fast transfer of photogenerated electrons. Electron paramagnetic resonance spectra and Mott-Schottky plots show that the generation of ･O2− and ･OH active species via Z-scheme route on TiO2@g-C3N4/SiO2-12% are responsible for the decomposition of formaldehyde under visible light. For practical applications, the TiO2@g-C3N4/SiO2-12% photocatalyst is further employed to fabricate the sustainable coating (denoted as TGS coating), which exhibits a formaldehyde removal efficiency of 85.0% with outstanding humidity control performance over ten times higher than commercial coatings. The remarkable improvement of humidity control performance on TGS coatings is due to the effect of better textural properties. More importantly, this study demonstrates the valorization of waste silicas to fabricate sustainable TGS coatings with great stability, which may provide the practical applications in the indoor environment.

Suppression of beta oscillations by delayed feedback in a cortex-basal ganglia-thalamus-pedunculopontine nucleus neural loop model.

Excessive neural synchronization of neural populations in the beta (β) frequency range (12-35 Hz) is intimately related to the symptoms of hypokinesia in Parkinson's disease (PD). Studies have shown that delayed feedback stimulation strategies can interrupt excessive neural synchronization and effectively alleviate symptoms associated with PD dyskinesia. Work on optimizing delayed feedback algorithms continues to progress, yet it remains challenging to further improve the inhibitory effect with reduced energy expenditure. Therefore, we first established a neural mass model of the cortex-basal ganglia-thalamus-pedunculopontine nucleus (CBGTh-PPN) closed-loop system, which can reflect the internal properties of cortical and basal ganglia neurons and their intrinsic connections with thalamic and pedunculopontine nucleus neurons. Second, the inhibitory effects of three delayed feedback schemes based on the external globus pallidum (GPe) on β oscillations were investigated separately and compared with those based on the subthalamic nucleus (STN) only. Our results show that all four delayed feedback schemes achieve effective suppression of pathological β oscillations when using the linear delayed feedback algorithm. The comparison revealed that the three GPe-based delayed feedback stimulation strategies were able to have a greater range of oscillation suppression with reduced energy consumption, thus improving control performance effectively, suggesting that they may be more effective for the relief of Parkinson's motor symptoms in practical applications.

An Intelligent Robust Operator-Based Sliding Mode Control for Trajectory Tracking of Nonlinear Uncertain Systems

This paper investigates the problem of trajectory tracking control in the presence of bounded model uncertainty and external disturbance. To cope with this problem, we propose a novel intelligent operator-based sliding mode control scheme for stability guarantee and control performance improvement in the closed-loop system. Firstly, robust stability is guaranteed by using the operator-based robust right coprime factorization method. Secondly, in order to further achieve the asymptotic tracking and enhance the responsiveness to disturbance, a finite-time integral sliding mode control law is designed for fast convergence and non-zero steady-state error in accordance with Lyapunov stability analysis. Lastly, the controller’s parameters are automatically adjusted by the proved stabilizing particle swarm optimization with the linear time-varying inertia weight, which significantly saves tuning time with a remarkable performance guarantee. The effectiveness and efficiency of the proposed method are verified on a highly nonlinear ionic polymer metal composite application. The extensive numerical simulations are conducted and the results show that the proposed method is superior to the state-of-the-art methods in terms of tracking accuracy and high robustness against disturbances.

Multi-objective optimisation of K-shape notch multi-way spool valve using CFD analysis, discharge area parameter model, and NSGA-II algorithm

Multi-way spool valves (MWSVs) with K-shape notches (KSNs) provide advantages such as improvement of the actuator speed control, micro-action, and response performance. However, the pressure drop (PD) associated with the energy consumption is larger of MWSVs under the high-pressure and large-flow condition. Meanwhile, extremely complex flow coefficient and multi-parameter, highly coupled KSNs are the chief factors restricting the flow-pressure characteristics exploration and optimisation design of MWSVs. To address these problems, complete numerical research and experiment are performed in this study, especially concerning the method of MWSV flow-pressure characteristics modelling, and surrogated model-based optimal design of KSN structures. First, the relationships between KSN structure parameters and flow-pressure properties of MWSV are modelled on the innovative discharge area parameter model (DAPM) and response surface methodology (RSM) (RSM-DPAM) using the CFD dataset. Second, to reduce the PD combining the flow control performance, surrogate model-based optimisation design is addressed. During optimisation, six KSN structure parameters are chosen as design variables, PD and flow area relative deviation (FARD) are selected as objective functions, and the RSM is employed as the projected model. Depended on the created surrogate model, the non-dominated sorting genetic algorithm (NSGA-II) is established to search for the optimal KSN structure. To certify the performance of the optimisation, flow field characteristics are analysed. The results demonstrate that the proposed RSM-DAPM-RSM model achieves reliable prediction for PD and FARD with a great correlation coefficient (0.9757 and 0.9946). The average PD reduces as much as 7.23% while the FARD is only 1.28%. Moreover, the region of low-pressure, high-velocity, and high-turbulent kinetic energy in the flow field are reduced. The proposed framework enhances the performance in KSN spool optimisation and could be applied to other kinds of notches.Abbreviations: BOI: Body of influence; BSV: Bucket spool valve; CFD: Computational fluid dynamics; CM: Construction machinery; DAPM: Discharge area parameter model; FARD: Flow area relative deviation; FCC: Flow control characteristic; GSA: Global sensitivity analysis; KSN: K-shape notch; MHAs: Meta-heuristic algorithms; MODE: Multi-objective differential evolution; MOGA: Multi-objective genetic algorithm; MOO: Multi-objective optimisation; MOPSO: Multi-objective particle swarm optimisation; MWSV: Multi-way spool valve; NRMS: Non-road mobile source; NSGA-II: Non-dominated sorting genetic algorithm; OLHD: Optimal Latin hypercube design; PD: Pressure drop; PDCs: Pressure drop characteristics; RSM: Response surface methodology; SA: Sensitivity analysis; TKE: Turbulent kinetic energy; TOPSIS: Technique for order preference by similarity to ideal solution; VFR: Volume flow rate

Uniaxial attitude control of uncrewed aerial vehicle with thrust vectoring under model variations by deep reinforcement learning and domain randomization

The application of neural networks for nonlinear control has been actively studied in the field of aeronautics. Successful techniques have been demonstrated to achieve improved control performance in simulation using deep-reinforcement learning. To transfer the controller learnt in the simulation of real systems, domain randomization is an approach that encourages the adaptiveness of neural networks to changing environments through training with randomized parameters in environments. This approach applies to an extended context, with changing working environments, including model configurations. In previous studies, the adaptive performance of the domain-randomization-based controllers was studied in a comparative fashion over the model variations. To understand the practical applicability of this feature, further studies are necessary to quantitatively evaluate the learnt adaptiveness with respect to the training conditions. This study evaluates deep-reinforcement-learning and the domain-randomization-based controller, with a focus on its adaptive performance over the model variations. The model variations were designed to allow quantitative comparisons. The control performances were examined, with a specific highlight of whether the model variation ranges fell within or exceeded the randomization range in training.