Model Parameters Research Articles

Vector Autoregressive Model Using Non-Normal Copula Errors

This article focuses on a bivariate vector autoregressive model of lag 1 with non-normal errors. We propose a bivariate error distribution using two identical marginals through a copula function. The copula used for the study is the Farlie-Gumbel-Morgenstern copula, which is considered to be one of the efficient class of copula in describing the dependence between two random variables. The model parameters are estimated using the method of inference functions for margins, and the finite sample properties of the model is illustrated through simulation studies. A real life example is considered to illustrate the applications of the proposed model. The adequacy of the copula model is examined using the two sample version of kolmogorov smirnov test statistic.

Research on SOC estimation of lithium-ion batteries based on robust full order proportional integral observer

Accurate state of charge (SOC) estimation of lithium-ion batteries is vital for the reliable and safe operation of electric vehicles. This paper introduces a novel SOC estimation method, the robust full-order proportional integral observer (RF-PIO), designed to overcome SOC estimation misalignment challenges in electric vehicles during high load shocks and temperature fluctuations. These challenges arise from the degradation of proportional integral observer stability. The RF-PIO method incorporates a novel proportional link into the disturbance estimation, significantly improving the observer's robustness without increasing computational complexity. This enhancement allows for more accurate tracking of model parameters under dynamic conditions. Extensive comparison experiments, in conjunction with a variety of driving data, validate the RF-PIO method. The results indicate that the SOC estimation error remains below 2.11%, even amidst unknown model parameters and high-frequency noise interference.

EXPRESS: Robust Demand Estimation with Customer Choice-Based Models for Sales Transaction Data

We develop a novel statistical method to estimate customer choice among a firm’s portfolio of offerings when the firm cannot directly observe customers who choose not to purchase any product. This censored demand problem is prevalent in many industries such as hotels, airlines, and retail. Although several methods have been proposed to address this problem, they require some level of data aggregation across arrivals and/or choice sets, which results in information loss and potentially biased estimates. Therefore, they have limited applicability in an environment where the prices of a firm’s portfolio of offerings vary over time and sometimes even across different customers. Our proposed method combines several desirable properties, which makes it a better fit for realistic datasets where the available choice sets or attributes of the products in the choice sets change over time. We consider two additional types of information for identification of our model parameters: 1) additional mild assumptions on the customers’ utility function, and 2) external information about a firm’s market share. We then develop a robust estimation procedure that accounts for inaccuracies in either information type and let the data determine the best approach. Through Monte-Carlo simulations, we show that our approach provides promising predictions of customer choice behavior when compared with other generally used methods and clearly outperforms those methods in scenarios where the product prices change frequently over time. Utilizing a real hotel transaction dataset provided by Oracle Labs, we further illustrate the improved estimation accuracy of our method compared to benchmark methods. Relative to existing approaches for estimating customer choice-based models, our proposed methodology better suits environments employing dynamic pricing and personalized offering practices, such as hospitality or online retailing.

Energy Bus-Based Matrix Modeling and Optimal Scheduling for Integrated Energy Systems

Integrated energy systems (IESs) can easily accommodate renewable energy resources (RESs) and improve the utilization efficiency of fossil energy by integrating various energy production, conversion, and storage technologies. However, the coupled multi-energy flows and the uncertainty of RESs bring challenges regarding optimal scheduling. Therefore, this study proposes an energy bus-based matrix-modeling method and a coordinated scheduling strategy for the IES. The matrix-modeling method can be used to formulate the steady- and transient-state balances of the multi-energy flows, and the transient model can clearly express the multi-time-scale characteristics of the different energy flows. The model parameters are fitted with data from experiments and the literature. To address the inherent randomness of the RESs and loads, a coordinated scheduling strategy is designed that contains two components: day-ahead optimization and rolling optimization. Day-ahead optimization uses the system steady-state model and multiple scenarios from the RES and load forecast data to minimize the operation cost while rolling optimization is based on the system’s transient-state model and aims to achieve the optimal real-time scheduling of the energy flows. Finally, a case study is conducted to verify the advantages and effectiveness of the proposed model and optimization method. The results show that stochastic optimization reduces the total daily cost by 1.48% compared to deterministic optimization when considering the prediction errors associated with the RESs and loads, highlighting the stronger adaptability of stochastic optimization to prediction errors. Moreover, rolling optimization based on the system’s transient-state model can reduce the errors between day-ahead scheduling and rolling correction.

A Long-Term Video Tracking Method for Group-Housed Pigs

Pig tracking provides strong support for refined management in pig farms. However, long and continuous multi-pig tracking is still extremely challenging due to occlusion, distortion, and motion blurring in real farming scenarios. This study proposes a long-term video tracking method for group-housed pigs based on improved StrongSORT, which can significantly improve the performance of pig tracking in production scenarios. In addition, this research constructs a 24 h pig tracking video dataset, providing a basis for exploring the effectiveness of long-term tracking algorithms. For object detection, a lightweight pig detection network, YOLO v7-tiny_Pig, improved based on YOLO v7-tiny, is proposed to reduce model parameters and improve detection speed. To address the target association problem, the trajectory management method of StrongSORT is optimized according to the characteristics of the pig tracking task to reduce the tracking identity (ID) switching and improve the stability of the algorithm. The experimental results show that YOLO v7-tiny_Pig ensures detection applicability while reducing parameters by 36.7% compared to YOLO v7-tiny and achieving an average video detection speed of 435 frames per second. In terms of pig tracking, Higher-Order Tracking Accuracy (HOTA), Multi-Object Tracking Accuracy (MOTP), and Identification F1 (IDF1) scores reach 83.16%, 97.6%, and 91.42%, respectively. Compared with the original StrongSORT algorithm, HOTA and IDF1 are improved by 6.19% and 10.89%, respectively, and Identity Switch (IDSW) is reduced by 69%. Our algorithm can achieve the continuous tracking of pigs in real scenarios for up to 24 h. This method provides technical support for non-contact pig automatic monitoring.

Dark energy nature of logarithmic f(R,Lm)-gravity models with observational constraints

This work explores the dark energy nature of logarithmic [Formula: see text]-gravity models with observational constraints, where [Formula: see text] represents the matter Lagrangian for perfect fluid and R is the Ricci-scalar curvature. With a matter Lagrangian [Formula: see text], a flat FLRW space–time metric and an arbitrary function [Formula: see text], where [Formula: see text] is a positive model parameter, we have derived the field equations of this model. By using the Hubble function, we have been able to solve the energy conservation equation and create a relationship between [Formula: see text], [Formula: see text] and [Formula: see text]. Using the most recent two observational datasets as 32 [Formula: see text] and 1048 Pantheon SNe Ia datasets, we conducted MCMC analysis. We have obtained best fit values of model parameters with [Formula: see text] errors and using these values, we have explored the cosmological properties of the model. We have performed om diagnostic analysis for the model and estimated the present age of the universe. Thus our derived model presents a transit phase decelerating to accelerating model without dark energy term [Formula: see text]. We found that the effective equation of state parameter is in the range [Formula: see text] over [Formula: see text] with present value [Formula: see text].

Probability Density Functions with Correlations of Experimental and Evaluated 235U(nth,f) Fission Yields and Their Impacts on Reactivity Loss with Burnup

The study of fission yields has a major impact on the characterization and understanding of the fission process and its applications. For the latter, it is crucial to provide fission yields with their associated correlation matrix in order to estimate precisely the uncertainties of crucial quantities, such as the reactivity loss. In the last decade, different works have been proposed to estimate the correlations of the independent fission yields satisfying the consistency of the cumulative yield evaluations. In these previous works, only model parameters and conservation laws have driven the correlations. The novelty of the present work consists of new complete and consistent evaluations of 235U(nth,f) independent and cumulative yields and their correlation matrices, starting from experimental data. The characterization of the probability density functions of fission yields validates the multivariate Gaussian assumption and constitutes a major issue in the validation of the uncertainty propagation tools of the applications. In addition, the new 235U(nth,f) fission yield covariance data have resulted in a decrease in nuclear data related to uncertainty in associated burnup calculations.

Study of equivalent circuit of GaN based laser chip and packaged laser.

High-speed GaN-based lasers play a pivotal role in visible light communication (VLC) systems; however, the causes of the limited modulation response of our fabricated laser diode (LD) are not fully understood. Accordingly, we constructed an equivalent circuit model for both the LD and its packaging. This model enabled us to analyze the series resistance and parallel capacitance of the LD at different injection currents. Experiments and simulations were performed to investigate the intrinsic responses of the LD. The series resistance and parallel capacitance are responsible for S21 roll-off at low frequencies. Determination of the packaging design parameters on the modulation response of a transistor outline (TO)-can packaged LD was investigated which is important to achieve the impedance match in the future. The value of each discrete component was determined by fitting the scattering parameters of the equivalent circuit model to the packaged LD. Reducing the series resistance and parallel capacitance improved the modulation response. Our study firstly illustrates the design and manufacture of violet-blue-green laser transmitters with a large modulation bandwidth for ultra-high-speed VLC from the point of the impedance influence.

Respiratory Condition Detection Using Audio Analysis and Convolutional Neural Networks Optimized by Modified Metaheuristics

Respiratory conditions have been a focal point in recent medical studies. Early detection and timely treatment are crucial factors in improving patient outcomes for any medical condition. Traditionally, doctors diagnose respiratory conditions through an investigation process that involves listening to the patient’s lungs. This study explores the potential of combining audio analysis with convolutional neural networks to detect respiratory conditions in patients. Given the significant impact of proper hyperparameter selection on network performance, contemporary optimizers are employed to enhance efficiency. Moreover, a modified algorithm is introduced that is tailored to the specific demands of this study. The proposed approach is validated using a real-world medical dataset and has demonstrated promising results. Two experiments are conducted: the first tasked models with respiratory condition detection when observing mel spectrograms of patients’ breathing patterns, while the second experiment considered the same data format for multiclass classification. Contemporary optimizers are employed to optimize the architecture selection and training parameters of models in both cases. Under identical test conditions, the best models are optimized by the introduced modified metaheuristic, with an accuracy of 0.93 demonstrated for condition detection, and a slightly reduced accuracy of 0.75 for specific condition identification.

Thermodynamic assessment of the Ce[sbnd]H and CeNi5[sbnd]H system

Interstitial metal hydrides (MHs) have attracted considerable attention in the field of hydrogen technology, particularly in the context of storage and compression applications. Because of their minor hysteresis effects, good cyclability, activation simplicity, and high volumetric storage density, LaNi5-based alloys are recognized as prominent candidates for hydrogen storage application. Additionally, the system’s thermodynamic and electrochemical properties can be modified to suit the requirements of a particular application by alloying specific substituents. To ascertain the thermodynamic effects of Ce addition within LaNi5, in this work the CeH and CeNi5H systems have been modeled with the CALPHAD method. For this reason, in this work, two different thermodynamic models have been developed and assessed using the same pressure-composition isotherms (PCIs) datasets obtained from literature and theoretical formation energies newly calculated employing periodic density functional theory (DFT). Direct comparison of the models against each other in terms of accuracy and physical plausibility revealed that extrapolation of thermodynamic properties to data-scarce regions is more reasonable with fewer model parameters and in agreement with other similar systems within the rare-earth (RE) metal-hydride class. In addition, the CeNi5H system was investigated by assessing the (Ce)(Ni)5(V a,H)7 phase model, which could accurately predict hydrogen storage properties while being compatible with previously developed LaNi5H models. Ultimately, the models developed in this study may be employed and extended to describe multi-component REH systems and allow for thermodynamic computations that are highly desirable for accurate predictions of hydrogen absorption/desorption properties and degradation characteristics within the (La,Ce)Ni5H metal hydride family.

Calibration of Decision-Based Crowd-Behaviour Model

Various methods of calibration are used depending on the model type, application, and individual preferences. While there is no universally applicable method, statistical techniques became popular in recent decades. Introduced calibration concept consists of separate calibration episodes to avoid choosing only a few metrics to describe the whole system and a high computational time increasing exponentially with the number of parameters. These episodes are designed to be separated from each other and to cover one type of pedestrian behaviour captured by some model parameters. The design of the calibration quantities; estimate of the needed simulation time to get stationary results; and the number of iterations by Chebyshev's inequality influencing the quality of the results are discussed. Furthermore, hypothesis testing (James' test) is used to compare the model and experimental data. This calibration process can be applied for any pedestrian model; this paper deals with its application on the crowd-behaviour phase in the author's decision based model.

Short Fiber-Reinforced Polymer Polyamide 6 Lugs and Selective Laser-Melted Ti-6Al-4V Bushing Contact Cohesive Zone Model Mode II Parameters’ Evaluation

This paper discusses an approach to estimating the parameters of the cohesive zone model (CZM) by mode II by extruding the bushing along the lug axis. This method of evaluation requires small samples, which is particularly relevant when investigating short fiber-reinforced polymers (SFRPs) with additively manufactured embedded elements. Adhesion is investigated on the example of 30% carbon fiber-reinforced polyamide-6 molded to Ti-6Al-4V (VT6) selective laser-melted (SLM) alloy bushing in cases of a roughness Ra = 2.66 μm (vibratory finishing), Ra = 8.79 μm (sandblasting), and Ra = 10.02 (directly from SLM). The values of the maximum equivalent tangential contact stress were in a range from 1.1 MPa to 9.5 MPa, while the critical fracture energy for tangential slip was estimated at 15 N/mm for all cases. Experimental validation of the obtained CZM mode II was carried out by evaluating the load-carrying capacity of the lugs with different bushings. In both the experiment and the calculation, greater bushing roughness provides greater lug load-bearing capacity. The ribbed bushings added significant strength in the experiments, which confirmed the importance of considering the tangential mode in the contact model. The presented models can be used for the preliminary evaluation of short fiber-reinforced polyamide-6 parts with titanium-embedded elements bearing capacity.

Fractional stochastic volatility model

This article introduces a discrete‐time fractional stochastic volatility model (FSV) based on fractional Gaussian noise. The new model includes the standard stochastic volatility model as a special case and has the same limit as the fractional integrated stochastic volatility (FISV) model, which is the continuous‐time fractional Ornstein–Uhlenbeck process. A simulated maximum likelihood method, which maximizes the time‐domain log‐likelihood function calculated by the importance sampling technique, and a frequency‐domain quasi maximum likelihood method (or quasi Whittle) are employed to estimate the model parameters. Simulation studies suggest that, while both estimation methods can accurately estimate the model, the simulated maximum likelihood method outperforms the quasi Whittle method. As an illustration, we fit the FSV and FISV models with the proposed estimation techniques to the S&P 500 composite index over a sample period spanning 45 years.

Linking cognitive integrity to working memory dynamics in the aging human brain.

Aging is accompanied by a decline of working memory, an important cognitive capacity that involves stimulus-selective neural activity that persists after stimulus presentation. Here, we unraveled working memory dynamics in older human adults (male and female) including those diagnosed with mild cognitive impairment (MCI) using a combination of behavioral modeling, neuropsychological assessment, and magnetoencephalographic (MEG) recordings of brain activity. Younger adults (male and female) were studied with behavioral modeling only. Participants performed a visuo-spatial delayed match-to-sample task under systematic manipulation of the delay and distance between sample and test stimuli. Their behavior (match/non-match decisions) was fit with a computational model permitting the dissociation of noise in the internal operations underlying the working memory performance from a strategic decision threshold. Task accuracy decreased with delay duration and sample/test proximity. When sample/test distances were small, older adults committed more false alarms than younger adults. The computational model explained the participants' behavior well. The model parameters reflecting internal noise (not decision threshold) correlated with the precision of stimulus-selective cortical activity measured with MEG during the delay interval. The model uncovered an increase specifically in working memory noise in older compared to younger participants. Furthermore, in the MCI group, but not in the older healthy controls, internal noise correlated with the participants' clinically assessed cognitive integrity. Our results are consistent with the idea that the stability of working memory contents deteriorates in aging, in a manner that is specifically linked to the overall cognitive integrity of individuals diagnosed with MCI.Significance statement Several cognitive functions decline during aging, and this process is aggravated in MCI - a condition constituting a primary risk factor for developing dementia. One function susceptible to age-related cognitive decline is working memory: the ability to maintain information online for the flexible control of behavior, which entails persistent stimulus-selective neural activity in different regions of the cerebral cortex. We used computational modeling of behavioral and neural recordings to show that the stability of working memory contents is reduced in older human subjects and predicts overall cognitive decline in MCI patients. Our findings provide new mechanistic insight into cognitive aging and MCI and highlight working memory stability as an objective marker of the mechanisms underlying cognitive impairment.

Policy, practice, and prediction: model-based approaches to evaluating N. gonorrhoeae antibiotic susceptibility test uptake in Australia.

Antimicrobial resistance (AMR) represents a significant threat to global health with Neisseria gonorrhoea emerging as a key pathogen of concern. In Australia, the Australian Gonococcal Surveillance Program (AGSP) plays a critical role in monitoring resistance patterns. However, antibiotic susceptibility test (AST) uptake - a crucial component for effective resistance surveillance - remains to be a limiting factor. The study aims to model the processes involved in generating AST tests for N. gonorrhoea isolates within the Australian healthcare system and assess the potential impact of systematic and policy-level changes. Two models were developed. The first model was a mathematical stochastic health systems model (SHSM) and a Bayesian Belief Network (BBN) to simulate the clinician-patient dynamics influencing AST initiation. Key variables were identified through systematic literature review to inform the construction of both models. Scenario analyses were conducted with the modification of model parameters. The SHSM and BBN highlighted clinician education and the use of clinical support tools as effective strategies to improve AST. Scenario analysis further identified adherence to guidelines and changes in patient-level factors, such as persistence of symptoms and high-risk behaviours, as significant determinants. Both models supported the notion of mandated testing to achieve higher AST initiation rates but with considerations necessary regarding practicality, laboratory constraints, and culture failure rate. The study fundamentally demonstrates a novel approach to conceptualising the patient-clinician dynamic within AMR testing utilising a model-based approach. It suggests targeted interventions to educational, support tools, and legislative framework as feasible strategies to improve AST initiation rates. However, the research fundamentally highlights substantial research gaps in the underlying understanding of AMR.

Lightweight-Improved YOLOv5s Model for Grape Fruit and Stem Recognition

Mechanized harvesting is the key technology to solving the high cost and low efficiency of manual harvesting, and the key to realizing mechanized harvesting lies in the accurate and fast identification and localization of targets. In this paper, a lightweight YOLOv5s model is improved for efficiently identifying grape fruits and stems. On the one hand, it improves the CSP module in YOLOv5s using the Ghost module, reducing model parameters through ghost feature maps and cost-effective linear operations. On the other hand, it replaces traditional convolutions with deep convolutions to further reduce the model’s computational load. The model is trained on datasets under different environments (normal light, low light, strong light, noise) to enhance the model’s generalization and robustness. The model is applied to the recognition of grape fruits and stems, and the experimental results show that the overall accuracy, recall rate, mAP, and F1 score of the model are 96.8%, 97.7%, 98.6%, and 97.2% respectively. The average detection time on a GPU is 4.5 ms, with a frame rate of 221 FPS, and the weight size generated during training is 5.8 MB. Compared to the original YOLOv5s, YOLOv5m, YOLOv5l, and YOLOv5x models under the specific orchard environment of a grape greenhouse, the proposed model improves accuracy by 1%, decreases the recall rate by 0.2%, increases the F1 score by 0.4%, and maintains the same mAP. In terms of weight size, it is reduced by 61.1% compared to the original model, and is only 1.8% and 5.5% of the Faster-RCNN and SSD models, respectively. The FPS is increased by 43.5% compared to the original model, and is 11.05 times and 8.84 times that of the Faster-RCNN and SSD models, respectively. On a CPU, the average detection time is 23.9 ms, with a frame rate of 41.9 FPS, representing a 31% improvement over the original model. The test results demonstrate that the lightweight-improved YOLOv5s model proposed in the study, while maintaining accuracy, significantly reduces the model size, enhances recognition speed, and can provide fast and accurate identification and localization for robotic harvesting.

MERA: Meta-Learning Based Runtime Adaptation for Industrial Wireless Sensor-Actuator Networks

IEEE 802.15.4-based industrial wireless sensor-actuator networks (WSANs) have been widely deployed to connect sensors, actuators, and controllers in industrial facilities. Configuring an industrial WSAN to meet the application-specified quality of service (QoS) requirements is a complex process, which involves theoretical computation, simulation, and field testing, among other tasks. Since industrial wireless networks become increasingly hierarchical, heterogeneous, and complex, many research efforts have been made to apply wireless simulations and advanced machine learning techniques for network configuration. Unfortunately, our study shows that the network configuration model generated by the state-of-the-art method decays quickly over time. To address this issue, we develop a ME ta-learning based R untime A daptation (MERA) method that efficiently adapts network configuration models for industrial WSANs at runtime. Under MERA, the parameters of the network configuration model are explicitly trained such that a small number of optimization steps with only a few new measurements will produce good generalization performance after the network condition changes. We also develop a data sampling method to reduce the measurements required by MERA at runtime without sacrificing its performance. Experimental results show that MERA achieves higher prediction accuracy with less physical measurements, less computation time, and longer adaptation intervals compared to a state-of-the-art baseline.

Approach for determining micro-strength parameters of rock based on particle flow code

Discrete Element Method (DEM) has been successfully utilized to model rock behavior based on particle flow code (PFC), which is extensively employed in solving various problems related to rock engineering and geomechanics. Therefore, a convenient method for selecting appropriate microparameters of PFC for model generation is necessary. The present study aims to develop a novel approach that calculates proper micro-strength parameters for the contact bond model (CBM). Firstly, based on Plackett–Burman (PB) design, qualitative research is conducted and it is found that the main factors that influence the Brazilian tensile strength is microscopic tensile strength. We analyzed the stress conditions of a Brazilian disc’s vertical diameter using both continuum models and DEM. From this analysis, we establish a theoretical relationship between rock tensile strength and micro-strength parameters. Subsequently, a large number of numerical Brazilian tests were conducted to obtain the statistical relationship between the geometric parameters of balls, micro-strength parameters and the Brazilian tension strength. The results of the numerical simulation were then used to refine the theoretical equation mentioned above, resulting in a modified equation for rock tensile strength and micro-strength parameters. Finally, after verification, we confirm the feasibility of the method in this paper.

Time-frequency analysis of nonlinear structures under nonstationary excitation by directly solving structural dynamic equation through absolute displacement

The time-frequency evolution of seismic ground motion energy under strong earthquakes, which can be described by the evolutionary power spectral density (EPSD) matrix, will amplify the most unfavorable responses of members in nonlinear structural systems. However, the existing general finite element software fails to reduce the dimension of the EPSD matrix and then decouple time from frequency in frequency domain analysis. This failure greatly limits the simulation and calculation of multi-dimensional nonlinear structures with multiple degrees of freedom by the stochastic vibration theory. In this study, the pseudo excitation method (PEM), which can direct solve structural dynamic equations using absolute displacement, is used to derive the self-spectral and cross-spectral densities of seismic ground motions in one-dimensional and multi-dimensional cases. In MATLAB, the EPSD matrix is transformed into a four-dimensional uniform modulation excitation matrix independent of the time variable. Nonlinear iteration is conducted and the precise integration method (PIM) is employed through a transient analysis module. Furthermore, a simple one-dimensional example is presented to verify the correctness of the proposed algorithm herein. Finally, as an example, we select important parameters of the coherence model at different supports of a half-through three-span concrete-filled steel tubular (CFST) tied-arch bridge in view of real engineering conditions, and calculate the time-varying power spectrum and variance of the responses of arch ribs, arch feet and the bridge deck system. The results show that the theoretical derivation and the algorithm constructed in this paper can simulate the time-delay effect of the nonlinear structural system. This proves the feasibility of general finite element software in solving and analyzing random responses to multi-dimensional and multi-support non-stationary excitation of nonlinear structures.

Optimization of the concentration of ozone generated by DBD using PSO algorithm for water treatment process

The water treatment process with ozone is influenced by various operating parameters and environmental factors that can impact its efficiency. In this study, experiments were conducted using a Venturi pumping frame to investigate the effects of three controllable variables: oxygen flow height, applied voltage level, and water flow rate. The tests aimed to develop a mathematical model that accurately represents the relationship between these input variables and the resulting ozone concentration in the treated water. The experimental data was analyzed using the MODDE 5.0 software, a specialized application for statistical modeling and design of experiments. By fitting the data to appropriate model equations, a mathematical model was obtained that quantifies the influence of each variable and their interactions on the ozone concentration response. To optimize the process performance, a particle swarm optimization (PSO) algorithm was employed to extract the best-fit parameters for the mathematical model. PSO is a computational technique inspired by the social behavior of bird flocks or fish schools, utilizing a population of candidate solutions that evolve iteratively to converge on the global optimum solution. In this case, PSO searched for the model parameter values that minimized the error between predicted and experimentally measured ozone concentrations, rapidly converging to an accurate solution. The optimized mathematical model enables predicting the ozone concentration under any combination of oxygen flow height, voltage, and water flow rate within the experimental range. This predictive capability facilitates identifying the optimum operating conditions to maximize ozone concentration, thereby enhancing the efficiency of the water treatment process. The model serves as a valuable tool for process control, monitoring, and optimization, ensuring consistent treatment quality while minimizing resource consumption and operational costs.