Nonlinear Techniques Research Articles

Performance improvement of a DPC-FPID strategy with matrix converter using CDFIG in wind power system

This study focuses on optimizing energy extraction from Wind Power Generation Systems (WPGS) using a cascaded Doubly Fed Induction Generator (CDFIG) amidst variable wind speed operation. The aim of this study is to provide a new robust nonlinear control technique. The proposed method is founded on a fractional-order Proportional–Integral–Derivative controller (FPID). To well control the injection of both active and reactive power into the electrical grid and respond to the needs of consumers despite the changes in environmental conditions, a robust Direct Power Control (DPC) is employed with FPID (DPC-FPID) associated with Matrix Converter (MC). To extract the greatest aerodynamic power Maximum Power Point Tracking (MPPT), is employed. We compare the suggested method’s outcomes with traditional PID results in order to confirm and validate the findings. It can be argued that the DPC-FPID method exhibits superior performance compared to the DPC-PI method. In terms of Total Harmonic Distortion (THD), the outcomes indicate that the proposed technique utilizing FPID (1.20%) outperforms the conventional technique relying on PID (1.87%). The DPC-FPID approach gives a reduction in ripple values in comparison to the DPC-PI strategy in terms of ratios for the torque (6.25%), active power (14.28%), and reactive power (14.705%).

Combining algorithm techniques with mechanical and acoustic profiles for the prediction of apples sensory attributes

The research work shows the potentiality of advanced linear and nonlinear learning algorithm techniques in the prediction of apples texture sensory attributes as “hardness”, “crunchiness”, “flouriness”, “fibrousness”, and “graininess”. Starting from the information contained in the entire mechanical and acoustic curves acquired during samples compression test, the prediction performances of five different statistical tools as Partial Least Squares regression (PLS), Multilayer Perceptron (MLP), Support Vector Regression (SVR) and Gaussian Process Regression (GPR) are shown and discussed.All Predictive models validations evidence best accuracies for texture sensory attributes “hardness” and “crunchiness” and in general for GPR learning algorithm. By combining mechanical and acoustic profiles, 5-fold cross validations produce values of coefficient of determination R2 up to 0.885 (GPR) and 0.840 (GPR), respectively for “hardness” and “crunchiness”. These results, comparable to those obtained by considering a large number of mechanical and acoustic parameters extracted from acquired profiles as predictive factors, evidence a new and reliable way for the prediction of texture sensory attributes of apples. The proposed approach can overcome the necessity to define, in advance, number and type of features to be calculated from instrumental texture profiles and can be easily implemented in an automatic process.

Nonlinear ensemble techniques and reliability to estimate oxygen transfer efficiency of rectangular venturi flumes for free flow

ABSTRACT In this study, we investigate assessing the oxygen transfer efficiency of a rectangular venturi flume (VFOTF20), employing machine learning ensemble models. Our investigation revolves around how models like gradient boosting machine (GBM), stacked ensemble (SE), extreme gradient boosting (XRT), M5 (Pruned and Unpruned), and random forest (RF) estimate the oxygen transfer efficiency of a rectangular venturi flume. Key input parameters, including discharge per unit width (q), throat width (W), throat length (F), and water depth (Ha), are scrutinized. Laboratory experiments furnish the datasets essential for our analysis. During the testing phase, these modelling ensembles are rigorously evaluated. The findings unequivocally demonstrate that the GBM model surpasses all other contenders in performance. Nevertheless, it is noteworthy that all proposed ensemble models, alongside conventional models like linear regression (LR) and nonlinear regression (NLR), exhibit commendable performance, albeit with variations. The correlation diagram and sensitivity analysis underscore the pivotal role of discharge per unit width (q) as the most significant variable impacting the VFOTF20. Additionally, we conduct a one-way analysis of variance (ANOVA) and an uncertainty study to enrich our understanding of the subject matter further.

تحسين علاقة المرهون لضغط نقطة الفقاعة للنفط الخام الليبي

Accurate estimation of crude oil bubble point pressure plays a vital role in many petroleum engineering calculations, such as reserve estimation, material balance, reservoir simulation, production equipment design, and optimization of well performance. The Pb can be measured in the pressure-volume-temperature (PVT) experiments. Nonetheless, the PVT measurements have limitations, such as being costly and time-consuming. In this paper, the Al-Marhoun correlation for bubble point pressure for black oil reservoirs is improved using the linearization of non-linear regression techniques to fit Libyan crudes accurately. A total of 62 PVT data reports taken from various Libyan oil fields were used in the study. The PVT data consist of an oil gravity range of 24.7 ºAPI to 46.8 ºAPI and bubble point pressures of 123 psig to 6100 psig. Statistical error analyses and graphical methods were used to evaluate the original and modified Al-Marhoun correlations. The results showed that the improved Al-Marhoun correlation exhibits significantly lower average absolute error and deviation than the published ones. The correlation coefficient of R2 of the improved Al-Marhoun correlation is 96.70%, and the average percent error (APE) is 0.70% with a standard deviation (SD) of 14.70.

On-the-Fly Simulation of Two-Dimensional Fluorescence-Excitation Spectra.

Two-dimensional (2D) fluorescence-excitation (2D-FLEX) spectroscopy is a recently proposed nonlinear femtosecond technique for the detection of photoinduced dynamics. The method records a time-resolved fluorescence signal in its excitation- and detection-frequency dependence and hence combines the exclusive detection of excited state dynamics (fluorescence) with signals resolved in both excitation and emission frequencies (2D electronic spectroscopy). In this work, we develop an on-the-fly protocol for the simulation of 2D-FLEX spectra of molecular systems, which is based on interfacing the classical doorway-window representation of spectroscopic responses with trajectory surface hopping simulations. Applying this methodology to gas-phase pyrazine, we show that femtosecond 2D-FLEX spectra can deliver detailed information that is otherwise obtainable via attosecond spectroscopy.

Control of DC-DC boost converter in discontinuous conduction mode feeding a constant power load

This article presents a new control strategy for a DC-DC boost converter used to supply a constant power load. The designed controller allows regulates the converter output voltage to a required reference value. By designing the controller based on the reduced order averaged model of the converter and using a nonlinear control technique based on feedback linearization, a simple-to-implement and stable controller for both operating modes of the converter (continuous and discontinuous conduction modes respectively) is obtained. The designed control strategy is validated through simulation and experimental results, demonstrating good dynamic performance and stability in both conduction modes, under variations in reference values and significant load changes. In addition, a comparison of the performance and implementation costs between the control strategy proposed in this paper and two strategies proposed by other authors is included.

A methodology for evaluating damage in thin-walled cylindrical shells using bounded ultrasonic beam scattering

This paper introduces an ultrasonic detection methodology specifically designed to assess damage in thin-walled cylindrical shells, which crucially relies on the interaction between a bounded ultrasonic beam and a thin-walled cylindrical shell immersed in fluid, considering both water-filled and air-filled cavities. Initially, we derive the scattered sound field expression for a bounded ultrasonic beam obliquely striking the shell. Subsequently, through finite element simulations and experimental verification, we observe that when the incident bounded beam is emitted at the critical angles defined in this study, early damage significantly enhances the received sound pressure amplitude detected by a symmetrically positioned receiver. Notably, a mere 5 % decrease in the shell's elastic modulus leads to a notable 233.69 % increase in the area under the amplitude-frequency curve of the received sound pressure for water-filled cavities and a remarkable 642.85 % surge in area for air-filled cavities. Experimental data further validates the sensitivity of this method towards varying corrosion damage states. This approach combines the reliability of linear ultrasonic methods with the enhanced sensitivity of nonlinear ultrasonic techniques, offering a significant advancement over traditional ultrasonic detection methods for inspecting cylindrical shells. The proposed assessment method holds immense potential in providing novel insights for inspecting cylindrical shells in practical applications.

Optimizing stock market volatility predictions based on the SMVF-ANP approach

The stock market is considered one of the most complicated financial systems, comprising several components or inventories, whose prices vary substantially over time. Bursaries include revealing market tendencies over time. All investors in the stock market aim to maximize profits and reduce the associated risks. Stock currency forecasts are a significant financial concern that is being handled even more closely. In recent years, various neural network and hybrid models have surpassed classic linear and non-linear techniques to produce reliable prediction outcomes. This study investigates the efficacy of dynamic and effective stock market forecasting using neural network models. This study examines market transmission mechanisms and assesses the predicted links between multiple financial and economic factors. A stock market volatility and artificial network prediction (SMVF–ANP) approach is presented. The models analyzed included a multi-layer perceptron (MLP), dynamic artificial neural network, and generalized autoregressive conditional heteroscedasticity to extract additional input variables. The results reveal that the trade strategies led by the classification models yield superior risk-adjusted returns compared to the buy-and-hold approach and those led by the neural network and linear regression model-level estimate predictions. The numerical results show that the proposed SMVF-ANP method achieved a high performance ratio of 94.1%, an enhanced prediction ratio of 98.4%, a high stock market volatility rate of 96.7%, a reduced mean square percentage error ratio of 16.3%, a probability rate of 32.7%, an increased efficiency rate of 96.9%, and an accuracy ratio of 97.2% compared to other methods.

Frontoparietal-Striatal Network and Nucleus Basalis Modulation in Patients With Parkinson Disease and Gait Disturbance.

Neural computations underlying gait disorders in Parkinson disease (PD) are multifactorial and involve impaired expression of stereotactic locomotor patterns and compensatory recruitment of cognitive functions. This study aimed to clarify the network mechanisms of cognitive contribution to gait control and its breakdown in patients with PD. Patients with PD were instructed to walk at a comfortable pace on a mat with pressure sensors. The characterization of cognitive-motor interplay was enhanced by using a gait with a secondary cognitive task (dual-task condition) and a gait without additional tasks (single-task condition). Participants were scanned using 3-T MRI and 123I-ioflupane SPECT. According to gait characteristics, cluster analysis assisted by a nonlinear dimensionality reduction technique, t-distributed stochastic neighbor embedding, categorized 56 patients with PD into 3 subpopulations. The preserved gait (PG) subgroup (n = 23) showed preserved speed and variability during gait, both with and without additional cognitive load. Compared with the PG subgroup, the mildly impaired gait (MIG) subgroup (n = 16) demonstrated deteriorated gait variability with additional cognitive load and impaired speed and gait variability without additional cognitive load. The severely impaired gait (SIG) subgroup (n = 17) revealed the slowest speed and highest gait variability. In addition, group differences were found in attention/working memory and executive function domains, with the lowest performance in the SIG subgroup than in the PG and MIG subgroups. Using resting-state functional MRI, the SIG subgroup demonstrated lower functional connectivity of the left and right frontoparietal network (FPN) with the caudate than the PG subgroup did (left FPN, d = 1.21, p < 0.001; right FPN, d = 1.05, p = 0.004). Cortical thickness in the FPN and 123I-ioflupane uptake in the striatum did not differ among the 3 subgroups. By contrast, the severity of Ch4 density loss was significantly correlated with the level of functional connectivity degradation of the FPN and caudate (left FPN-caudate, r = 0.27, p = 0.04). These findings suggest that the functional connectivity of the FPN with the caudate, as mediated by the cholinergic Ch4 projection system, underlies the compensatory recruitment of attention and executive function for damaged automaticity in gait in patients with PD.

Data-driven transient lift attenuation for extreme vortex gust–airfoil interactions

We present a data-driven feedforward control to attenuate large transient lift experienced by an airfoil disturbed by an extreme level of discrete vortex gust. The current analysis uses a nonlinear machine-learning technique to compress the high-dimensional flow dynamics onto a low-dimensional manifold. While the interaction dynamics between the airfoil and extreme vortex gust are parametrized by its size, gust ratio and position, the wake responses are well captured on this simple manifold. The effect of extreme vortex disturbance about the undisturbed baseline flows can be extracted in a physically interpretable manner. Furthermore, we call on phase-amplitude reduction to model and control the complex nonlinear extreme aerodynamic flows. The present phase-amplitude reduction model reveals the sensitivity of the dynamical system in terms of the phase shift and amplitude change induced by external forcing with respect to the baseline periodic orbit. By performing the phase-amplitude analysis for a latent dynamical model identified by sparse regression, the sensitivity functions of low-dimensionalized aerodynamic flows for both phase and amplitude are derived. With the phase and amplitude sensitivity functions, optimal forcing can be determined to quickly suppress the effect of extreme vortex gusts towards the undisturbed states in a low-order space. The present optimal flow modification built upon the machine-learned low-dimensional subspace quickly alleviates the impact of transient vortex gusts for a variety of extreme aerodynamic scenarios, providing a potential foundation for flight of small-scale air vehicles in adverse atmospheric conditions.

Nonlinear MPPT techniques to control hybrid power systems

In recent years, grid-connected multifunctional photovoltaic (PV) systems have proven to be highly efficient. This system integrates PV panels with a DC–DC boost converter (DC–DC–BC) and the electrical distribution grid (DEG). Linking the PV to the AC-DEG is accomplished through a three-level multifunctional voltage source inverter (MVSI). The DC–DC–BC component in this study is engineered to perform maximum power point tracking (MPPT) irrespective of normal or abnormal conditions. The conventional MPPT technique poses several challenges and constraints on system usage. Hence, the suggestion is to adopt synergetic control (SC) and sliding mode control (SMC) to enhance the MPPT technique's performance within the proposed system framework. Moreover, predictive direct power control is applied to the MVSI-based shunt active power filter, utilizing a phase-locked loop technique to achieve multiple objectives: minimizing energy fluctuations, injecting active power, correcting power factors, compensating reactive power, and mitigating harmonic currents. To implement the proposed system, the MATLAB is used for this purpose, with several tests used to study the behavior of the controls proposed in this work. Numerical results indicate significant reductions in active and reactive power fluctuations, with estimated rates of 38.46% and 15.30%, respectively, compared to traditional strategies. Moreover, the total harmonic distortion (THD) of the source current after filtering is reduced by 31.88% under solar irradiation of G = 1000 Wm2. Before filtering, the THD of current experiences a reduction estimated at 97.65%. These findings underscore the superior performance of the proposed control technique across all evaluated aspects.

Proposing a novel nonlinear integrated control technique for an electric power steering system to improve automotive dynamic stability

This article proposes a new control solution for an electric power steering (EPS) system to ensure the stability of car's dynamic behaviours. This work provides two new contributions which differ from previously existing publications. Firstly, a novel control method for the steering system is designed in this article based on a combination of proportional-integral-derivative (PID) and backstepping control techniques. The input to the backstepping algorithm is the output of the PID controller, whose parameters are tuned by a complex fuzzy algorithm with two inputs. Secondly, values of road reaction torque and other dynamic effects are calculated using a complex automotive dynamics model based on a nonlinear motion model and a spatial oscillation model. The stability of the control system is evaluated through the Lyapunov control function and the error between the output signals, while the dynamic stability is evaluated through the changes in car's dynamic behaviours. According to the simulation results, output values always closely follow ideal values with negligible errors if and only when the steering system is controlled by the proposed algorithm. In some conditions, the steering motor angle error achieved by the proposed controller does not exceed 0.022 rad, much lower than the fault scenario. In addition, the vehicle's roll angle and motion trajectory always follow the desired value with minimal errors. In conclusion, if the EPS system is controlled by the new control technique shown in this article, car dynamic stability will be guaranteed under all investigated conditions.

Exploring New Traveling Wave Solutions to the Nonlinear Integro-Partial Differential Equations with Stability and Modulation Instability in Industrial Engineering

In this research article, we demonstrate the generalized expansion method to investigate nonlinear integro-partial differential equations via an efficient mathematical method for generating abundant exact solutions for two types of applicable nonlinear models. Moreover, stability analysis and modulation instability are also studied for two types of nonlinear models in this present investigation. These analyses have several applications including analyzing control systems, engineering, biomedical engineering, neural networks, optical fiber communications, signal processing, nonlinear imaging techniques, oceanography, and astrophysical phenomena. To study nonlinear PDEs analytically, exact traveling wave solutions are in high demand. In this paper, the (1 + 1)-dimensional integro-differential Ito equation (IDIE), relevant in various branches of physics, statistical mechanics, condensed matter physics, quantum field theory, the dynamics of complex systems, etc., and also the (2 + 1)-dimensional integro-differential Sawda–Kotera equation (IDSKE), providing insights into the several physical fields, especially quantum gravity field theory, conformal field theory, neural networks, signal processing, control systems, etc., are investigated to obtain a variety of wave solutions in modern physics by using the mentioned method. Since abundant exact wave solutions give us vast information about the physical phenomena of the mentioned models, our analysis aims to determine various types of traveling wave solutions via a different integrable ordinary differential equation. Furthermore, the characteristics of the obtained new exact solutions have been illustrated by some figures. The method used here is candid, convenient, proficient, and overwhelming compared to other existing computational techniques in solving other current world physical problems. This article provides an exemplary practice of finding new types of analytical equations.

Plug-and-play learnable EMD module for time-domain speech separation

This paper presents a learnable empirical mode decomposition (EMD) module tailored for single channel speech separation. The proposed EMD module exhibits a flexible plug-and-play characteristic, enabling its integration into various speech separation networks. Conventionally, non-learnable EMD algorithms, as a nonlinear time-domain adaptive techniques, aimed at decomposing speech signals into a set of oscillatory intrinsic mode functions (IMFs) and a residual component. However, the inherent non-differentiability of the interpolation operation in these algorithms restricts their integration into neural networks, thus the EMD algorithm only exists in the preprocessing step and cannot be integrated into the neural network to form an end-to-end trainable speech separation network. In order to mitigate this issue, we use the max pooling layer and the deconvolution network to replace the envelope solving algorithm in the EMD method and build a trainable EMD neural network module. Multiple sets of experiments have shown that the integrating of EMD module brings the improvement to different separation systems.

Streamlining NMR Chemical Shift Predictions for Intrinsically Disordered Proteins: Design of Ensembles with Dimensionality Reduction and Clustering.

By merging advanced dimensionality reduction (DR) and clustering algorithm (CA) techniques, our study advances the sampling procedure for predicting NMR chemical shifts (CS) in intrinsically disordered proteins (IDPs), making a significant leap forward in the field of protein analysis/modeling. We enhance NMR CS sampling by generating clustered ensembles that accurately reflect the different properties and phenomena encapsulated by the IDP trajectories. This investigation critically assessed different rapid CS predictors, both neural network (e.g., Sparta+ and ShiftX2) and database-driven (ProCS-15), and highlighted the need for more advanced quantum calculations and the subsequent need for more tractable-sized conformational ensembles. Although neural network CS predictors outperformed ProCS-15 for all atoms, all tools showed poor agreement with HN CSs, and the neural network CS predictors were unable to capture the influence of phosphorylated residues, highly relevant for IDPs. This study also addressed the limitations of using direct clustering with collective variables, such as the widespread implementation of the GROMOS algorithm. Clustered ensembles (CEs) produced by this algorithm showed poor performance with chemical shifts compared to sequential ensembles (SEs) of similar size. Instead, we implement a multiscale DR and CA approach and explore the challenges and limitations of applying these algorithms to obtain more robust and tractable CEs. The novel feature of this investigation is the use of solvent-accessible surface area (SASA) as one of the fingerprints for DR alongside previously investigated α carbon distance/angles or ϕ/ψ dihedral angles. The ensembles produced with SASA tSNE DR produced CEs better aligned with the experimental CS of between 0.17 and 0.36 r2 (0.18-0.26 ppm) depending on the system and replicate. Furthermore, this technique produced CEs with better agreement than traditional SEs in 85.7% of all ensemble sizes. This study investigates the quality of ensembles produced based on different input features, comparing latent spaces produced by linear vs nonlinear DR techniques and a novel integrated silhouette score scanning protocol for tSNE DR.

Wavenumber dynamic stiffness formulation for exact dispersion analysis of moderately thick symmetric cross-ply laminated plate built-up waveguides

A wavenumber dynamic stiffness (WDS) formulation for exact dispersion analysis of moderately thick symmetric cross-ply laminated plate built-up waveguides is presented. The effects of shear deformation and rotatory inertia are considered in the formulation by adopting the first order shear deformation theory. The elemental WDS matrix is derived from the exact general solutions of the governing differential equations and can be assembled to model complex plate built-up waveguides using the assembly procedure similar to that of the finite element method. The nonlinear eigen-solution technique, the Wittrick–Williams (WW) algorithm, is employed to compute dispersion curves from the obtained WDS matrices. To enhance computational efficiency, the J0 count problem of the WW algorithm is addressed by developing explicit expressions for the J0 term. This eliminates the need for mesh refinement over the entire frequency/wavenumber range. The accuracy and efficiency of the proposed method are demonstrated through comparisons with analytical solutions based on the classical laminated plate theory and the first order shear deformation theory, as well as numerical results obtained from the wave and finite element method.

A Sustainable Inventory Model with Advertisement Effort for Imperfect Quality Items under Learning in Fuzzy Monsoon Demand

In this paper, we proposed a sustainable inventory model with a learning effect for imperfect quality items under different kinds of fuzzy environments like crisp, general fuzzy, cloudy fuzzy, and monsoon fuzzy. We divided the mathematical model into three parts under the learning effect according to the real-time fuzzy components (crisp, cloudy, and monsoon environments) of the demand rate of the items. We minimized the total inventory cost with respect to cycle length in each environment under the proposed assumptions. The non-linear optimization technique is applied for the algorithm and the solution method to find the decision variable. Finally, we compared the total inventory cost under different fuzzy environments and our finding is that the fuzzy monsoon environment is a more effective fuzzy environment than crisp and cloudy fuzzy environments. We have presented a numerical example for the validation of the proposed model and have shown the impact of the inventory input parameters on the cycle length and total inventory fuzzy cost. The managerial insights and future scope of this proposed study have been shown in the sensitivity analysis and conclusion. The limitations, application, future extension and scope, and social implementation have been shown in this research study.

Phased array-based nonlinear wave mixing technique: Application to lack-of-fusion porosity characterization in additively manufactured metals.

The objective of this research is to demonstrate the effectiveness of a phased array-based nonlinear wave mixing technique to characterize internal, localized microscale damage in an additively manufactured (AM) component. By using phased arrays for the generation of the incident waves, it is possible to produce a nonlinear wave mixing scanning technique without the need for immersion or changing coupling conditions. The phased arrays can be configured to generate incident waves in multiple directions that meet the resonance conditions required for nonlinear wave mixing at a variety of internal locations. This allows for the scanning of a specimen without the removal and re-coupling of the source transducers, leading to greater scanning speed and repeatability. To demonstrate the accuracy of this phased array wave mixing approach, measurements of acoustic nonlinearity in an AM component are first made with a bulk wave second harmonic generation through thickness measurement. Next, nonlinear wave mixing measurements are made with single element transducers to confirm the sensitivity of the proposed nonlinear wave mixing approach to lack-of-fusion porosity in AM metals. Finally, phased arrays are used to highlight the effectiveness of the proposed nonlinear wave mixing technique in these same AM components.

Sideband Peak Count – a new nonlinear ultrasonic technique for monitoring damage progression in engineering materials

Linear ultrasonic (LU) techniques used by majority of the researchers working in material damage monitoring, are reliable for detecting relatively large defects. If the defect dimensions are in the range of the ultrasonic wavelength or larger, then those defects can be detected by analyzing the scattered ultrasonic fields. Material damage affects LU parameters such as ultrasonic wave speed and attenuation and their changes are detectable for relatively large defects. However, for small defects (when defect dimensions are significantly smaller than the wavelength of the propagating signal) the changes in the LU parameters are too small to detect or measure reliably. For detecting small defects engineers often use high frequency ultrasonic signals to make the defect dimensions greater than the wavelength. However, high frequency signals attenuate quickly and therefore, only very small regions near the ultrasonic probe can be inspected in this manner. Inspecting large structures by high frequency ultrasonic signals requires moving the probe mechanically from one point to the next and therefore, can be very time consuming. Nonlinear ultrasonic (NLU) technique on the other hand does not need to satisfy this restricting condition that the wavelength of the signal must be smaller than the defect size. NLU works well when the signal wavelength is much larger than the defect size. Therefore, relatively low frequency signals that can propagate a long distance and monitor a large area of a structure can be used for NLU measurements. Different NLU techniques can be used for detection and monitoring of small damages in a specimen. A relatively new NLU technique called the Sideband Peak Count-Index or SPC-I technique has been developed by the author and his collaborators. SPC-I technique for monitoring different types of materials – composites, metals, concrete, and other cement-based materials has been found to be effective. Along with those success stories of SPC-I the effect of topography and the advantage of topological sensing is also discussed in this presentation.

A multi reaction kinetic model to describe the enzymatic transesterification reaction of jatropha oil using a fermented solid containing lipases

The advancement of more precise tools for sustainable process design in enzymatic biodiesel synthesis from renewable sources is crucial. Kinetics of solvent-free transesterification reactions were conducted across a temperature spectrum from 30 °C to 60 °C, utilizing Jatropha curcas oil (TG) and ethanol as substrates, alongside a fermented solid by Rhizopus homothallicus as the biocatalyst. The dynamics of chemical species concentrations were monitored through High-performance Thin-Layer Chromatography. Maximum productivities were achieved at 35 °C and 60 °C for biodiesel (293.24 and 299.02 g kg biocat−1 h−1, respectively), at 40 °C for diglycerides (1018.36 g kg biocat−1 h−1), and at 35 °C for monoglycerides (560.75 g kg biocat−1 h−1). Maximum yields were determined at 30 °C for fatty acid ethyl esters (0.56 g gTG−1), and at 40 °C for diglycerides (0.53 g gTG−1) and monoglycerides (0.30 g gTG−1). Based on the experimental findings, a kinetic model was formulated encompassing three reversible transesterification reactions. Individual reactions were structured following classical biochemical kinetics, inclusive of ethanol inhibition. Model fitting was executed through non-linear multivariable regression techniques, with the minimum of the average coefficient of variation of the residuals (ACVR) serving as the objective function. The resulting fit of the kinetic model to the experimental data proved satisfactory, with an ACVR of less than 5 % across all instances. Notably, the maximum biodiesel productivity, obtained in this work, represented the highest value, compared to other related studies, using a fermented solid as a biocatalyst.