Nonlinear Nature Research Articles

Exploring the Performance of Whale Optimization Algorithm on Rosenbrock's Function

Optimization of complex and nonlinear functions is essential across various domains, from engineering and finance to artificial intelligence and machine learning. Rosenbrock's function stands as a fundamental benchmark for evaluating optimization algorithms due to its highly nonlinear and multimodal nature. Among the multitude of optimization algorithms, the Whale Optimization Algorithm (WOA) has garnered attention for its inspiration from the social behavior of humpback whales. However, its performance on Rosenbrock's function remains relatively unexplored. This paper aims to investigate the effectiveness of the WOA specifically on Rosenbrock's function through rigorous experimentation and analysis. By evaluating convergence speed, solution accuracy, and robustness, this study sheds light on WOA's behavior when confronted with the challenges posed by Rosenbrock's function. Comparative analysis with other optimization algorithms further elucidates WOA's adaptability and scalability. The findings contribute valuable insights for selecting suitable optimization algorithms in real-world applications and advance understanding of optimization algorithms' behavior in challenging landscapes.

Hamiltonian formalism for bistable-multilayered plates under non-mechanical stimuli

Bistable multilayered plates have attracted significant attention as morphing and adaptive structures, renowned for their unprecedented exceptional performance. However, accurately predicting both their shape and internal stresses poses formidable challenges due to their geometrically nonlinear nature. For the first time, this paper introduces a Hamiltonian formalism aimed at achieving high-resolution analysis of nonlinear multilayered plates subjected to non-mechanical stimuli, including hygro-thermo-electro-magneto-elastic responses. A canonical system is strategically developed to compute membrane behaviors, yielding symplectic dual differential equations for in-plane field variables. This method elegantly decouples out-of-plane variables from the full-state vector, leading to an exact analytical solution in the membrane problem. To predict the bending behaviors, the first variation of the Hamiltonian energy density function, expressed as a power series of the transverse deflection, ensures flexural equilibrium. The power series effectively captures all admissible out-of-plane deformations, enabling a smooth transition between linear and nonlinear plate responses, including pitchfork bifurcation and limit points. The validity and accuracy of the proposed method are rigorously assessed through convergence tests and satisfaction of boundary conditions across various equilibria, ranging from monostability to bistability. It is cross-verified with high-fidelity finite-element methods (FEM), showing excellent agreements in both deformations and stress resultants. This research presents a physics-based methodology that unveils a parametric interplay between in-plane and out-of-plane field variables, serving as an efficient approach for analyzing adaptive and morphing structures.

Complete Ensemble Empirical Mode Decomposition with Adaptive Noise to Extract Deep Information of Bearing Fault in Steam Turbines via Deep Belief Network

Extracting to enhance the accuracy of diagnosing bearing faults in steam turbines, a novel approach focused on extracting key fault features from vibration signals is introduced. Recognizing the complex, non-linear, and non-stationary nature of bearing vibration signals, our strategy involves a sensitivity analysis utilizing a multivariate diagnostic algorithm. The process begins with collecting vibration data from defective bearings via the TMI system. This data is then subjected to Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), enabling the integration of adaptive noise for the extraction of in-depth information. Following this, an analysis in both time and frequency domains — post Fast Fourier Transform (FFT) — is conducted on the decomposed signals, forming the basis of a diagnostic features database. To streamline data analysis and boost the model’s computational efficiency, a combination of eXtreme Gradient Boosting (XGBoost) and Mutual Information Criterion (MIC) is applied for dimensionality reduction. Furthermore, a deep belief network (DBN) is implemented to develop a precise fault diagnosis model for the bearings in rotating machinery. By incorporating sensitivity analysis, a diagnostic matrix is crafted, facilitating highly accurate fault identification. The superiority of this diagnostic algorithm is corroborated by testing with real on-site data and a benchmark database, demonstrating its enhanced diagnostic capabilities relative to other feature selection techniques.

Functional responses of a medium-ranging marine predator highlight the importance of frontal zones as foraging locations

The distribution of marine predators is linked to bio-physical processes that structure the spatio-temporal availability of prey species. Within shelf seas, tidal fronts are highly productive regions occurring at the interface between mixed and stratified waters. Fronts are predictable but dynamic features, with their timing and strength varying seasonally and annually. The availability of frontal habitats will also vary between animal populations depending on geographic location. Thus, understanding the associations between marine predators and frontal habitats across a range of environmental conditions will assist marine management and conservation. Here, we assessed functional responses of breeding black-legged kittiwakes Rissa tridactyla to environmental covariates related to tidal fronts (front strength, distance to fronts, sea surface temperature [SST] and surface chlorophyll concentration) from 10 UK colonies located throughout the North Sea. Kittiwakes showed a tendency to forage in areas of higher, but not maximal, front strength when such areas were available. Areas closer to fronts (<10 km) were selected when available, though we also observed increased usage of areas distant from fronts (30-50 km). Kittiwakes tended to forage in cooler, mixed waters, particularly as average SST rose. When average chlorophyll concentrations were low, habitat usage peaked in areas of higher chlorophyll. The results highlight the importance of frontal habitats and the dynamic, non-linear nature of seabird responses to habitat. Accounting for dynamic changes in habitat availability will play a key role in future conservation efforts, particularly as marine renewable installations and climate change may influence water stratification patterns.

Multi-condensate state as a functional strategy to optimize the cell signaling output

The existence of multiple biomolecular condensates inside living cells is a peculiar phenomenon not compatible with the predictions of equilibrium statistical mechanics. In this work, we address the problem of multiple condensates state (MCS) from a functional perspective. We combine Langevin dynamics, reaction-diffusion simulation, and dynamical systems theory to demonstrate that MCS can indeed be a function optimization strategy. Using Arp2/3 mediated actin nucleation pathway as an example, we show that actin polymerization is maximum at an optimal number of condensates. For a fixed amount of Arp2/3, MCS produces a greater response compared to its single condensate counterpart. Our analysis reveals the functional significance of the condensate size distribution which can be mapped to the recent experimental findings. Given the spatial heterogeneity within condensates and non-linear nature of intracellular networks, we envision MCS to be a generic functional solution, so that structures of network motifs may have evolved to accommodate such configurations.

Association Between Osteoporosis and Adiposity Index Reveals Nonlinearity Among Postmenopausal Women and Linearity Among Men Aged over 50 Years

PurposePrevious research shows conflicting views on the relationship between obesity and osteoporosis, partly due to variations in obesity classification and the nonlinear nature of these relationships. This study investigated the association between adiposity indices and osteoporosis, diagnosed using dual-energy X-ray absorptiometry (DXA), employing nonlinear models and offering optimal thresholds to prevent further bone mineral density decline.MethodsIn 2019, a prospective study enrolled males over 50 years and postmenopausal women. Anthropometric measurements, blood biochemistry, and osteoporosis measured by DXA were collected. Associations between adiposity indices and osteoporosis were analyzed using a generalized additive model and segmented regression model.ResultsThe study included 872 women and 1321 men. Indices such as abdominal volume index (AVI), visceral adiposity index (VAI), waist circumference (WC), hip circumference, body mass index (BMI), waist-to-hip ratio, and waist-to-height ratio (WHtR) were inversely associated with osteoporosis. In women, the relationship between the risk of osteoporosis and the adiposity indices was U-shaped, with thresholds of WC = 94 cm, AVI = 17.67 cm2, BMI = 25.74 kg/m2, VAI = 4.29, and WHtR = 0.61, considering changes in bone mineral density. Conversely, men exhibited a linear patterns for the inverse association.ConclusionThe impact of obesity and adiposity on osteoporosis varies significantly between women and men. In postmenopausal women, the relationship is nonlinear (U-shaped), with both very low and very high adiposity linked to higher osteoporosis risk. In men over 50, the relationship is linear, with higher adiposity associated with lower osteoporosis risk. The study suggests that maintaining specific levels of adiposity could help prevent osteoporosis in postmenopausal women.

Behavior of Economic Agents With Bounded Rationality in a Semi-open New Keynesian Model

The purpose of the article is to analyze the behavior of economic agents with limited rationality in a New Keynesian model which postulates that imported equipment and technology are one of the factors of production and that households consume only domestic products. Economic agents’ expectations are based on stationary values for the output gap and inflation and also on extrapolation of the latest available data on these variables. The weighted shares of agents applying these rules change endogenously. Histograms of the frequency distribution of the degree of optimism and the impulse responses of monetary policy shocks and technology shocks to the variables under study indicate that a less open economy tends to undergo an economic cycle with a smaller amplitude than a more rigid economy. An analysis of the trade-offs between inflation volatility and the output gap established their non-linear nature (in contrast to standard models with rational expectations). The results from analysis of trade-offs was that stabilization of inflation in models with limited rational expectations requires an increased interest rate reaction compared to a similar reaction for a model in which agents have rational expectations. The results obtained may be useful in designing monetary policy to stabilize inflation and output gaps.

Predicting multiphase flow behavior of methane in shallow unconfined aquifers using conditional deep convolutional generative adversarial network

Numerical modeling is an essential tool for geoscience applications involving multiphase flow behavior. Performing numerical simulation is, however, computationally intensive due to multi-scale, non-linear, and multi-physics nature of mechanisms controlling multiphase flow dynamics. Additionally, the computational challenges associated with traditional numerical simulations limit their applicability for repetitive simulations required in inverse modeling, uncertainty analysis, and optimization tasks. To overcome these limitations, surrogate modeling has recently emerged as a viable solution. A surrogate model, which functions as a regression model, is trained using numerical simulation data. It approximates the input–output relationships within a dynamic fluid environment. We design surrogate models, based on conditional deep convolutional generative adversarial network (cDC-GAN), to map the cross-domain between input and output pairs in a multiphase multicomponent system, focusing on methane (CH4) migration in shallow unconfined aquifers. The cDC-GAN technique is selected due to its ability to generate high-fidelity surrogate models that effectively capture complex spatial distributions and heterogeneities. This technique excels in handling high-dimensional data, learning the intricate relationships between inputs and outputs, and producing realistic representations of subsurface phenomena. The trained cDC-GANs consider capillary entry pressure heterogeneity as input because this geologic attribute places first-order control on CH4 migration in subsurface. The outputs include CH4 saturation, water saturation, residual saturation of CH4, CH4 mole fraction, and CH4 molality. For each output, a separate cDC-GAN model is trained. Once trained, cDC-GANs can at any given time determine CH4 distribution in a shallow unconfined aquifer, both qualitatively and quantitatively. The cDC-GAN approach can be considered as a valuable complement to numerical simulations for predicting multiphase flow behavior in other geoscience-, energy-, and environmental applications such as contaminant transport, hydrocarbon production, and geological carbon dioxide and hydrogen storage.

An explicit finite element discrete crack analysis of open hole tension failure in composites

Developing efficient, robust methods for predicting the progressive failure of carbon fiber composites under tension is essential for optimal design, balancing weight reduction, damage tolerance, and service life. Implicit finite element (FE) methods struggle with the complex interplay of failure mechanisms, leading to a heavy reliance on costly, time-consuming experimental testing. This study introduces a novel explicit algorithm designed for laminate-level mesh models, capable of simulating cohesive cracks without predefined paths. Utilizing an explicit finite element software approach, our method effectively addresses convergence issues associated with the non-linear and unstable nature of composite failures during quasi-static loading. Contrasting with implicit FE method, this mesh-independent approach is both practical and numerically robust. The algorithm’s performance, tested on carbon-fiber reinforced composites with varying ply configurations [452/-452]s, [45n/90n/-45n/0n]s and [45/90/-45/0]ns (n=1/2/4/8), demonstrates improved simulation accuracy and efficiency over implicit FE methods, aligning well with prior experimental and simulation data. This advancement offers a promising solution for accurately simulating and understanding the complex failure behavior of these composites.

Strong nonlinear mixing evolutions within phononic frequency combs

Phononic frequency combs (PFCs) represent an emerging attractive nonlinear vibrational phenomenon characterized by equidistant spectral lines. Despite the extensive experimental studies, the complex nonlinear mixing nature of PFCs continues to present significant challenges in solving and investigating their complete dynamics, which is difficult to achieve by existing computational approaches. In this paper, the entire solution space within a representative PFC induced by a 1:2 internal resonance is elucidated by conducting continuation computations and numerical long-time integrations. The proposed continuation approach is achieved by integrating our developed semi-analytical residue-regulating homotopy method (RRHM) with a pseudo arc-length continuation technique. In this solution space, we unearth wide-range nonlinear evolutions including overlapping intervals between the periodic and quasi-periodic branches, abundant multivalued sub-intervals, cyclic-fold (CF) bifurcations, and torus-doubling (TD) routes to chaos. In addition, multiple coexistences of a chaotic attractor and a periodic orbit, a chaotic attractor and a quasi-periodic orbit, as well as a periodic orbit and three quasi-periodic orbits are identified. Furthermore, we meticulously dissect and distinguish non-smooth variations in PFC morphology, which manifest as multiple jumps in comb spacing as the excitation frequency is swept across. This study could serve as a general guide for a comprehensive exploration of PFC dynamics and can offer insights to inform and inspire related experimental studies.

Application of Functional Resonance Analysis and fuzzy TOPSIS to identify and prioritize factors affecting newly emerging risks

Conventional safety analyses in complex systems like air separation units (ASUs) often attributed accidents to linear, deterministic causes, such as operator error. However, acknowledging the intricate interdependence of process components necessitates a shift towards recognizing the complexity of incident causation. This study proposes a novel model that integrates Function Resonance Analysis Method (FRAM) and fuzzy logic analysis to address this growing need. The model facilitates the identification of emerging risks and assesses the impact of influential factors within a mixed qualitative and quantitative framework. The FRAM method is initially employed to identify emerging risks within the ASU. Subsequently, fuzzy multi-criteria decision-making methods are utilized to establish the relationships and weightage of influential factors. Data collection encompasses semi-structured interviews, direct observation, process workflow analysis, and the involvement of a panel of engineers and operators from the investigated ASU. Utilizing FMV software for FRAM analysis, functions associated with air compression, distribution, and storage exhibit high resonance. This signifies substantial variability and a heightened potential for incidents or deviations in these functions and higher-level tasks. Furthermore, Fuzzy TOPSIS analysis reveals that education and experience emerge as the most impactful factors governing newly emerging risk. This model demonstrates significant merit for risk assessment and incident investigation. Its non-linear and dynamic nature empowers the proactive identification and examination of processes, incidents, and emerging risks before deviations or accidents occur.

New Solitary Waves for Thin-Film Ferroelectric Material Equation Arising in Dielectric Materials

Abstract In this paper, the thin-film ferroelectric material equation (TFFME), which enables the propagation of solitary polarisation in thin-film ferroelectric materials is investigated, will be expressed through the non-linear evolution models. Ferroelectrics are dielectric materials that explain wave propagation non-linear demeanors. The non-linear wave propagation form is administrated by TFFME. To investigate the characterisations of new waves and solitonic properties of the TFFME, the modified exponential Jacobi technique and rational exp(−ϕ(η))-expansion technique are used. Plenty of alternative responses may be achieved by employing individual formulas; each of these solutions is offered by some plain graphs. The validity of such schemes and solutions may be exhibited by assessing how well the relevant schemes and solutions match up. The effect of the free variables on the manner of acting of reached plots to a few solutions in the exact forms was also explored depending upon the nature of non-linearities. The descriptive characteristics of the reached results are presented and analysed by some density, two- and three-dimensional figures. We believe that our results would pave the way for future research generating optical memories based on non-linear solitons.

‘No One Is Left Behind?’: A Mixed-Methods Case Study of Equity and Inclusion in Physical Education Teacher Education

Equity and inclusion are requisites of high-quality Physical Education (PE). However, there is a substantial gap in understanding PE Teacher Education’s (PETE) effectiveness in preparing Preservice Teachers (PSTs) to implement equity-driven pedagogies. Moreover, focused on individual retrospective gameplay engagement rates (participation time), current research fails to provide a holistic perspective of the practical manifestations of equity and inclusion in PE. This study fills this void with novel insights offered by a mixed-methods case study examining the following: (i) the process-oriented teaching strategies employed by a PST trained to deliver inclusive pedagogies, alongside student voices on lived experiences; and (ii) the outcome-oriented gameplay patterns across two teaching units (Basketball and Volleyball). Participants included one PST and 26 students. Extensive observations and focus groups mapped the applied teaching strategies and student responses. Video-based social network analysis captured equity and inclusion in students’ gameplay patterns, using metrics such as degree prestige. Findings indicate the PETE impact in inducing PSTs’ inclusive manipulation of learning activities and the fostering of inclusive team membership and positive collaboration. SNA metrics evidenced equitable and inclusive gameplay patterns. Despite pedagogical efforts, content-specific factors may influence students’ gameplay inclusion. Hence, a reflection on the multifaceted and non-linear nature of promoting inclusive participation is prompted.

Deep learning systems for forecasting the prices of crude oil and precious metals

Commodity markets, such as crude oil and precious metals, play a strategic role in the economic development of nations, with crude oil prices influencing geopolitical relations and the global economy. Moreover, gold and silver are argued to hedge the stock and cryptocurrency markets during market downsides. Therefore, accurate forecasting of crude oil and precious metals prices is critical. Nevertheless, due to the nonlinear nature, substantial fluctuations, and irregular cycles of crude oil and precious metals, predicting their prices is a challenging task. Our study contributes to the commodity market price forecasting literature by implementing and comparing advanced deep-learning models. We address this gap by including silver alongside gold in our analysis, offering a more comprehensive understanding of the precious metal markets. This research expands existing knowledge and provides valuable insights into predicting commodity prices. In this study, we implemented 16 deep- and machine-learning models to forecast the daily price of the West Texas Intermediate (WTI), Brent, gold, and silver markets. The employed deep-learning models are long short-term memory (LSTM), BiLSTM, gated recurrent unit (GRU), bidirectional gated recurrent units (BiGRU), T2V-BiLSTM, T2V-BiGRU, convolutional neural networks (CNN), CNN-BiLSTM, CNN-BiGRU, temporal convolutional network (TCN), TCN-BiLSTM, and TCN-BiGRU. We compared the forecasting performance of deep-learning models with the baseline random forest, LightGBM, support vector regression, and k-nearest neighborhood models using mean absolute error (MAE), mean absolute percentage error, and root mean squared error as evaluation criteria. By considering different sliding window lengths, we examine the forecasting performance of our models. Our results reveal that the TCN model outperforms the others for WTI, Brent, and silver, achieving the lowest MAE values of 1.444, 1.295, and 0.346, respectively. The BiGRU model performs best for gold, with an MAE of 15.188 using a 30-day input sequence. Furthermore, LightGBM exhibits comparable performance to TCN and is the best-performing machine-learning model overall. These findings are critical for investors, policymakers, mining companies, and governmental agencies to effectively anticipate market trends, mitigate risk, manage uncertainty, and make timely decisions and strategies regarding crude oil, gold, and silver markets.

Predicting Crop Yield Productivity Using Machine Learning Algorithms: A Comparison of Linear and Non-linear Approaches

Predicting crop yield productivity is crucial for farmers and the agricultural sector to gain insights into crop productivity and returns. With advancements in technology and artificial intelligence, predicting crop yield using machine learning algorithms has become an important innovation. This study aimed to predict crop yield productivity using various machine learning algorithms and techniques. The dataset was sourced from Kaggle, preprocessed, and analyzed using linear algorithms such as Linear Regression, LASSO, and Ridge, as well as non-linear algorithms including SVR, KNN Regressor, and Polynomial Regression. Mean Squared Error (MSE) was computed to evaluate algorithms performance. Comparing the efficacy of linear versus non-linear algorithms on the dataset revealed that non-linear algorithms outperformed linear ones, indicating that the dataset's non-linear nature. Therefore, non-linear machine learning algorithms like SVR, KNN Regressor, and Polynomial Regression were recommended for better accuracy. Among these, KNN Regressor performed the best with an MSE of 0.00025, followed by SVR and Polynomial Regression with MSE values of 0.00142 and 0.0024, respectively.

Advanced Machine Learning Techniques for Predicting Gold and Silver Futures

This research focuses on predicting the future values of gold and silver futures by employing advanced machine learning algorithms. Traditional econometric models often struggle with commodity prices’ non-linear and dynamic nature. To address this, the study evaluates the performance of four unconventional machine learning algorithms: Gaussian Processes, Quantile Regression Forests, Extreme Learning Machines, and Support Vector Regression with an RBF kernel. The dataset used includes monthly trading data for gold and silver futures. The research findings indicate that these machine- learning models significantly enhance prediction accuracy. Support Vector Regression with an RBF kernel demonstrated the highest accuracy for gold futures predictions, while Extreme Learning Machines performed competitively for silver futures. This study highlights the potential of advanced machine learning techniques in financial forecasting, providing valuable insights for traders and investors in optimizing their strategies.

Continuous-time Hammerstein model identification utilizing hybridization of Augmented Sine Cosine Algorithm and Game-Theoretic approach

The widespread use of dynamic systems has greatly simplified various human-operated tasks. However, the complex and nonlinear nature of these systems has posed challenges in determining their structure due to heavy reliance on modeling for theoretical and empirical purposes in academic and practical contexts. This challenge is particularly evident in the Hammerstein model, which is well-known for its recognition of structural nonlinearity. To address the limitations of uncovering an optimized continuous-time Hammerstein model, researchers have explored the practical application of the Augmented Sine Cosine Algorithm-Game Theoretic (ASCA-GT). By combining the Game Theoretic (GT) and Sine Cosine Algorithm (SCA), this hybrid approach aims to achieve a nonlinear position-updated process for improved exploration and exploitation, while effectively overcoming issues like local optima trapping. The performance of ASCA-GT was evaluated using 13 benchmark functions and mathematical scenarios, as well as the Twin-Rotor System (TRS) and Electro-Mechanical Positioning System (EMPS). The effectiveness of the proposed technique was assessed using Wilcoxon's rank test, which confirmed the superior performance of ASCA-GT compared to other metaheuristic optimization methods in determining the continuous-time Hammerstein model.

Comparison of the performances of Statistical and Artificial Neural Network models in the prediction of geometry and density of PLA/wood biocomposite cubes manufactured by FDM

The present study investigates the impact of scanning speed, printing temperature, and layer height on the density, dimensions, errors of parallelism, and surface finish of cubical specimens made of PLA/wood biocomposite and manufactured by Fused Deposition Modelling (FDM). The study examined 64 specimens, each produced with a unique set of process parameters. The Response Surface Methodology (RSM) was employed to evaluate the effects of process parameters on the examined properties of the manufactured cubes. RSM analysis revealed the statistical significance of direct proportion between the layer height, printing temperature, and x-and y-dimensions of the manufactured specimens (with P-values of 0, 0, 0.002, and 0, respectively). Also, the scanning speed and error of parallelism in z-oriented faces were statistically correlated (with a P-value of 0.035). For layer height and cube density, an indirect proportion was observed (with a P-value of 0). Compared to the regression model, ANN exhibited better performance at process parameters effect evaluation. The worse performance of regression models can be attributed to their limited capacity to represent non-linear relationships, while ANN models can capture the complex non-linear nature of the process, leading to better performances (R2 close to 100%). An evaluation of the defects in the specimens was carried out using the go/no-go diagram.

Nonlinear analysis of ion‐acoustic solitary waves in an unmagnetized highly relativistic quantum plasma

AbstractThe present paper explores the dynamics of ion‐acoustic solitary waves (IASWs) within an unmagnetized, highly relativistic quantum plasma containing positive and negative ions alongside electrons, employing the quantum hydrodynamic model. The treatment accounts for the inertial characteristics of negative and positive ions, considering electrons as inertialess. The nonlinear nature of quantum IASWs is investigated through the derivation of the Korteweg–de Vries equation using the reductive perturbation method. The investigation highlights how wave propagation characteristics, whether compressive or rarefactive, are substantially modulated by several parameters, such as the quantum diffraction parameter , relativistic effects , equilibrium density , and ion mass ratio . The analysis identifies the existence of both slow and fast wave modes, heavily influenced by the relativistic parameters involved. Our findings have significant implications for the understanding of both laboratory and space plasmas, especially in contexts where negative ions are present.

Deep deterministic policy gradient for adaptive power system stabilization and voltage regulation

This paper focuses on the challenges posed by the time-variable and nonlinear nature of energy systems. In this systems set points fluctuate due to load variations, generator losses, and disturbances such as short circuit faults. Maintaining power system stability and effectively damping low-frequency oscillations are crucial objectives. To enhance damping and dynamic stability in modern systems power system stabilizers (PSSs) are typically employed. These facilities generate auxiliary control signals for the generator excitation system, diminishing oscillations. In this study, by involving a deep deterministic policy gradient (DDPG) based on a synergetic control approach to the excitation system of synchronous generators, a novel approach to achieving fast and adaptive stability improvement and voltage regulation is suggested. The presented technique incorporates an intelligent synergetic PSS that effectively stabilizes the voltage response of a single machine connected to an infinite bus power system. To leverage its adaptive capability in controller parameter adjustments, an auxiliary deep DDPG algorithm with an Actor-Critic architecture is designed. The suggested procedure offers a promising avenue for effectively handling electromechanical oscillations and achieving improved voltage regulation and transient stability in power systems.