Nonlinear Parameters Research Articles

To Evaluate the Degradation of Heat Damaged Concrete Specimens after Curing Using Non-Linear Ultrasound Technique

In this research, Non-linear Ultrasound (NLU) technique was used to evaluate the degradation on heat damaged cement mortar specimen behaving explicit nonlinear. Mortars of Portland cement type I (or normal cement, NC) were chosen to mold the specimens with water cement ratios of 0.4, 0.5 and 0.6, and size of 5x5x5cm-cube and 5x5x2cm-brick. The specimens were grouped for heating at different temperatures (30, 200, 300, 400, 600, 800℃ for 24 hours) to create degradations of different levels. After curing process in water for 28 days, mechanical property tests were carried out on each cube to get its stress-strain relation and strength. NLU tests were conducted on the brick specimens. The RITEC SNAP System with 250kHz/transmit and 500kHz/receive transducers was used to conduct the measurement of harmonics. The obtained amplitudes in spectrum of fundamental, 2nd and 3rd harmonics (A1, A2 and A3) and the amplitudes due to the background nonlinearity by facility (A01, A02 and A03) were analyzed to approach the nonlinear parameters for each specimen, such as the β and γ. The [(A01- A1),(A03/A 3 2 01 -A3/A13)] and[(A01-A1), |A02/A01 -A2/A12|] were applied as a nonlinear characteristic index to mark the quality of the microstructure of material, which could be related to the durability and workability of the material. The results showed a promised quantification method using NLU. Extended application can be expected.

Formation mechanism of loess-mudstone landslides in the Weibei Tableland Fault Active Zone of Baoji, China - Taking Wolongsi landslide as an example

The geomorphologic and environmental evolution of the Loess Plateau is greatly affected by the strong fault activity, leading to the frequent occurrence of geological hazards, particularly the loess-mudstone landslide (LML). Thus, it is crucial to investigate the formation mechanism of such landslides in active fault zones. In this study, a field survey was conducted in the Weibei tableland of Baoji where the active fault zone is developed. To study the creep behavior of LML sliding zone soil, the triaxial creep tests of multi-stage loading under different water content, confining pressure, dry density, loess-mudstone binary structure (LMBS) contact surface angle, and thickness were carried out using the sliding zone soil samples (loess, mudstone, and LMBS samples) obtained from Wolongsi landslide in the study area as an example. Experimental results revealed that: (1) Water content has a significant weakening effect on the strength of LML sliding zone soil. The strength of the LMBS sample is extremely water-sensitive. The weakening effect of water on the long-term strength of LML sliding zone soil mainly manifested in promoting the elastoplastic deformation of loess and the viscoplastic deformation of mudstone. (2) The long-term strength of the LML slip zone soil increases linearly with the increase in confining pressure and increases exponentially with the dry density. (3) The degrading effect of the stratigraphic interface dip angle on the long-term slope strength is mainly reflected in the change in the weakening degree of water on the strength of the LML sliding zone. In addition, according to the test results, the traditional Nishihara model is improved by introducing nonlinear parameters, and a new constitutive equation describing LML sliding zone soil is established. The new constitutive model can accurately describe the creep curve's whole process especially sensitively identifying the accelerated creep stage. Finally, after conducting a field investigation and laboratory tests, the main hazard factors affecting the occurrence of the LML were analyzed in the presence of fault activity on the Weibei Plateau of Baoji, China, and its formation mechanism was revealed as well.

A comprehensive evaluation of linear and non-linear HRV parameters between paced breathing and stressful mental state

BackgroundHeart rate variability (HRV) is a crucial metric that provides valuable insight into the balance between relaxation and stress. Previous research has shown that most HRV parameters improve during periods of mental relaxation, while decreasing during tasks involving cognitive workload. Although a comprehensive analysis of both linear and non-linear HRV parameters has been carried out in existing literature, there still exists a need for further research in this area. Additionally, limited knowledge exists regarding how specific interventions may influence the interpretation of these parameters and how the different parameters correlate under different interventions. This study aims to address these gaps by conducting a thorough comparison of different linear and non-linear HRV parameters under mentally relaxed versus stressful states. MethodologyParticipants were randomly and equally divided among two between-subjects groups: relaxed-stress (RS) (N = 22) and stress-relaxed (SR) (N = 22). In the RS group, a paced breathing task was given for 5 min to create relaxation, and was followed by a 5-min time-based mental calculation task to create stress. In the SR group, the order of the stress and relaxed tasks was reversed. There was a washout period of 15 min after the first task in both groups. ResultsOf the 37 HRV parameters, 33 differed significantly between the two interventions. The majority of the parameters exhibited an improving and degrading tendency of HRV parameters in the relaxed and stressed states, respectively. The correlation of the majority of HRV parameters decreases during stress, while prominent time domain and geometric domain parameters stand out in the correlation. ConclusionOverall, HRV parameters can be reliably used to assess a person's relaxed and stressed mental states during paced breathing and mental arithmetic task respectively. Furthermore, non-linear HRV parameters provide accurate estimators of the mental state, in addition to the commonly used linear parameters.

Application of multi-objective artificial gorilla troops optimization algorithm in intelligent evacuation path planning for building fires

In the event of a sudden incident in large buildings, optimizing personnel evacuation paths has a direct and significant impact on overall evacuation efficiency. To address personnel evacuation scenarios caused by building fires in complex environments, this study presents a path planning approach based on the Multi-Objective Gorilla Optimization (MIGTO) algorithm. The objective function comprises path risk, congestion cost, and path length. However, traditional GTO algorithms face limitations in addressing such problems, including slow convergence, premature convergence, and susceptibility to local optima. To address the aforementioned challenges, this study introduces variable updates to the spiral position during the algorithm development phase to improve search efficiency. The nonlinear parameters are adjusted to achieve a harmonious balance between global and local search capabilities. In addition, the alert perturbation mechanism is implemented before each optimization iteration, which improves the algorithm's ability to overcome local optima. Furthermore, a compound chaotic mapping is introduced to increase the diversity of the population. Experimental results demonstrate the outstanding performance of the MIGTO algorithm in various grid map path planning scenarios. Whether faced with complex obstacles, multiple exits, or multiple fire sources, the path inferiority indices of MIGTO in path planning are significantly superior to other algorithms. The MIGTO algorithm is not only suitable for dynamic planning of fire evacuation paths, but can also be used in the Pathfinder evacuation simulation software, where it outperforms the software's built-in algorithms.

Forecasting the potential of global marine shipping carbon emission under artificial intelligence based on a novel multivariate discrete grey model

PurposeTo achieve sustainable development in shipping, accurately identifying the impact of artificial intelligence on shipping carbon emissions and predicting these emissions is of utmost importance.Design/methodology/approachA multivariable discrete grey prediction model (WFTDGM) based on weakening buffering operator is established. Furthermore, the optimal nonlinear parameters are determined by Grey Wolf optimization algorithm to improve the prediction performance, enhancing the model’s predictive performance. Subsequently, global data on artificial intelligence and shipping carbon emissions are employed to validate the effectiveness of our new model and chosen algorithm.FindingsTo demonstrate the applicability and robustness of the new model in predicting marine shipping carbon emissions, the new model is used to forecast global marine shipping carbon emissions. Additionally, a comparative analysis is conducted with five other models. The empirical findings indicate that the WFTDGM (1, N) model outperforms other comparative models in overall efficacy, with MAPE for both the training and test sets being less than 4%, specifically at 0.299% and 3.489% respectively. Furthermore, the out-of-sample forecasting results suggest an upward trajectory in global shipping carbon emissions over the subsequent four years. Currently, the application of artificial intelligence in mitigating shipping-related carbon emissions has not achieved the desired inhibitory impact.Practical implicationsThis research not only deepens understanding of the mechanisms through which artificial intelligence influences shipping carbon emissions but also provides a scientific basis for developing effective emission reduction strategies in the shipping industry, thereby contributing significantly to green shipping and global carbon reduction efforts.Originality/valueThe multi-variable discrete grey prediction model developed in this paper effectively mitigates abnormal fluctuations in time series, serving as a valuable reference for promoting global green and low-carbon transitions and sustainable economic development. Furthermore, based on the findings of this paper, a grey prediction model with even higher predictive performance can be constructed by integrating it with other algorithms.

Data-driven online prediction of remaining fatigue life of a steel plate based on nonlinear ultrasonic monitoring

Online monitoring fatigue damage and remaining fatigue life (RFL) prediction of engineering structures are essential to ensure safety and reliability. A data-driven online prediction method based on nonlinear ultrasonic monitoring was developed to predict the RFL of the structures in real-time. Nonlinear ultrasonic parameters were obtained to monitoring the fatigue degradation. A Bayesian framework was employed to continuously compute and update the RFL distributions of the structures. Nonlinear ultrasonic experiments were performed on the fatigue damaged Q460 steel to validate the developed prediction methodology. The result indicates that the developed method has high prediction accuracy and can provide effective information for subsequent decision-making.

Overdistention Accelerates Electrophysiological Changes in Uterine Muscle Towards Labour in Multiple Gestations

Background for the researchPremature birth and its associated complications are one of the biggest global health problems, since there is currently no effective screening method in clinical practice to accurately identify the true Preterm Birth (PTB) from the false threatened ones. Despite the high prevalence of PTB in multiple gestation (MG) women which amounted up to 60%, in the literature there is any work about their uterine myoelectric activities in vivo system. Electrohysterography (EHG) has been emerged as an alternative technique for predicting PTB in single gestation (SG) women. PurposeThe aim of this study was to characterize and compare the uterine myoelectrical activity in vivo system of SG and MG women in regular check-ups, to provide the basis for early detection and prevention of preterm labour in MG. Basic proceduresA prospective observational cohort study was conducted on 31 SG and 18 MG women between the 28th and 32th WoG who underwent regular check-ups in the Polytechnic and University Hospital La Fe (Valencia, Spain). The 30-minute bipolar recording was filtered in the 0.1-4 Hz bandwidth and downsampled to 20 Hz. Signal analysis was performed in 120-second moving windows with 50% overlap, after removing artefacts by a double- blind expert process. A set of 8 temporal, spectral and non-linear parameters were calculated: root mean square (RMS), kurtosis of the Hilbert envelope (KHE), median frequency (MDF), H/L ratio, and sample entropy (SampEn) and bubble entropy (BubbEn) calculated in the whole bandwidth (WBW) and the fast wave high (FWH). The 10th, 50th and 90th percentiles of all windows analysed were calculated to obtain representative values of the recordings. For each parameter and percentile, statistically significant differences between the SG and MG groups and their statistical power (SP) were analysed to determine both the existence of an effect and substantive significance, respectively. Main findingsIn comparison to SG, MG EHG exhibited significant higher impulsiveness and higher predictability than SG which was reflected in the KHE (SP10 = 85.2, p10 < 0.001) and entropy measures (SampEn FWH: SP50 = 62.0, p50 = 0.0.016; SP90 = 52.5, p90 = 0.059. BubbEn FWH: SP50 = 75.2, p50 < 0.001; SP90 = 60.3, p90 = 0.002), suggesting an accelerated evolution of uterine electrophysiological condition. In addition, several EHG parameters were found to significantly correlate with foetal weight such as amplitude (RMS: r90 = 0.311, p90 = 0.006), signal impulsiveness (KHE: r10 = 0.311, p10 = 0.006) and entropy measures (SampEn FWH: r50 = −0.317, p50 = 0.005*; r90 = −0.279, p90 = 0.013*. BubbEn FWH: r50 = −0.370, p50 = 0.001*; r90 = −0.313, p90 = 0.005*), suggesting an electromechanical coupling between uterine overdistension and contractile activity in vivo system. Principal conclusionsIn comparison to SG women, MG showed higher impulsiveness and predictability in early third gestational trimester, as reflected in KHE, SampEn and BubbEn, respectively. We found similar cell excitability between SG and MG women far from delivery. In addition, we confirmed the relationship between uterine overdistension and surface myoelectric activity, revealing the electromechanical coupling pathway in uterine smooth muscle. Therefore, contextualized EHG-biomarkers would provide valuable information for early detection of PTB risk, which would allow clinicians better PTB management through personalised therapeutic interventions.

Whole Body Control of Mobile Manipulators With Series Elastic Actuators for Cart Pushing Tasks.

Human-centered environments provide affordance for the use of two-handed mobile manipulators. Yet robots designed to function in and physically interact with such environments are not yet capable of meeting human users' requirements. This work proposes a whole body control framework of a two-handed mobile manipulator driven by series elastic actuators (SEAs) for cart pushing tasks. A whole body dynamic model for an integrated mobile platform and on-board arms is revealed, which takes into account the interaction forces with the cart. Then, the explicit force/position control of the mobile manipulator is performed. It enables the robot to interact dynamically with the environment while providing motion, i.e., the manipulators provide both output force control and motion control for pushing a cart. To cope with the highly nonlinear system dynamics and parameter variation of a SEA-driven mobile manipulator, this work proposes an adaptive robust controller based on a novel integral barrier Lyapunov function for cart pushing tasks by considering model uncertainty. The proposed controller enables the mobile manipulator to complete cart pushing tasks by regulating the position and output force of the mobile base and arms. The experimental results show the effectiveness of this approach in cart pushing tasks.

Elongational rheology of 2, 3 and 4 polymer stars connected by linear backbone chains

We consider the elongational rheology of model polystyrene topologies with 2, 3 and 4 stars, which are connected by one (2-star or “Pom-Pom”), two (3-star) and three (4-star) linear backbone chains. The number of arms of each star varies from qa = 3 to 24, the molecular weight of the arms from Mw,a = 25 kg/mol to 300 kg/mol, and the backbone chains from Mw,b = 100 kg/mol to 382 kg/mol. If the length of the arm is shorter than the length of the backbone, i.e. Mw,a < Mw,b, and despite the vastly different topologies considered, the elongational stress growth coefficient can be modeled by the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model, based exclusively on the linear-viscoelastic characterization and a single nonlinear parameter, the dilution modulus. If the length of the arms of the stars is similar or longer than the length of the backbone chain (Mw,a ≥ Mw,b) connecting two stars, the impact of the backbone chain on the rheology vanishes and the elongational stress growth coefficient is dominated by the star topology showing similar features of the elongational stress growth coefficient as those of linear polymers.Graphical

Parameterisation and evolution of non-breaking wave nonlinearity over flexible vegetation

Wave nonlinearity significantly influences wave attenuation and can cause sediment transport imbalances in vegetated zones, impacting shoreline stability and ecosystem-based coastal defences. Despite its importance, the parameterisation and mechanisms of wave nonlinearity evolution over flexible vegetation remain unclear. This study examines the mechanisms behind non-breaking wave nonlinearity evolution over flexible vegetation and provides parameterisation of wave nonlinearity, based on experimental data collected by Anderson and Smith (2014). The study derives a new set of empirical formulae for predicting wave nonlinearity in Spartina alterniflora, which considers Ursell number, relative vegetation width, vegetation submergence, and vegetation density. The predictions made using these formulae are in good agreement with the measurements. The results indicate a decrease in wave skewness across the span of vegetation, whereas wave asymmetry increases until it reaches a maximum before decreasing. The findings suggest a preferential dissipation of high harmonics compared to low harmonics in the vegetation zone. Additionally, bispectrum analysis reveals that vegetation enhances the difference interaction while suppressing the sum interaction between wave components. The findings enable improvements in our understanding of wave nonlinearity in vegetation, providing better predictive capabilities for wave attenuation and sediment transport, which are crucial for the design and optimization of coastal defence systems.

Soft tissue material properties based on human abdominal in vivo macro-indenter measurements

Simulations of human-technology interaction in the context of product development require comprehensive knowledge of biomechanical in vivo behavior. To obtain this knowledge for the abdomen, we measured the continuous mechanical responses of the abdominal soft tissue of ten healthy participants in different lying positions anteriorly, laterally, and posteriorly under local compression depths of up to 30 mm. An experimental setup consisting of a mechatronic indenter with hemispherical tip and two time-of-flight (ToF) sensors for optical 3D displacement measurement of the surface was developed for this purpose. To account for the impact of muscle tone, experiments were conducted with both controlled activation and relaxation of the trunk muscles. Surface electromyography (sEMG) was used to monitor muscle activation levels. The obtained data sets comprise the continuous force-displacement data of six abdominal measurement regions, each synchronized with the local surface displacements resulting from the macro-indentation, and the bipolar sEMG signals at three key trunk muscles. We used inverse finite element analysis (FEA), to derive sets of nonlinear material parameters that numerically approximate the experimentally determined soft tissue behaviors. The physiological standard values obtained for all participants after data processing served as reference data. The mean stiffness of the abdomen was significantly different when the trunk muscles were activated or relaxed. No significant differences were found between the anterior-lateral measurement regions, with exception of those centered on the linea alba and centered on the muscle belly of the rectus abdominis below the intertubercular plane. The shapes and areas of deformation of the skin depended on the region and muscle activity. Using the hyperelastic Ogden model, we identified unique material parameter sets for all regions. Our findings confirmed that, in addition to the indenter force-displacement data, knowledge about tissue deformation is necessary to reliably determine unique material parameter sets using inverse FEA. The presented results can be used for finite element (FE) models of the abdomen, for example, in the context of orthopedic or biomedical product developments.

Pump and probe wave mixing for imaging nonlinear features embedded into a massive concrete block

Abstract Nonlinear ultrasonic parameters are known to be highly sensitive to the presence of damage in materials, and numerous methods have already been reported. This study proposes a way to image a nonlinear defect embedded into a nonlinear medium. The nonlinear defect is mimicked by a Berea sandstone sphere (high nonlinearity). It is placed into a large concrete block (average nonlinearity) during casting. The proposed pump and probe propagating wave interaction method allows imaging the presence of the highly nonlinear region. The image contrast is magnified by a factor 8 in the defective zone. The results are validated using a model and the individual mechanical properties of both concrete and Berea Sandstone. These findings open perspectives for application to civil engineering concrete structures such as the assessment of durability distresses involving internal swelling.

A novel fractional multivariate grey prediction model for forecasting hydroelectricity consumption

PurposeThis study aims to enhance the prediction accuracy of hydroelectricity consumption in China, with a focus on addressing the challenges posed by complex and nonlinear characteristics of the data. A novel grey multivariate prediction model with structural optimization is proposed to overcome the limitations of existing grey forecasting methods.Design/methodology/approachThis paper innovatively introduces fractional order and nonlinear parameter terms to develop a novel fractional multivariate grey prediction model based on the NSGM(1, N) model. The Particle Swarm Optimization algorithm is then utilized to compute the model’s hyperparameters. Subsequently, the proposed model is applied to forecast China’s hydroelectricity consumption and is compared with other models for analysis.FindingsTheoretical derivation results demonstrate that the new model has good compatibility. Empirical results indicate that the FMGM(1, N, a) model outperforms other models in predicting the hydroelectricity consumption of China. This demonstrates the model’s effectiveness in handling complex and nonlinear data, emphasizing its practical applicability.Practical implicationsThis paper introduces a scientific and efficient method for forecasting hydroelectricity consumption in China, particularly when confronted with complexity and nonlinearity. The predicted results can provide a solid support for China’s hydroelectricity resource development scheduling and planning.Originality/valueThe primary contribution of this paper is to propose a novel fractional multivariate grey prediction model that can handle nonlinear and complex series more effectively.

A model-based proportional-integral observer design for adhesion estimation in the wheel-rail interface: LMI approach

Adhesion estimation in wheel and rail interface is a crucial element as it has a direct effect on the locomotive characteristics and performance. Since the adhesion condition depends on unpredictable factors and dynamic models, its estimation is a complex task. In this paper, a dynamic model for a single wheelset including parameters in detail is developed to improve the accuracy of the model. Then, a model-based Proportional–Integral Observer (PIO) is designed to estimate adhesion during uncertainties and nonlinear parameters. The stability of the proposed PI observer is proved with Lyapunov theory and Linear Matrix Inequality (LMI). Finally, the performance of the method is evaluated via numerical simulation in MATLAB software, and it is validated with a model set-up in the SIMPACK Multibody Simulation (MBS) software.

Lie group analysis and SQLM of entropy generation of MHD nonlinear radiative micropolar nanofluid flow with thermophoresis and Brownian motion

This study investigates the entropy generation in hydromagnetic mixed convection of a micropolar fluid flowing over a stretchable sheet, taking into account various influential factors such as nonlinear thermal radiation, Ohmic dissipation, uniform heat source/sink effects, chemical reaction, thermophoresis, and Brownian motion. The Spectral Quasilinearization Method (SQLM) is employed, which transforms nonlinear equations into a series of linearized ones, streamlining the solving process. Additionally, Lie group analysis is utilized to identify symmetries and derive similarity transformations crucial for converting partial differential equations into coupled ordinary differential equations, which are then solved numerically. A comprehensive sensitivity analysis is conducted on critical parameters, including the Darcy parameter, Biot number, Brinkman number, nonlinear convection parameter, and chemical reaction parameter. This analysis explores the impacts of these parameters on various flow profiles, such as velocity, temperature, microrotation, concentration, and entropy generation, enriching the depth and practical relevance of the findings. The results reveal that increasing the Brinkman and Reynolds numbers enhances entropy generation profiles while increasing the coupling parameter reduces them. The focus on entropy generation analysis provides valuable insights into energy utilization and system efficiency, particularly in micropolar fluid dynamics. Furthermore, the study underscores the practical implications of its findings by highlighting their relevance in evaluating the effectiveness of industrial processes, especially those related to energy conversion and heat transfer phenomena.

High‐Dissolution Mechanism of Ti–48Al–2Cr–2Nb Alloy in Electrochemical Machining from a Nonlinear Dynamic Perspective

High‐rate dissolution process of Ti–48Al–2Cr–2Nb alloy in electrochemical machining exhibits strong nonlinear dynamic characteristics, but the quantitative relationship between these nonlinear characteristics and surface topography, as well as the electro‐dissolution mechanism, is unknown. Therefore, the fractal and recursive features of dissolution behavior and quantitative characterization of the dissolved surface topography were investigated. Additionally, an electro‐dissolution mechanism model in electrochemical machining process was presented. Applying a higher potential of 11 V can enhance the stability of the electrochemical system, resulting in a smoother and uniform surface. The saturation correlation dimension, surface roughness, and integral area of lacunarity initially decrease before increasing with higher electrolytic pressure, while laminarity and determinism show an initial increase followed by a decrease. These five characteristic parameters reach their optimal values at an electrolyte pressure of 0.4 MPa, indicating that achieving a stable and deterministic electrochemical system is crucial for obtaining a uniform smooth surface. These nonlinear dynamic characteristic parameters can be considered as in‐situ monitoring parameters for surface quality in ECM. The anodic dissolution process comprises three stages: initial passive film dissolution and breakdown, rapid dissolving with surface coarsening, and stable dissolving with polishing.

The electronic, structural and nonlinear optical properties of licochalcone L in the aqueous solution and gaseous phase: A DFT study

In the present article, various conformers of licochalcone L, a chalcone derivative extracted from the G. inflata root, have been analyzed in the aqueous solution and gaseous phase using calculation based on density functional theory (DFT). Nonlinear optical parameters such as dipole moment (μ), mean polarizability (α), polarizability anisotropy (Δα) and the first order hyperpolarizability (β) have been estimated to examine the NLO properties of the title molecule. These parameters were found to be significantly higher than those of standard molecules, indicating the potential NLO applications of licochalcone L. The analysis of natural bond orbitals (NBO) has been carried out to characterize various intramolecular interactions. The nucleus-independent chemical shift (NICS) technique has been used to investigate the aromaticity. Further, the pKa values have been computed for each hydroxyl group, revealing that the neutral form predominates at physiological pH, while the monoanionic form becomes predominant at pH greater than 9. The impact of solvation on the molecular electrostatic potentials and frontier molecular orbitals has been investigated for the neutral as well as monoanionic form of licochalcone L. A variety of global chemical reactivity descriptors have been calculated to highlight the structure-activity relationship.

Braneworld black holes with ModMax electrodynamics on the brane

In this study, we investigate ModMax electrodynamics localized within the Randall–Sundrum II and Dvali–Gabadadze–Porrati branes, deriving corresponding 3-brane spacetime solutions that conform to the effective Einstein equations in each specific scenario. We construct solutions for charged black holes within the effective Einstein equation framework in both braneworld scenarios. The examination explores the trajectories of charged objects in this spacetime, underscoring the significance of the nonlinear parameter. Our analysis uncovers the fact that, similar to the prior ModMax black hole investigation, the nonlinear parameter plays a pivotal role in suppressing the effective charge of the black hole, due to its definite positive value.

High Perturbations of a Fractional Kirchhoff Equation with Critical Nonlinearities

This paper concerns a fractional Kirchhoff equation with critical nonlinearities and a negative nonlocal term. In the case of high perturbations (large values of α, i.e., the parameter of a subcritical nonlinearity), existence results are obtained by the concentration compactness principle together with the mountain pass theorem and cut-off technique. The multiplicity of solutions are further considered with the help of the symmetric mountain pass theorem. Moreover, the nonexistence and asymptotic behavior of positive solutions are also investigated.

Non-linear Kernel Optimisation of Support Vector Machine Algorithm for Online Marketplace Sentiment Analysis

Twitter is a social media platform that is very important in the digital world. Fast communication and interaction make Twitter a vital information center in sentiment analysis. The purpose of this research is to classify public opinion about the presence of marketplaces in Indonesia, both positive and negative sentiments, using a Non-linear SVM algorithm based on 1276 tweets. This research involves the stages of data pre-processing, labeling, feature extraction using TF-IDF, and data division into three scenarios: 80% training data and 20% test data, 50% training data and 50% test data scenario, and 20% training data and 80% test data scenario. The last process, GridSearchCV, combines cross-validation and non-linear SVM parameters for model evaluation using a confusion matrix. The best SVM model resulting from the scenario was 80% training and 20% test data, with hyperparameters Gamma = 100 and C = 0.01, achieving 89% accuracy. When tested on never-before-seen data, the accuracy increased to 90%, with an f1-score of 91%, precision of 88%, and recall of 95% on negative sentiments. In conclusion, evaluating the performance of non-linear SVM kernels with a combination of hyperparameter values can improve accuracy, especially on public response information about online marketplaces and public sentiment.