Nonlinear Support Research Articles

Quantitative physics-physiology relationship modeling of human emotional response to Shu music.

Music perception is one of the most complex human neurophysiological phenomena invoked by sensory stimuli, which infers an internal representation of the structured events present in a piece of music and then forms long-term echoic memory for the music. An intrinsic relationship between the basic acoustic property (physics) of music and human emotional response (physiology) to the music is suggested, which can be statistically modeled and explained by using a novel notion termed as quantitative physics-physiology relationship (QPPR). Here, we systematically analyzed the complex response profile of people to traditional/ancient music in the Shu area, a geographical concept located in the Southwest China and one of three major origins of the Chinese nation. Chill was utilized as an indicator to characterize the response strength of 18 subjects to an in-house compiled repertoire of 86 music samples, consequently creating a systematic subject-to-sample response (SSTSR) profile consisting of 1,548 (18 × 86) paired chill elements. The multivariate statistical correlation of measured chill values with acoustic features and personal attributes was modeled by using random forest (RF) regression in a supervised manner, which was compared with linear partial least square (PLS) and non-linear support vector machine (SVM). The RF model exhibits possessed strong fitting ability (r F 2 = 0.857), good generalization capability (r P 2 = 0.712), and out-of-bag (OOB) predictability (r O 2 = 0.731) as compared to SVM and, particularly, PLS, suggesting that the RF-based QPPR approach is able to explain and predict the emotional change upon musical arousal. It is imparted that there is an underlying relationship between the acoustic physical property of music and the physiological reaction of the audience listening to the music, in which the rhythm contributes significantly to emotional response relative to timbre and pitch. In addition, individual differences, characterized by personal attributes, is also responsible for the response, in which gender and age are most important.

Multivariable prediction of functional outcome after first-episode psychosis: a crossover validation approach in EUFEST and PSYSCAN.

Several multivariate prognostic models have been published to predict outcomes in patients with first episode psychosis (FEP), but it remains unclear whether those predictions generalize to independent populations. Using a subset of demographic and clinical baseline predictors, we aimed to develop and externally validate different models predicting functional outcome after a FEP in the context of a schizophrenia-spectrum disorder (FES), based on a previously published cross-validation and machine learning pipeline. A crossover validation approach was adopted in two large, international cohorts (EUFEST, n = 338, and the PSYSCAN FES cohort, n = 226). Scores on the Global Assessment of Functioning scale (GAF) at 12 month follow-up were dichotomized to differentiate between poor (GAF current < 65) and good outcome (GAF current ≥ 65). Pooled non-linear support vector machine (SVM) classifiers trained on the separate cohorts identified patients with a poor outcome with cross-validated balanced accuracies (BAC) of 65-66%, but BAC dropped substantially when the models were applied to patients from a different FES cohort (BAC = 50-56%). A leave-site-out analysis on the merged sample yielded better performance (BAC = 72%), highlighting the effect of combining data from different study designs to overcome calibration issues and improve model transportability. In conclusion, our results indicate that validation of prediction models in an independent sample is essential in assessing the true value of the model. Future external validation studies, as well as attempts to harmonize data collection across studies, are recommended.

Quantitative prediction of minced chicken gel strength under ultrasonic treatment by NIR spectroscopy coupled with nonlinear chemometric tools evaluated using APaRPs

Achieving the ideal gel strength is essential for desired texture in minced chicken products. This study developed a rapid, non-destructive method using near-infrared (NIR) spectroscopy and nonlinear chemometric modeling to predict minced chicken gel strength under ultrasonic treatment. Initially, minced chicken samples were subjected to high-intensity ultrasound for 0–50 min. This was followed by heat-induced gelation. Gel strength was conventionally measured, and NIR spectra were collected. Nonlinearity between gel strength and spectral data was confirmed using augmented partial residual plots (APaRPs). Subsequently, nonlinear support vector machine (SVM) and extreme learning machine (ELM) models were developed using full NIR spectra and variable selection methods, including uninformative variable elimination (UVE), competitive adaptive reweighting (CARS), and genetic algorithms (GA). GA proved most effective for enhancing model performance, achieving the highest predicted coefficient of determination (Rp2 = 0.8772) with the ELM model, demonstrating potential for rapid, non-destructive prediction of minced chicken gel strength quality.

Toward coupling of nonlinear support vector regression and crowd intelligence optimization algorithms in estimation of suspended sediment load

Sediment phenomenon is very important in hydraulic and water resources issues. The existence of this phenomenon causes many problems in water storage. Sediment simulation in rivers helps in controlling sediment as well as reducing damages. In this study, an attempt was made to estimate the suspended sediment load using the corresponding river flow rate in the Zohreh River, Iran using the newest intelligent simulation methods. This study seeks to couple the nonlinear support vector regression (SVR) with crowd intelligence optimization algorithms. For this purpose, support vector regression was optimized using four new crowd optimization algorithms including the ant colony optimizer (ACO), the ant lion optimizer (ALO), the dragonfly algorithm (DA), and the salp swarm algorithm (SSA). Simulation was done in the two phases of train and test. Due to the integration of the nonlinear support vector regression with the optimization algorithms, the model train phase requires more time than usual situations. Therefore, in the current study, taking into account the number of different iterations including 25, 50, 100 and 200 iterations to perform the optimization of the model and tried to find the best optimizer by considering the calculated error and the run time. It was generally found that the SVR model is accurate in estimating the suspended sediment load. Finally, according to the calculated error as well as the run time, the support vector regression model optimized with the salp swarm algorithm with 25 iterations was chosen as the best model. Also, the values of R2, NSE, and RMSE for the best model in the test phase were calculated as 1, 1, and 10.2 tons per day, respectively, and the algorithm run time was 252 s.

Surface quality evaluation through new optical imaging system-based objective speckle for additive manufactured titanium samples

Laser cladding is an effective additive manufacturing technology used for materials’ surface modification to enhance their surface and mechanical properties. Surface roughness is a crucial feature that affects the materials’ quality and lifespan. Additionally, it is a real indicator of hardness and wear resistance. Although the existing methods may precisely measure surface roughness, they require delicate adjustment, can damage surfaces, and have limited working distances. This study presents a novel optical imaging system to quantitatively estimate the quality modifications of additive manufacturing samples by measuring their surface roughness based on objective speckle and advanced multivariate analysis methods. The raw speckle patterns are generated from deposited layers on Ti6Al4V titanium alloys obtained at different laser processing parameters. The proposed analysis approach produces collections of local statistical matrices from which histogram features are extracted. Canonical correlation analysis (CCA) is then proposed to distinguish the most significant features. The correlation between the features (with and without applying CCA) and surface roughness is established by using two machine learning regression algorithms, nonlinear support vector regression (SVR), random forest regression (RF), and k-nearest neighbor regression (kNN). The results confirmed that combining RF and CCA provided a feasible regression model to estimate the surface roughness, with 0.998 for R2 in training samples and maximum values of 0.258, 0.484, and 4.593 %, respectively, for MAE, RMSE, and MAPE in test samples. This demonstrates that the proposed objective speckle imaging system is effective in estimating the quality modification of additive manufacturing samples by measuring their surface roughness.

Prediction of blast-hole utilization rate using structured nonlinear support vector machine combined with optimization algorithms

Prediction of blast-hole utilization rate using structured nonlinear support vector machine combined with optimization algorithms

Klasifikasi Gender Berdasarkan Sidik Jari Menggunakan Principal Component Analysis dan Support Vector Machine

Most fingerprint classification research uses features such as core and delta as its basis. Before extracting fingerprint features, various preprocessing steps are usually performed first. This study differs from other studies in that classification is performed directly on the fingerprint image without going through a detailed preprocessing step and only a pixel size change is performed to 96x103. Fingerprint features are not determined manually, but are extracted automatically using the Principal Component Analysis (PCA) method which produces the 4200 best features. For feature perfection reasons, feature normalization has been performed using StandardScaler. The classification of this study uses a nonlinear Support Vector Machine (SVM) method with a Polynomial kernel. This study uses 6000 data samples from the SOCOFing database. This model obtains a classification accuracy of up to 88.75%.

Chaotic Vortex-Induced Vibrations of Rigid Cylinders with Nonlinear Snapping Support

Vortex-Induced Vibration (VIV) is a complex fluid–structure interaction in offshore structures. Traditionally, this phenomenon is considered periodic; however, many of its signals show chaotic behavior. The basic model already employed by other researchers is a rigid circular cylinder with linear springs and dampers. In this work, nonlinear snapping support is used to model nonlinearity in the system. To numerically simulate the flow, Reynolds-Averaged Navier–Stokes (RANS) equations for two-dimensional incompressible unsteady flows are applied. The degree of nonlinearity of the system can be changed by manipulating [Formula: see text], which is one of the geometric properties of the spring and takes values between 0 and 1. The 0–1 test, Poincaré section, and Fast Fourier Transform are used to analyze the cylinder and lift force behavior. Also, the Hilbert transform is applied to the signals, and the phase shift between displacement and lift force is obtained. The results show that the system behavior consists of branches: branch I and branch II. The large amplitudes occur in branch II. It is found that chaos emerges at the beginning of branch II, regardless of the value of [Formula: see text]. By raising the [Formula: see text] value, the span of branch II becomes more expansive, and its first point is placed at lower reduced velocities. Also, the wake dynamics becomes more regular at the end of branch I and more irregular at the beginning of branch II with the increase in [Formula: see text]. When the cylinder displacement signal is chaotic, the lift force behavior is also chaotic, but not vice versa.

Rapid pH Value Detection in Secondary Fermentation of Maize Silage Using Hyperspectral Imaging

As pH is a key factor affecting the quality of maize silage, its accurate detection is essential to ensuring product quality. Although traditional methods for testing the pH of maize silage feed are widely used, the procedures are often complex and time-consuming and may damage the sample. This study presents a non-destructive hyperspectral imaging (HSI) technology that provides a more efficient and cost-effective method of monitoring pH by capturing the spectral information of samples and analyzing their chemical and physical properties rapidly and without contact. We applied four spectral preprocessing methods, among which the multiplicative scatter correction (MSC) preprocessing method yielded the best results. To minimize model redundancy and enhance predictive performance, we utilized six feature extraction methods for characteristic wavelength extraction, integrating these with partial least squares (PLS), non-linear support vector machine regression (SVR), and extreme learning machine (ELM) algorithms to construct a quantitative pH value prediction model. The results showed that the model based on the bootstrapping soft shrinkage (BOSS) feature wavelength extraction method outperformed the other feature extraction methods, selecting 20 pH value-related feature wavelengths from 256 bands and building a stable BOSS–ELM model with prediction set determination coefficient (RP2), root-mean-square error of prediction (RMSEP), and relative percentage deviation (RPD) values of 0.9241, 0.4372, and 3.6565, respectively. To further optimize the model for precisely predicting pH at each pixel in hyperspectral images, we employed three algorithms: the genetic algorithm (GA), whale optimization algorithm (WOA), and bald eagle search (BES). These algorithms optimized and compared the BOSS–ELM model to obtain the best model for predicting maize silage pH: the BOSS–BES–ELM model. This model achieved a determination coefficient (RP2) of 0.9598, an RMSEP of 0.3216, and an RPD of 5.1448. We generated a visualized distribution map of pH value variation in maize silage using the BOSS–BES–ELM model. This study provides strong technical support and a reference for the rapid, non-destructive detection of maize silage pH from an image, an advancement of great significance to ensuring the quality of maize silage.

Potential of hyperspectral imaging for nondestructive determination of α-farnesene and conjugated trienol content in ‘Yali’ pear

The sesquiterpene α-farnesene and its corresponding oxidation products, namely conjugated trienols (CTols) is well known to be correlated with the development of superficial scald, a typical physiological disorder after a long term of cold storage in pear fruit. In this work, hyperspectral imaging (HSI) technology was used for nondestructive predicting of α-farnesene and CTols [CT258, CT281 and CT(281-290)] content in ‘Yali’ pear. In order to obtain the best performance of calibration model and simplify the calibration model further, various preprocessing methods together with their combinations and different wavelength selection algorithms, including successive projections algorithm (SPA), competitive adaptive reweighted sampling (CARS) and uninformative variable elimination (UVE), were investigated and compared based on linear partial least square regression (PLSR) and nonlinear least square support vector machine (LS-SVM) models, respectively. In conclusion, compared to the PLSR models, the results of LS-SVM models based on original and preprocessing methods performed better for the prediction of α-farnesene and CTols, while the performance of LS-SVM models based on the selected characteristic wavelengths were worse. For α-farnesene, the best result was obtained by LS-SVM model based on MSC-FD pretreatment with the RPD value of 2.6, Rp = 0.925 and RMSEP = 4.387 nmol cm−2. And for CTols, CT281 performed better compared with CT258 and CT(281-290), achieving the result with RPD = 2.4, Rp = 0.913 and RMSEP = 2.734 nmol cm−2 based on LS-SVM model combined with SD pretreatment. The overall results illustrated HSI technology could be used for rapid and nondestructive prediction of α-farnesene and CTols in ‘Yali’ pear, which would be helpful for supporting postharvest decision systems.

Predicting anti-trypanosome effect of carbazole-derived compounds by powerful SVM with novel kernel function and comprehensive learning PSO.

In order to predict the anti-trypanosome effect of carbazole-derived compounds by quantitative structure-activity relationship, five models were established by the linear method, random forest, radial basis kernel function support vector machine, linear combination mix-kernel function support vector machine, and nonlinear combination mix-kernel function support vector machine (NLMIX-SVM). The heuristic method and optimized CatBoost were used to select two different key descriptor sets for building linear and nonlinear models, respectively. Hyperparameters in all nonlinear models were optimized by comprehensive learning particle swarm optimization with low complexity and fast convergence. Furthermore, the models' robustness and reliability underwent rigorous assessment using fivefold and leave-one-out cross-validation, y-randomization, and statistics including concordance correlation coefficient (CCC), [Formula: see text] , [Formula: see text] , and [Formula: see text] . Among all the models, the NLMIX-SVM model, which was established by support vector regression using a nonlinear combination of radial basis kernel function, sigmoid kernel function, and linear kernel function as a new kernel function, demonstrated excellent learning and generalization abilities as well as robustness: [Formula: see text] = 0.9581, mean square error (MSE) = 0.0199 for the training set and [Formula: see text] = 0.9528, MSE = 0.0174 for the test set. [Formula: see text] , [Formula: see text] , CCC, [Formula: see text] , [Formula: see text], and [Formula: see text] are 0.9539, 0.8908, 0.9752, 0.9529, 0.9528, and 0.9633, respectively. The NLMIX-SVM method proved to be a promising way in quantitative structure-activity relationship research. In addition, molecular docking experiments were conducted to analyze the properties of new derivatives, and a new potential candidate drug molecule was ultimately found. In summary, this study will provide help for the design and screening of novel anti-trypanosome drugs.

Near-Infrared Spectroscopy Analysis of the Phytic Acid Content in Fuzzy Cottonseed Based on Machine Learning Algorithms.

Cottonseed is rich in oil and protein. However, its antinutritional factor content, of phytic acid (PA), has limited its utilization. Near-infrared (NIR) spectroscopy, combined with chemometrics, is an efficient and eco-friendly analytical technique for crop quality analysis. Despite its potential, there are currently no established NIR models for measuring the PA content in fuzzy cottonseeds. In this research, a total of 456 samples of fuzzy cottonseed were used as the experimental materials. Spectral pre-treatments, including first derivative (1D) and standard normal variable transformation (SNV), were applied, and the linear partial least squares (PLS), nonlinear support vector machine (SVM), and random forest (RF) methods were utilized to develop accurate calibration models for predicting the content of PA in fuzzy cottonseed. The results showed that the spectral pre-treatment significantly improved the prediction performance of the models, with the RF model exhibiting the best prediction performance. The RF model had a coefficient of determination in prediction (R2p) of 0.9114, and its residual predictive deviation (RPD) was 3.9828, which indicates its high accuracy in measuring the PA content in fuzzy cottonseed. Additionally, this method avoids the costly and time-consuming delinting and crushing of cottonseeds, making it an economical and environmentally friendly alternative.

Study on the Vibration Characteristics of the Helical Gear-Rotor-Bearing Coupling System of a Wind Turbine with Composite Faults

As the core component of the wind turbine generation gearbox, the gear-rotor-bearing transmission system typically operates in harsh environments, inevitably leading to the occurrence of composite faults in the system, which exacerbates system vibration. Therefore, it is necessary to study the vibration characteristics of wind turbine helical gear-rotor-bearing transmission systems with composite faults. This paper uses an improved energy method to calculate the theoretical time-varying mesh stiffness of a helical gear with a root crack failure. On the premise of considering the time-varying meshing stiffness of the faulty helical gear, the gear eccentric fault, and the nonlinear support force of the faulty bearing, a multi-degree-of-freedom helical gear-rotor-bearing transmission system with compound faults was established by using the lumped parameter method. The dynamic model of the system was solved based on the Runge–Kutta method, and the vibration response of the system under healthy conditions, single faults with gear eccentricity, single faults with tooth root cracks, and coupled bearing composite faults were simulated and analyzed. The results show that the simulation results based on KISSsoft software 2018 version verify the effectiveness of the improved energy method; the existence of single faults and composite faults will cause the fault characteristics in the time domain and frequency domain responses. In this paper, the influence of a single fault and a complex fault on the time domain and frequency domain of the system is mainly discovered through the fault study of the helical rotor-bearing system, and the influence of the fault degree on the vibration of the gear motion system is discussed. The greater the degree of the fault, the more vibration of the system occurs; accordingly, when the system is under the coupling of tooth root crack and bearing fault, there is a significant difference compared with the healthy system and the single fault system. The system vibration has obvious time domain and frequency domain signal characteristics, including periodic pulse impacts caused by gear faults and time domain impact caused by bearing. The fault characteristic frequencies can also be found in the frequency domain. In this paper, the fault study of a helical gear of wind turbine generation provides a reference for the theoretical analysis of the vibration characteristics of the helical gear-rotor-bearing system under various fault conditions, lays a solid foundation for the simulation and subsequent diagnosis of the composite fault signal of the system, and provides help for the fault diagnosis of wind turbine gearboxes in the future.

Cortical signals analysis to recognize intralimb mobility using modified RNN and various EEG quantities

Electroencephalogram (EEG) signals are critical in interpreting sensorimotor activities for predicting body movements. However, their efficacy in identifying intralimb movements, such as the dorsiflexion and plantar flexion of the foot, remains suboptimal. This study aims to explore whether various EEG signal quantities can effectively recognize intralimb movements to facilitate the development of Brain-Computer Interface (BCI) devices for foot rehabilitation. This research involved twenty-two healthy, right-handed participants. EEG data were collected using 21 electrodes positioned over the motor cortex, while two electromyography (EMG) electrodes recorded the onset of ankle joint movements. The study focused on analyzing slow cortical potential (SCP) and sensorimotor rhythms (SMR) in alpha and beta bands from the EEG. Five key features—fourth-order Autoregressive feature, variance, waveform length, standard deviation, and permutation entropy—were extracted. A modified Recurrent Neural Network (RNN) including Long Short-term Memory (LSTM) and Gated Recurrent Unit (GRU) algorithms was developed for movement recognition. These were compared against conventional machine learning algorithms, including nonlinear Support Vector Machine (SVM) and k Nearest Neighbourhood (kNN) classifiers. The performance of the proposed models was assessed using two data schemes: within-subject and across-subjects. The findings demonstrated that the GRU and LSTM models significantly outperformed traditional machine learning algorithms in recognizing different EEG signal quantities for intralimb movement. The study indicates that deep learning models, particularly GRU and LSTM, hold superior potential over standard machine learning techniques in identifying intralimb movements using EEG signals. Where the accuracies of LSTM for within and across subjects were 98.87 ± 1.80 % and 87.38 ± 0.86 % respectively. Whereas the accuracy of GRU within and across subjects were 99.18 ± 1.28 % and 86.44 ± 0.69 % respectively. This advancement could significantly benefit the development of BCI devices aimed at foot rehabilitation, suggesting a new avenue for enhancing physical therapy outcomes.

Forecasting Chinese crude oil futures volatility: New evidence based on dual feature processing of large‐scale variables

AbstractThis paper aims to study the volatility forecasting of Chinese crude oil futures from the large‐scale variables perspective by considering both the information on international futures markets volatility and technical indicators of Chinese crude oil futures. We employ the dual feature processing method (LASSO‐PCA) by integrating least absolute shrinkage and selection operator (LASSO) and principal component analysis (PCA) to extract important factors of the large‐scale exogenous variables. Besides the traditional ordinary least squares (OLS) estimation, the nonlinear support vector regression (SVR) approach is employed to integrate with the LASSO‐PCA method. The empirical results show that both the OLS and SVR combined with LASSO‐PCA can improve the forecasting accuracy, especially SVR‐LASSO‐PCA owns the best forecasting performance. The analysis of the selected variables finds international futures volatility is chosen more frequently. These results are further validated through a series of robust experiments. Finally, the time difference between China and the United States is also considered in order to obtain more reasonable out‐of‐sample forecasting.

An intelligent fuzzy enabled parent node selection approach in low power networks

The Internet of Things lies in establishing low-power and lossy networks created by interconnecting many wireless devices with limited resources. Fascinatingly, an IPv6 routing protocol for low-power and lossy networks has become a common practice for these applications. Even though this protocol addresses the challenges of low-power networks, many issues concerning the quality of service and energy consumption are open to the research community. The protocol relies on a destination-oriented directed acyclic graph, and the root selection depends on some constraints and metrics associated with an objective function (OF). The conventional OFs select parents based on a single metric, such as the expected transmission count or the number of nodes to travel. The current paper proposes an enhancement to the OF metric, aiming to decrease node energy and enhance the quality of service. This improvement is achieved by the factors, including the received signal strength indicator, node distance, power, link quality indicator, and expected transmission count, to select reliable communication links. The minimum power needed for reliable communication is predicted from the received signal strength indicator, node distance, receiver power, and link quality indicator using a nonlinear support vector machine. The OF value of the candidate node is computed from the power level and expected transmission count combined using the Takagi-Sugeno fuzzy model. The proposed OF is implemented in the Cooja simulator and compared against minimum rank with hysteresis OF and OF zero. A considerable improvement in the packet delivery ratio and a 37.5% reduction in energy consumption is obtained.

Experimental and Theoretical Insights into the Intermolecular Interactions in Saturated Systems of Dapsone in Conventional and Deep Eutectic Solvents.

Solubility is not only a crucial physicochemical property for laboratory practice but also provides valuable insight into the mechanism of saturated system organization, as a measure of the interplay between various intermolecular interactions. The importance of these data cannot be overstated, particularly when dealing with active pharmaceutical ingredients (APIs), such as dapsone. It is a commonly used anti-inflammatory and antimicrobial agent. However, its low solubility hampers its efficient applications. In this project, deep eutectic solvents (DESs) were used as solubilizing agents for dapsone as an alternative to traditional solvents. DESs were composed of choline chloride and one of six polyols. Additionally, water-DES mixtures were studied as a type of ternary solvents. The solubility of dapsone in these systems was determined spectrophotometrically. This study also analyzed the intermolecular interactions, not only in the studied eutectic systems, but also in a wide range of systems found in the literature, determined using the COSMO-RS framework. The intermolecular interactions were quantified as affinity values, which correspond to the Gibbs free energy of pair formation of dapsone molecules with constituents of regular solvents and choline chloride-based deep eutectic solvents. The patterns of solute-solute, solute-solvent, and solvent-solvent interactions that affect solubility were recognized using Orange data mining software (version 3.36.2). Finally, the computed affinity values were used to provide useful descriptors for machine learning purposes. The impact of intermolecular interactions on dapsone solubility in neat solvents, binary organic solvent mixtures, and deep eutectic solvents was analyzed and highlighted, underscoring the crucial role of dapsone self-association and providing valuable insights into complex solubility phenomena. Also the importance of solvent-solvent diversity was highlighted as a factor determining dapsone solubility. The Non-Linear Support Vector Regression (NuSVR) model, in conjunction with unique molecular descriptors, revealed exceptional predictive accuracy. Overall, this study underscores the potency of computed molecular characteristics and machine learning models in unraveling complex molecular interactions, thereby advancing our understanding of solubility phenomena within the scientific community.

A study of analyzing longitudinal dynamic behavior of a double-rod system with longitudinal nonlinear supports

In engineering, shafting systems are typically subjected to longitudinal vibration excitations, which may result in unwanted vibration. To study the control of longitudinal vibration in shafting systems, they can be simplified to rod structures. Currently, engineers have attempted to apply the nonlinear principle to design nonlinear supports to control the vibration of flexible structures. However, the flexible structures referenced in the literature are usually composed of a single component, which limits the application of nonlinear supports to more complex structures. To explore the potential application of nonlinear supports in marine engineering, this work introduces a longitudinal vibration prediction model for a double-rod system equipped with longitudinal nonlinear supports. The generalized Hamilton principle is used to derive the governing equations for the double-rod system with longitudinal nonlinear supports. The longitudinal vibration responses of the double-rod system are numerically solved using the Galerkin truncation method. The numerical results confirm that a 1-term truncation number guarantees the stability of the longitudinal vibration prediction model. Under certain conditions, the longitudinal vibration responses are significantly affected by longitudinal nonlinear supports. It is recommended to install longitudinal nonlinear supports on both Rod 1 and Rod 2 simultaneously to suppress vibration in the first two main resonance orders. With reasonable excitations, the vibration state and magnitudes of the double-rod system can be effectively controlled by adjusting the longitudinal nonlinear supports. Complex longitudinal vibration responses are more readily induced by altering the parameters of the longitudinal nonlinear support installed on Rod 1. Choosing appropriate parameters for the nonlinear supports on Rod 1 and Rod 2 positively contributes to the reduction of vibration in the double-rod system.

A bilateral assessment of human activity recognition using grid search based nonlinear multi-task least squares twin support vector machine

A bilateral assessment of human activity recognition using grid search based nonlinear multi-task least squares twin support vector machine

A Bilateral Assessment of Human Activities Using PSO-Based Feature Optimization and Non-linear Multi-task Least Squares Twin Support Vector Machine

A Bilateral Assessment of Human Activities Using PSO-Based Feature Optimization and Non-linear Multi-task Least Squares Twin Support Vector Machine