Nonlinear Factors Research Articles

Optimization Design of PSS and SVC Coordination Controller Based on the Neighborhood Rough Set and Improved Whale Optimization Algorithm

Aimed at reducing the redundancy of parameters for the power system stabilizer (PSS) and static var compensator (SVC), this paper proposes a method for coordinated control and optimization based on the neighborhood rough set and improved whale optimization algorithm (NRS-IWOA). The neighborhood rough set (NRS) is first utilized to simplify the redundant parameters of the controller to improve efficiency. Then, the methods of the Sobol sequence initialization population, nonlinear convergence factor, adaptive weight strategy, and random differential mutation strategy are introduced to improve the traditional whale optimization algorithm (WOA) algorithm. Finally, the improved whale optimization algorithm (IWOA) is utilized to optimize the remaining controller parameters. The simulation results show that the optimization parameters were reduced from 12 and 18 to 3 and 4 in the single-machine infinity bus system and dual-machine power system, and the optimization time was reduced by 74.5% and 42.8%, respectively. In addition, the proposed NRS-IWOA method exhibits more significant advantages in optimizing parameters and improving stability than other algorithms.

Nonlinear Factor Returns in the US Equity Market

We examine nonlinear return-to-characteristic relationships for five equity market factors: value, momentum, small size, low beta, and profitability. Our study employs monthly returns and characteristics for the largest one thousand US stocks from 1964 to 2023 with a focus on average active returns over the last 20 years. Beyond simplicity in modeling the return-generating process, we find no reason to assume a linear relationship between characteristics and security returns. Allowance for nonlinearity leads to increases in information ratios for factor portfolios neutralized with respect to nonlinear exposure to the other factors.

Nonlinear disturbance observer-based finite-time prescribed performance control for MSVs with input saturation

ABSTRACT A finite-time prescribed performance control scheme based on an improved nonlinear disturbance observer is proposed for tracking the trajectory of marine surface vessels (MSVs) under the disturbance of the marine environment. The objective of this paper is to design a nonlinear disturbance observer based on state estimation error feedback that accurately estimates and compensates for the unknown disturbance problem. An adaptive law is applied to estimate the upper bound of its error, removing the requirement of a priori knowledge of the unknown lumped disturbance upper bound. This paper also introduces a non-logarithmic performance function in order to efficiently solve the problem of considering both transient and steady state MSVs performance simultaneously. In addition, the adaptive dynamic system is introduced to overcome the adverse effects caused by nonlinear saturation factors for the input-constrained problem. With this control strategy, the system output error converges to a pre-defined region within a finite amount of time and meets the prescribed performance requirements. Finally, simulation and comparison verify the control scheme's effectiveness and superiority.

Enhanced adaptive-convergence in Harris’ hawks optimization algorithm

This paper presents a novel enhanced adaptive-convergence in Harris’ hawks optimization algorithm (EAHHO). In EAHHO, considering that Harris’ hawks will adopt different perching strategies and chasing styles according to the value of the escaping energy parameter E, nonlinear adaptive-convergence factor a is designed and adjusted to enhance the convergence and robustness of the algorithm. Moreover, the convergence and stability of EAHHO are proved mathematically by using the Markov chain theory and Lyapunov stability theory respectively. Moreover, numerical simulation results of 14 HHOs with different nonlinear convergence factors on 23 benchmark functions show that the nonlinear convergence factor of EAHHO is applicable to challenging problems with unknown search spaces, and the comparisons with the selected well-established algorithms on 56 test functions demonstrate that EAHHO performs competitively and effectively. Finally, the experiment results show that EAHHO algorithm also has a good performance to solve the optimization problems with relatively high dimensions and graph size of Internet of Vehicles routing problem.

On the information content of explainable artificial intelligence for quantitative approaches in finance

AbstractWe simulate economic data to apply state-of-the-art machine learning algorithms and analyze the economic precision of competing concepts for model agnostic explainable artificial intelligence (XAI) techniques. Also, we assess empirical data and provide a discussion of the competing approaches in comparison with econometric benchmarks, when the data-generating process is unknown. The simulation assessment provides evidence that the applied XAI techniques provide similar economic information on relevant determinants when the data generating process is linear. We find that the adequate choice of XAI technique is crucial when the data generating process is unknown. In comparison to econometric benchmark models, the application of boosted regression trees in combination with Shapley values combines both a superior fit to the data and innovative interpretable insights into non-linear impact factors. Therefore it describes a promising alternative to the econometric benchmark approach.

Modeling and parameter identification of rate-dependent hysteresis behavior based on modified-generalized Prandtl–Ishlinskii model

The intrinsic characteristic of piezoelectric actuators (PEA), known as hysteresis, has been demonstrated to diminish the capability and stability of the system significantly. This paper proposes a modified-generalized Prandtl–Ishlinskii (MGPI) model to describe the rate-dependent hysteresis in piezoelectric actuators. The developed model incorporates a voltage change rate function to replace the first part of the generalized Prandtl–Ishlinskii (GPI) model. Additionally, the model integrates the cubic polynomial into the envelope function, along with the dynamic thresholds and weights. When describing the hysteresis of the piezoelectric actuator (PEA), the model parameters are identified using the Improved Grey Wolf Optimizer (IGWO) algorithm. To prevent the algorithm from getting trapped in local optima, the cubic chaotic mapping is utilized for population initialization, as well as a nonlinear convergence factor, and the Levy flight strategy factor is introduced to update the Wolf pack’s position. The rate-dependent hysteresis behavior of a PEA under excitation in the 1–200 Hz frequency range was experimentally measured. The measured data were used to demonstrate the validity of the proposed MGPI model. The relative root-mean-square error and the relative maximum error of the MGPI model are 1.41% and 6.00%, respectively, which are lower than those of the GPI model, which are 3.15% and 10.58%. Under the composite frequency driving, the outputs of the GPI model and MGPI model were compared with the measured data of the PEA, the results suggest that the MGPI model and the IGWO algorithm can more accurately describe the rate-dependent hysteresis of the piezoelectric actuators.

Optimal design of robust control for belt conveyor systems based on fuzzy dynamic model and Nash game

An optimized robust control method is proposed in this paper to deal with the disturbances of nonlinear factors such as uncertainty in belt conveyor and to realize the speed control of belt conveyor. By controlling the subsystems to track the same desired speed, belt breaks and overlaps caused by varying belt speeds from one section to another are limited. First, a fuzzy model is developed by applying fuzzy set theory to describe uncertainties of belt conveyor such as masses, stiffness, damping and frictions. Second, a robust control is designed for the nominal system and compensating for the uncertainty. With the robust control, the belt conveyor system is proved to be uniformly bounded and uniformly ultimately bounded by the Lyapunov approach. Third, the parameters of controller are optimized based on a non-cooperative game approach. The optimal solution is the Nash equilibrium. Optimal solution allows the controller system to perform better and decrease the cost of control. Finally, by comparing with LQR control and different parameters, the feasibility of robust control and the rationality of the optimal parameters are proven.

Improved negative sampling method in collaborative filtering recommendation based on Generative adversarial network

ObjectiveThe problem of low model performance caused by the lack of negative samples in the recommendation method based on implicit feedback information can be solved. MethodsThe implicit feedback recommendation model DAEGAN is constructed based on the conditional generative adversarial network framework. The Denoising Auto-Encoder is used as a generator to capture nonlinear potential factors in the interaction and improve the robustness of model. In this paper, a strong and weak negative sampling strategy is proposed, which combines the visibility of user in time points to mine uninteresting items and acquire strong negative samples, and injects these information into the model by modifying the masking mechanism to solve the problem of missing negative samples. ResultsExperiments on MovieLens 100 K, Amazon Movie and TV, MovieLens 1 M datasets show that the recommendation accuracy of CFGAN based on strong and weak negative sampling and DAEGAN proposed in this paper has been improved. LimitationsThe generation of strong negative samples is based on user interaction records, which cannot solve effectively cold start problems in extremely sparse data. ConclusionsAfter DAEGAN application, the strong and weak negative sampling method proposed in this paper has generally higher recommendation accuracy than those mainstream recommendation algorithms. The code is available at https://github.com/nanjingzhuyuxuan/DAEGAN.

Research on wind farm power forecasting based on IGWO-CNN

Abstract An enhanced convolutional neural network (CNN) has been proposed to address the issue of low accuracy in wind farm power prediction using traditional methods, which leverages an improved version of the Gray Wolf Optimizer (IGWO). The standard Gray Wolf Optimizer (GWO) exhibits a linear change in the search range, which can limit its dynamic convergence capabilities. By incorporating nonlinear convergence factors and dynamic convergence strategies, the improved algorithm modulates the global search pace, effectively preventing it from getting stuck in local optima. The refined IGWO is subsequently applied to fine-tune the optimal CNN architecture, mitigating the uncertainty typically associated with the structural configuration of CNNs. When predicting the actual power measurements from a wind plant in Inner Mongolia, the results indicate that the IGWO-based CNN method outperforms both the conventional GWO-CNN approach and the standalone CNN regarding prediction accuracy.

Backstepping control based on adaptive neural network and disturbance observer for reconfigurable variable stiffness actuator

Reconfigurable variable stiffness actuator (RVSA) has attracted increasing attention in robotics due to its safety, compliance, and robustness. However, the control of the RVSA is challenging due to nonlinear factors such as high-order nonlinear dynamic, model uncertainties, time-varying model parameters, and disturbances. In this paper, firstly, a lightweight RVSA structure with both passive and active nonlinear variable stiffness characteristic is developed. Secondly, a dynamic surface backstepping control method based on a radial basis neural network and disturbance observer (DSBC-RBFNN-DOB) is proposed to achieve position control of the lightweight RVSA with matched and unmatched uncertainties. To address solve the “complexity explosion” and noise problems in traditional backstepping control, the dynamic surface backstepping control (DSBC) method is used to design the controller. Then, a method based on radial basis neural network (RBFNN) and disturbance observer (DOB) are used to compensate for the matched and unmatched uncertainties in the link and motor. In this method, the matched uncertainties are compensated using RBFNN, and the DOB is integrated to compensate RBFNN approximation errors and unmatched uncertainties. Through Lyapunov stability analysis, the semi-global boundedness of the controller is proven. Finally, the proposed method is simulated and actually implemented, verifying the effectiveness of the method. Simulation and experimental results show that the root mean square error (RMSE) of the proposed method is only 0.97277° and 0.6418°, respectively. Compared with PID, DSBC, and DSBC-RBFNN, the error reduction percentages in simulation (experiment) are 85.6 % (88.9 %), 49.4 % (88.4 %) and 36.1 % (80.0 %) respectively.

Analysis of optical solitons propagation in the dual-mode resonant nonlinear Schrödinger dynamical equation with assorted nonlinear interactions

This research explores the dual-mode manifestation within the nonlinear Schrödinger equation, elucidating the amplification or absorption of paired waves. This study delves into the simultaneous generation of two distinct waves associated with the dual-mode phenomenon with three crucial parameters: phase velocity, nonlinearity and dispersive factor. The resulting wave phenomena from these solutions have implications across various fields, including fluid dynamics, water wave mechanics, ocean engineering and scientific inquiry. The study employs the modified Sardar sub-equation method to obtain the optical soliton solutions, encompassing various types such as dark, bright, singular, combo dark–singular, periodic singular and dark–bright solitons. The obtained results highlight the reliability and simplicity of the modified Sardar sub-equation method. Additionally, the paper delves into the parametric conditions crucial for shaping and sustaining these solitons. The research explores the interaction of dual waves and the variation in wave speed. Furthermore, dynamic phenomena are illustrated, and the physical implications of the solutions are interpreted using 3D and 2D plots with different parameter values.

Improved Snake Optimizer Using Sobol Sequential Nonlinear Factors and Different Learning Strategies and Its Applications

The Snake Optimizer (SO) is an advanced metaheuristic algorithm for solving complicated real-world optimization problems. However, despite its advantages, the SO faces certain challenges, such as susceptibility to local optima and suboptimal convergence performance in cases involving discretized, high-dimensional, and multi-constraint problems. To address these problems, this paper presents an improved version of the SO, known as the Snake Optimizer using Sobol sequential nonlinear factors and different learning strategies (SNDSO). Firstly, using Sobol sequences to generate better distributed initial populations helps to locate the global optimum solution faster. Secondly, the use of nonlinear factors based on the inverse tangent function to control the exploration and exploitation phases effectively improves the exploitation capability of the algorithm. Finally, introducing learning strategies improves the population diversity and reduces the probability of the algorithm falling into the local optimum trap. The effectiveness of the proposed SNDSO in solving discretized, high-dimensional, and multi-constraint problems is validated through a series of experiments. The performance of the SNDSO in tackling high-dimensional numerical optimization problems is first confirmed by using the Congress on Evolutionary Computation (CEC) 2015 and CEC2017 test sets. Then, twelve feature selection problems are used to evaluate the effectiveness of the SNDSO in discretized scenarios. Finally, five real-world technical multi-constraint optimization problems are employed to evaluate the performance of the SNDSO in high-dimensional and multi-constraint domains. The experiments show that the SNDSO effectively overcomes the challenges of discretization, high dimensionality, and multi-constraint problems and outperforms superior algorithms.

Spatiotemporal Characteristics and Driving Factors of Ecosystem Regulation Services Value at the Plot Scale

The value of ecosystem regulation services (ERSV) is a crucial aspect of gross ecosystem product (GEP). Understanding and mastering the spatiotemporal evolution characteristics and driving factors of ERSV is essential for the efficient management of regional ecosystems. This study proposes an ERSV accounting model at the plot scale and uses the barycentric analysis method, the optimal parameters-based geographical detector model (OPGD), and the constraint line extraction method to analyze the spatiotemporal evolution characteristics, main driving factors, and constraint rules of ERSV in Yunyang District, Hubei Province in 2016, 2018, 2020, and 2021. The results show that (1) In the temporal dimension, the overall ERSV of the district increased by CNY 1.664 billion from 2016 to 2021, with an increase rate of 3.68%. The contribution values of climate regulation function and water retention function to ERSV was significant. (2) In the spatial dimension, the ERSV was high in the north and south and low in the middle, with high-value areas mainly located in woodland and wetland areas. The center of gravity of the ERSV increase shifted to the southwest by 12,455.42 m, while the center of gravity of the reduction shifted to the southwest by 3582.79 m from 2016 to 2021. (3) The interaction of any two driving factors had greater explanatory power for the spatial differentiation of ERSV than that of a single driving factor, and all of them showed nonlinear or double factor enhancement characteristics. The human active index (HAI) and construction land proportion (CLP) were the leading anthropogenic factors, while the land surface temperature (LST) and NDVI were the leading natural factors. (4) The ERSV could maintain a high and stable value output when the HAI was less than 0.3, CLP was less than 15%, LST was between 18 and 22 °C, and NDVI was greater than 0.5. These results can guide the practices of ecology, production, and life in Yunyang District and contribute to the high quality and sustainable development of the regional ecology and economy.

Adaptive RISE Control of Winding Tension with Active Disturbance Rejection

A winding system is a time-varying system that considers complex nonlinear characteristics, and how to control the stability of the winding tension during the winding process is the primary problem that has hindered development in this field in recent years. Many nonlinear factors affect the tension in the winding process, such as friction, structured uncertainties, unstructured uncertainties, and external interference. These terms severely restrict the tension tracking performance. Existing tension control strategies are mainly based on the composite control of the tension and speed loops, and previous studies involve complex decoupling operations. Owing to the large number of calculations required for this method, it is inconvenient for practical engineering applications. To simplify the tension generation mechanism and the influence of the nonlinear characteristics of the winding system, a simpler nonlinear dynamic model of the winding tension was established. An adaptive method was applied to update the feedback gain of the continuous robust integral of the sign of the error (RISE). Furthermore, an extended state observer was used to estimate modeling errors and external disturbances. The model disturbance term can be compensated for in the designed RISE controller. The asymptotic stability of the system was proven according to the Lyapunov stability theory. Finally, a comparative analysis of the proposed nonlinear controller and several other controllers was performed. The results indicated that the control of the winding tension was significantly enhanced.

Using moderated nonlinear factor models to adjust for differential item functioning in the Student-Teacher Relationship Scale from kindergarten to Grade 6

Prior research has demonstrated that children form developmentally salient relationships with teachers and that these relationships are uniquely predictive of subsequent functioning both in and outside of school. However, prior work estimating trajectories and predictors of teacher-student relationship quality has failed to test and adjust for bias in questionnaire items. The present study used longitudinal data from the NICHD Study of Early Child Care and Youth Development (SECCYD; N = 1140) to test and adjust for measurement bias in the Student-Teacher Relationship Scale (STRS; Pianta, 2001) across grades (K–6) and sociodemographic characteristics (i.e., birth sex, race/ethnicity, family income-to-needs ratio, and maternal education) to generate less biased estimates of trajectories of teacher-student relationship quality. Results identified differential item functioning for three of seven STRS items assessing conflict and three of eight STRS items assessing closeness, with items functioning differentially across child grade, birth sex, race/ethnicity, and maternal education level. Comparisons of growth models using non-adjusted and adjusted STRS scores highlight substantive differences between scoring approaches, such that the effects of race/ethnicity, maternal education, and maternal sensitivity on teacher-student relationship quality were masked prior to adjusting for item bias. These findings demonstrate the importance of testing and correcting for item bias in questionnaire-based assessments of teacher-student relationship quality to ensure valid conclusions.

Study on driving safety of vehicle-bridge interaction system based on ultra-high-dimensional point-selected extremum methods

ABSTRACT The driving safety indexes involve the geometric nonlinear contact relationship of the wheel and rail and the high-frequency vibration of the wheel-set. The calculation of their probability characteristic parameters requires very precise selection of random excitation samples. Track irregularity is an essential external excitation force in the vehicle-bridge interaction system (VBIS). Besides, many random phase angles must be considered when using the harmonic superposition method to simulate VBIS, leading to the ultra-high-dimensional random variables problem. Thus, this paper proposes a square power point method and a pseudo-random sequence (Sobol sequence) based on a number theoretic approach to model ultra-high dimensional random variables accurately. This strategy reduces the deviation between the representative track irregularity samples (TIS) and can be applied to fields of strongly nonlinear and high-frequency vibration. Then, by increasing the number of representative TIS, the deviation between response samples caused by non-linear factors can be significantly reduced. Finally, this paper proposes a threshold method for driving safety indexes that determines the service life of bridges, which can quickly obtain the threshold of its extreme value distribution through the cumulative distribution function, and establish the relationship between the threshold and the number of trains travelled. The above theories are verified by calculation examples, and some engineering suggestions are obtained.

Research on the EMA Control Method Based on Transmission Error Compensation

This research investigates the impact of nonlinear clearance factors on position tracking accuracy in the servo drive system of a harmonic reducer. The study introduces a technique for modeling and compensating for transmission errors, thereby improving position tracking accuracy through online compensation combined with an auto-disturbance rejection controller. Initially, the mathematical model of the permanent magnet synchronous motor is outlined, and the current loop and speed loop control models are derived. Subsequently, an electromechanical actuator (EMA) simulation model with clearance is established, and detailed simulation analysis is conducted to verify the impact of clearance on tracking accuracy. A model for online compensation of transmission errors is then developed. Following the principles of active disturbance rejection control (ADRC), a second-order ADRC is formulated for real-time compensation of transmission errors in EMA position mode. Finally, through no-load and load experiments, the change in position tracking error with and without transmission error compensation is compared and analyzed. The results demonstrate that utilizing automatic disturbance rejection control with transmission error compensation achieves the highest position tracking accuracy. Compared to the proportion integration differentiation (PID) control method, the root mean square of position tracking error is reduced by approximately 12.8% and 17.3% under no-load and load conditions, respectively. By compensating for position errors online, the accuracy of the EMA position can be improved.

Dynamics of heterogeneous Hopfield neural network with adaptive activation function based on memristor

Memristor and activation function are two important nonlinear factors of the memristive Hopfield neural network. The effects of different memristors on the dynamics of Hopfield neural networks have been studied by many researchers. However, less attention has been paid to the activation function. In this paper, we present a heterogeneous memristive Hopfield neural network with neurons using different activation functions. The activation functions include fixed activation functions and an adaptive activation function, where the adaptive activation function is based on a memristor. The theoretical and experimental study of the neural network’s dynamics has been conducted using phase portraits, bifurcation diagrams, and Lyapunov exponents spectras. Numerical results show that complex dynamical behaviors such as multi-scroll chaos, transient chaos, state jumps and multi-type coexisting attractors can be observed in the heterogeneous memristive Hopfield neural network. In addition, the hardware implementation of memristive Hopfield neural network with adaptive activation function is designed and verified. The experimental results are in good agreement with those obtained using numerical simulations.

Leakage Source Location of Hazardous Chemicals Based on the Improved Gray Wolf Optimization Algorithm

To accurately determine the leakage source location and strength during gas leakage accidents, this study compares the concentration obtained from the diffusion model with that measured by the sensor and proposes an improved gray wolf optimization algorithm for leakage source location. This algorithm introduces two improvement strategies. First, a nonlinear convergence factor is introduced to balance the global and local searches of the algorithm. Second, a reverse learning operation is performed on the three individuals with the worst fitness in the contemporary population. The results showed that the location results based on the improved gray wolf optimization algorithm exhibited high accuracy and stability, could quickly and accurately locate the leakage source, and provided data support for emergency disposal of accidents.

Seeing is believing: Forecasting crude oil price trend from the perspective of images

AbstractIn this paper, we propose a novel imaging method to forecast the daily price data of West Texas Intermediate (WTI) crude oil futures. We use convolutional neural networks (CNNs) for future price trend prediction and obtain higher prediction accuracy than other benchmark forecasting methods. The results show that images can contain more nonlinear information, which is beneficial for energy price forecasting. Nonlinear factors also have a strong influence during drastic fluctuations in crude oil prices. In the robustness tests, we find that the image‐based CNN is the most stable approach and can be applied in various futures forecasting scenarios. In the prediction of low‐frequency models for high‐frequency data, the CNN method still retains considerable predictive power, indicating the possibility of transfer learning of our novel approach. By unleashing the power of the picture, we open up a whole new perspective for forecasting future energy trends.