Hybrid Nonlinear Model Research Articles

Hybrid nonlinear probabilistic model using Monte Carlo simulation and hybrid support vector regression for evaporation predictions

This study presents a hybrid model combining Support Vector Regression (SVR) with the Gray Wolf Optimizer (GWO) for evaluating evaporation dynamics. The model was tested using 50 years of meteorological data from Zabol and Chabahar stations in Iran, and compared against standard SVR. Results show that the SVR-GWO significantly outperforms SVR, reducing predictive errors by over 41% on average. For Zabol, the SVR-GWO markedly improved performance, particularly in July where R2 increased from 0.867 to 0.973. The model more closely matched observed statistics, especially for mean and standard deviation, though challenges remain in reproducing higher-order statistics. Interestingly, 5,000 functions evaluation proved nearly as effective as 500,000 suggesting computational efficiency. This integrated approach, incorporating Monte Carlo simulations and kernel density estimation, provides valuable probabilistic insights into evaporation dynamics, offering a promising tool for drought vulnerability assessment and water resources planning in regions with complex climatic patterns.

A new short-term wind power prediction methodology based on linear and nonlinear hybrid models

Fast and accurate wind power prediction is of great significance for grid planning. However, wind power dataset tends to be highly stochastic and volatile, while showing more stable seasonal and cyclical changes, which is a linear and nonlinear superposition features, and it is difficult to use a single linear or nonlinear model to make accurate predictions. Considering these essential features of wind power data, a short-term wind power prediction method based on linear and nonlinear hybrid models is proposed in this paper. First, the complete ensemble empirical mode decomposition (CEEMD) is used to decompose and reconstruct the wind speed and direction in the original dataset to reduce the volatility. Then, to capture the linear features in the dataset, the autoregressive integrated moving average model with exogenous input variables (AIRMAX) is used for linear modeling, and the sparrow search algorithm optimized gated recurrent unit (SSA-GRU) is used to model the nonlinear features. At the same time, to improve the efficiency of model training, federated learning (FL) is utilized for distributed model training. Finally, the ARIMAX and SSA-GRU models are weighted and summed the prediction results to gain the final prediction results using equal weighted averaging (EWA), minimum sum of squares error (MSSE), and maximum grey relational analysis (MGRA), which are commonly used to compute the weights of the combined models, respectively. The wind power dataset from a wind farm in northwest China from January 1, 2022 to October 31, 2022 are used for experiments and analysis, and the results show that the root mean square error (RMSE), R-square (R2), and accuracy (ACC) of the proposed method are 11.944, 0.987, and 0.613, respectively, which are better than all the compared models. The main contribution of this paper is twofold, on the one hand, it indirectly proves that the wind power dataset is formed by the superposition of linear and nonlinear features, and on the other hand, it puts forward a theoretical model and research paradigm for predicting short-term wind power and presents a scientific basis for grid scheduling.

Data-driven aeroelastic analyses of structures in turbulent wind conditions using enhanced Gaussian Processes with aerodynamic priors

Recent advancements in data-driven aeroelasticity have been driven by the wealth of data available in the wind engineering practice, especially in modeling aerodynamic forces. Despite progress, challenges persist in addressing free-stream turbulence and incorporating physics knowledge into data-driven aerodynamic force models. This paper presents a hybrid Gaussian Process (GPs) methodology for non-linear modeling of aerodynamic forces induced by gusts and motion on bluff bodies. Building on a recently developed GP model of the motion-induced forces, we formulate a hybrid GP aerodynamic force model that incorporates both gust- and motion-induced angles of attack as exogenous inputs, alongside a semi-analytical quasi-steady (QS) model as a physics-based prior knowledge. In this manner, the GP model incorporates the absent physics of the QS model, and the non-dimensional hybrid formulation enhances its appeal from an aerodynamic perspective. We devise a training procedure that leverages simultaneous input signals of gust angles, based on random free-stream turbulence, and motion angles, based on random broadband signals. We verify the methodology through analytical linear aerodynamics of a flat plate and non-linear aerodynamics of a bridge deck using Computational Fluid Dynamics (CFD). The standout feature of the presented methodology is its applicability for aeroelastic buffeting analyses, showcasing robustness when handling broadband excitation. Importantly, the non-linear hybrid model preserves its capability to capture higher-order harmonics in the motion-induced forces and remains applicable for flutter analysis, while incorporating both motion and gust angles as input. Applications of the methodology are anticipated in the aeroelastic analysis and monitoring of slender line-like structures.

Hybrid nonlinear regression model versus MARS, MEP, and ANN to evaluate the effect of the size and content of waste tire rubber on the compressive strength of concrete

Tire rubber waste is globally accumulated every year. Therefore, a solution to this problem should be found since, if landfilled, it is not biodegradable and causes environmental issues. One of the most effective ways is recycling those wastes or using them as a replacement for normal aggregate in the concrete mixture, which has high impact resistance and toughness; thus, it will be a good choice. In this study, 135 data were collected from previous literature to develop a model for the prediction of rubberized concrete compressive strength; the database comprised different mixture proportions, the maximum size of the rubber (1–40 mm), and the rubber percentage (0–100%) replacing natural fine and coarse aggregates were among the input parameters in addition to cement content (380–500 kg/m3) water content (129–228 kg/m3), fine aggregate content (0–925 kg/m3), coarse aggregate content (0–1303 kg/m3), and curing time of the samples (1–96 Days); then the collected data were used in developing Multi Expression Programming (MEP), Artificial Neural Network (ANN), Multi Adaptive Regression Spline (MARS), and Nonlinear Regression (NLR) Models for predicting compressive strength (CS) of rubberized concrete. The parametric analysis reveals that as the maximum rubber size increases, the reduction in compressive strength becomes more pronounced. Notably, this strength decline is more significant when rubber replaces coarse aggregate than its replacement of fine aggregate. Among the input parameters considered, it is evident that the fine aggregate content exerts the most substantial influence on the compressive strength of rubberized concrete. Its impact on predicting compressive strength surpasses other factors, with the concrete samples' curing time ranking second in importance. According to the assessment tools, the ANN model performed better than other developed models, with high R2 and lower RMSE, MAE, SI, and MAPE. Additionally, ANN and MARS models predicted the CS of different sizes better than MEP and NLR models. Subsequently, we employed the collected data to develop predictive models using Multi Expression Programming (MEP), Artificial Neural Network (ANN), Multi Adaptive Regression Spline (MARS), and Nonlinear Regression (NLR) techniques to forecast the compressive strength (CS) of rubberized concrete. The statistical analysis tools assessed the performance of these developed models through various evaluation criteria, including the Coefficient of Determination (R2), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Scatter Index (SI), and Mean Absolute Percentage Error (MAPE). In summary, our study underscores the efficacy of recycling rubber materials in concrete production. It presents a powerful predictive model for assessing the compressive strength of rubberized concrete, with the ANN model standing out as the most accurate and reliable choice for this purpose.

An efficient nonlinear hybrid model of energy dissipation piers utilizing fiber beam and self-developed hysteretic spring elements

Energy dissipation piers comprised of concrete filled steel tubular (CFST) columns and steel shear links can exhibit good seismic performance by reasonable collaborative optimization design of columns and links. Considering the time and economic costs of experiments and fine element analysis (FEA), an efficient and accurate numerical model is critical to investigate the hysteretic behavior of energy dissipation piers under earthquake action. Therefore, a hysteretic constitutive law for steel shear links is first proposed including the theoretical shear force-deformation skeleton curve and the unloading and reloading rules during hysteretic loading. Next, a hysteretic spring model is developed for efficiently simulating the hysteretic mechanical behavior of steel shear links, which is validated to have good accuracy with comparison to fine FEA and experimental results. Then, a simplified hybrid model consisting of the self-developed spring model and fiber beam model and two multi-scale FEA models with different levels of refinement are established for nonlinear analysis of energy dissipation piers, respectively. The comparison of numerical and test results confirms that the innovative fiber beam-spring hybrid model can accurately describe the hysteretic performance of energy dissipation piers, especially the detailed mechanical behavior of steel shear links and column feet, which provides an efficient numerical tool for analysing the collaborative working mechanism of energy dissipation piers and similar energy dissipation structures.

A numerical analysis on the drainage capacity of a ropax vessel in the garage deck, in still water and in waves

The ropax vessels are designed to provide the transfer of vehicles, cargo, and passengers and to ensure maximum comfort and safety. The absence of a transversal subdivision for all vessel length poses serious threats to ship safety in case of flooding of the garage deck. When the floodwater is not properly and efficiently drained overboard it can have detrimental consequences both on ship stability, due to large free surface effects and, on loads on deck structures due to the pressure of the accumulated water.In this paper, we propose and apply a fast numerical method for the study of the drainage capacity in the garage deck of a ropax vessel assuming a passive drainage system i.e. comprising only scuppers, whereas the investigated flooding scenario depends on fire fighting operations.The effectiveness of the drainage system is simulated accounting for ship dynamics in calm water and in waves, by adopting a hybrid non-linear numerical model. Flooded water is modelled by lumped mass method; the couplings between ship and floodwater dynamics is achieved by the apparent gravity technique. Two scupper configurations are considered, by modifying scupper dimensions and positions on board. Several numerical simulations are carried out assuming also partially inefficient scuppers. The analysis of the obtained results can provide a general support for the design of passive drainage systems. Based on the outcomes of the case study, this research discloses an improvement in the drainage system when more scuppers are allocated at the stern zone.

Renewable Energy Forecasting with Hybrid Nonlinear Model (ANFIS): Case Study of Wind Speed in Thailand

Renewable Energy Forecasting with Hybrid Nonlinear Model (ANFIS): Case Study of Wind Speed in Thailand

Reverse logistics planning research of building waste from perspective of closed supply chain in urban sustainable environment governance.

The resource utilization of building waste in urban sustainable environment governance is significant, in view of the status of construction waste recycling; this article built a reverse logistics planning model in urban building waste from the perspective of a closed supply chain by means of a hybrid nonlinear programming model. Combining the simulated annealing algorithm with memory function and the genetic algorithm with global convergence performance, a new genetic simulated annealing algorithm is presented to optimize the model. The empirical study was then made for the system to verify the feasibility of the model. The proposed new planning method and its detailed steps can provide a meaningful reference value for resource utilization of building waste in urban sustainable environment governance.

Hybrid axisymmetric model for forced heave of a shallowly submerged cylindrical wave energy converter

Shallowly submerged oscillating structures may be found in wave energy devices or semi-submersible vessels. Predicting the force on such structures is critical for design purposes, but complicated due to nonlinear phenomena which can occur in shallow water, including wave breaking and bore formation. Such effects are particularly important around the first ‘resonance’ frequency of the fluid on top of the device, where linear theory predicts large flows on/off the cylinder and corresponding surface elevations and forces. In an effort to create a reliable and efficient model to predict the hydrodynamic force on a shallowly submerged truncated vertical cylinder, an axisymmetric nonlinear hybrid model is developed for forced heave oscillations. The flow above the cylinder is modelled using the nonlinear shallow water equations, and linear potential flow theory is used in the surrounding fluid. The model is compared with experimental results for forced heave oscillations and performs well for predicting the heave force. It is then used to examine linearised heave force for increasing amplitudes of (prescribed) harmonic heave motion. There is a significant reduction in the peaks of radiation damping and added mass coefficients with increasing amplitude, and associated shifts in the frequencies of the peaks.

Novel concept design of low energy hybrid battery thermal management system using PCM and multistage Tesla valve liquid cooling

To challenge the continuous operation performance of high energy density lithium-ion batteries at different ambient temperatures. A battery thermal management system combining Multi-stage tesla valve liquid cooling and Phase change material (MP) is proposed. After verification of the accuracy of the thermal model based on experimental measurements, numerical studies are performed at the end of 2C rate discharge. In addition, based on general full factorial design method, Kriging approximation model is used to construct complex nonlinear hybrid model between the spacing between batteries, the number of MSTV channels, coolant velocity and the performance of MP (pressure drop, standard deviation of surface temperature, and maximum temperature). At the same time, to avoid falling into local solutions, the adaptive simulated annealing (ASA) global search algorithm is integrated to optimize high-dimensionality multi-objective structural settings. The simulation results show that the designed MP-BTMS is connected with water/ethanol coolant and the inlet velocity is 0.193 m/s, the maximum temperature, standard deviation of surface temperature and pressure drop of the battery pack at 33.12 °C, 1.50 ℃ and 647.8 Pa, respectively. Finally, the optimised MP is used in continuous depth discharge conditions, as well as a range of simulation tests. The superiority of the optimum battery thermal management system in different application scenarios (liquid cooling/heating) is also verified. The cooling performance indicates that the use of MP reduces the total energy consumption required for coolant circulation by 79.9% compared to conventional BTMS. Moreover, it is found that at ambient temperature (Tamb = -10 °C), the use of MP can keep the battery module warm twice as long compared to conventional BTMS. This means that MP can significantly delay the temperature drop during cold stops of EVs, thus reducing the energy required for active battery heating after short-term parking.

Nonlinear Hybrid Model Predictive Control for building energy systems

This paper presents a nonlinear hybrid Model Predictive Control (MPC) approach for building energy systems based on Modelica. The MPC approach takes into account two characteristics that are very common for building energy systems: nonlinearities (inherent in the building envelope and Heating, Ventilation and Air Conditioning (HVAC) systems) and discontinuities (in the form of on/ off operation, discrete operation states and operation modes). The hybrid MPC approach integrates both continuous and discrete optimization variables into the control concept and thus is capable of controlling building energy systems with binary or integer decision variables, switching dynamics or logic if-then-else constraints. By employing a time-variant linearization approach, nonlinear Modelica optimization problems are approximated with high accuracy and transformed into a linearized state-space representation. Based on the linearization output, a linearized optimization problem is generated automatically in every MPC iteration, which is extensible by various integer characteristics and is accessible for a wide range of mixed-integer solvers. A simulation study on a nonlinear Modelica building energy system demonstrates the control quality of the proposed toolchain revealing a small linearization error and successful integration of multiple integer characteristics. The benefits of the approach are manifested by comparing its performance with different reference control strategies.

Dynamic responses of electromechanical transmission system based on a nonlinear hybrid model

A nonlinear hybrid model of electromechanical transmission system is proposed by combining finite element method and lumped parameter method, in which the flexible shaft model is established by using three-dimension nonlinear beam element based on the absolute node coordinate formulation and the gear mesh model is calculated by using nonlinear time-varying lumped parameter model. In the hybrid model, the coupling between the nonlinear deformation of shafts and excitation of gears is considered. The generalized- α implicit time stepping algorithm is used to study the dynamic responses of system. Then, comparisons and analyses are made of the dynamic responses of system between the hybrid model and previous lumped parameter model. Finally, the effects of flexibility of shafts, the geometrical parameters of shaft, the mounting position of the gear on the shaft and the operation conditions on the dynamic responses of system are analyzed. The results show that the presented nonlinear hybrid model is valid and effective in predicting the dynamic behavior of electromechanical transmission system. The gear meshing force is increased by 14.3% and new coupling frequencies are observed due to the effect of the shaft flexibility. Moreover, since the shaft radius of 0.05 m is the critical value for the accurate calculation of the proposed nonlinear hybrid model, the nonlinearity caused by the shaft vibration cannot be ignored. When the gear is installed at the midpoint of the shaft, the maximum von Mises stress of the shaft of 1.8 × 107 Pa is achieved and located at the connected point on the shaft. This study plays an important role in the field of electromechanical transmission design.

“EMD-SVR” Hybrid Machine Learning Model and its Application in Agricultural Price Forecasting

Timely and accurate price forecasting is one of challenges in agriculture. It helps both producer and consumer to make the efficient plan. The inherent nonstationarity and nonlinearity in price data makes problem in forecasting. A single forecasting model may not be able to tackle nonstationarity and nonlinearity, simultaneously. With this context, a nonlinear hybrid model called EMD-SVR has been proposed to deal the problem. The empirical mode decomposition (EMD) deals with nonstationarity by decomposing price data into a finite and small number of subsets. Further, these decomposed subsets are forecasted using Support Vector Regression (SVR) model and aggregated to make final forecast. The performance of the proposed hybrid model are evaluated in monthly price index of chili. The empirical results indicated the superiority of the EMD-SVR model.

A Hybrid LSTM-Based Genetic Programming Approach for Short-Term Prediction of Global Solar Radiation Using Weather Data

The integration of solar energy in smart grids and other utilities is continuously increasing due to its economic and environmental benefits. However, the uncertainty of available solar energy creates challenges regarding the stability of the generated power the supply-demand balance’s consistency. An accurate global solar radiation (GSR) prediction model can ensure overall system reliability and power generation scheduling. This article describes a nonlinear hybrid model based on Long Short-Term Memory (LSTM) models and the Genetic Programming technique for short-term prediction of global solar radiation. The LSTMs are Recurrent Neural Network (RNN) models that are successfully used to predict time-series data. We use these models as base predictors of GSR using weather and solar radiation (SR) data. Genetic programming (GP) is an evolutionary heuristic computing technique that enables automatic search for complex solution formulas. We use the GP in a post-processing stage to combine the LSTM models’ outputs to find the best prediction of the GSR. We have examined two versions of the GP in the proposed model: a standard version and a boosted version that incorporates a local search technique. We have shown an improvement in terms of performance provided by the proposed hybrid model. We have compared its performance to stacking techniques based on machine learning for combination. The results show that the suggested method provides significant improvement in terms of performance and consistency.

MODEL HYBRID NONLINEAR REGRESSION LOGISTIC (NLR) –DOUBLE EXPONENSIAL SMOOTHING (DES) DAN PENERAPANNYA PADA JUMLAH KASUS KUMULATIF COVID-19 DI INDONESIA DAN BELANDA

The economic relationship between Indonesia and the Netherlands is a good trade relationship, but the spread of COVID-19 disrupts the two countries' economies. Both countries need to have an explanation regarding the condition of COVID-19 to raise economic market sentiment. Based on this, Hybrid and non-hybrid models are used to predict the dispersion conditions and compare them through the MAPE value. The double-exponential nonlinear logistic regression hybrid model on the cumulative number of COVID-19 is not suitable for use in the Netherlands COVID-19 cases but is suitable for use in the cumulative number of COVID-19 cases Indonesia. The hybrid nonlinear regression logistic-double exponential model is one way to optimize MAPE, especially in training data. Based on the hybrid non-client regression logistic model, the peak incidence of Covid-19 in the Netherlands is estimated at 22 November 2020, and the hybrid nonlinear regression logistic-Double exponential model predicts that the peak of Covid-19 occurs in Indonesia on 28 November 2020. the Netherlands wave is around 2.83 percent and Indonesia 1.62 percent. Therefore the decline in Indonesia is predicted to be faster, but the Netherlands will reach the peak of the Indonesian news wave.

Research on coupled vibrations of driveshaft–rear axle system based on nonlinear hybrid model

The transmission shaft–rear axle system is consisted of universal joint, hypoid gear pair, tapered roller bearing, and half shaft. In this article, as a combination of system dynamics and structure dynamics, a hybrid dynamic model of the bending–torsional–shaft vibration of the driveshaft main reducer was established to study its noise vibration harshness performance. Through dynamic frequency sweep analysis, it is found that the natural frequency of torsional vibration of the system is 53.96 Hz. Getting the natural frequency of the torsional vibration of the systems being 57 Hz by the bench tests and Adams simulations. The correctness of the nonlinear hybrid model of the driveshaft–rear axle system is proved. This research will be beneficial to the design, monitoring, and fault detection of the automobile transmission system.

A nonlinear hybrid model to assess the impacts of climate variability and human activities on runoff at different time scales

Understanding the contributions of potential drivers on runoff is essential for the sustainable management of water resources; however, the impacts of climate variability and human activities on runoff at inter-annual and inter-decadal scales have rarely been assessed quantitatively. To achieve this goal, this study develops a nonlinear hybrid model, which integrates extreme-point symmetric mode decomposition (ESMD), back propagation artificial neural networks (BPANN) and weights connection method. ESMD allows to separate the times series of drivers and runoff into different time scales. BPANN is then used to simulate the relation between the drivers and runoff at each time scale separately. Weights connection method is employed to quantify the impacts of climate variability and human activities on runoff. The performance of this proposed model is compared with multiple linear regression (MLR). The mountainous area of the Hotan River Basin is selected as case study area. Results reveal that runoff exhibits significant fluctuations at inter-annual (2 and 9 years) and inter-decadal (14 years) scales. Climate variables are responsible for 81% of the runoff variations, while human activities account for 8%. The nonlinear hybrid model substantially outperforms MLR in all performance measures. We attribute this improvement to the ability of the proposed model to represent nonlinear relations and to simulate the association between drivers and runoff at different time scales. For instance, water vapor affects runoff positively at the inter-annual time scale but negatively at the inter-decadal time scale. Such opposing relations cannot be represented by MLR or many other, more traditional methods.

Effects of DC-Field Excitation on the Incremental Inductance of a Variable Flux Reluctance Machine

This article presents a method for the computation of the incremental inductances in a 12/10 variable flux reluctance machine (VFRM) using the hybrid analytical modeling coupled with a fixed-point nonlinear solver. The variation of incremental and apparent inductance with respect to the dc-field excitation is investigated for both zero and non-zero ac-field excitations. The results show that the difference between both inductance values is not negligible after 25 A/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> dc-current density for the investigated benchmark without the ac field. Moreover, when a non-zero ac field is introduced in addition to the dc-field, the apparent inductance becomes misleading not only under magnetic saturation but also under low excitation in the linear region of the saturation curve. The results obtained with the proposed nonlinear hybrid model are compared with the finite element method in terms of magnetic flux density distribution and incremental inductance value. The root-mean-square discrepancy of magnetic flux density distribution is found to be 37.6 mT. Furthermore, the discrepancy between incremental inductance results of the proposed method and the finite element model is calculated as 1.43%, while the proposed approach requires less post-processing and necessitates ten times less number of degrees-of-freedom.

Nonlinear Adaptive Robust Precision Pointing Control of Tank Servo Systems

This paper focuses on the high performance pointing control of tank servo systems with parametric uncertainties and uncertain nonlinearities including nonlinear friction, backlash and structural flexibility. A comprehensive dynamic nonlinear mathematical model of the two-DOF tank servo system is established. Specifically, to accurately describe the nonlinear friction characteristics in actual systems, a continuous friction model is employed. Moreover, a hybrid nonlinear model combining structural flexibility and transmission backlash is constructed to characterize the nonlinear characteristics of the backlash and flexible coupling between the input and output shafts of the drive end for the tank servo system. By using the backstepping method, a nonlinear adaptive robust controller is presented. In the controller, the adaptive law is compounded to dispose of parametric uncertainties and a well-designed continuous nonlinear robust control law is developed for the purpose of coping with unmodeled disturbances. The closed-loop system stability analysis indicates that the presented controller achieves an asymptotic tracking performance with parametric uncertainties and ensures the robustness against unmodeled disturbances theoretically. The effectiveness of the proposed control strategy is verified by a large number of comparative simulation results.

A new hybrid model for wind speed forecasting combining long short-term memory neural network, decomposition methods and grey wolf optimizer

Reliable and accurate wind speed forecasting (WSF) is fundamental for efficient exploitation of wind power. In particular, high accuracy short-term WSF (ST-WSF) has a significant impact on the efficiency of wind power generation systems. Due to the non-stationarity and stochasticity of the wind speed (WS), a single model is often not sufficient in practice for the accurate estimation of the WS. Hybrid models are being proposed to overcome the limitations of single models and increase the WS forecasting performance. In this paper, a new hybrid WSF model is developed based on long short-term memory (LSTM) network and decomposition methods with grey wolf optimizer (GWO). In the pre-processing stage, the missing data is filled by the weighted moving average (WMA) method, the WS time series (WSTS) data are smoothed by WMA filtering and the smoothed data are used as model input after Z-score normalization. The forecasting model is formed by the combination of a single model, a decomposition method and an advanced optimization algorithm. Successively, the hybrid WSF model is developed by combining the LSTM and decomposition methods, and optimizing the intrinsic mode function (IMF) estimated outputs with a grey wolf optimizer (GWO). The developed non-linear hybrid model is utilized on the data collected from five wind farms in the Marmara region, Turkey. The obtained experimental results indicate that the proposed combined model can capture non-linear characteristics of WSTS, achieving better forecasting performance than single forecasting models, in terms of accuracy.