Complex Nonlinear Characteristics Research Articles

A classification-driven neuron-grouped SAE for feature representation and its application to fault classification in chemical processes

Recently, deep learning has become a popular tool for fault detection and diagnosis in chemical processes to learn complex nonlinear features. However, the features extracted from most traditional deep networks are only good representation for the raw input data, which may contain irrelevant information with the faults and are not beneficial for the fault classification task. Thus, a novel classification-driven neuron-grouped stacked autoencoder (CG-SAE) is proposed for hierarchical fault-related feature representation in this paper. During the pre-training phase of CG-SAE, the hidden neurons in each CG-AE are divided into several groups, the number of which is equal to that of the data categories. Each group is mainly associated to one type of fault. Moreover, the supervised information is introduced without additional weights by comparing the error between the actual label and the average activation of the corresponding group. In this way, the extracted deep features can contain category-related information and be clustered to different categories. In terms of the classification accuracy and training efficiency, CG-SAE performs better than some advanced supervised methods as verified by the Tennessee Eastman (TE) benchmark and an industrial hydrocracking process.

Double memristors oscillator with hidden stacked attractors and its multi-transient and multistability analysis

Abstract In this paper, by replacing the two linear resistors in the RLC oscillator with flux-controlled and charge-controlled memristors, a novel double memristors nonlinear circuit system is proposed. From the oscillator circuit, we established the mathematical model of the system and proved that it is a hidden system without equilibrium. The numerical simulation results of the mathematical model are consistent with the circuit. What is more, we also find that one state variable of the system has the typical slow change behavior, which is reflected in the form of step-like or square-like waves, thus forming a novel stacked attractor. Then, through studying the Poincare map, phase diagram, bifurcation diagram, Lyapunov exponents (LEs), it was proved that the system has multi-transient behaviors such as chaos to another chaos, chaos to period, chaos to quasi-period, quasi-period to period. Besides, the memristive oscillator has quasi-periodic multistability when changing the initial values, which is a rare phenomenon for a chaotic system. These findings indicate that the proposed memristive hidden oscillator has complex nonlinear dynamic characteristics. Finally, the Digital Signal Processing (DSP) hardware platform confirms the physical realizability of the oscillator, offering the possibility of engineering applications.

Body height robust control of automotive air suspension system using finite‐time approach

AbstractOne of the essential characteristics of electronically controlled air suspension (ECAS) is that the automotive height is adjustable. Because ECAS system has complex nonlinearity and noticeable hysteresis, it is easy to make the vehicle oscillate near the target height due to the overcharge/discharge of air springs, which would cause the instability of vehicle body posture. More than that, the existence of external disturbances and uneven loads has impacts on body height control. The complex nonlinear characteristics and the existence of external interference put forward higher requirements for the design of ECAS body height controller. In this paper, by non‐singular coordinate transformation, the nonlinear model of the 1/4 ECAS body height regulation system is transformed into a linear model with a third‐order integral chain firstly, which is closer to the real dynamic characteristics of the suspension system than the linear system with low order. Secondly, based on continuous finite‐time theory, a continuous finite‐time feedback stabilization controller with small parameters is designed, and it turned out that the height regulation system can achieve finite‐time stability. Finally, the simulation results under sinusoidal and random disturbances show that with the comparison with the traditional PD control, the designed finite‐time controller can not only guarantee the system faster response speed and better control accuracy but also obtain the better anti‐jamming performance. By innovatively applying the finite‐time theory to the ECAS system, the designed control system in this paper can afford good robustness for ECAS height adjustment and has great significance to improve the overall performance of ECAS system.

A Novel Decomposition-Ensemble Learning Model Based on Ensemble Empirical Mode Decomposition and Recurrent Neural Network for Landslide Displacement Prediction

As vital comments on landslide early warning systems, accurate and reliable displacement prediction is essential and of significant importance for landslide mitigation. However, obtaining the desired prediction accuracy remains highly difficult and challenging due to the complex nonlinear characteristics of landslide monitoring data. Based on the principle of “decomposition and ensemble”, a three-step decomposition-ensemble learning model integrating ensemble empirical mode decomposition (EEMD) and a recurrent neural network (RNN) was proposed for landslide displacement prediction. EEMD and kurtosis criteria were first applied for data decomposition and construction of trend and periodic components. Second, a polynomial regression model and RNN with maximal information coefficient (MIC)-based input variable selection were implemented for individual prediction of trend and periodic components independently. Finally, the predictions of trend and periodic components were aggregated into a final ensemble prediction. The experimental results from the Muyubao landslide demonstrate that the proposed EEMD-RNN decomposition-ensemble learning model is capable of increasing prediction accuracy and outperforms the traditional decomposition-ensemble learning models (including EEMD-support vector machine, and EEMD-extreme learning machine). Moreover, compared with standard RNN, the gated recurrent unit (GRU)-and long short-term memory (LSTM)-based models perform better in predicting accuracy. The EEMD-RNN decomposition-ensemble learning model is promising for landslide displacement prediction.

State of charge estimation for lithium-ion batteries using dynamic neural network based on sine cosine algorithm

State of charge (SOC) of the lithium-ion batteries is one of the key parameters of the battery management system, which the performance of SOC estimation guarantees energy management efficiency and endurance mileage of electric vehicles. However, accurate SOC estimation is a difficult problem owing to complex chemical reactions and nonlinear battery characteristics. In this paper, the method of the dynamic neural network is used to estimate the SOC of the lithium-ion batteries, which is improved based on the classic close-loop nonlinear auto-regressive models with exogenous input neural network (NARXNN) model, and the open-loop NARXNN model considering expected output is proposed. Since the input delay, feedback delay, and hidden layer of the dynamic neural network are usually selected by empirically, which affects the estimation performance of the dynamic neural network. To cover this weakness, sine cosine algorithm (SCA) is used for global optimal dynamic neural network parameters. Then, the experimental results are verified to obtain the effectiveness and robustness of the proposed method under different conditions. Finally, the dynamic neural network based on SCA is compared with unscented Kalman filter (UKF), back propagation neural network based on particle swarm optimization (BPNN-PSO), least-squares support vector machine (LS-SVM), and Gaussian process regression (GPR), the results show that the proposed dynamic neural network based on SCA is superior to other methods.

Identification modeling and prediction of ship maneuvering motion based on LSTM deep neural network

This paper proposes a novel system identification scheme to obtain a MIMO model of ship maneuvering motion, which can leverage the temporal correlation from the constructed training data to learn the underlying feasible model robust to extraneous noise. The scheme is based on long–short-term-memory (LSTM) deep neural network, which is more easily trained than traditional feedforward neural network with more complicated network structure. First, multiple datasets of simulated standard maneuvers (10°/10° and 20°/20° zigzag, 35° turning circle) of a KVLCC2 model are artificially polluted with white noise of various levels and used simultaneously to train the deep neural network model. Meanwhile, the data of 15°/15° zigzag maneuver are used to facilitate the training process to alleviate overfitting problem. Second, different datasets of modified zigzag tests are used to validate the generalization performance and robustness to noise of the trained neural network model. The training and validation results demonstrate that a mapping between the dynamics of ship motion and the computation in LSTM deep neural network is correctly identified. This mapping indicates that the complex nonlinear features of ship maneuvering motion can be learned from the measured temporal data, using standard training techniques for deep neural networks. An equivalent LSTM deep neural network model with better generalization performance and robustness is established, and its accuracy in predicting ship maneuvering motion is validated.

Accurate Pressure Control Based on Driver Braking Intention Identification for a Novel Integrated Braking System

<div class="section abstract"><div class="htmlview paragraph">With the development of intelligent and electric vehicles, higher requirements are put forward for the active braking and regenerative braking ability of the braking system. The traditional braking system equipped with vacuum booster has difficulty meeting the demand, therefore it has gradually been replaced by the integrated braking system. In this paper, a novel Integrated Braking System (IBS) is presented, which mainly contains a pedal feel simulator, a permanent magnet synchronous motor (PMSM), a series of transmission mechanisms, and the hydraulic control unit. As an integrative system of mechanics-electronics-hydraulics, the IBS has complex nonlinear characteristics, which challenge the accurate pressure control. Furthermore, it is a completely decoupled braking system, the pedal force doesn’t participate in pressure-building, so it is necessary to precisely identify driver’s braking intention. To improve the control accuracy of the system, this paper proposed a novel pressure control strategy based on driver braking intention identification. Firstly, the structure and working principle of the novel integrated braking system was introduced. Secondly, the driver's braking intention identification strategy was designed. Thirdly, Considering the nonlinear and dynamic characteristics of the system, a cascade closed-loop control strategy including a pressure loop by the feedforward-feedback method, a position loop by the sliding-mode control method, and current loop with friction compensation was proposed. Finally, based on dSPACE products, a hardware-in-the-loop (HiL) experimental bench was built for algorithm verification. The HiL experiment results show that the pressure control strategy has the advantages of accurate response, the braking system pressure follows the driver's expected pressure well.</div></div>

Systematic simplification of the Anaerobic Digestion Model No. 1 (ADM1) – Model development and stoichiometric analysis

Rigorous process models provide a reliable basis for model-based monitoring and control of anaerobic digestion plants. Due to the complex model structure and non-linear system characteristics, the established Anaerobic Digestion Model No. 1 (ADM1) is rarely applied in industrial plant operation. The present investigation proposes a systematic procedure for successive model simplification and presents the description of five model variants of a mass-based ADM1. Individual model structures greatly differ in their number of implemented process phases, characteristic components and required parameters. Simplified model variants combine nutrient degradation and biogas formation based on first-order sum reactions, whereas complex model structures describe individual degradation pathways and intermediates during acido- and acetogenesis. Characteristic features of the derived model structures as well as the stoichiometric methane potentials and microbial biomass yields of the underlying degradation pathways of individual model variations are evaluated and discussed in detail.

An Intelligent Passenger Flow Prediction Method for Pricing Strategy and Hotel Operations

Hospitality industry plays a crucial role in the development of tourism. Predicting the future demand of a hotel is a key step in the process of hotel revenue management. Hotel passenger flow prediction plays an important role in guiding the formulation of hotel pricing and operating strategies. On the one hand, hotel passenger flow prediction can provide decision support for hotel managers and effectively avoid the waste of hotel resources and loss of revenue caused by the loss of customers. On the other hand, it is the guarantee of the priority occupation of business opportunities by hotel enterprises, which can help hotel enterprises adjust their operation strategies reasonably to better adapt to the market situation. In addition, hotel passenger flow prediction is helpful to judge the overall operating condition of the hotel industry and assess the risk level of the hotel project to be built. Hotel passenger flow is affected by many factors, such as weather, environment, season, holidays, economy, and emergencies, and has the characteristics of complex nonlinear fluctuation. The existing demand predicting methods include linear methods and nonlinear methods. The linear prediction methods rely on the stability of environment and time series, so they cannot completely simulate the complex nonlinear fluctuations characteristics of hotel passenger flow. Traditional nonlinear prediction methods need to improve the prediction accuracy, and they are difficult to deal with the increasing data of hotel passenger flow. Based on the above analysis, this paper constructs a deep learning prediction model based on Long Short-Term Memory (LSTM) to predict the number of actual monthly arrival bookings. The number of actual monthly arrival bookings can reflect the actual monthly passenger flow of a hotel. The prediction model can effectively reduce the loss caused by cancellation or nonarrival of bookings due to various reasons and improve the hotel revenue. The experimental part of this paper is based on the booking demand dataset of a resort hotel in Portugal from July 1, 2015, to August 31, 2017. Artificial neural network (ANN) and support vector regression (SVR) are built as benchmark models to predict the number of actual monthly arrival bookings of this hotel. The experimental results show that, compared with the benchmark models, the LSTM model can effectively improve the prediction ability and provide necessary reference for the hotel's future pricing decision and operation mode arrangement.

Nonlinear responses of suspended cable under phase-differed multiple support excitations

Cable structures may be subjected to multiple support excitations and exhibit complex nonlinear dynamic characteristics. To study the influence of phase-differed support excitations on the responses of suspended cable, a model with both ends subjected to 3-D non-uniform excitations is established, and the infinite-dimensional discrete motion equations are obtained. The in-plane primary resonance and out-of-plane primary resonance are studied using the multiple scales method. The general expressions of the equivalent excitation amplitude and the response phase of the multi-excitation system are obtained. The effects of different combinations of horizontal, vertical, and transverse excitations on the response amplitude and phase are analyzed theoretically, and the multi-scale solutions are verified by numerical integration. The results show that the multi-excited cable can be regarded as a nominal single excitation system (NSES). The effect of multiple support excitations on the cable response is mainly reflected in two aspects: First, these excitations make the response phase of the system shift based on the response phase of the NSES; second, these support excitations affect the equivalent excitation amplitude of the NSES. Both the response phase’s shift and the equivalent excitation amplitude depend on the combination of the excitations and the parity of the excited modes. When the phase difference between the two excitations is gradually changed from 0 to $$\pi $$ , the phase–frequency curve is also shifted by $$\pi $$ . However, the shifting process is not necessarily linear. The excitation phase difference does not change the soft and hard properties of the system. However, it can simultaneously change the response amplitude and the resonance region’s width so that the amplitude–frequency curve changes with a period of $$2\pi $$ in a specific region.

Forecasting China’s sovereign CDS with a decomposition reconstruction strategy

Precisely predicting sovereign credit default swaps (CDS) is important for preventing sovereign risks. However, sovereign CDS exhibit complex nonlinear characteristics, which make accurate predictions challenging. As a result, this paper proposes a hybrid ensemble forecasting framework based on a decomposition reconstruction strategy that considers multiple factors. The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is used to decompose the sovereign CDS into different components, and the reconstruction method based on sample entropy is employed to reconstruct the components into trend items, market fluctuation items and noise items. Motivated by the features of components reconstructed, we utilize the autoregressive integrated moving average (ARIMA) and relevance vector machine (RVM) models to predict each component. Finally, the forecasting results of the three sub-sequences are integrated as the final forecast. For verification, China’s 5-year daily sovereign CDS is used as sample data, and the empirical results reveal that the proposed model performs better than all benchmark models in terms of forecasting accuracy, including horizon and directional. Furthermore, the results indicate that the proposed model can be regarded as an effective and promising tool for forecasting China’s sovereign CDS.

Does China’s OFDI Successfully Promote Environmental Technology Innovation?

Environmental technology innovation is a crucial measure of the quality of China’s economic development and sustainable environmental protection. Based on the 2009–2017 provincial panel data from China, this article used the modified projection pursuit model to measure the environmental technology innovation capabilities of various regions. Moreover, this article empirically investigates the threshold effect of outward foreign direct investment on China’s environmental technology innovation under different intellectual property protection levels. The results are as follows. First, the environmental technology innovation capabilities of China’s regions vary significantly, showing an “east-middle-west” gradient decline trend similar to levels of economic development. Second, outward foreign direct investment has a significant reverse environmental technology innovation effect, but this effect has complex nonlinear characteristics. Third, in the process of outward foreign direct investment affecting environmental technology innovation, intellectual property protection has a significant double threshold effect. As the level of intellectual property protection continues to cross the threshold value, the effect direction of outward foreign direct investment on environmental technology innovation undergoes a sudden change from inhibition to promotion. However, when intellectual property protection is too high, the promotion effect is relatively limited. This paper provides some reference points and insights that should aid in establishing a scientific intellectual property protection system and raising the level of environmental technology innovation.

Analysis of Air Mean Temperature Anomalies by Using Horizontal Visibility Graphs.

The last decades have been successively warmer at the Earth’s surface. An increasing interest in climate variability is appearing, and many research works have investigated the main effects on different climate variables. Some of them apply complex networks approaches to explore the spatial relation between distinct grid points or stations. In this work, the authors investigate whether topological properties change over several years. To this aim, we explore the application of the horizontal visibility graph (HVG) approach which maps a time series into a complex network. Data used in this study include a 60-year period of daily mean temperature anomalies in several stations over the Iberian Peninsula (Spain). Average degree, degree distribution exponent, and global clustering coefficient were analyzed. Interestingly, results show that they agree on a lack of significant trends, unlike annual mean values of anomalies, which present a characteristic upward trend. The main conclusions obtained are that complex networks structures and nonlinear features, such as weak correlations, appear not to be affected by rising temperatures derived from global climate conditions. Furthermore, different locations present a similar behavior and the intrinsic nature of these signals seems to be well described by network parameters.

Estimation of Reference Evapotranspiration Using Spatial and Temporal Machine Learning Approaches

Evapotranspiration (ET) is widely employed to measure amounts of total water loss between land and atmosphere due to its major contribution to water balance on both regional and global scales. Considering challenges to quantifying nonlinear ET processes, machine learning (ML) techniques have been increasingly utilized to estimate ET due to their powerful advantage of capturing complex nonlinear structures and characteristics. However, limited studies have been conducted in subhumid climates to simulate local and spatial ETo using common ML methods. The current study aims to present a methodology that exempts local data in ETo simulation. The present study, therefore, seeks to estimate and compare reference ET (ETo) using four common ML methods with local and spatial approaches based on continuous 17-year daily climate data from six weather stations across the Red River Valley with subhumid climate. The four ML models have included Gene Expression Programming (GEP), Support Vector Machine (SVM), Multiple Linear Regression (LR), and Random Forest (RF) with three input combinations of maximum and minimum air temperature-based (Tmax, Tmin), mass transfer-based (Tmax, Tmin, U: wind speed), and radiation-based (Rs: solar radiation, Tmax, Tmin) measurements. The estimates yielded by the four ML models were compared against each other by considering spatial and local approaches and four statistical indicators; namely, the root means square error (RMSE), the mean absolute error (MAE), correlation coefficient (r2), and scatter index (SI), which were used to assess the ML model’s performance. The comparison between combinations showed the lowest SI and RMSE values for the RF model with the radiation-based combination. Furthermore, the RF model showed the best performance for all combinations among the four defined models either spatially or locally. In general, the LR, GEP, and SVM models were improved when a local approach was used. The results showed the best performance for the radiation-based combination and the RF model with higher accuracy for all stations either locally or spatially, and the spatial SVM and GEP illustrated the lowest performance among the models and approaches.

Application of Three Deep Machine-Learning Algorithms in a Construction Assessment Model of Farmland Quality at the County Scale: Case Study of Xiangzhou, Hubei Province, China

Constructing a scientific and quantitative quality-assessment model for farmland is important for understanding farmland quality, and can provide a theoretical basis and technical support for formulating rational and effective management policies and realizing the sustainable use of farmland resources. To more accurately reflect the systematic, complex, and differential characteristics of farmland quality, this study aimed to explore an intelligent farmland quality-assessment method that avoids the subjectivity of determining indicator weights while improving assessment accuracy. Taking Xiangzhou in Hubei Province, China, as the study area, 14 indicators were selected from four dimensions—terrain, soil conditions, socioeconomics, and ecological environment—to build a comprehensive assessment index system for farmland quality applicable to the region. A total of 1590 representative samples in Xiangzhou were selected, of which 1110 were used as training samples, 320 as test samples, and 160 as validation samples. Three models of entropy weight (EW), backpropagation neural network (BPNN), and random forest (RF) were selected for training, and the assessment results of farmland quality were output through simulations to compare their assessment accuracy and analyze the distribution pattern of farmland quality grades in Xiangzhou in 2018. The results showed the following: (1) The RF model for farmland quality assessment required fewer parameters, and could simulate the complex relationships between indicators more accurately and analyze each indicator’s contribution to farmland quality scientifically. (2) In terms of the average quality index of farmland, RF > BPNN > EW. The spatial patterns of the quality index from RF and BPNN were similar, and both were significantly different from EW. (3) In terms of the assessment results and precision characterization indicators, the assessment results of RF were more in line with realities of natural and socioeconomic development, with higher applicability and reliability. (4) Compared to BPNN and EW, RF had a higher data mining ability and training accuracy, and its assessment result was the best. The coefficient of determination (R2) was 0.8145, the mean absolute error (MAE) was 0.009, and the mean squared error (MSE) was 0.012. (5) The overall quality of farmland in Xiangzhou was higher, with a larger area of second- and third-grade farmland, accounting for 54.63%, and the grade basically conformed to the trend of positive distribution, showing an obvious pattern of geographical distribution, with overall high performance in the north-central part and low in the south. The distribution of farmland quality grades also varied widely among regions. This showed that RF was more suitable for the quality assessment of farmland with complex nonlinear characteristics. This study enriches and improves the index system and methodological research of farmland quality assessment at the county scale, and provides a basis for achieving a threefold production pattern of farmland quantity, quality, and ecology in Xiangzhou, while also serving as a reference for similar regions and countries.

Nonlinear Vibration Mechanism of the Marine Rotating Machinery with Airbag Isolation Device under Heaving Motion

In this paper, we put an investigation into the nonlinear vibration mechanism of the marine rotating machinery with an airbag isolation device under heaving motion. First, we consider the effects of mass unbalance and heaving motion and propose a mathematical model of the marine rotating mechanical system with airbag vibration isolation. Then, the multiple-scale method is conducted to analyze the nonlinear dynamic characteristics of the mechanical system; the frequency-response curves are mainly studied under different parameters, such as the heave excitation, rotor speed, and damping; and the numerical method is also introduced to analyze its dynamic behaviors, such as the steady-state response and its corresponding phase diagram, Poincaré section. The dynamic stability of the system is investigated based on the bifurcations and the largest Lyapunov exponent about rotor speed and heaving frequency. The obtained results indicate complex nonlinear characteristics of the system compared to the system without heaving excitation, which can help us fully understand the dynamic characteristics and parametric optimization as well as structural design of the marine mechanical isolation system.

Complex circuit simulation and nonlinear characteristics analysis of GaN power switching device

Abstract To overcome the problem of energy losses in the electrical circuits and to improve the energy conversion efficiency, it is necessary to increase the power switch frequency and reduce the open resistance of the power switch. Moreover, based on energy saving, failure protection, circuit design and other aspects of the research of enhanced devices are also essential, a new static and dynamic model of GaN power transistor is proposed, and the steady-state and dynamic characteristics of GaN power transistors are simulated and tested. The GaN power transistor used in the test has a constant voltage of 450 V and a current of 4 A. By changing the driving power U, G (take 2, 3, 4V) and the stray inductance Ls (take 2 μH, 5 μH), the switching characteristics of the simulation model were studied, and the simulation was carried out by changing the absorption capacitance Cc (select 1.5 μF and 3.0 μF). This proposed simulation model can be used to analyze the protection effect of the buffer circuit under various stray inductors and help to guide the design of the buffer circuit. The simulation results of the static and dynamic models of the new GaN power transistor agree well with the experimental results. With the increase of Ug , the opening speed is faster, but the turn-off delay is longer. With the increase of Ls , the peak of the turn-off voltage increases. After increasing the absorption capacitance, the peak voltage during the turnoff is limited to the rated voltage, and the buffer circuit plays a protective role and the greater the Cc , the better the protection. The simulation results are consistent with the theoretical analysis, which verifies the effectiveness of the model.

Study on the Improvement of the Application of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise in Hydrology Based on RBFNN Data Extension Technology

The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult. Currently, some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method, a new time-frequency analysis method based on the empirical mode decomposition (EMD) algorithm, to decompose non-stationary raw data in order to obtain relatively stationary components for further study. However, the endpoint effect in CEEMDAN is often neglected, which can lead to decomposition errors that reduce the accuracy of the research results. In this study, we processed an original runoff sequence using the radial basis function neural network (RBFNN) technique to obtain the extension sequence before utilizing CEEMDAN decomposition. Then, we compared the decomposition results of the original sequence, RBFNN extension sequence, and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method. The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect. At both ends of the components, the extension sequence more accurately reflected the true fluctuation characteristics and variation trends. These advances are of great significance to the subsequent study of hydrology. Therefore, the CEEMDAN method, combined with an appropriate extension of the original runoff series, can more precisely determine multi-time scale characteristics, and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting.

Hybrid recommendation model based on deep learning and Stacking integration strategy

In the traditional recommendation algorithms, due to the rapid development of deep learning and Internet technology, user-item rating data is becoming increasingly sparse. The simple inner product interaction mode adopted by the collaborative filtering method has a cold start problem and cannot learn the complex nonlinear structural features between users and items, while the content-based algorithm encounters the difficulty of effective feature extraction. In response to this problem, a hybrid model is proposed based on deep learning and Stacking integration strategy. The traditional recommendation algorithm is first fused by using the Stacking integration strategy to make up for the shortcomings of the single recommendation algorithm to achieve better recommendation performance. The fusion-based model learns the more abstract and deeper nonlinear interaction features by deep learning technology, which makes the model performance gain further. The experiment comparison on the MovieLens-1m dataset shows that the proposed hybrid recommendation model can significantly improve the accuracy of rating prediction.

Flexural wave band structure of magneto-elastic phononic crystal nanobeams based on the nonlocal theory

Phononic crystals are widely researched for new kinds of functional composites. However, studies on magneto-elastic PCs at nanoscale that show special superiorities are quite limited. Considering the nonlocal effect and nonlinear magneto-mechanical coupling, this work establishes a theoretical model for size-dependent flexural wave band structure of magneto-elastic PC nanobeams with magnetostrictive materials according to the Euler–Bernoulli beam model and nonlocal theory. The influence of nonlocal parameter, pre-stress and magnetic field on band structure of Titanium/Terfenol-D PC nanobeams is analyzed. The results show that the nonlocal effect has a remarkable weakening impact on the dispersion curve of high order band gap. In addition, band gap exhibits complex nonlinear coupling characteristics due to the consideration of pre-stress and magnetic field. Moreover, geometric parameter plays an important role in determining the size-dependent band structure. Consequently, the research may be helpful for flexible regulation of elastic wave propagation in PC nanobeam-based devices.