Nonlinear Mapping Research Articles

Fractional-Order Modeling and Nonlinear Dynamic Analysis of Forward Converter

To accurately investigate the nonlinear dynamic characteristics of a forward converter, a fractional-order state-space averaged model of a forward converter in continuous conduction mode (CCM) is established based on the fractional calculus theory. And nonlinear dynamical bifurcation maps which use PI controller parameters and a reference current as bifurcation parameters are obtained. The nonlinear dynamic behavior is analyzed and compared with that of an integral-order forward converter. The results show that under certain operating conditions, the fractional-order forward converter exhibits bifurcations characterized by low-frequency oscillations and period-doubling as certain circuit and control parameters change. Under the same circuit conditions, there is a difference in the stable parameter region between the fractional and integral-order models of the forward converter. The stable zone of the fractional-order forward converter is larger than that of the integral-order one. Therefore, the circuit struggles to enter states of bifurcation and chaos. The stability domain for low-frequency oscillations and period-doubling bifurcations can be accurately predicted by using a small signal model and a predictive correction model of the fractional-order forward converter, respectively. Finally, by performing circuit simulations and hardware-in-the-loop experiments, the rationality and correctness of the theoretical analysis are verified.

Digital Visualization of Environmental Risk Indicators in the Territory of the Urban Industrial Zone

This study focused on predicting the spatial distribution of environmental risk indicators using mathematical modeling methods including machine learning. The northern industrial zone of Pavlodar City in Kazakhstan was used as a model territory for the case. Nine models based on the methods kNN, gradient boosting, artificial neural networks, Kriging, and multilevel b-spline interpolation were employed to analyze pollution data and assess their effectiveness in predicting pollution levels. Each model tackled the problem as a regression task, aiming to estimate the pollution load index (PLI) values for specific locations. It was revealed that the maximum PLI values were mainly located to the southwest of the TPPs over some distance from their territories according to the average wind rose for Pavlodar City. Another area of high PLI was located in the northern part of the studied region, near the Hg-accumulating ponds. The high PLI level is generally attributed to the high concentration of Hg. Each studied method of interpolation can be used for spatial distribution analysis; however, a comparison with the scientific literature revealed that Kriging and MLBS interpolation can be used without extra calculations to produce non-linear, empirically consistent, and smooth maps.

Research on deep-sea terrain refinement methods based on satellite remote sensing data

Bathymetric data is crucial for navigation safety and various applications. However, only a small portion of the seafloor has been systematically mapped through direct measurement. The remaining bathymetry is estimated from satellite altimeter data, providing only an approximate representation of the seafloor's shape. To address this issue, the convolutional neural network (CNN) is introduced for the analysis of seabed topography. To the best of our knowledge, this marks the first attempt to incorporate the CNN into the definitive map of the world ocean floor. By employing skip connections based on residual learning, we construct a deeper CNN layer that effectively reduces training complexity. The deeper convolutional neural network layer is used to create a more complex nonlinear mapping model, which is then employed to downscale low-resolution seabed topographic data in order to obtain high-precision seabed topographic information. This process enhances the representation of seabed topographic data to reflect the actual terrain more accurately. The results are compared with those obtained using the bicubic difference method. Conducting tests near the Gulf of Thailand, where Malaysia Airlines Flight MH370 was lost, the results demonstrate that the method proposed in this paper achieves higher accuracy in processing the downscaling of seabed topographic data.

A novel method for settlement imputation and monitoring of earth-rockfill dams subjected to large-scale missing data

Various missing values inevitably exist in the settlement monitoring data of prolonged operation of earth-rockfill dams, which delays or even interrupts the dam structure analytical procedure. This study aims to develop a reliable method for addressing the missing data problem and monitoring earth-rockfill dam settlement behavior. First, an imputation model, support vector regression based on the finite element method and time input (FEMTSVR), is proposed and offers superior performance when capturing complex nonlinear mappings from environmental variables to settlement on small sample data. Herein, an improved particle swarm optimization algorithm (IPSO) is developed, realizing the nonlinear adjustment of weights and parameter reduction during hyperparameter optimization. Then, this study establishes a sequential prediction model based on gate recurrent unit (GRU) networks to monitor dam behavior on the imputed and complete dataset. Eventually, the proposed method is evaluated using real-world earth-rockfill dam monitoring data with the help of statistical indicators, demonstrating its efficiency in monitoring settlement data subjected to large-scale missingness. This study provides a robust database for dam structural health monitoring, while also providing a promising framework for the safety assessment of other civil or hydraulic engineering based on raw monitoring data.

Decision-making Support Platform and Security Design for Rural Leisure Tour Industry based on SEA Method and SVR Model

An accurate short-term passenger flow forecast of rural tourism can avoid accidents as much as possible. However, the short-term passenger flow of rural leisure tourism shows nonlinear, seasonal, random, and other complex characteristics. Meanwhile, the traditional forecasting methods are often difficult to achieve accurate forecasting. Therefore, this study now used the nonlinear mapping function in the support vector regression to convert the passenger traffic training sample into a high-dimensional feature space and established a linear decision function. Then the influence of periodicity on the prediction effect through seasonal index adjustment was reduced. Finally, event triggering combined with core embedding technology for tamper-proof detection was adopted to improve the security of the platform. The results showed that the minimum absolute error of prediction with improved SVM model was 0.27% compared with traditional model and autoregressive integrated moving average model. After the introduction of the Internet search factor, the traffic prediction result was more accurate, which was 0.0425 smaller than that without the introduction of the Internet search factor. When the concurrency was less than 100 times/s, the average response time difference before and after adding the core embedded program was small, indicating that the security of page tampering technology was high. This research method can effectively predict the passenger flow of rural leisure tourism industry and ensure the safety of the platform.

Large-scale photonic computing with nonlinear disordered media.

Neural networks find widespread use in scientific and technological applications, yet their implementations in conventional computers have encountered bottlenecks due to ever-expanding computational needs. Photonic computing is a promising neuromorphic platform with potential advantages of massive parallelism, ultralow latency and reduced energy consumption but mostly for computing linear operations. Here we demonstrate a large-scale, high-performance nonlinear photonic neural system based on a disordered polycrystalline slab composed of lithium niobate nanocrystals. Mediated by random quasi-phase-matching and multiple scattering, linear and nonlinear optical speckle features are generated as the interplay between the simultaneous linear random scattering and the second-harmonic generation, defining a complex neural network in which the second-order nonlinearity acts as internal nonlinear activation functions. Benchmarked against linear random projection, such nonlinear mapping embedded with rich physical computational operations shows improved performance across a large collection of machine learning tasks in image classification, regression and graph classification. Demonstrating up to 27,648 input and 3,500 nonlinear output nodes, the combination of optical nonlinearity and random scattering serves as a scalable computing engine for diverse applications.

Fuel cell temperature control based on nonlinear transformation mitigating system nonlinearity

The operational temperature significantly impacts the efficiency and lifespan of fuel cells. However, precise fuel cell temperature control poses a challenge due to the inherent nonlinear characteristics within the thermal management system. In this study, an in-depth quantitative analysis is undertaken to dissect the intricacies of nonlinearity embedded in temperature control. The results show that the nonlinearity arises from the nonlinear mapping between the thermostat opening and the distribution of coolant flow between the inner and outer loops. To address this nonlinearity, a pre-experiment is implemented to determine the flow ratio of the outer loop coolant flow rate concerning the total stack coolant flow rate under different thermostat openings. Furthermore, a robust temperature control method based on nonlinear transformation is designed, ensuring that stack coolant inlet temperature quickly tracks the target value when load currents change. The proposed control method is verified on a 5 kW fuel cell test bench, and the results demonstrate improvement in dynamic characteristics and enhanced system's robustness. Small-step tests indicate stable tracking of the stack coolant inlet temperature, with a steady-state error of less than 0.2 °C. Besides, under a large-load step response test, the thermostat exhibits a rapid response with merely a 0.6 °C temperature overshoot.

Effect Evaluation of Staged Fracturing and Productivity Prediction of Horizontal Wells in Tight Reservoirs

In this paper, the effect evaluation and production prediction of staged fracturing for horizontal wells in tight reservoirs are studied. Firstly, the basic characteristics and value of horizontal wells in tight reservoirs are introduced, their geological characteristics, flow mechanism and permeability model are analyzed and the application of grey theory in effect analysis is discussed. Considering the problems of staged fracturing effect evaluation and the production prediction of horizontal wells in tight reservoirs, a BP neural network model based on deep learning is proposed. Due to the interference of multiple physical parameters and the complex functional relationship in the development of tight reservoir fracturing, the traditional prediction method has low accuracy and it is difficult to establish an accurate mapping relationship. In this paper, a BP neural network is used to simulate multivariable nonlinear mapping by modifying the model, and its advantages in solving the coupling relationship of complex functions are brought into play. A neural network model with fracturing parameters as input and oil and gas production as output is designed. Through the training and testing of data sets, the accuracy and applicability of the proposed model for effect evaluation and yield prediction are verified. The research results show that the model can fit the complex mapping relationship between fracturing information and production and provide an effective evaluation and prediction tool for the development of the staged fracturing of horizontal wells in tight reservoirs.

Exploration of deep learning-driven multimodal information fusion frameworks and their application in lower limb motion recognition

Research on Lower Limb Motion Recognition (LLMR) based on various wearable sensors has been widely applied in exoskeleton robots, exercise rehabilitation, etc. Typically, employing multimodal information tends to yield higher accuracy and stronger robustness compared to using unimodal information. Due to the inevitable reliance on feature engineering in shallow machine learning-based LLMR methods, this study leverages the powerful non-linear feature mapping capability of deep learning (DL) to construct several end-to-end LLMR frameworks, including: Convolutional Neural Networks (CNNs), CNN-Recurrent Neural Networks (RNNs) and CNN-Graph Neural Networks (GNNs). The effectiveness of the proposed frameworks is verified in distinct tasks, including the recognition of seven types of lower limb motions in healthy subjects and three types of motions in patients with stroke, as well as the phase recognition task during the sit-to-stand (SitTS) process in patients with stroke, achieving the highest mean accuracy of 95.198 %, 99.784 %, and 99.845 %, respectively. Further research and integration of two transfer learning techniques, adaptive Batch Normalization (BN) and model fine-tuning, significantly enhance the applicability of the proposed frameworks in inter-subject prediction. Additionally, systematic analyses are conducted to assess the strengths and weaknesses of different models in terms of recognition performance, complexity, and adaptability to variations in the number of modalities and sensor channels. Experimental results indicate that the proposed frameworks hold promise in providing potential support for the development of human-robot collaborative lower limb exoskeletons or rehabilitation robots.

Metric multidimensional scaling for large single-cell datasets using neural networks

Metric multidimensional scaling is one of the classical methods for embedding data into low-dimensional Euclidean space. It creates the low-dimensional embedding by approximately preserving the pairwise distances between the input points. However, current state-of-the-art approaches only scale to a few thousand data points. For larger data sets such as those occurring in single-cell RNA sequencing experiments, the running time becomes prohibitively large and thus alternative methods such as PCA are widely used instead. Here, we propose a simple neural network-based approach for solving the metric multidimensional scaling problem that is orders of magnitude faster than previous state-of-the-art approaches, and hence scales to data sets with up to a few million cells. At the same time, it provides a non-linear mapping between high- and low-dimensional space that can place previously unseen cells in the same embedding.

Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation

Despite their remarkable success in approximating a wide range of operators defined by PDEs, existing neural operators (NOs) do not necessarily perform well for all physics problems. We focus here on high-frequency waves to highlight possible shortcomings. To resolve these, we propose a subfamily of NOs enabling an enhanced empirical approximation of the nonlinear operator mapping wave speed to solution, or boundary values for the Helmholtz equation on a bounded domain. The latter operator is commonly referred to as the “forward” operator in the study of inverse problems, and we propose a hypernetwork version of the subfamily of NOs as a surrogate model. Our methodology draws inspiration from transformers and techniques such as stochastic depth. Experiments reveal certain surprises in the generalization and the relevance of introducing stochastic depth. Our NOs show superior performance as compared with standard NOs, not only for testing within the training distribution but also for out-of-distribution scenarios. To delve into this observation, we obtain a novel out-of-distribution risk bound tailored to Gaussian measures on Banach spaces, relating stochastic depth with the bound. We conclude by offering an in-depth analysis of the Rademacher complexity associated with our modified models and prove an upper bound tied to their stochastic depth that existing NOs do not satisfy.

Evaluation and Screening of Technological Innovation and Entrepreneurship Based on Improved BPNN Model

Aiming at the low success rate of incubation investment of China’s technology-based start-ups, how to scientifically evaluate technology-based start-ups has become an important issue that needs to be faced. Considering the expert consultation characteristics of the Delphi method is extremely suitable for decision-making problems in the field of uncertainty, as well as the strong nonlinear mapping ability and learning ability of the backpropagation neural network (BPNN). According to the characteristics of the evaluation object and following the principle of index selection, the study uses the Delphi method to determine the evaluation index system suitable for technology-based entrepreneurial enterprises in the current environment and obtain the scores of each index. Based on the established evaluation index system, the BPNN evaluation model is further constructed, and its parameters are optimised to improve its performance. Aiming at the problem that it is easy to fall into a local optimal, a genetic algorithm (GA) is used to optimise it, and a GA-BPNN model is constructed. The comprehensive capability of GA-BPNN is evaluated by using the excellent nonlinear characteristic analysis ability of GA-BPNN to provide a reference for important decisions such as investment. Using BPNN simulation, it was concluded that the correct rate of evaluation of qualified enterprises was between 23.32% and 89.99%, with an average correct rate of 58.32%. The average correct rate was 80.99%. The evaluation accuracy rate was unstable and the average accuracy rate was low. The optimised GA-BPNN model had an average evaluation accuracy rate of 80.32% for qualified enterprises and 93.66% for unqualified enterprises, and the average evaluation accuracy rate increased by 21.99% and 12.66%, respectively. The effectiveness of the model and algorithm was verified. It shows that the GA-BPNN model can be used as an effective tool for the evaluation and screening of technology-based entrepreneurial enterprises. The evaluation system of technology-based entrepreneurial enterprises established by research is scientific and can be applied in practice.

Data-driven contract design for supply chain coordination with algorithm sharing and algorithm competition

Supply chain members can intelligently learn their decisions based on historical data by using Machine-Learning (ML) algorithms. To coordinate the supply chain, the data-driven contract design problems for three contracts—buyback, quantity flexibility, and combined quantity flexibility and rebate—were investigated for a supply chain with one manufacturer and multiple retailers under algorithm sharing and algorithm competition. The problems were formulated as bi-level optimization models by introducing nonlinear mapping from historical demand data to ordering decisions and using ML algorithms to learn the mapping parameters. The bi-level optimization models were transformed into semi-infinite programming models and solved using the (nested) cutting plane methods. Empirical studies using data from two databases showed that algorithm sharing or algorithm competition, the type of contract used, and learning algorithms were the three factors influencing the performance of supply chain coordination when using a data-driven contract design. Algorithm sharing was found to be more beneficial to the supply chain members than algorithm competition in promoting supply chain coordination. An effective incentive mechanism, such as an individualized buyback ratio and a rebate from the manufacturer to the retailers with a good forecast performance, can encourage the retailers to participate in algorithm sharing and improvement.

Intelligent Sensing of Thermal Error of CNC Machine Tool Spindle Based on Multi-Source Information Fusion.

Aiming at the shortcomings of single-sensor sensing information characterization ability, which is easily interfered with by external environmental factors, a method of intelligent perception is proposed in this paper. This method integrates multi-source and multi-level information, including spindle temperature field, spindle thermal deformation, operating parameters, and motor current. Firstly, the internal and external thermal-error-related signals of the spindle system are collected by sensors, and the feature parameters are extracted; then, the radial basis function (RBF) neural network is utilized to realize the preliminary integration of the feature parameters because of the advantages of the RBF neural network, which offers strong multi-dimensional solid nonlinear mapping ability and generalization ability. Thermal-error decision values are then generated by a weighted fusion of different pieces of evidence by considering uncertain information from multiple sources. The spindle thermal-error sensing experiment was based on the spindle system of the VMC850 (Yunnan Machine Tool Group Co., LTD, Yunnan, China) vertical machining center of the Yunnan Machine Tool Factory. Experiments were designed for thermal-error sensing of the spindle under constant speed (2000 r/min and 4000 r/min), standard variable speed, and stepped variable speed conditions. The experiment's results show that the prediction accuracy of the intelligent-sensing model with multi-source information fusion can reach 98.1%, 99.3%, 98.6%, and 98.8% under the above working conditions, respectively. The intelligent-perception model proposed in this paper has higher accuracy and lower residual error than the traditional BP neural network perception and wavelet neural network models. The research in this paper provides a theoretical basis for the operation, maintenance management, and performance optimization of machine tool spindle systems.

Head pose estimation with particle swarm optimization‐based contrastive learning and multimodal entangled GCN

AbstractHead pose estimation is an especially challenging task due to the complexity nonlinear mapping from 2D feature space to 3D pose space. To address the above issue, this paper presents a novel and efficient head pose estimation framework based on particle swarm optimized contrastive learning and multimodal entangled graph convolution network. Firstly, a new network, the region and difference‐aware feature pyramid network (RD‐FPN), is proposed for 2D keypoints detection to alleviate the background interference and enhance the feature expressiveness. Then, particle swarm optimized contrastive learning is constructed to alternatively match 2D and 3D keypoints, which takes the multimodal keypoints matching accuracy as the optimization objective, while considering the similarity of cross‐modal positive and negative sample pairs from contrastive learning as a local contrastive constraint. Finally, multimodal entangled graph convolution network is designed to enhance the ability of establishing geometric relationships between keypoints and head pose angles based on second‐order bilinear attention, in which point‐edge attention is introduced to improve the representation of geometric features between multimodal keypoints. Compared with other methods, the average error of our method is reduced by 8.23%, indicating the accuracy, generalization, and efficiency of our method on the 300W‐LP, AFLW2000, BIWI datasets.

An Implicit Transformer-based Fusion Method for Hyperspectral and Multispectral Remote Sensing Image

There is an effective way to enhance the spatial resolution of hyperspectral remote sensing images by fusing them with multispectral remote sensing images. However, most of the existing deep fusion techniques adopt discretized explicit models to approximate the complex continuous nonlinear mapping in the fusion process, leading to limitations in enhancing the fidelity of spatial details. Additionally, existing algorithms commonly utilize discrete methods such as bilinear or bicubic interpolation during the hyperspectral upsampling process, leading to the loss of crucial spatial-spectral features. To this end, this study proposes a novel Implicit Transformer Fusion Generative Adversarial Network (ITF-GAN), which incorporates the continuity perception mechanism of implicit neural representation with the powerful self-attention mechanism of the Transformer architecture, which uses point-to-point implicit functions aiming to efficiently process information in both spatial and spectral dimensions. Besides, a guided implicit neural sampling module is introduced in the hyperspectral image up-sampling process to enhance the coordinated expression of features in the spatial and spectral domains, which improves the spatial resolution and spectral fidelity of the fused image during the upsampling process. A series of fusion experiments including 4x, 8x, and 16x scale factors have shown that ITF-GAN has significant advantages over current popular fusion algorithms in both objective evaluation indicators and subjective visual evaluation.

Enhancing mix proportion design of low carbon concrete for shield segment using a combination of Bayesian optimization-NGBoost and NSGA-III algorithm

The demand for segment concrete increases rapidly with the expansion of urban rail transit and underground space, which may lead to carbon emissions (CE). In the production of segment concrete, using supplement cementitious materials (SCM) can be used to reduce CE instead of cement. However, SCM contents are usually determined by many orthogonal experiments, which are often time-consuming and only consider the limited experimental variables. Therefore, a novel hybrid intelligent algorithm combining Bayesian optimization (BO), natural gradient boosting (NGBoost) and non-dominated sorting genetic algorithm (NSGA)-III is proposed, which overcomes these disadvantages. Firstly, NGBoost model after hyperparameter optimization using BO is used to establish a nonlinear mapping relationship between segment concrete mix proportion and performance, which was used as the fitness function of the non-dominated sorting genetic algorithm (NSGA-III). Secondly, the optimal Pareto solutions were obtained through NSGA-III, and the reasonable range of segment concrete mixing proportion was obtained. Finally, a segment concrete production case was used to verify the effectiveness of the proposed algorithm. The results showed that the proposed hybrid algorithm combining proposed scheme decision strategy can obtain an optimal design scheme for concrete mix proportion. In addition, the comprehensive optimization rate of the obtained optimal scheme compared to the experimental optimal group was 11.5%. Moreover, the amount of phosphorous slag (PS) and granulated blast furnace slag (GBFS) in the optimal scheme was 26%, with a mass ratio of 1:2. Compared to the experimental optimal group, the optimal scheme can reduce the cost and CE per cubic meter by 31.64 yuan and 31.04 kg, respectively. Furthermore, the hybrid algorithm proposed can accurately obtains an optimal amount of SCM, which could be used as a supporting tool to reduce the production cost and CE of segment concrete. Overall, this research contributes to combining machine learning algorithms with actual production processes, which overcomes the data limitations of traditional experiments. It also provides a new intelligent approach and reference cases for the low-carbon design and sustainable development of building materials such as concrete.

On multiple impacts of functional gradient magneto-electro-elastic plates with convex and concave configurations and prediction based on PSO-BPNN

Revealing the coupling mechanism between the nonlinear effect and the multi-physical fields in the bistable plate, as well as the interaction between multiple impacts, promotes the innovative development of morphing structures. Improved neural network technology contributes to the adaptive design and functional integration of morphing structures. The multiple impacts of functional gradient magneto-electro-elastic (FG-MEE) plates with convex and concave configurations are investigated. In the Reddy high-order shear plate theory considering the bistable configuration, functional gradient models and magneto-electro-mechanical effect models are constructed. To measure the contact forces in the multi-impact process, the modified Hertz contact model is introduced. Through the Hamiltonian variational principle, the nonlinear multiple impact dynamics of the FG-MEE plates with convex and concave configurations are modeled. To obtain the bistable configuration induced by the magneto-electro-mechanical coupling effects, the two-step perturbation method is extended in multiple physical fields. Further, the two-step perturbation method and the Galerkin method are extended to acquire the higher-order truncated solutions for the multiple impact responses of FG-MEE plates with convex and concave configurations. Based on the numerical result database of multiple impact response, the nonlinear mapping relationship between the structure characteristics, load characteristics and multiple impact responses of bistable FG-MEE plate is constructed by the particle swarm optimization-back propagation (PSO-BP) technology. Ultimately, the coupling effects between the multi-physical fields and nonlinear behaviors in FG-MEE plates with convex and concave configurations are comparatively analyzed, and the interactions between multiple impacts are systematically revealed.

Distributed adaptive finite-time output feedback containment control for nonstrict-feedback stochastic multi-agent systems via command filters

In this paper, distributed adaptive finite-time output feedback containment control based on command filters is proposed for nonstrict-feedback stochastic multi-agent systems (SMASs) with unmodeled dynamics, input quantization and prescribed performance. The unknown states are estimated using a high-gain observer, the unmodeled dynamics is handled by introducing a measurable dynamic signal, and the input signal is processed using an integrated quantizer that combines the advantages of uniform quantizer and hysteretic quantizer. The hyperbolic tangent function and time-varying function are applied to construct the performance function, and the constrained containment error is transformed into an unconstrained system through nonlinear mapping (NM). Unknown smooth functions are handled with the superb approximation capability of radial basis function neural networks (RBFNNs). Based on stochastic finite-time theory and dynamic surface control (DSC) method, nonlinear command filters are introduced to reduce the use of black-box functions and simplify the controller design. Finally, the theoretical analysis and two sets of experimental results demonstrate that all signals in the controlled system are semi-global finite-time stability in probability (SGFSP) and the designed controller works well.

Low-Rank Multilabel Learning Based on Nonlinear Mapping

Low-Rank Multilabel Learning Based on Nonlinear Mapping