Multivariate Time Series Anomaly Detection Based on Spatial-Temporal Network and Transformer in Industrial Internet of Things

In the Industrial Internet of Things(IIoT),sensors generate time series data to reflect the working state.When the systems are attacked,timely identification of outliers in time series is critical to ensure security.Although many anomaly detection methods have been proposed,the temporal correlation of the time series over the same sensor and the state(spatial)correlation between different sensors are rarely considered simultaneously in these methods.Owing to the superior capability of Transformer in learning time series features.This paper proposes a time series anomaly detection method based on a spatial-temporal network and an improved Transformer.Additionally,the methods based on graph neural networks typically include a graph structure learning module and an anomaly detection module,which are interdependent.However,in the initial phase of training,since neither of the modules has reached an optimal state,their performance may influence each other.This scenario makes the end-to-end training approach hard to effectively direct the learning trajectory of each module.This interdependence between the modules,coupled with the initial instability,may cause the model to find it hard to find the optimal solution during the training process,resulting in unsatisfactory results.We introduce an adaptive graph structure learning method to obtain the optimal model parameters and graph structure.Experiments on two publicly available datasets demonstrate that the proposed method attains higher anomaly detection results than other methods.

Comprehensive evaluation and spatial-temporal evolution characteristics of urban resilience in Chengdu-Chongqing Economic Circle

To clarify the connotations and extensions of urban resilience,this study focuses on the Chengdu-Chongqing Economic Circle with 16 cities as research subjects.A comprehensive evaluation index system was constructed to measure the resilience of each city from 2003 to 2020.The spatial-temporal evolution characteristics were analyzed using Kernel density estimation,standard deviation ellipse,and spatial Markov chain analysis,and the spatial Tobit model was introduced to discover the influencing factors.The results indicate the following:①Urban resilience in the Chengdu-Chongqing Economic Circle displays an upward trend,with the center of gravity moving to the southwest,and the polarization phenomenon intensifying.②The urban resilience level in a region has certain spatial and geographical dependence,while the probability of urban resilience transfer differs in adjacent cities with different resilience levels.③Urban centrality,economic scale,openness level,and financial development promote urban resilience,whereas government scale significantly inhibits it.Finally,this paper proposes countermeasures and suggestions to improve the urban resilience of the Chengdu-Chongqing Economic Circle.

AFSTGCN:Prediction for multivariate time series using an adaptive fused spatial-temporal graph convolutional network

The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.

Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression

In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.

Convergent Data-Driven Regularizations for CT Reconstruction

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography(CT).As the(naive)solution does not depend on the measured data continuously,regularization is needed to reestablish a continuous dependence.In this work,we investigate simple,but yet still provably convergent approaches to learning linear regularization methods from data.More specifically,we analyze two approaches:one generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of our previous work,and one tailored approach in the Fourier domain that is specific to CT-reconstruction.We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on.Finally,we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically,discuss their advantages and disadvantages and investigate the effect of discretization errors at differentresolutions.

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

Trigonometric Regularization and Continuation Method Based Time-Optimal Control of Hypersonic Vehicles

Aiming at the time-optimal control problem of hypersonic vehicles(HSV)in ascending stage,a trigonometric regularization method(TRM)is introduced based on the indirect method of optimal control.This method avoids analyzing the switching function and distinguishing between singular control and bang-bang control,where the singular control problem is more complicated.While in bang-bang control,the costate variables are unsmooth due to the control jumping,resulting in difficulty in solving the two-point boundary value problem(TPBVP)induced by the indirect method.Aiming at the easy divergence when solving the TPBVP,the continuation method is introduced.This method uses the solution of the simplified problem as the initial value of the iteration.Then through solving a series of TPBVP,it approximates to the solution of the original complex problem.The calculation results show that through the above two methods,the time-optimal control problem of HSV in ascending stage under the complex model can be solved conveniently.

Spatial-temporal distribution and geochemistry of highly evolved Mesozoic granites in Great Xing’an Range,NE China:Discriminant criteria and geological significance

Highly evolved granite is an important sign of the mature continent crust and closely associated with deposits of rare metals.In this work,the authors undertake systematically zircon U-Pb ages and whole rock elemental data for highly evolved granitic intrusions from the Great Xing’an Range(GXR),NE China,to elucidate their discriminant criteria,spatial-temporal distribution,differentiation and geodynamic mecha-nism.Geochemical data of these highly evolved granites suggest that high w(SiO_(2))(>70%)and differentiation index(DI>88)could be quantified indicators,while strong Eu depletion,high TE_(1,3),lowΣREE and low Zr/Hf,Nb/Ta,K/Rb could only be qualitative indicators.Zircon U-Pb ages suggest that the highly evolved gran-ites in the GXR were mainly formed in Late Mesozoic,which can be divided into two major stages:Late Ju-rassic-early Early Cretaceous(162-136 Ma,peak at 138 Ma),and late Early Cretaceous(136-106 Ma,peak at 126 Ma).The highly evolved granites are mainly distributed in the central-southern GXR,and display a weakly trend of getting younger from northwest to southeast,meanwhile indicating the metallogenic potential of rare metals within the central GXR.The spatial-temporal distribution,combined with regional geological data,indicates the highly evolved Mesozoic granites in the GXR were emplaced in an extensional environ-ment,of which the Late Jurassic-early Early Cretaceous extension was related to the closure of the Mongol-Okhotsk Ocean and roll-back of the Paleo-Pacific Plate,while the late Early Cretaceous extension was mainly related to the roll-back of the Paleo-Pacific Plate.

Spatial-temporal Divergence Characteristics and Driving Factors of Green Economic Efficiency in the Yangtze River Economic Belt of China

The spatial and temporal variation of green economic efficiency and its driving factors are of great significance for the con-struction of high-efficiency and low-consumption green development model and sustainable socio-economic development.The research focused on the Yangtze River Economic Belt(YREB)and employed the miniumum distance to strong efficient frontier DEA(MinDs)model to measure the green economic efficiency of the municipalities in the region between 2008 and 2020.Then,the spatial autocorrel-ation model was used to analyze the evolution characteristics of its spatial pattern.Finally,Geodetector was applied to reveal the drivers and their interactions on green economic efficiency.It is found that:1)the overall green economic efficiency of the YREB from 2008 to 2020 shows a W-shaped fluctuating upward trend,green economic efficiency is greater in the downstream and smallest in the upstream;2)the spatial distribution of green economic efficiency shows clustering characteristics,with multi-core clustering based on‘city clusters-central cities'becoming more obvious over time;the High-High agglomeration type is mainly clustered in Jiangsu and Zheji-ang,while the Low-Low agglomeration type is clustered in the western Sichuan Plateau area and southwestern Yunnan;3)from input-output factors,whether it is the YREB as a whole or the upper,middle and lower reaches regions,the economic development level,labor input,and capital investment are the leading factors in the spatial-temporal evolution of green economic efficiency,with the com-prehensive influence of economic development level and pollution index being the most important interactive driving factor;4)from so-cio-economic factors,information technology drivers such as government intervention,transportation accessibility,information infra-structure,and Internet penetration are always high impact influencers and dominant interaction factors for green economic efficiency in the YREB and the three major regions in the upper,middle and lower reaches.Accordingly,the article puts forward relevant policy re-commendations in terms of formulating differentiated green transformation strategies,strengthening network leadership and informa-tion technology construction and coordinating multi-factor integrated development,which could provide useful reference for promoting synergistic green economic efficiency in the YREB.

Adaptive spatial-temporal graph attention network for traffic speed prediction

Considering the nonlinear structure and spatial-temporal correlation of traffic network,and the influence of potential correlation between nodes of traffic network on the spatial features,this paper proposes a traffic speed prediction model based on the combination of graph attention network with self-adaptive adjacency matrix(SAdpGAT)and bidirectional gated recurrent unit(BiGRU).First-ly,the model introduces graph attention network(GAT)to extract the spatial features of real road network and potential road network respectively in spatial dimension.Secondly,the spatial features are input into BiGRU to extract the time series features.Finally,the prediction results of the real road network and the potential road network are connected to generate the final prediction results of the model.The experimental results show that the prediction accuracy of the proposed model is im-proved obviously on METR-LA and PEMS-BAY datasets,which proves the advantages of the pro-posed spatial-temporal model in traffic speed prediction.

Spatial-temporal Variation Characteristics of Water Quality in the Lower Reaches of the Nenjiang River

As an important river in the western part of Jilin Province,the lower reach of the Nenjiang River is an important wetland water source conservation area in Jilin Province.Within the watershed,it governs the Momoge Wetland,the Xianghai Wetland,and the Danjiang Wetland in Jilin Province.The main problem in the lower reaches of the Nenjiang River is the uneven distribution of water resources in time and space,and the intensification of land salinization.Zhenlai County and Da an City in the Nenjiang River Basin have sufficient surface water resources,with surface water as the drinking water source.Baicheng City and Tongyu County have scarce surface water resources,and both use groundwater as their domestic water source.The main polluted section in the basin is the Xianghai Reservoir,and the annual water quality evaluation is Class V.However,the water quality of the Tao er River,the main stream of the Nenjiang River,is significantly better than that of the Xianghai Reservoir.In order to better study the water environmental pollution situation in the Nenjiang River basin,monitoring data from five sections of non seasonal rivers in the basin from 2012 to 2021 were selected for studying water quality.This in-depth exploration of the water pollution status and river water quality change trends in the Nenjiang River basin is of great significance for future rural development,agricultural pattern transformation,and the promotion of water ecological civilization construction.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Spatial-temporal difference between nitrate in groundwater and nitrogen in soil based on geostatistical analysis

The study of temporal and spatial variations of nitrate in groundwater under different soil nitrogen environments is helpful to the security of groundwater resources in agricultural areas.In this paper,based on 320 groups of soil and groundwater samples collected at the same time,geostatistical analysis and multiple regression analysis were comprehensively used to conduct the evaluation of nitrogen contents in both groundwater and soil.From May to August,as the nitrification of groundwater is dominant,the average concentration of nitrate nitrogen is 34.80 mg/L;The variation of soil ammonia nitrogen and nitrate nitrogen is moderate from May to July,and the variation coefficient decreased sharply and then increased in August.There is a high correlation between the nitrate nitrogen in groundwater and soil in July,and there is a high correlation between the nitrate nitrogen in groundwater and ammonium nitrogen in soil in August and nitrate nitrogen in soil in July.From May to August,the area of low groundwater nitrate nitrogen in 0-5 mg/L and 5-10 mg/L decreased from 10.97%to 0,and the proportion of high-value area(greater than 70 mg/L)increased from 21.19%to 27.29%.Nitrate nitrogen is the main factor affecting the quality of groundwater.The correlation analysis of nitrate nitrogen in groundwater,nitrate nitrogen in soil and ammonium nitrogen shows that they have a certain period of delay.The areas with high concentration of nitrate in groundwater are mainly concentrated in the western part of the study area,which has a high consistency with the high value areas of soil nitrate distribution from July to August,and a high difference with the spatial position of soil ammonia nitrogen distribution in August.

STGSA:A Novel Spatial-Temporal Graph Synchronous Aggregation Model for Traffic Prediction

The success of intelligent transportation systems relies heavily on accurate traffic prediction,in which how to model the underlying spatial-temporal information from traffic data has come under the spotlight.Most existing frameworks typically utilize separate modules for spatial and temporal correlations modeling.However,this stepwise pattern may limit the effectiveness and efficiency in spatial-temporal feature extraction and cause the overlook of important information in some steps.Furthermore,it is lacking sufficient guidance from prior information while modeling based on a given spatial adjacency graph(e.g.,deriving from the geodesic distance or approximate connectivity),and may not reflect the actual interaction between nodes.To overcome those limitations,our paper proposes a spatial-temporal graph synchronous aggregation(STGSA)model to extract the localized and long-term spatial-temporal dependencies simultaneously.Specifically,a tailored graph aggregation method in the vertex domain is designed to extract spatial and temporal features in one graph convolution process.In each STGSA block,we devise a directed temporal correlation graph to represent the localized and long-term dependencies between nodes,and the potential temporal dependence is further fine-tuned by an adaptive weighting operation.Meanwhile,we construct an elaborated spatial adjacency matrix to represent the road sensor graph by considering both physical distance and node similarity in a datadriven manner.Then,inspired by the multi-head attention mechanism which can jointly emphasize information from different r epresentation subspaces,we construct a multi-stream module based on the STGSA blocks to capture global information.It projects the embedding input repeatedly with multiple different channels.Finally,the predicted values are generated by stacking several multi-stream modules.Extensive experiments are constructed on six real-world datasets,and numerical results show that the proposed STGSA model significantly outperforms the benchmarks.

Spatial-temporal variations and driving factors of soil organic carbon in forest ecosystems of Northeast China

Forest soil carbon is a major carbon pool of terrestrial ecosystems,and accurate estimation of soil organic carbon(SOC)stocks in forest ecosystems is rather challenging.This study compared the prediction performance of three empirical model approaches namely,regression kriging(RK),multiple stepwise regression(MSR),random forest(RF),and boosted regression trees(BRT)to predict SOC stocks in Northeast China for 1990 and 2015.Furthermore,the spatial variation of SOC stocks and the main controlling environmental factors during the past 25 years were identified.A total of 82(in 1990)and 157(in 2015)topsoil(0–20 cm)samples with 12 environmental factors(soil property,climate,topography and biology)were selected for model construction.Randomly selected80%of the soil sample data were used to train the models and the other 20%data for model verification using mean absolute error,root mean square error,coefficient of determination and Lin's consistency correlation coefficient indices.We found BRT model as the best prediction model and it could explain 67%and 60%spatial variation of SOC stocks,in 1990,and 2015,respectively.Predicted maps of all models in both periods showed similar spatial distribution characteristics,with the lower SOC in northeast and higher SOC in southwest.Mean annual temperature and elevation were the key environmental factors influencing the spatial variation of SOC stock in both periods.SOC stocks were mainly stored under Cambosols,Gleyosols and Isohumosols,accounting for 95.6%(1990)and 95.9%(2015).Overall,SOC stocks increased by 471 Tg C during the past 25 years.Our study found that the BRT model employing common environmental factors was the most robust method for forest topsoil SOC stocks inventories.The spatial resolution of BRT model enabled us to pinpoint in which areas of Northeast China that new forest tree planting would be most effective for enhancing forest C stocks.Overall,our approach is likely to be useful in forestry management and ecological restoration at and beyond the regional scale.

A Hybrid Regularization-Based Multi-Frame Super-Resolution Using Bayesian Framework

The prime purpose for the image reconstruction of a multi-frame super-resolution is to reconstruct a higher-resolution image through incorporating the knowledge obtained from a series of relevant low-resolution images,which is useful in numerousfields.Nevertheless,super-resolution image reconstruction methods are usually damaged by undesirable restorative artifacts,which include blurring distortion,noises,and stair-casing effects.Consequently,it is always challenging to achieve balancing between image smoothness and preservation of the edges inside the image.In this research work,we seek to increase the effectiveness of multi-frame super-resolution image reconstruction by increasing the visual information and improving the automated machine perception,which improves human analysis and interpretation processes.Accordingly,we propose a new approach to the image reconstruction of multi-frame super-resolution,so that it is created through the use of the regularization framework.In the proposed approach,the bilateral edge preserving and bilateral total variation regularizations are employed to approximate a high-resolution image generated from a sequence of corresponding images with low-resolution to protect significant features of an image,including sharp image edges and texture details while preventing artifacts.The experimental results of the synthesized image demonstrate that the new proposed approach has improved efficacy both visually and numerically more than other approaches.

Regularization by Multiple Dual Frames for Compressed Sensing Magnetic Resonance Imaging With Convergence Analysis

Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual,which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering(BM3D)denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging(CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.

Distributed Optimal Formation Control for Unmanned Surface Vessels by a Regularized Game-Based Approach

Dear Editor,This letter explores optimal formation control for a network of unmanned surface vessels(USVs).By designing an individual objective function for each USV,the optimal formation problem is transformed into a noncooperative game.Under this game theoretic framework,the optimal formation is achieved by seeking the Nash equilibrium of the regularized game.A modular structure consisting of a distributed Nash equilibrium seeker and a regulator is proposed.

Dense Spatial-Temporal Graph Convolutional Network Based on Lightweight OpenPose for Detecting Falls

Fall behavior is closely related to high mortality in the elderly,so fall detection becomes an important and urgent research area.However,the existing fall detection methods are difficult to be applied in daily life due to a large amount of calculation and poor detection accuracy.To solve the above problems,this paper proposes a dense spatial-temporal graph convolutional network based on lightweight OpenPose.Lightweight OpenPose uses MobileNet as a feature extraction network,and the prediction layer uses bottleneck-asymmetric structure,thus reducing the amount of the network.The bottleneck-asymmetrical structure compresses the number of input channels of feature maps by 1×1 convolution and replaces the 7×7 convolution structure with the asymmetric structure of 1×7 convolution,7×1 convolution,and 7×7 convolution in parallel.The spatial-temporal graph convolutional network divides the multi-layer convolution into dense blocks,and the convolutional layers in each dense block are connected,thus improving the feature transitivity,enhancing the network’s ability to extract features,thus improving the detection accuracy.Two representative datasets,Multiple Cameras Fall dataset(MCF),and Nanyang Technological University Red Green Blue+Depth Action Recognition dataset(NTU RGB+D),are selected for our experiments,among which NTU RGB+D has two evaluation benchmarks.The results show that the proposed model is superior to the current fall detection models.The accuracy of this network on the MCF dataset is 96.3%,and the accuracies on the two evaluation benchmarks of the NTU RGB+D dataset are 85.6%and 93.5%,respectively.