Research And Application Of Complex System Time Series Data Spatio-temporal Characteristic Modeling

Complex temporal data in complex systems often exhibit characteristics such as nonlinearity,strong coupling,and large time delays,which pose significant challenges for modeling and analysis.This paper focuses on the modeling and analysis of spatiotemporal characteristics in complex system temporal data,including temporal chaos analysis,multivariate coupling and long-range causal time-delay feature extraction,and multi-scale feature fusion.The main contributions and innovations of this study are as follows:(1)For the problem that machine learning or deep learning models do not take full advantage of the inherent domain characteristics of time series data,based on the inherent invariance and separability of the shape of high-dimensional chaotic attractors,a method for extracting temporal nonlinear dynamical features based on chaos analysis is proposed,which analyzes the attractor in both the temporal(trajectory evolution)and spatial(attractor shape)dimensions.Firstly,from the perspective of dynamic system analysis,the parameter calculation method for reconstructing the high-dimensional chaotic attractor of univariate temporal data is determined,and its high-dimensional phase space reconstruction is performed.Secondly,the representation methods for high-dimensional phase space embedding are studied,and a qualitative analysis of the high-dimensional chaotic attractor in both the temporal and spatial dimensions is conducted.Finally,a quantitative representation is designed for the attractor trajectory evolution features and morphological features with higher separability,serving as a robust chaotic feature representation for temporal data.Ultimately,the proposed method is applied to coal combustion flame videos for combustion stability analysis,achieving robust and accurate temporal classification.(2)In response to the limitations of existing models in adequately capturing variable coupling relationships and long-term memory,a long-range prediction method based on the small-world spatiotemporal graph convolutional network is proposed.This method transforms multivariate temporal data into graph data and utilizes spatiotemporal graph convolutional networks to handle their coupled time-delay characteristics.Firstly,for multivariate temporal data without a predefined topology structure,a graph construction method is developed that considers both information propagation efficiency and structural redundancy,creating a graph structure that represents the coupling relationships between variables.Secondly,a node attention layer guided by importance is designed to capture the temporal variations in spatial coupling relationships,combined with Chebyshev graph convolutional layers.A gate-controlled dilated causal convolution is used to expand the model’s receptive field and extract the nonlinear temporal relationships over long-term sequences,enhancing the model’s ability to retain historical data while reducing computational complexity and addressing the issue of decreased accuracy in long-range prediction.Finally,dynamic system analysis methods and information entropy are introduced to guide the selection of key hyperparameters for gate-controlled dilated causal convolution,enabling the training and optimization of the small-world spatiotemporal graph convolutional network.The proposed method is applied to four common data sets of complex systems to realize long-range multi-variable and multi-step prediction,which provides a way to solve the difficult modeling problem of multi-variable timing fitting with large time delay and strong coupling.(3)To address the long-range causal temporal characteristics of multivariate time series,an improved heuristic spatiotemporal graph attention network is proposed for dynamic modeling of multivariate temporal data.Firstly,the causal relationships between variables are transformed into a directed graph structure.A dynamic directed similarity calculation function is designed,considering the clustering effect caused by varying strengths of coupling relationships between variables.Based on this,a heuristic clustering algorithm is employed to generate a sparse and connected directed graph structure,which represents the causal relationships between variables in complex system operation.Secondly,a gate-controlled convolutional attention unit is introduced,leveraging the excellent extraction capability of Transformers for long-term dependencies.The model combines convolutional attention to enhance sensitivity to local context,addressing the challenges posed by causal time delays between variables.It integrates with multi-head graph attention layers to extract time-varying delays and coupling features due to system operational fluctuations.Lastly,a set of system-level operational state features based on complex network topological characteristics is proposed to improve the model’s sensitivity in recognizing changes in system operational states.Finally,the proposed method is applied to anomaly detection and compared with the baseline method in four common data sets of complex systems to verify the ability of the proposed method to fit the causal time-delay relationship.(4)To address the issue of inconsistent information granularity between domain knowledge and deep features,a feature dynamic fusion method based on the Transformer network framework is designed.This method adaptively explores the associated characteristics between handcrafted features and deep features,achieving dynamic fusion of highly complementary features with different granularities.Firstly,considering the varying contributions of different handcrafted and deep features to classification accuracy,a feature reduction module based on low-rank matrix decomposition is designed to achieve low-redundancy dimensionality reduction and enhancement of features.Secondly,to tackle the problem of inconsistent information granularity between handcrafted and deep features,a dynamic feature fusion module is designed based on cross-modal cross-correlation computation,enabling adaptive alignment of different granularities of information.Subsequently,aiming to improve the separability of fused features and reduce redundant information,methods for designing fusion model loss functions and training strategies based on the separability and sparsity of fused features are explored.This ultimately achieves adaptive complementary fusion of handcrafted and deep features.Lastly,addressing the problem of identifying the operating conditions in coalfired rotary kiln sintering,considering the characteristics of the rotary kiln process and on-site operations,domain knowledge features of coal combustion flame videos are extracted using the method of extracting temporal nonlinear dynamical features.Deep features of thermodynamic process data are extracted using a heuristic spatiotemporal graph attention network.The domain knowledge features and deep features are then multimodally fused using the Transformer network framework.A high-precision sintering condition recognition algorithm is developed,specifically for coal-fired rotary kilns,providing a viable solution for accurate condition detection in other complex systems based on temporal data analysis.