Non-stationary Characteristics Research Articles

Carbon emissions trading price forecasts by multi-perspective fusion

<p>The precise prediction of carbon emissions trading prices is the foundation for the stable and sustainable development of the carbon financial market. In recent years, influenced by a combination of factors such as the pandemic, trading regulations, and policies, carbon prices have exhibited strong random volatility and clear non-stationary characteristics. Traditional single-perspective prediction methods based on conventional statistical models are increasingly inadequate due to the homogenization of features and are struggling to adapt to China's regional carbon emissions trading market. Therefore, this paper proposes a multi-perspective fusion-based prediction method tailored to the Chinese market. It leverages carbon emissions trading information from key cities as relevant features to predict the price changes in individual cities. Inspired by the development of artificial intelligence, this paper implements various time series models based on deep neural networks. The effectiveness of the multi-perspective approach is validated through multiple metrics. It provides scientific decision-making tools for domestic carbon emissions trading investors, making a significant contribution to strengthening carbon market risk management and promoting the establishment and rational development of a unified carbon market in China.</p>

A Stock Index Futures Price Prediction Approach Based on the MULTI-GARCH-LSTM Mixed Model

As a type of financial derivative, the price fluctuation of futures is influenced by a multitude of factors, including macroeconomic conditions, policy changes, and market sentiment. The interaction of these factors makes the future trend become complex and difficult to predict. However, for investors, the ability to accurately predict the future trend of stock index futures price is directly related to the correctness of investment decisions and investment returns. Therefore, predicting the stock index futures market remains a leading and critical issue in the field of finance. To improve the accuracy of predicting stock index futures price, this paper introduces an innovative forecasting method by combining the strengths of Long Short-Term Memory (LSTM) networks and various Generalized Autoregressive Conditional Heteroskedasticity (GARCH)-family models namely, MULTI-GARCH-LSTM. This integrated approach is specifically designed to tackle the challenges posed by the nonstationary and nonlinear characteristics of stock index futures price series. This synergy not only enhances the model’s ability to capture a wide range of market behaviors but also significantly improves the precision of future price predictions, catering to the intricate nature of financial time series data. Initially, we extract insights into the volatility characteristics, such as the aggregation of volatility in futures closing prices, by formulating a model from the GARCH family. Subsequently, the LSTM model decodes the complex nonlinear relationships inherent in the futures price series and incorporates assimilated volatility characteristics to predict future prices. The efficacy of this model is validated by applying it to an authentic dataset of gold futures. The empirical findings demonstrate that the performance of our proposed MULTI-GARCH-LSTM hybrid model consistently surpasses that of the individual models, thereby confirming the model’s effectiveness and superior predictive capability.

EDA-Graph: Graph Signal Processing of Electrodermal Activity for Emotional States Detection.

The continuous detection of emotional states has many applications in mental health, marketing, human-computer interaction, and assistive robotics. Electrodermal activity (EDA), a signal modulated by sympathetic nervous system activity, provides continuous insight into emotional states. However, EDA possesses intricate nonstationary and nonlinear characteristics, making the extraction of emotion-relevant information challenging. We propose a novel graph signal processing (GSP) approach to model EDA signals as graphical networks, termed EDA-graph. The GSP leverages graph theory concepts to capture complex relationships in time-series data. To test the usefulness of EDA-graphs to detect emotions, we processed EDA recordings from the CASE emotion dataset using GSP by quantizing and linking values based on the Euclidean distance between the nearest neighbors. From these EDA-graphs, we computed the features of graph analysis, including total load centrality (TLC), total harmonic centrality (THC), number of cliques (GNC), diameter, and graph radius, and compared those features with features obtained using traditional EDA processing techniques. EDA-graph features encompassing TLC, THC, GNC, diameter, and radius demonstrated significant differences (p<0.05) between five emotional states (Neutral, Amused, Bored, Relaxed, and Scared). Using machine learning models for classifying emotional states evaluated using leave-one-subject-out cross-validation, we achieved a five-class F1 score of up to 0.68.

Multi-step forecasting of dissolved oxygen in River Ganga based on CEEMDAN-AdaBoost-BiLSTM-LSTM model

Accurate prediction of Dissolved Oxygen (DO) is an integral part of water resource management. This study proposes a novel approach combining Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) with AdaBoost and deep learning for multi-step forecasting of DO. CEEMDAN generates Intrinsic Mode Functions (IMFs) with different frequencies, capturing non-linear and non-stationary characteristics of the data. The high-frequency and medium-frequency IMFs, characterized by complex patterns and frequent changes over time, are predicted using Adaboost with Bidirectional Long Short-Term Memory (BiLSTM) as the base estimator. The low-frequency IMFs, characterized by relatively simple patterns, are predicted using standalone Long Short-Term Memory (LSTM). The proposed CEEMDAN-AdaBoost-BiLSTM-LSTM model is tested on data from ten stations of river Ganga. We compare the results with six models without decomposition and four models utilizing decomposition. Experimental results show that using a tailored prediction technique based on each IMF’s distinctive features leads to more accurate forecasts. CEEMDAN-AdaBoost-BiLSTM-LSTM outperforms CEEMDAN-BiLSTM with an average improvement of 25.458% for RMSE and 37.390% for MAE. Compared with CEEMDAN-AdaBoost-BiLSTM, an average improvement of 20.779% for RMSE and 28.921% for MAE is observed. Diebold-Mariano test and t-test suggest a statistically significant difference in performance between the proposed and compared models.

A data-driven soft sensor model for coal-fired boiler SO2 concentration prediction with non-stationary characteristic

Environmental issues have received significant global attention, and achieving ultra-low emission has become a crucial goal for thermal power plant. Pollutant prediction is essential to achieving ultra-low emission control. Due to the frequent adjustment of operating conditions, the coal-fired power generation process is a typical non-stationary process with complex changes along the time direction. A single model cannot effectively portray the complex non-stationary characteristics and model mismatch may occur in the prediction, which brings new challenges for modeling coal-fired SO2 emission. Therefore, the condition-driven category boosting (CatBoost) soft sensor model is proposed for real-time prediction of SO2 concentration. First, the thermal process time series is rearranged into different data slices. These data slices vary along the direction of the condition indicator, which can characterize the process characteristics on different slices. Second, the load-based sequential condition division (LSCD) algorithm is designed to realize the division of boiler operation process. The characteristics of process are effectively captured by variational auto-encoder (VAE), and the data slices with similar process characteristics are merged into the same mode. Non-stationary process along the time direction is reorganized into different condition modes along the load direction. Finally, the high-resolution local CatBoost models under different modes are constructed to achieve fine-grained prediction of SO2 concentration. The effectiveness of the proposed condition-driven model is verified by an industrial example of 1000 MW coal-fired boiler. The prediction results show that the proposed model can effectively divide the operation conditions and achieve accurate prediction of SO2 concentration. In the typical models in SO2 predicting, the proposed model has better performance with a determination coefficient of 0.92.

Interpretable and explainable hybrid model for daily streamflow prediction based on multi-factor drivers.

Streamflow time series data typically exhibit nonlinear and nonstationary characteristics that complicate precise estimation. Recently, multifactorial machine learning (ML) models have been developed to enhance the performance of streamflow predictions. However, the lack of interpretability within these ML models raises concerns about their inner workings and reliability. This paper introduces an innovative hybrid architecture, the TCN-LSTM-Multihead-Attention model, which combines two layers of temporal convolutional networks (TCN) followed by one layer of long short-term memory (LSTM) units, integrated with a Multihead-Attention mechanism for predicting streamflow with streamflow causation-driven prediction samples (RCDP), employing local and global interpretability studies through Shapley values and partial dependency analysis. The find_peaks method was used to identify peak flow events in the test dataset, validating the model's generality and uncovering the physical causative patterns of streamflow. The results show that (1) compared to the LSTM model with the same hyperparameter settings, the proposed TCN-LSTM-Multihead-Attention hybrid model increased the R2 by 52.9%, 2.5%, 43.1%, and 10.7% respectively at four stations in the test set predictions using RCDP samples. Moreover, comparing the prediction results of the hybrid model under different samples in Hengshan station, the R2 for RCDP increased by 5.06% and 1.22% compared to streamflow autoregressive prediction samples (RAP) and meteorological-soil volumetric water content coupled autoregressive prediction samples (MCSAP) respectively. (2) Historical streamflow data from the preceding 3days predominantly influences predictions due to strong autocorrelation, with flow quantity (Q) typically emerging as the most significant feature alongside precipitation (P), surface soil moisture (SSM), and adjacent station flow data. (3) During periods of low and normal flow, historical data remains the most crucial factor; however, during flood periods, the roles of upstream inflow and precipitation become significantly more pronounced. This model facilitates the identification and quantification of various hydrodynamic impacts on flow predictions, including upstream flood propagation, precipitation, and soil moisture conditions. It also elucidates the model's nonlinear relationships and threshold responses, thereby enhancing the interpretability and reliability of streamflow predictions.

Two-layer elastic models for single-yeast compressibility with flat microlevers.

Unicellular organisms such as yeast can survive in very different environments, thanks to a polysaccharide wall that reinforces their extracellular membrane. This wall is not a static structure, as it is expected to be dynamically remodeled according to growth stage, division cycle, environmental osmotic pressure and ageing. It is therefore of great interest to study the mechanics of these organisms, but they are more difficult to study than other mammalian cells, in particular because of their small size (radius of a few microns) and their lack of an adhesion machinery. Using flat cantilevers, we perform compression experiments on single yeast cells (S. cerevisiae) on poly-L-lysine-coated grooved glass plates, in the limit of small deformation using an atomic force microscope (AFM). Thanks to a careful decomposition of force-displacement curves, we extract local scaling exponents that highlight the non-stationary characteristic of the yeast behavior upon compression. Our multi-scale nonlinear analysis of the AFM force-displacement curves provides evidence for non-stationary scaling laws. We propose to model these phenomena based on a two-component elastic system, where each layer follows a different scaling law..

Amplitude-Time Dual-View Fused EEG Temporal Feature Learning for Automatic Sleep Staging.

Electroencephalogram (EEG) plays an important role in studying brain function and human cognitive performance, and the recognition of EEG signals is vital to develop an automatic sleep staging system. However, due to the complex nonstationary characteristics and the individual difference between subjects, how to obtain the effective signal features of the EEG for practical application is still a challenging task. In this article, we investigate the EEG feature learning problem and propose a novel temporal feature learning method based on amplitude-time dual-view fusion for automatic sleep staging. First, we explore the feature extraction ability of convolutional neural networks for the EEG signal from the perspective of interpretability and construct two new representation signals for the raw EEG from the views of amplitude and time. Then, we extract the amplitude-time signal features that reflect the transformation between different sleep stages from the obtained representation signals by using conventional 1-D CNNs. Furthermore, a hybrid dilation convolution module is used to learn the long-term temporal dependency features of EEG signals, which can overcome the shortcoming that the small-scale convolution kernel can only learn the local signal variation information. Finally, we conduct attention-based feature fusion for the learned dual-view signal features to further improve sleep staging performance. To evaluate the performance of the proposed method, we test 30-s-epoch EEG signal samples for healthy subjects and subjects with mild sleep disorders. The experimental results from the most commonly used datasets show that the proposed method has better sleep staging performance and has the potential for the development and application of an EEG-based automatic sleep staging system.

Magnetic Field Mutation Mechanism and Its Non-Stationary and Stationary State Analysis in Power and "Ring" Applications

The phenomenon of magnetic field mutation, a complex yet pivotal aspect in various scientific and engineering domains, has garnered significant attention due to its profound implications on system behavior and performance. Magnetic fields, inherently dynamic in nature, exhibit mutations characterized by temporal variations in strength, direction, and spatial distribution. These mutations can stem from diverse sources, including external environmental factors, system dynamics, and material properties.This paper presents a comprehensive investigation into the magnetic field mutation mechanism and its implications for power and "ring" applications. The study encompasses theoretical analysis, simulation studies, and experimental validation to elucidate the dynamic behavior of magnetic fields in various contexts. The findings reveal insights into the temporal evolution and state analysis of magnetic fields, highlighting both stationary and non-stationary characteristics. Through analysis tables, we demonstrate the varying magnetic field strengths observed at different nodes within a ring application over consecutive time intervals. The implications of these findings for the stability and performance of magnetic field systems, particularly in power applications. The study underscores the importance of considering non-stationary factors in magnetic field analysis, emphasizing the need for adaptive modeling techniques and real-time monitoring strategies. The insights gained from this research contribute to a deeper understanding of magnetic field dynamics and offer valuable implications for the design, optimization, and operation of magnetic field-based systems in diverse applications.

Multivariate USV Motion Prediction Method Based on a Temporal Attention Weighted TCN-Bi-LSTM Model

Unmanned surface vehicle (USV)’s motion is represented by time-series data that exhibit highly nonlinear and non-stationary features, significantly influenced by environmental factors, such as wind speed and waves, when sailing on the sea. The accurate prediction of USV motion, particularly crucial parameters, such as the roll angle and pitch angle, is imperative for ensuring safe navigation. However, traditional and single prediction models often struggle with low accuracy and fail to capture the intricate spatial–temporal dependencies among multiple input variables. To address these limitations, this paper proposes a prediction approach integrating temporal convolutional network (TCN) and bi-directional long short-term memory network (Bi-LSTM) models, augmented with a temporal pattern attention (TPA) mechanism, termed the TCN-Bi-LSTM-TPA (TBT) USV motion predictor. This hybrid model effectively combines the strengths of TCN and Bi-LSTM architectures to extract long-term temporal features and bi-directional dependencies. The introduction of the TPA mechanism enhances the model’s capability to extract spatial information, crucial for understanding the intricate interplay of various motion data. By integrating the features extracted by TCN with the output of the attention mechanism, the model incorporates additional contextual information, thereby improving prediction accuracy. To evaluate the performance of the proposed model, we conducted experiments using real USV motion data and calculated four evaluation metrics: mean square error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and R-squared (R2). The results demonstrate the superior accuracy of the TCN-Bi-LSTM-TPA hybrid model in predicting USV roll angle and pitch angle, validating its effectiveness in addressing the challenges of multivariate USV motion prediction.

Dynamic responses of the floatover system with nonstationary mating processes: An experimental study

Floatover method has been widely applied in the installation of both fixed and floating platforms, which has the advantages of high efficiency, economy, and large lifting capacity compared with other installation methods. Few studies could numerically and experimentally simulate the continuous load transfer process which shows significant nonstationary characteristics. This paper conducts experimental research on the nonstationary mating process of the floatover system. The ballasting system based on the control logic of feedback adjustment is developed to adjust the draft and inertia properties of the floatover vessel, and the validation tests are conducted to verify the feasibility and reliability of the system. The load buffer devices are designed carefully and the piecewise linear spring simulation method is applied to simulate the nonlinear stiffnesses of the elastic cushion. The stationary model for 0% and 100% load transfer stages and the nonstationary model for continuous load transfer process are established and tested in the model tests, and the dynamic responses are analyzed by using statistical and spectral methods respectively. Stationary model tests indicate that the spectral characteristics and distribution of LMU (Leg Mating Unit) dynamic loads in transverse symmetric positions are similar, and the statistical values are also relatively close under different wave heads. The nonstationary dynamic responses are segmented according to the physical process, time-frequency spectrum and piecewise statistics diagram to find the critical stage. The greatest dynamic load occurs in the intermediate stage of the mating process when the larger stiffness of the LMU acts and the steel-to-steel contact will also occur.

A combined framework for carbon emissions prediction integrating online search attention

As CO2 emissions continue to rise, the problem of global warming is becoming increasingly serious. It is important to provide a robust management decision-making basis for the reductions of carbon emissions worldwide by predicting carbon emissions accurately. However, affected by various factors, the prediction of carbon emissions is challenging due to its nonlinear and nonstationary characteristics. Thus, we propose a combination forecast model, named CEEMDAN-GWO-SVR, which incorporates multiple features to predict trends in China’s carbon emissions. First, the impact of online search attention and public health emergencies are considered in carbon emissions prediction. Since the impact of different variables on carbon emissions is lagged, the grey relational degree is used to identify the appropriate lag series. Second, irrelevant features are eliminated through RFECV. To address the issue of feature redundancy of online search attention, we propose a dimensionality reduction method based on keyword classification. Finally, to evaluate the features of the proposed framework, four evaluation indicators are tested in multiple machine learning models. The best-performed model (SVR) is optimized by CEEMDAN and GWO to enhance prediction accuracy. The empirical results indicate that the proposed framework maintains good performance in both multi-scenario and multi-step prediction.

Agricultural price prediction based on data mining and attention-based gated recurrent unit: a case study on China’s hog

Under the influence of the coronavirus disease and other factors, agricultural product prices show non-stationary and non-linear characteristics, making it increasingly difficult to forecast accurately. This paper proposes an innovative combinatorial model for Chinese hog price forecasting. First, the price is decomposed using the Seasonal and Trend decomposition using the Loess (STL) model. Next, the decomposed data are trained with the Long Short-term Memory (LSTM) and Seasonal Autoregressive Integrated Moving Average (SARIMA) models. Finally, the prepared data and the multivariate influence factors after Factor analysis are predicted using the gated recurrent neural network and attention mechanisms (AttGRU) to obtain the final prediction values. Compared with other models, the STL-FA-AttGRU model produced the lowest errors and achieved more accurate forecasts of hog prices. Therefore, the model proposed in this paper has the potential for other price forecasting, contributing to the development of precision and sustainable agriculture.

Structural seismic response reconstruction method based on multidomain feature-guided generative adversarial neural networks

Structural seismic response reconstruction is important to assess the safety of structures. This study presents a novel multidomain feature-guided generative adversarial neural network model (MWGAN-TF) for reconstructing the seismic responses of structures, which takes into account the joint non-stationarity of the seismic response in the time-frequency statistical domain. It innovatively incorporates time, frequency, and statistical-domain feature constraints into the multiscale generative adversarial neural network, which guides the model to learn the multidomain feature information of the seismic response at different time scales. A statistical indicator (CNCSI) was proposed to evaluate the performance of the model in capturing nonstationary characteristics. The effectiveness of the MWGAN-TF was verified using response data from numerical models of a three-story moment-resisting frame and reinforced concrete frame structures, as well as the field measurement data of an actual building. Thereafter, the effects of different domain feature-guided models on the reconstruction response accuracy are discussed. The results show that embedding multidomain feature constraints can provide a more reliable response reconstruction by improving the ability of the model to capture nonstationary characteristics. Thus, the deep learning paradigm based on multidomain feature guidance outperforms the classical neural network guided only by time-domain features.

Multi-temporal Scale Wind Power Forecasting Based on Lasso-CNN-LSTM-LightGBM

Due to the increasingly severe climate problems, wind energy has received widespread attention as the most abundant energy on Earth. However, due to the uncertainty of wind energy, a large amount of wind energy is wasted, so accurate wind power prediction can greatly improve the utilization of wind energy. To increase the forecast for wind energy accuracy across a range of time scales, this paper presents a multi-time scale wind power prediction by constructing an ICEEMDAN-CNN-LSTM-LightGBM model. Initially, feature selection is performed using Lasso regression to identify the most significant variables affecting the forecast for wind energy across distinct time intervals. Subsequently, the ICEEMDAN is utilized to break down the wind power data into various scales to capture its nonlinear and non-stationary characteristics. Following this, a deep learning model based on CNN and LSTM networks is developed, with the CNN responsible for extracting spatial features from the time series data, and the LSTM designed to capture the temporal relationships. Finally, the outputs of the deep learning model are fed into the LightGBM model to leverage its superior learning capabilities for the ultimate prediction of wind power. Simulation experiments demonstrate that the proposed ICEEMDAN-CNN-LSTM-LightGBM model achieves higher accuracy in multi-time scale wind power prediction, providing more reliable decision assistance with the management and operation of wind farms.

Bearing Fault Diagnosis Based on Parameter-Optimized Variational Mode Extraction and an Improved One-Dimensional Convolutional Neural Network

When faults occur in rolling bearings, vibration signals exhibit sensitivity to periodic impact components, susceptibility to complex background noise, and non-stationary and nonlinear characteristics. Consequently, using traditional signal processing methods to effectively identify bearing faults presents significant challenges. To facilitate the accurate fault diagnosis of bearings in noisy conditions, we propose an intelligent fault diagnosis method using the Archimedes optimization algorithm (AOA), coupled with a one-dimensional multi-scale residual convolutional neural network (1D-MRCNN), to optimize the variational mode extraction (VME) parameters. First, we introduce a weighted correlated kurtosis (WCK) indicator, formulated using the correlation coefficient and correlated kurtosis as the objective function, to optimize the VME’s center frequency ω and penalty factor α, enabling targeted signal extraction. Second, deep learning techniques are employed to construct the 1D-MRCNN. The neural network then processes the extracted signal for feature extraction and automated fault-type identification. Our simulation results show that the WCK objective function effectively isolates impact components under fault conditions, and our experimental validation confirms that the proposed method accurately identifies diverse fault types across multiple noise levels.

Rotating Machinery Fault Diagnosis under Time–Varying Speed Conditions Based on Adaptive Identification of Order Structure

Rotating machinery fault diagnosis is of key significance for ensuring safe and efficient operation of various industrial equipment. However, under nonstationary operating conditions, the fault–induced characteristic frequencies are often time–varying. Conventional Fourier spectrum analysis is not suitable for revealing time–varying details, and nonstationary fault feature extraction methods are still in desperate need. Order spectrum can reveal the rotational–speed–related time–varying frequency components as spectral peaks in order domain, thus facilitating fault feature extraction under time–varying speed conditions. However, the speed–unrelated frequency components are still nonstationary after angular–domain resampling, thus causing wide–band features and interferences in the order spectrum. To overcome such a drawback, this work proposes a rotating machinery fault diagnosis method based on adaptive separation of time–varying components and order feature extraction. Firstly, the rotational speed is estimated by the multi–order probabilistic approach (MOPA), thus eliminating the inconvenience of installing measurement equipment. Secondly, adaptive separation of the time–varying frequency component is achieved through time–varying filtering and surrogate test. It effectively eliminates interference from irrelevant components and noise. Finally, a high–resolution order spectrum is constructed based on the average amplitude envelope of each mono–component. It does not involve Fourier transform or angular–domain resampling, thus avoiding spectral leakage and resampling errors. By identifying the fault–related spectral peaks in the constructed order spectrum, accurate fault diagnosis can be achieved. The Rényi entropy values of the proposed order spectrum are significantly lower than those of the traditional order spectrum. This result verifies the effective energy concentration and high resolution of the proposed order spectrum. The results of both numerical simulation and lab experiments confirm the effectiveness of the proposed method in accurately presenting the time–varying frequency components for rotating machinery diagnosing faults.

Multi-scale reconstruction of rolling mill vibration signal based on fuzzy entropy clustering

The mill vibration signals collected during mill operation are often affected by complex working conditions and various disturbances, thus presenting strong non-stationary characteristics. After the vibration signal is processed by noise reduction, although the noise interference and modal aliasing phenomenon are solved, the extracted vibration signal of the rolling mill still has the problems of strong non-stationarity, high complexity, and great difficulty in analyzing, which largely affects the prediction model construction. To address the above problems, this study proposes a multi-scale signal reconstruction method based on Fuzzy Entropy and Gath-Geva fuzzy clustering algorithm, which effectively reduces the complexity of the original sequence, reduces the number of predictive modellings, and improves the signal predictability and prediction accuracy. The sequence reconstruction of such non-stationary vibration signals based on their internal characteristics has obvious advantages for the problem of mill vibration prediction and analysis.

Research on the spatiotemporal evolution and non-stationarity effect of urban carbon balance: Evidence from representative cities in China

Accelerating the attainment of carbon balance in Chinese cities has become pivotal in addressing global climate change and promoting green, low-carbon development. This study, encompassing 277 prefecture-level and above cities from 2007 to 2020, reveals a positive overall trend in China's urban carbon balance index. The evolution unfolds in two stages, demonstrating a distinct “tiered development” pattern across the eastern, central and western regions. Moreover, significant spatial agglomeration characteristics characterize China's carbon balance hot and cold spots throughout the study period, with their spatial agglomeration degree remaining stable. The standard deviation ellipse analysis confirms these hot and cold spots' alignment with China's economic development level and population distribution. The GTWR test results highlight the pronounced non-stationary characteristics of different driving factors in space and time, exhibiting variations in strength and direction among regions. Consequently, enhancing China's urban carbon balance requires tailored measures based on different areas' unique conditions and development characteristics, emphasizing a hierarchical and classified approach to leverage distinct driving factors and foster a green development system in China.

Early Fault Diagnosis of Bearings Based on Symplectic Geometry Mode Decomposition Guided by Optimal Weight Spectrum Index

When the rotating machinery fails, the signal generated by the faulty component often no longer maintains the original symmetry, which makes the vibration signal with nonlinear and non-stationary characteristics, and is easily affected by background noise and other equipment excitation sources. In the early stage of fault occurrence, the fault signal is weak and difficult to extract. Traditional fault diagnosis methods are not able to easily diagnose fault information. To address this issue, this paper proposes an early fault diagnosis method for symplectic geometry mode decomposition (SGMD) based on the optimal weight spectrum index (OWSI). Firstly, using normal and fault signals, the optimal weight spectrum is derived through convex optimization. Secondly, SGMD is used to decompose the fault signal, obtaining a series of symplectic geometric modal components (SGCs) and calculating the optimal weight index of each component signal. Finally, using the principle of maximizing the OWSI, sensitive components reflecting fault characteristics are selected, and the signal is reconstructed based on this index. Then, envelope analysis is performed on the sensitive components to extract early fault characteristics of rolling bearings. OWSI can effectively distinguish the interference components in fault signals using normal signals, while SGMD has the characteristic of unchanged phase space structure, which can effectively ensure the integrity of internal features in data. Using actual fault data of rolling bearings for verification, the results show that the proposed method can effectively extract sensitive components that reflect fault characteristics. Compared with existing methods such as Variational Mode Decomposition (VMD), Feature Mode Decomposition (FMD), and Spectral Kurtosis (SK), this method has better performance.