Low-frequency Components Research Articles

Characteristics of facial electromyography during cold exposure and feasibility of evaluating thermal comfort

A comfortable building environment plays a vital role in enhancing both the physical and mental well-being of its occupants. In recent years, the assessment of building thermal environments has gained significant attention. The assessment methodology is shifting from subjective evaluations to more physiological assessments. However, the exploration of facial muscles in this context has remained largely uncharted territory. The primary objective of this research was to investigate the characteristics of facial electromyography (fEMG) in a cold environment and examine its potential for assessing thermal comfort. The experiment was divided into two parts. The first part focused on understanding fEMG characteristics in the time domain, frequency domain, and phase during activities like speaking, expressing emotions, and exposure to cold conditions. The second part aimed to study the recovery process of fEMG after cold exposure, achieved by increasing clothing insulation and raising air temperature. The findings revealed significant distinctions in fEMG characteristics when subjects engaged in speaking (notably in the low-frequency component of the anguli oris muscle), expressing emotions (with a prominent low-frequency component in the zygomatic muscle), or experiencing cold conditions (highlighted by the high-frequency component of the masseter muscle). Interestingly, augmenting clothing insulation in the body region posed challenges in improving facial muscle electrical activity, while raising air temperature effectively alleviated facial muscle tension. This study represents the pioneering application of fEMG in indoor thermal comfort evaluation. It offers a physiological foundation for assessing thermal comfort based on facial skin temperature and facial expressions. Furthermore, the research contributes valuable data that can support the advancement of wearable devices and smart building systems.

Dynamic response of a pump-turbine runner during turbine's mode starting up

With an increase in head and rotational speed, pumped storage units, particularly the runner, experience higher pressure and centrifugal force. In this study, a combination of the 1D method of characteristics (MOC), 3D computational fluid dynamics (CFD) as well as computational structure dynamics (CSD) was employed to examine the dynamic response of a pump turbine runner during turbine's mode starting up. A detailed analysis of the transient characteristics during this process was conducted. Initially, the high-pressure zone concentrated on the pressure surface of the runner's inlet side. However, this zone gradually expanded over time and shifted to the suction surface. The time-frequency of pressure pulsation showed significant low-frequency and second harmonic frequency components. Different monitoring points exhibited different sensitivities to rotational speed and torque. It can be assumed that runner's blade stress is proportional to the square of the rotational speed. The sensitivity of blade stress related to runner speed and torque provides important results and analysis. P2 is the most sensitive to changes in rotational speed, while P1 is the most sensitive to changes in torque. These findings enhance our understanding of the dynamic behavior of the RPT runner and contribute to potential improvements in design and operation.

Research on the intelligent teaching mode of college piano classroom based on big data technology

Abstract In this paper, firstly, under the perspective of big data, the innovation research of piano intelligent teaching mode and the application strategy of intelligent piano teaching mode under big data thinking are explained, respectively. Secondly, in music recognition in a college piano classroom, the piano music signal needs to be sampled, quantized and pre-processed to avoid the frequency bias caused by the low-frequency components of the piano music signal. Then, based on the big data technology, the piano intelligent teaching note recognition system is constructed by using the improved time domain algorithm and the improved time-frequency domain combination algorithm, and the recognition of note time value in piano intelligent teaching and the piano intelligent teaching note recognition system are studied and analyzed. The results show that the improved time-frequency domain combination is more effective in responding to the time-value information of piano music signals in recognition simulation. The note recognition system studied in this project has seen a recognition rate increase of almost 5% in system performance. This paper studies the application of intelligent piano teaching in professional learning in universities, which can lead to the development and popularity of intelligent teaching methods in piano classrooms.

Short-term power load forecasting based on the CEEMDAN-TCN-ESN model.

Ensuring an adequate electric power supply while minimizing redundant generation is the main objective of power load forecasting, as this is essential for the power system to operate efficiently. Therefore, accurate power load forecasting is of great significance to save social resources and promote economic development. In the current study, a hybrid CEEMDAN-TCN-ESN forecasting model based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and higher-frequency and lower-frequency component reconstruction is proposed for short-term load forecasting research. In this paper, we select the historical national electricity load data of Panama as the research subject and make hourly forecasts of its electricity load data. The results show that the RMSE and MAE predicted by the CEEMDAN-TCN-ESN model on this dataset are 15.081 and 10.944, respectively, and R2 is 0.994. Compared to the second-best model (CEEMDAN-TCN), the RMSE is reduced by 9.52%, and the MAE is reduced by 17.39%. The hybrid model proposed in this paper effectively extracts the complex features of short-term power load data and successfully merges subseries according to certain similar features. It learns the complex and varying features of higher-frequency series and the obvious regularity of the lower-frequency-trend series well, which could be applicable to real-world short-term power load forecasting work.

Single-Molecule Methane Sensing Using Palladium-Functionalized nIR Fluorescent Single-Walled Carbon Nanotubes.

There has been considerable interest in detecting atmospheric and process-associated methane (CH4) at low concentrations due to its potency as a greenhouse gas. Nanosensor technology, particularly fluorescent single-walled carbon nanotube (SWCNT) arrays, is promising for such applications because of their chemical sensitivities at single-molecule detection limits. However, the methodologies for connecting the stochastic molecular fluctuations from gas impingement on such sensors require further development. In this work, we synthesize Pd-conjugated ss(GT)15-DNA-wrapped SWCNTas near-infrared (nIR) fluorescent, single-molecule sensors of CH4. The complexes are characterized using X-ray photoelectron spectroscopy (XPS) and spectrophotometry, demonstrating spectral changes between the Pd2+ and Pd0 oxidation states. The nIR fluctuations generated upon exposure from 8 to 26 ppb of CH4 were separated into high- and low-frequency components. Aggregating the low-frequency components for an array of sensors showed the most consistent levels of detection with a limit of 0.7 ppb. These results advance the hardware and computational methods necessary to apply this approach to the challenge of environmental methane sensing.

Fault Section Recognition within Duration of Power Swing Using Teager–Kaiser Energy Operator and Sequence Components

Relaying operation is not reliable during power swing due to the presence of additional lower-frequency components of electrical signals. Relay operation is prohibited during Power swing blocking (PSB) operation to restrict the malfunctioning of the distance relay. During such periods, fault section identification (FSI) schemes need to work for safeguarding the electrical power system from disturbances. Fault detection and fault direction estimation are part of FSI. This article proposes a protection algorithm within the period of power swing where a Teager–Kaiser energy operator (TKEO) of superimposed negative sequence admittance (SNSA) is utilized for fault detection and an integrated scheme for determining their direction. In this integrated direction estimation approach, the direction of fault is recognized by calculating the phases of negative sequence admittance (NSA) and positive sequence admittance (PSA). The proposed technique is verified and tested on a WSCC 9-bus, 400 kV, 50 Hz system for different balanced and unbalanced fault cases with different fault conditions. Even, in some scenarios like CT saturation and single pole tripping (SPT), the proposed approach performs accurately. The results are simulated using EMTDC/PSCAD software.

Parametric study of the effects of clump weights on the performance of a novel wind-wave hybrid system

This paper presents a novel catenary mooring system incorporating multiple clump weights (CWs) designed for a SPIC-Wavestar wind-wave energy hybrid system. To enhance the performance of the hybrid system, a parametric analysis was performed on mooring CWs. The motions of the SPIC platform, along with the power absorbed by the Wavestar wave energy converters (WECs), specifically in response to the operational regular wave, were simulated. The hydrodynamic analysis program AQWA was used for the analysis. The results indicated that the surge and pitch motions of the platform comprised low-frequency and wave-frequency components, whereas the heave motion only comprised a wave-frequency component. However, the low-frequency responses of the surge and pitch motions were substantially smaller than their wave-frequency counterparts. In addition, the properties of the CW exerted notable influence on both platform motion and the overall power absorption by the WEC array. The variation trends with respect to the CW weight, location, and number were complex. Overall, the results of this study provide valuable insights into the mooring design of ocean energy hybrid systems.

Coping und vegetative Reaktivität bei Aderhautmelanomen

Summary Background We aimed to assess coping and vegetative reactivity in uveal melanoma (UM) patients compared to controls with benign nevi of the uvea. Material and methods In total, 20 patients with recently diagnosed uveal melanoma were recruited and matched for age and gender to 20 controls with benign nevi of the uvea. Heart rate variability (HRV) and blood pressure variability (BPV) were monitored throughout an initial period of rest (POR1), a mental stress test (DT), and another period of rest (POR2). Coping strategies were assessed for both groups using a stress-coping questionnaire. Results The LF/HF ratio (low-/high-frequency component of total spectral power) of HRV showed decreasing values in the UM group and increasing values in controls throughout the measurement sequence (p = 0.025). Diastolic BPV revealed declining values of the low-frequency component in normalized units (LFnu) between POR1 and DT in UM patients compared to rising values between POR1 and DT in controls (p = 0.006). There were no intergroup differences in coping strategies (p > 0.05). Conclusions Coping mechanisms are unaltered in patients with uveal melanoma compared to controls, but vegetative reactivity may show a different pattern once patients are diagnosed.

Coarse-to-fine interaction on perceived depth in compound grating.

To encode binocular disparity, the visual system uses a pair of left eye and right eye bandpass filters with either a position or a phase offset between them. Such pairs are considered to exit at multiple scales to encode a wide range of disparity. However, local disparity measurements by bandpass mechanisms can be ambiguous, particularly when the actual disparity is larger than a half-cycle of the preferred spatial frequency of the filter, which often occurs in fine scales. In this study, we investigated whether the visual system uses a coarse-to-fine interaction to resolve this ambiguity at finer scales for depth estimation from disparity. The stimuli were stereo grating patches composed of a target and comparison patterns. The target patterns contained spatial frequencies of 1 and 4 cycles per degree (cpd). The phase disparity of the low-frequency component was 0° (at the horopter), -90° (uncrossed), or 90° (crossed), and that of the high-frequency components was changed independent of the low-frequency disparity, in the range between -90° (uncrossed) and 90° (crossed). The observers' task was to indicate whether the target appeared closer to the comparison pattern, which always shared the disparity with the low-frequency component of the target. Regardless of whether the comparison pattern was a 1-cpd + 4-cpd compound or a 1-cpd simple grating, the perceived depth order of the target and the comparison varied in accordance with the phase disparity of the high-frequency component of the target. This effect occurred not only when the low-frequency component was at the horopter, but also when it contained a large disparity corresponding to one cycle of the high-frequency component (±90°). Our findings suggest a coarse-to-fine interaction in multiscale disparity processing, in which the depth interpretation of the high-frequency changes based on the disparity of the low-frequency component.

Extended-Range Forecast of Regional Persistent Extreme Cold Events Based on Deep Learning

Regional persistent extreme cold events are meteorological disasters that cause serious harm to people’s lives and production; however, they are very difficult to predict. Low-temperature weather systems and their effects have a significant low-frequency oscillation period (10–20 d and 30–60 d). This paper uses deep learning to analyze the extended-range time scale and predict regional persistent extreme cold events. The dominant low-frequency oscillation components of cold events are obtained via wavelet transform and Butterworth filtering. The low-frequency oscillation component is decomposed via empirical orthogonal function decomposition to extract the main spatial mode and time coefficient. A convolutional neural network is used to establish the correlation between large-scale circulations and the time coefficient of the low-frequency oscillation component of the lowest temperature. The proposed deep learning model exhibits good prediction accuracy for regional persistent extreme cold events with low-frequency oscillations.

Generation and periodic evolution of third harmonics carrying transverse orbital angular momentum in air-plasma filaments.

Spatiotemporal optical vortex (STOV) pulses, possessing inherent transverse orbital angular momentum (OAM) and exhibiting phase singularity and intensity null in the spatiotemporal (ST) domain, have received increasing attention in recent years. Here, we investigate theoretically the third harmonic generation and evolution properties of STOV pulses via the interaction of 800-nm-STOV pulses with air-plasma filaments. We show that beautiful third harmonic STOV pulses are generated at a propagation distance of several millimeters. During further propagation, the ST intensity profiles of the third harmonics undergo variations in a periodic way, leading to the distortion and subsequent restoration to the initial ring pattern. The periodic evolution is a result of the interference effects between the third harmonics generated with different phases. Consequently, the evolution period is roughly twice the dephasing length of the third harmonics. Meanwhile, additional singularities emerge in the intensity patterns due to destructive interference occurring at specific dephasing lengths for the specific frequency components. The high-frequency components experience destructive interference earlier than the low-frequency components during each evolution period because the dephasing length decreases with frequency. This results in the sequentially appearance of the additional singularities from top to bottom in the ST intensity patterns. The proposed scheme demonstrates a way for higher-order STOV generation and manipulation in air-plasma filaments, which can be of interest for experiments related to vortex light science.

Experimental study on load characteristics of vehicle during high-speed water entry

During the process of high-speed water entry, the vehicle will bear large loads. Obtaining and analysing the time-frequency characteristics of loads is of great engineering significance for the protection of shell and equipment. The high-speed camera is used to capture the evolution of cavity and the accelerometer is used to collect the acceleration of model during water entry. The time-frequency characteristics of acceleration are obtained based on the short-time Fourier transform and discrete wavelet transform. The results indicate that the cavity exhibits an asymmetric shape and shrinks near free surface during the oblique high-speed water entry. When the cavity undergoes closure and collapse, the collapsing order of the upper and lower parts is opposite. Through the short time Fourier transform, it was found that the loads contain components of different frequency at different periods. When the model collides with free surface, the frequency contained in acceleration are more complex, reflecting the complexity of mechanical environment. The discrete wavelet transform is used to extract the components with more time-resolution and obtain the relative energy of each component. It is found that the relative energy of low-frequency components increases with the increase of water entry speed.

Investigation of High-Speed Dynamic Transmission Error Testing Using Gear Strain

The difficulties of testing the dynamic transmission errors of gears in complex environments, such as high-speed operations or situations with oil contamination, and the limited variety of available testing methods have been recognized as issues which this study endeavors to tackle. In this study, a testing method for evaluating high-speed dynamic transmission errors of spur gears through the use of strain sensors is proposed. To reduce the interference of environmental noise on testing signals, physical measures, such as the use of copper foil to shield signal wires and the grounding of data acquisition equipment, were implemented during the testing process. Utilizing wavelet decomposition to distinguish between the high- and low-frequency components of the testing signals, the transmission error of gears during high-speed operation was calculated. After confirming the feasibility of the stress–strain stiffness approach in gear transmission error testing using the magnetic grid method, tests on modified and non-modified gears at various speeds and loads were carried out. The two types of test data were processed and evaluated to determine the effect of speed and load on gear dynamic transmission error. It was possible to conduct research on the testing technique of gear dynamic transmission errors utilizing strain sensors, which provides a new, fast, simple, and practical testing strategy for gear transmission error testing.

Nonlinear dynamics and acoustic radiation of coherent structures consisting of multiple ring–helical modes in the near-nozzle region of a subsonic turbulent circular jet

This paper investigates the nonlinear evolution and acoustic radiation of coherent structures (CS) in the near-nozzle region of a subsonic turbulent circular jet. A CS is taken to be a wavepacket consisting of multiple ring/helical modes, which are considered to be inviscid instability waves supported by the mean-flow profile. As the three-dimensionality of helical modes is weak in the near-nozzle region, the ring and helical modes with the same frequency have nearly the same growth rates and critical levels. They coexist and interact with each other in their common critical layer at high Reynolds numbers. The self and mutual quadratic interactions generate a mean-flow distortion and streaks, which act back on the fundamental components through the cubic interaction. The amplitude of the CS is governed by an integro-partial-differential equation, a significant feature of which is that differentiations with respect to the azimuthal coordinate appear in the history-dependent nonlinear terms. The non-parallelism of the mean flow as well as the impact of fine-scale turbulence on CS are taken into account and found to affect the nonlinear terms. By solving the amplitude equation, the development of the constituting modes, streamwise vortices and streaks are described. For CS consisting of frequency sideband, low-frequency components are excited nonlinearly and amplify to reach a considerable level. By analysing the large-distance asymptote of the perturbation, the low-frequency acoustic waves are found to be emitted by the temporally–spatially varying mean-flow distortion and streaks generated by the nonlinear interactions of the CS, and are thereby determined on the basis of first principles. Interestingly, the energetic part of the streaky structure that contributes to the nonlinear dynamics does not radiate directly, and instead the Reynolds stresses driving the subdominant radiating components represent the true physical sources.

Development of control strategy for community battery energy storage system in grid-connected microgrid of high photovoltaic penetration level

The focus of this paper is to develop a control strategy for a community battery bank in a grid-connected microgrid in which a significant level of photovoltaic generation is embedded. In order to minimize the capacity of the community battery, the power transfer capacity of the interconnection link between the microgrid and the external grid system is utilized to safe maximum levels. Through Empirical Mode Decomposition analysis of the net power flows of the microgrid, the daily and seasonal modes of the net power oscillations are identified as the two dominant low-frequency components. Whence a rule-based operational strategy is developed to control the power flows of the community battery via a novel dynamic referencing scheme for the state-of-charge of the battery bank. The battery control scheme counteracts the dominant daily and seasonal modes of oscillations of the net power. The numerical calculations performed for a case study shows that the proposed scheme leads to an approximately 16% decrease in the required battery capacity for particular growth rate of solid-electrolyte interphase film in the battery bank. The scheme does not require the forecasting of the net power, and thus, it has an increased degree of robustness when the community battery undertakes the power buffering task.

Study on dynamic characteristics of the gear-dual-rotor system with multi-position rubbing

To reveal the mechanism of gear meshing induced rubbing and investigate the nonlinear dynamic response characteristics of a gear-dual-rotor system with multi-position rubbing, a new finite element model (FEM) of the gear-dual-rotor system considering the gear meshing excitation is established based on the in-house beam element code. Then, the fixed interface component mode synthesis method (FICMSM) is used to establish the reduced gear-dual-rotor dynamic model. A rotor-rotor rubbing model between the inner and outer rotors (IORs) and a rotor-stator rubbing model are built through vectors considering whirling velocities. In addition to the general concern about the low-frequency components around rotating frequencies and transversal responses with rubbing, more attention is given to the high-frequency components around the gear meshing frequency and the torsional responses. Finally, some interesting phenomena are found as follows: gear meshing is a new cause of partial rubbing. Some combined frequencies between the rotating frequencies of IORs and modulation frequencies between the meshing frequency and rotating frequencies are found in the transversal and torsional responses.

Spectral representation of EEG data using learned graphs with application to motor imagery decoding

Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organization of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines. We present a novel method for transforming EEG data into a spectral representation. First, we learn subject-specific graphs from each subject’s EEG data. Second, by eigendecomposition of the normalized Laplacian matrix of each subject’s graph, an orthonormal basis is obtained using which any given EEG map of the subject can be decomposed, providing a spectral representation of the data. We show that energy of EEG maps is strongly associated with low frequency components of the learned basis, reflecting the smooth topography of EEG maps. As a proof-of-concept for this alternative view of EEG data, we consider the task of decoding two-class motor imagery (MI) data. To this aim, the spectral representations are first mapped into a discriminative subspace for differentiating two-class data using a projection matrix obtained by the Fukunaga–Koontz transform (FKT). An SVM classifier is then trained and tested on the resulting features to differentiate MI classes. The method is benchmarked against features extracted from a subject-specific functional connectivity matrix as well as four alternative MI-decoding methods on Dataset IVa of BCI Competition III. Experimental results show the superiority of the proposed method over alternative approaches in differentiating MI classes, reflecting the added benefit of (i) decomposing EEG data using data-driven, subject-specific harmonic bases, and (ii) accounting for class-specific temporal variations in spectral profiles.

ICEEMDAN-based Combined Wind Power Forecasting

Background:: With the depletion of fossil energy and the increasingly serious environmental pollution, the task of developing renewable energy is imminent. As a green and pollutionfree renewable energy, the penetration of wind energy in the power grid continues to rise. Objective:: In order to reduce the volatility and randomness of wind power series and increase the accuracy of wind power prediction, a wind power combination model based on the ICEEMDAN (improved adaptive noise full set empirical mode decomposition) method is proposed. objective: In order to reduce the volatility and randomness of wind power series and increase the accuracy of wind power prediction, a wind power combination model based on ICEEMDAN (improved adaptive noise full set empirical mode decomposition) method is proposed Methodology:: First, the complex original wind power data have been decomposed into several relatively simple subsequences using the ICEEMDAN method. Aiming at the different lengths of coarse grain time series and data loss in traditional multi-scale entropy, a fine composite multiscale dispersion entropy is proposed to calculate the entropy value of each decomposition component, and divide the high- and low-frequency modal components to predict the modal components of different frequencies; secondly, differential moving autoregressive model (ARIMA) and shortterm memory neural network (LSTM) are used to establish the prediction models of high- and low-frequency components, respectively. Results:: Finally, the prediction results of each component have been superimposed and reconstructed to obtain the final prediction results. The effectiveness of the combined model is verified by the actual operation data of a European wind farm. result: The effectiveness of the combined model is verified by the actual operation data of a European wind farm. The results show that compared with the other four single and combined forecasting models, the combined model in this paper has higher forecasting accuracy. Conclusion:: As the effectiveness of the combined model is verified by the actual operation data of a European wind farm, the results have shown that compared to the other four single and combined forecasting models, the combined model in this paper has higher forecasting accuracy. Therefore, the model proposed in this article can be used for predicting wind power with significant fluctuations, which will help to provide support for optimized scheduling and energy storage configuration of wind farms, thereby reducing costs and increasing income for the power grid and wind farms. conclusion: ICEEMDAN decomposition algorithm can effectively reduce the influence of white noise on mode decomposition, and the prediction accuracy of wind power can be better improved by putting different frequency power components into different prediction models

Signal Processing Application Based on a Hybrid Wavelet Transform to Fault Detection and Identification in Power System

The power system is one of the most susceptible systems to failures, which are most frequently caused by transmission line faults. Transmission line failures account for 85% of all power system malfunctions. However, over the last decade, numerous fault detection methods have been developed to ensure the reliability and stability of power systems. A hybrid detection method based on the idea of redundancy property is presented in this paper. Because the continuous wavelet transform itself does not extract fault features for small defects effectively, the stationary wavelet transform approach is employed to assist in their detection. As a result of its ability to decompose the signal into high- and low-frequency components, undecimated reconstruction by using the algebraic summation operation (ASO) is used. This approach creates redundancy, which is useful for the feature extraction of small defects and makes faulty parts more evident. The numerical value of the redundancy ratio’s contribution to the original signal is approximately equal to 36%. Following this method for redundant signal reconstruction, a continuous wavelet transform is used to extract the fault characteristic significantly easier in the time-scale (frequency) domain. Finally, the suggested technique has been demonstrated to be an efficient fault detection and identification tool for use in power systems. In fact, using this advanced signal processing technique will help with early fault detection, which is mainly about predictive maintenance. This application provides more reliable operation conditions.

A novel non-ferrous metal price hybrid forecasting model based on data preprocessing and error correction

Accurately forecasting the price of non-ferrous metals is of great significance for traders to avoid risks, enterprises to arrange production plans, and countries to formulate economic policies. In order to improve the forecasting accuracy of non-ferrous metal prices, this paper proposes a novel non-ferrous metal price hybrid forecasting model named IVWAIEE (IVMD-WPD-ARIMA-IELM-ECD). Firstly, the original price series is decomposed into several smoother IMFs using variational mode decomposition (VMD). Simultaneously, the improved sparrow search algorithm (IFASSA) is used to optimize the parameters of VMD to improve the adaptability of VMD. Secondly, wavelet packet decomposition (WPD) is used to decompose the residual sequence generated by VMD to further extract the information in the residual sequence. Then, the components generated by VMD and WPD are defined as high frequency components and low frequency components according to the zero-crossing rate. ARIMA is used to forecast the low frequency components with gentle fluctuations, and extreme learning machine optimized by IFASSA (IELM) is used to forecast the high frequency components with strong fluctuations. The forecasting results of each component are accumulated to obtain the initial forecasting results and error sequence of the non-ferrous metal price. Next, WPD is used to further decompose the error sequence, and the error subsequence is predicted by ARIMA and IELM to obtain the error prediction results. Finally, the error prediction results are used to correct the initial forecasting results, and the final forecasting results of non-ferrous metal prices are obtained. In order to verify the superiority of the proposed model, the copper, aluminum, and zinc futures prices of the London Metal Exchange (LME) are selected as empirical data to verify the model. The results show that the proposed IVWAIEE model has better prediction accuracy and robustness than other benchmark models. Its RMSE values in predicting copper, aluminum, and zinc futures prices are 0.2238, 0.1863, and 0.2137, respectively, and MAE values are 0.1696, 0.1171, and 0.1644, respectively, which are lower than those of other benchmark models; The proposed model not only enriches the application of secondary decomposition and error correction in the field of non-ferrous metal price forecasting, but also solves the problems of insufficient adaptability and underutilization of residual sequence in the traditional variational mode decomposition method; The research results of this paper can provide scientific and effective guidance for the investment, production, and decision-making of non-ferrous metal stakeholders.