Signal Decomposition Algorithm Research Articles

Differential learning model for carbon emission allowance prices prediction based on adaptive decomposition and joint feature contribution

Currently, how to effectively control carbon emissions is a global concern. Accurate carbon price prediction can help us more effectively control carbon emissions and reduce environmental pollution. Due to the complexity of carbon valence, this study proposes an improved decomposition ensemble prediction model. Firstly, a novel signal decomposition algorithm is designed to adaptively determine the number of decomposition modes for carbon price sequences, obtaining a set of intrinsic mode functions (IMFs). Secondly, a creative method for assessing the contribution of feature components is developed. It utilizes a genetic algorithm-based mutual-information method to calculate the contribution of each IMFs to the original sequence, classifying all feature components into high and low contribution components. Then, this study developed a differential learning method that partitions the contribution of feature components and applies targeted learning and integration using temporal convolutional network with different structures. Compared to traditional forecasting frameworks, this framework improves prediction performance while reducing structural complexity and computational costs. Empirical results demonstrate the superiority and robustness of the proposed model with the outcomes of this study present the performances that the proposed model outperforms the others with Guangzhou's mean absolute percentage error of 3.30313%, which are beneficial for governments and enterprises to predict adverse signals in the carbon market in a more timely manner, and to take measures in advance to maintain the stability of carbon emissions.

Exploring the potential of pretrained CNNs and time-frequency methods for accurate epileptic EEG classification: a comparative study

Prompt diagnosis of epilepsy relies on accurate classification of automated electroencephalogram (EEG) signals. Several approaches have been developed to characterize epileptic EEG data; however, none of them have exploited time-frequency data to evaluate the effect of tweaking parameters in pretrained frameworks for EEG data classification. This study compares the performance of several pretrained convolutional neural networks (CNNs) namely, AlexNet, GoogLeNet, MobileNetV2, ResNet-18 and SqueezeNet for the localization of epilepsy EEG data using various time-frequency data representation algorithms. Continuous wavelet transform (CWT), empirical Fourier decomposition (EFD), empirical mode decomposition (EMD), empirical wavelet transform (EWT), and variational mode decomposition (VMD) were exploited for the acquisition of 2D scalograms from 1D data. The research evaluates the effect of multiple factors, including noisy versus denoised scalograms, different optimizers, learning rates, single versus dual channels, model size, and computational time consumption. The benchmark Bern-Barcelona EEG dataset is used for testing purpose. Results obtained show that the combination of MobileNetV2, Continuous Wavelet Transform (CWT) and Adam optimizer at a learning rate of 10−4, coupled with dual-data channels, provides the best performance metrics. Specifically, these parameters result in optimal sensitivity, specificity, f1-score, and classification accuracy, with respective values of 96.06%, 96.15%, 96.08%, and 96.10%. To further corroborate the efficacy of opted pretrained models on exploited Signal Decomposition (SD) algorithms, the classifiers are also being simulated on Temple University database at pinnacle modeling composition. A similar pattern in the outcome readily validate the findings of our study and robustness of deep learning models on epilepsy EEG scalograms.The conclusions drawn emphasize the potential of pretrained CNN-based models to create a robust, automated system for diagnosing epileptiform. Furthermore, the study offers insights into the effectiveness of varying time-frequency techniques and classifier parameters for classifying epileptic EEG data.

New formulation for predicting total dissolved gas supersaturation in dam reservoir: application of hybrid artificial intelligence models based on multiple signal decomposition

Total dissolved gas (TDG) concentration plays an important role in the control of the aquatic life. Elevated TDG can cause gas-bubble trauma in fish (GBT). Therefore, controlling TDG fluctuation has become of great importance for different disciplines of surface water environmental engineering.. Nowadays, direct estimation of TDG is expensive and time-consuming. Hence, this work proposes a new modelling framework for predicting TDG based on the integration of machine learning (ML) models and multiresolution signal decomposition. The proposed ML models were trained and validated using hourly data obtained from four stations at the United States Geological Survey. The dataset are composed from: (i) water temperature (Tw), (ii) barometric pressure (BP), and (iii) discharge (Q), which were used as the input variables for TDG prediction. The modelling strategy is conducted based on two different steps. First, six singles ML model namely: (i) multilayer perceptron neural network, (ii) Gaussian process regression, (iii) random forest regression, (iv) random vector functional link, (v) adaptive boosting, and (vi) Bootstrap aggregating (Bagging), were developed for predicting TDG using Tw, BP, and Q, and their performances were compared. Second, a new framework was introduced based on the combination of empirical mode decomposition (EMD), the variational mode decomposition (VMD), and the empirical wavelet transform (EWT) preprocessing signal decomposition algorithms with ML models for building new hybrid ML models. Hence, the Tw, BP, and Q signals were decomposed to extract the intrinsic mode functions (IMFs) by using the EMD and VMD methods and the multiresolution analysis (MRA) components by using the EWT method. Then after, the IMFs and MRA components were selected and regraded as new input variables for the ML models and used as an integral part thereof. The single and hybrid prediction models were compared using several statistical metrics namely, root mean square error, mean absolute error, coefficient of determination (R2), and Nash–Sutcliffe efficiency (NSE). The single and hybrid models were trained several times with high number of repetitions, depending on the kind of modeling process. The obtained results using single models gave good agreement between the predicted TDG and the situ measured dataset. Overall, the Bagging model performed better than the other five models with R2 and NSE values of 0.906 and 0.902, respectively. However, the extracted IMFs and MRA components using the EMD, VMD and the EWT have contributed to an improvement of the hybrid models’ performances, for which the R2 and NSE were significantly increased reaching the values of 0.996 and 0.995. Experimental results showed the superiority of hybrid models and more importantly the importance of signal decomposition in improving the predictive accuracy of TDG.Graphical abstract

Adaptive Fault Components Extraction by Using an Optimized Weights Spectrum Based Index for Machinery Fault Diagnosis

Machinery condition monitoring and fault diagnosis has attracted much attention because it is beneficial to reducing maintenance costs and improving industrial profits. Adaptive fault components extraction (AFCE) is the most crucial step for machinery fault diagnosis, and its core is statistical indices. Existing statistical indices including kurtosis and correlated kurtosis are empirical statistical indices (ESIs), and they cannot exactly quantify fault-related information in signals and distinguish fault components from interferential components. Thus, the ESIs might be easily affected by random impulsive noise, low frequency components, etc. To solve this problem, a new statistical index named optimized weights spectrum based index (OWSI) is proposed in this paper. The OWSI satisfies two good properties to guarantee exact quantification of fault components and effectively distinguish interferential components. Moreover, a new OWSI-based methodology is proposed to realize AFCE, and it can be implemented with signal decomposition algorithms such as variational mode decomposition without needing careful parameters tuning. Bearing and gear real-world fault signals are studied to verify the effectiveness of the proposed methodology. Results show that the proposed methodology is superior to ESI-based methods including classic fast kurtogram and newly developed feature mode decomposition.

River water temperature prediction using hybrid machine learning coupled signal decomposition: EWT versus MODWT

Accurate prediction of water temperature (Tw) will greatly help in improving our understanding of the overall thermal regime fluctuation, and it can help in making sound decisions. While great efforts have been devoted to the development of Tw models, further improvement in the prediction accuracy is challenging. Here, we propose a new hybrid machine learning (ML) models for predicting Tw from air temperature (Ta). First, two signal decomposition algorithms, i.e., the empirical wavelet transform (EWT) and maximum overlap discrete wavelet transform (MODWT) are used for decomposing the Ta into several subsequences. Second, the obtained subsequences are used as input variables for four ML models, i.e., the feedforward neural network (FFNN), the optimally pruned extreme learning machine (OPELM), the adaptive boosting (AdaBoost), and the bootstrap aggregating (Bagging). The development of the hybrid models is based on measured data form five measurement stations distributed over Poland. The experimental results show that, the new hybrid ML models achieved high predictive accuracies with Pearson correlation coefficient (R), Nash-Sutcliffe efficiency (NSE), root mean square error (RMSE) and mean absolute error (MAE) of approximately ≈0.99, ≈0.98, ≈0.718 °C, and ≈0.599 °C, respectively. Finally, the experimental results have demonstrated that, the MAE and RMSE of the single models were reduced by 66.12% and 65.30%, while the R and NSE values were improved by 4.85% and 10.02%, respectively, showing a very promising prediction performance. Our new modelling approach proposed in the present study clearly highlight the high contribution of the EWT and MODWT in improving the Tw estimation that is most strongly influenced by Ta. The significant difference between single and hybrid models can be explained by the ability of the EWT and MODWT to capture the high nonlinearity between Ta and Tw. Our new approach is of interest for water resources management and for assessing the variability of Tw over time and space. Finally yet importantly, this is the first study in the literature for which EWT and MODWT were used for modelling Tw, through which we have demonstrated that, an important amount of information is available and cannot be captured using single ML models, and signal decomposition have helped to overcome this challenge.

A Short-term solar irradiance forecasting modelling approach based on three decomposition algorithms and Adaptive Neuro-Fuzzy Inference System

In this study, a case study of four Indian cities i.e. Ajmer, Jaipur, Jodhpur and Kota in the state of Rajasthan are considered wherein 30 min ahead data have been obtained via the data site of the National Institute of Wind Energy and Wind Resource (NIWE) on which a proposed Global Horizontal Irradiance (GHI) prediction technique for all seasons is applied. Here, data has been pre-processed using three different signal decomposition algorithms in parallel i.e. Empirical Mode Decomposition (EMD), Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Ensemble Empirical Mode Decomposition (EEMD). Further, based on Pearson's Correlation Coefficient (PCC), corresponding IMFs & corresponding Residual obtained using the three decomposition algorithms are compared amongst each other respectively and that corresponding IMFs & corresponding Residual are chosen for signal reconstruction which are having highest correlation coefficient values. Thereafter, these selected IMFs and Residual from each algorithm are combined to form single input. In this way, three inputs formed from three decomposition algorithms based on the PCC values are fed to Adaptive Neuro-Fuzzy Inference System (ANFIS) for solar irradiance forecasting. The proposed technique shows significantly higher accurate results with less than 2% MAPE for different seasons considered at the site locations considered. Further, it terms of performance, the proposed technique is found to be independent of site location.

Time-varying uncertainty evaluation of the shock wave pressure measurements with small samples in an aerospace shock tube

Shock tube is a crucial device for the dynamic calibration of pressure sensors in aerospace and defense fields. Accurate measurement of the shock wave pressure (SWP) in the shock tube and reliable evaluation of the measurement uncertainty are the basis for improving the calibration accuracy of pressure sensors. However, the repeated measurement results of the SWP in shock tube have typical features of time-varying and small samples, leading to a poor reliability of the measurement uncertainty evaluation. To address this issue, an improved method is proposed to accurately evaluate the time-varying uncertainty of the SWP measurement results with small samples in an aerospace shock tube. The time-varying SWP measurement signals are firstly decomposed into four components by the multicomponent extraction based on signal decomposition algorithms. For the repeated SWP measurement data with small samples, a sample size expansion based on the bootstrap method is presented to reduce the mean estimation error of the four components. A time-varying uncertainty evaluation model of the four components is established based on the conjugate prior Bayesian theory. The reliable evaluation of the time-varying uncertainty of the SWP measurements is finally realized according to the uncertainty propagation principle. Simulations and the SWP measurement experiments in an aerospace shock tube are carried out to validate the performance of the proposed method. The results show that the proposed method works well in the time-varying uncertainty evaluation of the SWP measurements with small samples. Furthermore, the comparative experiments demonstrate the superiority of the proposed method over the Bessel method and the Bayesian method for the SWP measurement uncertainty evaluation in both accuracy and reliability.

A Content-Assisted Dynamic PUF Key Generation Scheme Using Compressive Autoencoder for Internet-of-Things

A physical unclonable function (PUF) is broadly investigated as a secret key generator for internet-of-things (IoT) devices because of its uniqueness and randomness. Security vulnerability may occur in conventional PUF-based schemes if an attacker eavesdrops on the challenge and response pair (CRP) associated with PUF. To mitigate the impact of such key compromise, this study proposes a novel dynamic PUF key generation scheme, where the sensing data-based dynamic features are integrated to a static PUF-based key. The compressive autoencoders (AEs) typically employed for compressing the time-series data can be customized to extract data-based features. The dynamic features are quantized to generate the data-based key, and then combined with the PUF-based key for the dynamic key generation. An attacker finds it difficult to extract the PUF-based key from the synthesized ones; hence, CRPs cannot be estimated, even if the attacker can obtain the dynamic key through eavesdropping. The event signal decomposition algorithm, which disjoins the dominant event signal in the dataset, is proposed to enhance the data-based key diversity. For numerical evaluation, the static random access memory-PUF and the public energy dataset are used for the dynamic key generation. Numerical results show that the AE model can generate a data-based key that prohibits key leakage to the attacker while improving the reconstruction performance. The dynamic key is evaluated for diverse attack models (e.g., replay and modeling attacks), and the attacker cannot estimate the CRP tables.

Characteristic enhancement of RV reducer under non-stationary condition based on WDT-IF-SS-VMD

Because the working conditions of the rotate vector (RV) reducer are often reciprocating at variable speeds and the working environment is relatively complex, so the vibration signals collected have non-stationary vibration and complex environmental noise. A fault diagnosis method for RV reducer (WDT-IF-SS-VMD) is proposed, which combines instantaneous frequency (IF) trend graph based on current signal and the parameter adaptive variational mode decomposition (VMD) algorithm. Firstly, the current signal and vibration signal are collected synchronously, and the steady-state phase of vibration signal is intercepted according to the IF trend diagram obtained by wavelet decomposition transform (WDT) of the current signal. Secondly, the intercepted vibration signals are transformed into scale space, and the parameters of VMD are selected adaptively based on fuzzy C-means clustering. Then, the maximum kurtosis criterion is used to complete the extraction of sensitive components. Finally, the envelope analysis is carried out to complete the fault diagnosis. The measured signal analysis results show that this method can effectively separate and extract fault features of the RV reducer.

Speech Deception Detection Based on EMD and Temporal Neural Network

Deceptive behaviour is a common phenomenon in human society. Research has shown that humans are not good at distinguishing deception, so studying automated deception detection techniques is a critical task. Most of the relevant technologies are susceptible to personal and environmental influences: EEG-based technologies need large and expensive equipment, facial-based technologies are sensitive with the camera’s perspective, and these reasons have somewhat limited the development of applications for deception detection technologies. In contrast, the equipment required for speech deception detection is cheap and easy to use, and the capture of speech is highly covert. Based on the application of signal decomposition algorithms in other fields such as EEG signals and speech emotion recognition, this paper proposed a signal decomposition and reconstruction method based on EMD to process the speech signal and a better deception detection performance was obtained by improving the speech quality. The comparison results with other decomposition algorithms showed that the EMD decomposition algorithm is the most suitable for our method. Across many different classification algorithms, accuracy improved by an average of 2.05% and the F1 score improved by an average of 1.7%. In addition, a new deception detector, called the TCN-LSTM network, was proposed in this paper. Experiments showed that this network organically combines the processing capability of TCN and LSTM for time series data; the recognition rate of deception detection was greatly improved, with the highest accuracy and F1 score reaching 86.2% and 86.0% under the EMD-based signal decomposition reconstruction method. Based on the research in this paper, the signal decomposition algorithms need to be further optimised for speech signals and more classification algorithms not used for this task should be tried.

Comparison of hybrid machine learning models to predict short-term meteorological drought in Guanzhong region, China.

Reliable drought prediction plays a significant role in drought management. Applying machine learning models in drought prediction is getting popular in recent years, but applying the stand-alone models to capture the feature information is not sufficient enough, even though the general performance is acceptable. Therefore, the scholars tried the signal decomposition algorithm as a data pre-processing tool, and coupled it with the stand-alone model to build 'decomposition-prediction' model to improve the performance. Considering the limitations of using the single decomposition algorithm, an 'integration-prediction' model construction method is proposed in this study, which deeply combines the results of multiple decomposition algorithms. The model tested three meteorological stations in Guanzhong, Shaanxi Province, China, where the short-term meteorological drought is predicted from 1960 to 2019. The meteorological drought index selects the Standardized Precipitation Index on a 12-month time scale (SPI-12). Compared with stand-alone models and 'decomposition-prediction' models, the 'integration-prediction' models present higher prediction accuracy, smaller prediction error and better stability in the results. This new 'integration-prediction' model provides attractive value for drought risk management in arid regions.

Multivariate group-sparse mode decomposition

In signal decomposition, a complex and nonstationary signal is decomposed into a set of basic functions, usually called intrinsic mode functions (IMFs). In multivariate signal decomposition, it is assumed that analogous IMFs across all channels share common bandwidths (BWs). In this paper, a generic extension of the group-sparse mode decomposition (GSMD) for multivariate (multichannel) signal decomposition is developed. The univariate GSMD is based on the assumption that the spectral energy of the measured signal is concentrated in disjoint groups, and each group represents the spectral energy of one of the IMFs. This concept is generalized in the proposed algorithm to the multivariate measurements. Accordingly, the penalized least-squares objective function used for deriving GSMD is adapted in this paper to handle the multivariate measurements, where the weightedℓ0-norm is utilized as the penalty term, and the weighting parameters and the regularization parameter are calculated using techniques based on energy detection over short windows. In addition, two thresholding strategies were applied by the proposed algorithm to overcome the mode-mixing phenomenon. The derived algorithm is referred to as generalized GSMD (gGSMD). The gGSMD is further developed to handle the case when the analogous IMFs have disparate BWs across channels, and the resulting algorithm is referred to as multivariate GSMD (MvGSMD). The MvGSMD enjoys the following desired properties: robustness against noise, fast convergence, mode alignment, automatically estimating the number of IMFs, producing orthogonal IMFs, and efficiently adjusting the BW of each individual IMF even when analogous IMFs across channels have disparate BWs. All these properties were validated using numerical results on simulated data and real EEG and physiological data. The simulation results also show that the proposed algorithm outperforms many state-of-the-art multivariate signal decomposition algorithms.

Data-driven nonstationary signal decomposition approaches: a comparative analysis

Signal decomposition (SD) approaches aim to decompose non-stationary signals into their constituent amplitude- and frequency-modulated components. This represents an important preprocessing step in many practical signal processing pipelines, providing useful knowledge and insight into the data and relevant underlying system(s) while also facilitating tasks such as noise or artefact removal and feature extraction. The popular SD methods are mostly data-driven, striving to obtain inherent well-behaved signal components without making many prior assumptions on input data. Among those methods include empirical mode decomposition and variants, variational mode decomposition and variants, synchrosqueezed transform and variants and sliding singular spectrum analysis. With the increasing popularity and utility of these methods in wide-ranging applications, it is imperative to gain a better understanding and insight into the operation of these algorithms, evaluate their accuracy with and without noise in input data and gauge their sensitivity against algorithmic parameter changes. In this work, we achieve those tasks through extensive experiments involving carefully designed synthetic and real-life signals. Based on our experimental observations, we comment on the pros and cons of the considered SD algorithms as well as highlighting the best practices, in terms of parameter selection, for the their successful operation. The SD algorithms for both single- and multi-channel (multivariate) data fall within the scope of our work. For multivariate signals, we evaluate the performance of the popular algorithms in terms of fulfilling the mode-alignment property, especially in the presence of noise.

Fault detection of rotating machinery based on marine predator algorithm optimized resonance-based sparse signal decomposition and refined composite multiscale fluctuation dispersion entropy.

Feature extraction is the key to the fault detection of rotating machinery based on vibration signals, and the quality of the features influences the reliability of the detection. This paper develops a fault feature extraction method of rotating machinery based on optimized resonance-based sparse signal decomposition and refined composite multiscale fluctuation dispersion entropy. First, resonance-based sparse signal decomposition is used to decompose the vibration signals adaptively. In order to obtain the resonance-based sparse signal decomposition algorithm with optimal performance, the marine predator algorithm is used for the parameters optimization with correlation kurtosis as the fitness function. Subsequently, based on the refined composite coarse-grained process and fluctuation dispersion entropy, a refined composite multiscale fluctuation dispersion entropy is developed, enabling a more accurate and comprehensive measure of the complexity of time series. Then, all feature matrices are input to the support matrix machine for fault identification. Experiments are conducted using two typical rotating machinery datasets for the validity of the proposed method, and comparisons are made with other methods. The results show that the proposed scheme outperforms other comparative methods regarding classification accuracy and stability. In addition, the proposed scheme can obtain relatively reliable classification results even when the data volume is small and the background noise is significant, demonstrating the scheme's potential for application in practical engineering.

An adaptive spectrum segmentation-based optimized VMD method and its application in rolling bearing fault diagnosis

Variational mode decomposition (VMD) is a signal decomposition algorithm with excellent denoising ability. However, the drawback that VMD is unable to determine the input parameters adaptively seriously affects the decomposition results. For this issue, an optimized VMD method based on modified scale-space representation (MSSR-VMD) is proposed. Firstly, MSSR is proposed to segment the fault signal spectrum, acquiring modes’ number and the initial center frequency for each mode adaptively. Moreover, a pre-decomposition step is added to the original VMD, which selects a target mode from divided frequency bands. Finally, the penalty factor of the target mode is adjusted during the iterative update of the VMD to achieve accurate extraction for the fault features. MSSR-VMD and other adaptive decomposition algorithms are employed to handle the simulated and experimental signals separately. By comparing the analysis results, the method has certain superiority in rolling bearing fault feature extraction.

Radar Detection-Inspired Signal Retrieval from the Short-Time Fourier Transform.

This paper presents a novel adaptive algorithm for multicomponent signal decomposition from the time–frequency (TF) plane using the short-time Fourier transform (STFT). The approach is inspired by a common technique used within radar detection called constant false alarm rate (CFAR). The areas with the strongest magnitude are detected and clustered, allowing for TF mask creation and filtering only those signal modes that contribute the most. As a result, one can extract a particular component void of noise and interference regardless of the signal character. The superiority understood as an improved reconstructed waveform quality of the proposed method is shown using both simulated and real-life radar signals.

Enhanced Discrimination of Seismic Geological Channels Based on Multi-Trace Variational Mode Decomposition

The spectral decomposition is a valuable tool for improving the resolution of seismic interpretation, and thus can improve the accuracy of the subtle geo-features (thin and narrow channels, thin reservoirs, etc.). Variational mode decomposition (VMD) is an adaptive signal decomposition algorithm that non-recursively decomposes multicomponent signals into several band-limited intrinsic mode functions, which is competitive in enhancing time-frequency resolution. However, discontinuity is normally caused by the trace-by-trace process, making the 3D seismic interpretation difficult. To address this issue, we present a novel seismic geological channel detection method for 3D seismic dataset based on multi-trace variational mode decomposition (MTVMD). The proposed method decomposes the broadband seismic data into several intrinsic mode functions and then computes seismic attributes from each component for geological feature analysis. Further tested by field seismic case, the proposed method demonstrates strength in depicting the detailed edges and sedimentary signatures of paleochannels. Overall, the proposed method provides an alternative approach to identifying seismic channels, especially for the detailed portrayals of subtle geo-features in low-quality seismic data.

Spectral variational mode extraction and its application in fault detection of rolling bearing

The core of fault diagnosis of rolling bearing is to extract the narrowband sub-components containing fault feature information from the bearing fault signal. Variational mode extraction (VME), a novel single sub-component separation algorithm originated from variational mode decomposition (VMD), provides a promising solution to bearing fault detection. However, its performance is closely related to the hyperparameter selection, including the center frequency ω d and the penalty factor α. This paper proposes a non-recursive and adaptive signal decomposition algorithm termed spectral variational mode extraction (SVME). SVME can be seen as a spectral decomposition technique whose framework is composed of the adaptive spectral boundary division and boundary constrained VME. In the adaptive spectral boundary division, an adaptive iterative spectral envelope method referring to the continuous envelope correlation (CCE) index is developed to integrate with the parameterless scale-space division to adaptively locate the frequency band boundary. The presented adaptive spectral boundary division approach can effectively inhibit the spectral boundary over-division. In the boundary constrained VME, the dominant frequency of each frequency band determined by the optimal spectral division is distinguished as the preset center frequency. Meanwhile, the optimal penalty factor is determined based on the envelope spectral kurtosis (ESK) index and the boundary-constraint principle. The SVME method is utilized in the simulation and experimental case studies to investigate its capability. Furthermore, its superiority is highlighted through the comparison with the variational mode decomposition (VMD) and Autogram methods.

A multi-model fusion based non-ferrous metal price forecasting

Non-ferrous metals play a significant role in social development. It is important for policy makers and entrepreneurs to forecast non-ferrous metals price accurately. However, existing methods are hard to obtain satisfactory results because the fluctuation rule of non-ferrous metal price is increasingly complex. Therefore, it is necessary to develop more accurate and stable forecasting method. In this paper, a multi-model fusion based non-ferrous metal price forecasting method is proposed. The dual-stage signal decomposition algorithm which combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD) is innovatively introduced into non-ferrous metal price forecasting. First, CEEMDAN is used to decompose the original price into several subsequences. Second, the most complex subsequence with maximum sample entropy (SE) is further decomposed by VMD. Dual-stage decomposition reveals essential features such as long-term trend and periodic fluctuations hidden in original sequence and thus lowers prediction difficulty. Besides, particle swarm optimization (PSO) is used to select optimal parameters for VMD. Finally, all subsequences are predicted by long short-term memory network (LSTM) and the results are integrated as the final prediction result. In the empirical study of London Metal Exchange (LME)'s copper, aluminum and zinc price, the proposed method is superior to all benchmark methods in terms of RMSE, MAE and MAPE. The results demonstrate that the proposed method is effective and robust.

Robustified extreme learning machine regression with applications in outlier-blended wind-speed forecasting

Wind energy is a core sustainable source of electric power, and accurate wind-speed forecasting is pivotal to enhancing the power stability, efficiency, and utilization. The existing forecasting methods are still limited by the influence of outliers and the modelling difficulties caused by complex features in wind speed series. This paper proposes a new wind speed forecasting system based on a designed adaptive robust extreme learning machine (ARELM) model and signal decomposition algorithms. Firstly, the ARELM is designed to sufficiently lessen the violation of normality assumptions and contamination by outliers. ARELM takes an adaptive scaled Huber’s loss as its objective function, which can limit the influence of outliers and adaptively determine an appropriate mixture distribution of normal distribution and Laplace distribution at the same time. Secondly, the empirical mode decomposition (EMD) method and its improved methods (EEMD, CEEMD and CEEMDAN) are introduced to our wind-speed forecasting system, where the low-frequent sub-series are modelled by basic ELM and the high-frequent ones are modelled by ARELM. This can decompose the modelling complex wind speed series into modelling several simple sub-series and reduce the difficulty of modelling. Experimental results show that our combined forecasting system, ELM-ARELM, obtains up to 78% improvement in forecasting performance comparing with the methods using general Huber’s loss and other comparison methods, which show the superiority of the adaptive scaled Huber’s loss. The error indexes (MAE and RMSE) by the proposed system, which are (0.25, 0.34), (0.32, 0.45) and (0.38, 0.53) for 5 min head, 15 min ahead and 25 min ahead experiments respectively, demonstrate the effectiveness of decomposition methods on improving accuracy of wind speed prediction.