Computational Complexity Research Articles

Multi-stage planning of clean resources and energy storage assets with hybrid uncertainty modeling for low-carbon resilient distribution systems

Climate change drives the urgent need for low-carbon and resilient energy system transitions. However, current planning methods ignore the inherent conflicts between carbon emission reduction and resilience enhancement, failing to optimally balance asset allocation for both aspects. They also neglect the long-term dynamic and stochastic nature of transitions, exposing systems to hybrid uncertainties. This paper presents a multi-stage dynamic planning method for clean resources and energy storage assets in power distribution networks. First, to facilitate low-carbon and resilient transitions, adaptive, stage-wise planning decisions are optimally determined under various planning strategies to mitigate risks stemming from hybrid uncertainties. Second, to precisely quantify the impact of hybrid uncertainties on decision-making, a systematic hybrid-uncertainty modeling approach is designed to capture short- and long-term uncertainties arising from both exogenous and endogenous factors. Third, to alleviate computational complexity, a decomposition-based stochastic dynamic dual integer programming method with augmented cut generation is introduced, which decomposes the original problem into stage-wise subproblems coordinated through forward and backward steps. Numerical results show that the proposed method generates cost-effective planning schemes, yielding $60 K in savings and reducing carbon emissions by 3853 tons. The method also demonstrates strong scalability, with a 52% reduction in solution time for large-scale planning problems.

A Cooperative Multi-Agent Q-Learning Control Framework for Real-Time Energy Management in Energy Communities

Residential and commercial buildings are responsible for 35% of the EU energy-related greenhouse gas (GHG) emissions. Reducing their emissions is crucial for meeting the challenging EU objective of the agenda for becoming a net-zero continent by 2050. The diffusion and integration of distributed renewable energy sources (RESs) and energy storage systems (ESSs), as well as the creation of energy communities (ECs), have proven to be crucial aspects in reducing GHG emissions. In this context, this article proposes a multi-agent AI-based control framework to solve the EC’s energy management problem in the presence of distributed RESs and ESSs as well as considering a shared ESS. The objectives of the proposed control framework are to satisfy the EC members’ load demand to maximize self-consumption and to manage ESSs charging and discharging processes, to enforce cooperative behavior among the EC members by adopting fair and personalized strategies and to maximize EC members’ profits. The proposed control procedure is based on three sequential stages, each solved by a dedicated local RL agent exploiting the Q-Learning algorithm. To reduce the computational complexity of the proposed approach, specifically defined state aggregation criteria were defined to map the RL agents’ continuous state spaces into discrete state spaces of limited dimensions. During the training phase, the EC members’ profiles and the ESSs’ and RESs’ characteristics were randomly changed to allow the RL agents to learn the correct policy to follow in any given scenario. Simulations proved the effectiveness of the proposed approach for different costumers’ load demand profiles and different EC configurations. Indeed, the trained RL agents proved to be able to satisfy the EC members’ load demands to maximize self-consumption, to correctly use the distributed and shared ESSs, to charge them according to respective personalized criteria and to sell the energy surplus, prioritizing sales to the EC. The proposed control framework also proved to be a useful tool for understanding EC performance in different configurations and, thus, for properly dimensioning the EC elements.

Lightweight Optic Disc and Optic Cup Segmentation Based on MobileNetv3 Convolutional Neural Network.

Glaucoma represents a significant global contributor to blindness. Accurately segmenting the optic disc (OD) and optic cup (OC) to obtain precise CDR is essential for effective screening. However, existing convolutional neural network (CNN)-based segmentation techniques are often limited by high computational demands and long inference times. This paper proposes an efficient end-to-end method for OD and OC segmentation, utilizing the lightweight MobileNetv3 network as the core feature-extraction module. Our approach combines boundary branches with adversarial learning, to achieve multi-label segmentation of the OD and OC. We validated our proposed approach across three public available datasets: Drishti-GS, RIM-ONE-r3, and REFUGE. The outcomes reveal that the Dice coefficients for the segmentation of OD and OC within these datasets are 0.974/0.900, 0.966/0.875, and 0.962/0.880, respectively. Additionally, our method substantially lowers computational complexity and inference time, thereby enabling efficient and precise segmentation of the optic disc and optic cup.

LLD-GAN: An end-to-end network for low-light image demosaicking

Demosaicking of low and ultra-low light images has wide applications in the fields of consumer electronics, security, and industrial machine vision. Denoising is a challenge in the demosaicking process. This study introduces a comprehensive end-to-end low-light demosaicking framework called LLD-GAN (Low Light Demosaicking Generative Adversarial Network), which greatly reduces the computational complexity. Our architecture employs a Wasserstein GAN framework enhanced by a gradient penalty mechanism. We have redesigned the generator based on the UNet++ network as well as its corresponding discriminator, which makes the model learning more efficient. In addition, we propose a new loss metric grounded in the principles of perceptual loss to obtain images with better visual quality. The contribution of Wasserstein GAN with gradient penalty and perceptual loss function was proved to be beneficial by our ablation experiments. For RGB images, we tested the proposed model under a wide range of low light levels, from 1/30 to 1/150 of normal light level, for 16-bit images with added noise. For actual low-light raw sensor images, the model was evaluated under three distinct lighting conditions: 1/100, 1/250, and 1/300 of normal exposure. The qualitative and quantitative comparison against advanced techniques demonstrates the validity and superiority of the LLD-GAN as a unified denoising-demosaicking tool.

CosGCTFormer: An end-to-end driver state recognition framework

Driver state is critical for safety in mixed traffic environments with automated and human-driven vehicles. Recognizing and monitoring the driver’s state is essential to provide early warnings of abnormal driving performance. This paper proposes a driver state recognition framework called cosGCTFormer for end-to-end recognition of the driver’s emotional state and mental load. First, we employ an inverted residual convolution module to extract local features from physiological signal data. Second, the cosGCT module is introduced to extract global features. This module uses cos attention to address the high computational complexity of the Transformer in calculating attention weights. Additionally, it employs Gated Channel Transformation (GCT) to establish relationships between different channel dimensions, something the Transformer alone cannot do effectively. Finally, a simulated driving experiment was designed to collect data for training and testing the proposed method. Results demonstrate that our framework achieves higher accuracy and a more lightweight design compared to prevalent Convolution neural network-based (CNN-based) and Transformer-based methods. Additionally, the effectiveness of both modules was verified.

Research on operating characteristics of V-shaped ultrasonic motor based on improved electromechanical coupling model

Abstract As a complex electromechanical coupling system, evaluating the motion characteristics of an ultrasonic motor via an accurate theoretical model is challenging due to the strong coupling between its electrical and mechanical properties. To address this issue, the paper first establishes a complete dynamic model of the V-shaped ultrasonic motor (VUSM). In contrast to the traditional dynamic model, the proposed model incorporates the centroid vibration of the stator and applies the weighted residual method to reduce the computational complexity by simplifying the dynamic model from infinite-dimensional degrees of freedom to two degrees of freedom. Subsequently, the finite element method is employed to determine the vibration mode of the stator structure and derive the two-phase operational mode of the motor. Using these two-phase working modes, the model is then solved to predict the motor's output characteristics under any operational condition. Furthermore, an electrical model accounting for preload nonlinearity was developed based on the dynamic model and compared with the model without considering preload nonlinearity, supported by experimental verification. The findings demonstrate that the established dynamic model and electrical model can accurately simulate the changing laws of the input and output characteristics of the motor, which provides assistance for the subsequent operation status evaluation of the motor and fault diagnosis during operation.

Multi-scale dual-channel feature embedding decoder for biomedical image segmentation

Background and Objective:Attaining global context along with local dependencies is of paramount importance for achieving highly accurate segmentation of objects from image frames and is challenging while developing deep learning-based biomedical image segmentation. Several transformer-based models have been proposed to handle this issue in biomedical image segmentation. Despite this, segmentation accuracy remains an ongoing challenge, as these models often fall short of the target range due to their limited capacity to capture critical local and global contexts. However, the quadratic computational complexity is the main limitation of these models. Moreover, a large dataset is required to train those models. Methods:In this paper, we propose a novel multi-scale dual-channel decoder to mitigate this issue. The complete segmentation model uses two parallel encoders and a dual-channel decoder. The encoders are based on convolutional networks, which capture the features of the input images at multiple levels and scales. The decoder comprises a hierarchy of Attention-gated Swin Transformers with a fine-tuning strategy. The hierarchical Attention-gated Swin Transformers implements a multi-scale, multi-level feature embedding strategy that captures short and long-range dependencies and leverages the necessary features without increasing computational load. At the final stage of the decoder, a fine-tuning strategy is implemented that refines the features to keep the rich features and reduce the possibility of over-segmentation. Results:The proposed model is evaluated on publicly available LiTS, 3DIRCADb, and spleen datasets obtained from Medical Segmentation Decathlon. The model is also evaluated on a private dataset from Medical College Kolkata, India. We observe that the proposed model outperforms the state-of-the-art models in liver tumor and spleen segmentation in terms of evaluation metrics at a comparative computational cost. Conclusion:The novel dual-channel decoder embeds multi-scale features and creates a representation of both short and long-range contexts efficiently. It also refines the features at the final stage to select only necessary features. As a result, we achieve better segmentation performance than the state-of-the-art models.

Optimizing size and location of UPFC for enhanced system dynamic stability using hybrid approach

This paper proposed a novel hybrid optimization technique, combining the Enhanced Multi-Strategic Sparrow Search Algorithm (EMSA) and White Shark Optimizer (WSO), to determine the optimal location and size of a Unified Power Flow Controller (UPFC) for enhancing power system dynamic stability. The proposed method offers improved search capabilities, reduced randomness, and lower computational complexity compared to existing approaches. Generator faults can significantly impact system dynamic stability constraints, including voltage and power loss. EMSA algorithm is employed to identify optimal location for UPFC placement by selecting bus with minimum power loss. Subsequently, WSO algorithm is used to optimize UPFC's capacity, ensuring that affected system parameters and dynamic stability constraints are restored within safe limits. Optimized UPFC is then installed at identified location, and system's power flow is analyzed. Proposed method is implemented in MATLAB/Simulink environment and tested on both IEEE 30 and IEEE 14 standard benchmark systems. Proposed method's performance is evaluated by comparison with existing methods.

An Enhanced Direct Position Determination of Mixed Circular and Non-Circular Sources Using Moving Virtual Interpolation Array.

In this study, a moving single-station direct position determination (DPD) algorithm based on virtual interpolated arrays is proposed. Existing moving single-station algorithms face challenges such as the incomplete utilization of sparse array apertures and insufficient consideration of mixed circular and non-circular signals. To address these issues, we propose an enhanced gridless DPD algorithm, suitable for multiple mixed circular and non-circular sources. Through constructing a non-zero unconjugated covariance matrix from the non-circular components of the mixed signals, the data dimensionality is expanded, and the gridless method is used to fill the voids in the coarray, significantly improving localization performance. Additionally, a unitary transformation method is applied to reduce computational complexity. This method transforms complex operations into real operations by applying unitary transformations to steering vectors and subspaces. Simulation results demonstrate that the proposed algorithm offers significant advantages in terms of array degrees of freedom and localization accuracy.

VAN-DAMME: GPU-accelerated and symmetry-assisted quantum optimal control of multi-qubit systems

We present an open-source software package, VAN-DAMME (Versatile Approaches to Numerically Design, Accelerate, and Manipulate Magnetic Excitations), for massively-parallelized quantum optimal control (QOC) calculations of multi-qubit systems. To enable large QOC calculations, the VAN-DAMME software package utilizes symmetry-based techniques with custom GPU-enhanced algorithms. This combined approach allows for the simultaneous computation of hundreds of matrix exponential propagators that efficiently leverage the intra-GPU parallelism found in high-performance GPUs. In addition, to maximize the computational efficiency of the VAN-DAMME code, we carried out several extensive tests on data layout, computational complexity, memory requirements, and performance. These extensive analyses allowed us to develop computationally efficient approaches for evaluating complex-valued matrix exponential propagators based on Padé approximants. To assess the computational performance of our GPU-accelerated VAN-DAMME code, we carried out QOC calculations of systems containing 10 - 15 qubits, which showed that our GPU implementation is 18.4× faster than the corresponding CPU implementation. Our GPU-accelerated enhancements allow efficient calculations of multi-qubit systems, which can be used for the efficient implementation of QOC applications across multiple domains. Program summaryProgram Title: VAN-DAMMECPC Library link to program files::https://doi.org/10.17632/zcgw2n5bjf.1Licensing provisions: GNU General Public License 3Programming language: C++ and CUDANature of problem: The VAN-DAMME software package utilizes GPU-accelerated routines and new algorithmic improvements to compute optimized time-dependent magnetic fields that can drive a system from a known initial qubit configuration to a specified target state with a large (≈1) transition probability.Solution method: Quantum control, GPU acceleration, analytic gradients, matrix exponential, and gradient ascent optimization.

An optimization of the Fourier self-calibration algorithm for improved noise suppression capability

Abstract Self-calibration emerges as a promising approach in ultra-precision field, overcoming the limitations imposed by instrument capabilities in conventional calibration. In the self-calibration research, the algorithm based on the Fourier transform firstly established a rigorous theoretical framework. However, despite advancements in alternative self-calibration methods that have improved noise suppression, the traditional Fourier algorithm still faces challenges, particularly in mitigating random measurement noise in the separation results. In this study, we introduce methods on enhancing the noise suppression capabilities of the Fourier self-calibration algorithm. We investigate the hypothesis in the traditional algorithm and find that the computation of weighted averages had minimal effects. Then, we present our method by augmenting measurement positions. Considering both the increase in the number of measurement positions and the enhancement of noise suppression capabilities, augmenting translation positions in the opposite direction is proved to be the most effective strategy. Our algorithm can effectively suppress measurement noise when one-sided point number of the artifact is below 21. While the additional data processing slightly increases runtime, it does not alter the algorithm’s computational complexity, yet it significantly improves noise suppression. The effectiveness of our method is validated through a Monte Carlo comparison of uncertainties with the original algorithm. Experiments on Fizeau interferometer further prove robustness and practical feasibility of our proposed algorithm, with the measurement repeatability being reduced by 26.34% and 25.15% in the errors separated from the stage and the artifact.

Recent Progress in ECDSA and DSA Digital Signature Algorithms

Digital signatures are essential for verifying the authenticity and integrity of information, thus facilitating digital authentication. The Elliptic Curve Digital Signature Algorithm (ECDSA) and the Digital Signature Algorithm (DSA) play critical roles in the field of digital signatures. This paper explores the conceptual frameworks and mathematical underpinnings of these algorithms, providing an in-depth analysis of their advantages and disadvantages with a focus on computational time complexity and key length requirements. The distinct applications of ECDSA and DSA in various fields are examined, highlighting how the selection of an algorithm influences security and efficiency in different scenarios. This analysis also considers the algorithms' suitability for specific security applications, offering insights into their strategic deployment. By comparing these characteristics, the study aims to guide the selection of appropriate digital signature technology, tailored to meet operational needs and security specifications. This comparative approach not only elucidates the practical implications of each algorithm but also contributes to a broader understanding of their roles in securing digital transactions.

FV-DLV3+: a light-weight flooded vegetation extraction method with attention-based DeepLabv3+

ABSTRACT Climate change and human activities have led to a decline in wetland vegetation and sharp reduction of wetland area, which has caused considerable damage to the hydrological cycle and ecological functions of many wetlands. Flooded vegetation (FV) is an important wetland landscape, and strengthening the research on methods of the extracting FV using remote sensing or aerial photos plays an important role in monitoring changes to wetlands. This paper used optical satellite and synthetic aperture radar satellite images as data sources, construct a set of feature variable sets suitable for FV extraction; in addition, a deep learning method based on the semantic segmentation model DeepLabv3+, FV-DLV3+, is proposed for FV extraction. The method adopts the lightweight MobileNetV2 model as the backbone feature extraction network, introduces the SegFormer network to make up for the feature information loss caused by MobileNetV2, and further captures more effective features and suppresses the interference of the background through an attention mechanism to enhance the ability to extract feature boundaries, thereby improving the accuracy of FV extraction. Taking the wetland of Poyang Lake as the experimental area, Landsat 8 and Sentinel-1A satellite data were selected as the data sources to produce a deep learning dataset, and U-Net, DeepLabv3+, Swin-Unet, Swin Transformer, and CVTNet were selected for comparison when conducting model training and validating experiments. The results show that FV-DLV3+ has an excellent effect on FV extraction of the Poyang Lake wetland, which effectively reduces the computational complexity of the process while improving extraction accuracy; the mean intersection over union of this paper’s method was higher than the five above-mentioned methods, which was 12.93% and 5.85% higher than that of DeepLabv3+ and CVTNet, respectively.

UNeXt: An Efficient Network for the Semantic Segmentation of High-Resolution Remote Sensing Images

The application of deep neural networks for the semantic segmentation of remote sensing images is a significant research area within the field of the intelligent interpretation of remote sensing data. The semantic segmentation of remote sensing images holds great practical value in urban planning, disaster assessment, the estimation of carbon sinks, and other related fields. With the continuous advancement of remote sensing technology, the spatial resolution of remote sensing images is gradually increasing. This increase in resolution brings about challenges such as significant changes in the scale of ground objects, redundant information, and irregular shapes within remote sensing images. Current methods leverage Transformers to capture global long-range dependencies. However, the use of Transformers introduces higher computational complexity and is prone to losing local details. In this paper, we propose UNeXt (UNet+ConvNeXt+Transformer), a real-time semantic segmentation model tailored for high-resolution remote sensing images. To achieve efficient segmentation, UNeXt uses the lightweight ConvNeXt-T as the encoder and a lightweight decoder, Transnext, which combines a Transformer and CNN (Convolutional Neural Networks) to capture global information while avoiding the loss of local details. Furthermore, in order to more effectively utilize spatial and channel information, we propose a SCFB (SC Feature Fuse Block) to reduce computational complexity while enhancing the model’s recognition of complex scenes. A series of ablation experiments and comprehensive comparative experiments demonstrate that our method not only runs faster than state-of-the-art (SOTA) lightweight models but also achieves higher accuracy. Specifically, our proposed UNeXt achieves 85.2% and 82.9% mIoUs on the Vaihingen and Gaofen5 (GID5) datasets, respectively, while maintaining 97 fps for 512 × 512 inputs on a single NVIDIA GTX 4090 GPU, outperforming other SOTA methods.

MFHARFNet: Multi-branch feature hybrid and adaptive receptive field network for image segmentation

Abstract Accurate segmentation of medical images is crucial for disease diagnosis and understanding disease changes. Deep learning methods, utilizing encoder-decoder structures, have demonstrated cutting-edge performance in various medical image segmentation tasks. However, the pooling operation in the encoding stage results in feature loss, which makes the network lack the ability to fuse multi-scale information at different levels, hinders its effective perception of multi-scale information, and leads to poor segmentation performance. Drawing inspiration from the U-shaped network, this study introduces a multi-branch feature hybrid attention and adaptive receptive field network (MFHARFNet) for medical image segmentation. Building upon the encoder-decoder framework, we initially devise a multi-branch feature hybrid attention module (MFHAM) to seamlessly integrate feature maps of varying scales, capturing both fine-grained features and coarse-grained semantics across the entire scale. Furthermore, we redesign the skip connection to amalgamate feature information from different branches in the encoder stage and efficiently transmit it to the decoder, providing the decoder with global context feature maps at different levels. Finally, the adaptive receptive field (ARF) module is introduced in the decoder feature reconstruction stage to adapt and focus on related fields, ensuring the model's adaptation to different segmentation target features, and achieving different weights for the output of different convolution kernels to improve segmentation performance. We comprehensively evaluate our method on medical image segmentation tasks, by using four public datasets across CT and MRI. Remarkably, MFHARFNet method consistently outperforms other state-of-the-art methods, exceeding UNet by 2.1%, 0.9%, 6.6% and 1.0% on Dice on ATLAS, LiTs, BraTs2019 and Spine and intervertebral disc datasets, respectively. In addition, MFHARFNet minimizes network parameters and computational complexity as much as possible. The source codes are in https://github.com/OneHundred99/MFHARFNet.

Deep cryogenic silicon etching for 3D integrated capacitors: A numerical perspective

One promising approach to increase the capacity density of integral microcapacitors, microsupercapacitors, and microbatteries is three-dimensional structure design, where electrodes are exposed in three dimensions instead of conventional in-plane electrodes. Such structures include nanowires, nanotubes, nanopillars, nanoholes, nanosheets, and nanowalls. In this work, a cryogenic silicon etching process suitable for fabrication of structures with high electrode area is proposed. A numeric model of this process is experimentally calibrated and used for pillar array structure sidewall area optimization. The use of adaptive Runge–Kutta–Fehlberg time integrator allows to achieve almost linear overall computation complexity as a function of simulated etching time, despite the linear increase in conductance computation complexity with depth. A rule for choosing optimal geometric structure parameters under technological constraints is formulated. An optimized trefoil-like structure is proposed, resulting in a total 5.5% increase in sidewall area with respect to the hexagonal array of circular pillars, resulting in 20.33 sidewall area per unit chip area for 30 min long etch or 31.80 for 60 min long etch.

Microwave Coincidence Imaging with Phase-Coded Stochastic Radiation Field

Microwave coincidence imaging (MCI) represents a novel forward-looking radar imaging method with high-resolution capabilities. Most MCI methods rely on random frequency modulation to generate stochastic radiation fields, which introduces the complexity of radar systems and imposes limitations on imaging quality under noisy conditions. In this paper, microwave coincidence imaging with phase-coded stochastic radiation fields is proposed, which generates spatio-temporally uncorrelated stochastic radiation fields with phase coding. Firstly, the radiation field characteristics are analyzed, and the coding sequences are designed. Then, pulse compression is applied to achieve a one-dimensional range image. Furthermore, an azimuthal imaging model is built, and a reference matrix is derived from the frequency domain. Finally, sparse Bayesian learning (SBL) and alternating direction method of multipliers (ADMM)-based total variation are implemented to reconstruct targets. The methods have better imaging performance at low signal-to-noise ratios (SNRs), as shown by the imaging results and mean square error (MSE) curves. In addition, compared with the SBL and ADMM-based total variation methods based on the direct frequency-domain solution, the proposed method’s computational complexity is reduced, giving it great potential in forward-looking high-resolution scenarios, such as autonomous obstacle avoidance with vehicle-mounted radar and terminal guidance.

Investigation of non-equilibrium phenomena in nitrogen RF inductively coupled plasma discharges: a state-to-state approach

Abstract This work presents a vibrational and electronic (vibronic) state-to-state (StS) model for nitrogen plasmas implemented within a multi-physics modular computational framework to study non-equilibrium effects in inductively coupled plasma (ICP) discharges. The vibronic master equations are solved in a tightly coupled fashion with the flow governing equations eliminating the need for invoking any simplifying assumptions when computing the state of the plasma, leading to a high-fidelity physical modeling. The model’s computational complexity is reduced via a maximum entropy coarse-graining approach, verified through zero-dimensional isochoric calculations. The coarse-grained StS model is employed to study the plasma discharge in the ICP facility at the von Karman Institute for Fluid Dynamics, Belgium. Results reveal pronounced discrepancies between StS predictions and those obtained based on local thermodynamic equilibrium (LTE) models, which are conventionally used in the simulation of such facilities. The analysis demonstrates a substantial departure of the internal state populations of atoms and molecules from the Boltzmann distribution. This has significant implications for energy coupling dynamics, affecting the discharge morphology. Further analysis reveals a quasi-steady-state population distribution in the plasma core, allowing for the construction of an efficient and ‘self-consistent’ macroscopic two-temperature (2T) formulation. Non-LTE simulations indicate significant disparities between the StS model and the commonly used Park 2T model, whereas the newly proposed 2T model aligns closely with StS simulations, capturing key features of non-equilibrium plasma formation. In particular, the current study highlights the importance of the vibrational-translational energy transfer term in shaping the plasma core morphology, suggesting a notable sensitivity to heavy-impact vibrational excitations and dissociative processes.

Short-time adaptive compact kernel distribution for fault diagnosis under variable working condition bearing

Time-frequency distribution (TFD) methods are extensively employed in the diagnosis of bearings operating under variable working conditions. However, these methods often face high computational complexity, limited time-frequency resolution, and cross-terms. To address these issues, this paper presents a new approach called Short-Time Adaptive Compact Kernel Distribution (STACKD). Based on the characteristics of the vibration signals, we designed Chirp-modulated Gaussian Window and used them to segment the overall signal into small segments. Then, we used a two-step Bayesian optimization method to obtain adaptive compact kernel distributions (ACKD) for these small segments of the signal. Finally, we recombined the ACKD of these small segments into a global STACKD. Results from simulations and experiments demonstrate that STACKD offers improved robustness against interference signals, lower computational complexity, and higher time-frequency resolution without cross-term effects. This method is tailored for diagnosing rolling bearings under variable working conditions, providing enhanced visualization of diagnostic processes with superior time-frequency resolution.

A proportional fusion adaptation algorithm to reduce noise in sEMG signals of the lower limb

Abstract To address issues related to unknown noise pollution and the inadequate performance of single adaptive noise reduction algorithms in measuring lower limb surface electromyography (sEMG) signals, this paper proposes an algorithm that combines the fast convergence speed and strong noise reduction capability of recursive least-squares (RLS) with the low computational complexity of the normalized least-mean-square (NLMS) and improved proportionate NLMS (IPNLMS). Through the proportional fusion of RLS with NLMS and RLS with IPNLMS, the proposed algorithm greatly improves convergence speed, stability, and noise reduction performance while effectively reducing computational complexity. Moreover, considering the influence of the initial value of weights on the noise reduction performance during the updating process of the adaptive noise reduction algorithm, a weight initial value setting (WIS) module is proposed to optimize the initial value of the weights by the known amount of data. Based on 50 independent experiments, an adaptive noise reduction algorithm and WIS module were used to reduce the unknown noise in the lower limb sEMG signals, which was generated by white Gaussian noise, power line interference, or hybrid noise interfered by an unknown environment. The noise reduction performance was evaluated by using the average value of the signal-to-noise ratio (SNR), the root-mean-square error, and R-square. Compared with the RLS, NLMS, and IPNLMS algorithms for noise reduction of vastus lateralis, rectus femoris, and biceps femoris signals containing unknown noise, the SNR of RLS-NLMS, RLS-IPNLMS, WIS-RLS-NLMS, and WIS-RLS-IPNLMS is improved by an average of [7.92%, 55.54%, 55.63%], [7.45%, 54.90%, 54.99%], [19.70%, 72.38%, 72.71%], [19.32%, 71.84%, 72.19%]. The simulation results verify that the proportional fusion adaptive noise reduction algorithm and the WIS module effectively accelerate the convergence speed, enhance the noise reduction capability, and reduce the computational complexity.