Convergence Precision Research Articles

Plant-inspired decentralized controller for robust orientation control of soft robotic manipulators.

Due to the complexity of deformations in soft manipulators, achieving precise control of their orientation is particularly challenging, especially in the presence of external disturbances and human interactions. Inspired by the decentralized growth mechanism of plant gravitropism, which enables plants' roots and stems to grow in the direction of gravity despite complex environmental interactions, this study proposes a decentralized control strategy for robust orientation control of multi-segment soft manipulators. This gravitropism-inspired decentralized controller was validated through simulations for convergence and robustness, and benchmarked against the traditional inverse Jacobian-based controller on a large-scale multi-segment soft manipulator. Experimental results demonstrate that the decentralized controller achieves comparable convergence and better control precision to the inverse Jacobian-based controller, while significantly outperforming it in disturbance rejection. Even in the presence of partial damage and human interaction, the decentralized controller provides robust control. This study provides a robust new approach for managing disturbances in complex environments, laying the foundation for further exploration of decentralized control strategies in soft robotics.

An innovative complex-valued encoding black-winged kite algorithm for global optimization

The black-winged kite algorithm (BKA) constructed on the black-winged kites’ migratory and predatory instincts is a revolutionary swarm intelligence method that integrates the Leader tactic with the Cauchy variation procedure to retrieve the expansive appropriate convergence solution. The essential BKA exhibits marginalized resolution efficiency, inferior assessment precision, and stagnant sensitive anticipation. To foster aggregate discovery intensity and advance widespread computational efficacy, an innovative complex-valued encoding BKA (CBKA) is presented to resolve the global optimization. The complex-valued encoding manipulates the dual-diploid configuration to encode the black-winged kite, and the actual and fictitious portions are inserted into the BKA, which transforms dual-dimensional encoding into a single-dimensional manifestation. With the inherent parallelism and consistency, the actual and fictitious portions are renewed separately for each search agent, which reinforces population pluralism, restricts discovery stagnation, extends identification area, promotes estimation excellence, advances information resources, and fosters collaboration efficiency. The CBKA not only showcases abundant flexibility and compatibility to accomplish supplementary advantages and sharpen resolution precision but also incorporates localized exploitation and universal exploration to forestall exaggerated convergence and cultivate desirable solutions. The function evaluations, engineering layouts, and adaptive infinite impulse response system identification are executed to certify the suitability and affordability of the CBKA. The experimental results manifest that the computational accomplishment and convergence productivity of the CBKA are superior to those of other comparison algorithms, the CBKA delivers noteworthy stabilization and resilience to explore superior assessment precision and swifter convergence efficiency.

An Improved Human Evolution Optimization Algorithm for Unmanned Aerial Vehicle 3D Trajectory Planning.

To address the challenges of slow convergence speed, poor convergence precision, and getting stuck in local optima for unmanned aerial vehicle (UAV) three-dimensional path planning, this paper proposes a path planning method based on an Improved Human Evolution Optimization Algorithm (IHEOA). First, a mathematical model is used to construct a three-dimensional terrain environment, and a multi-constraint path cost model is established, framing path planning as a multidimensional function optimization problem. Second, recognizing the sensitivity of population diversity to Logistic Chaotic Mapping in a traditional Human Evolution Optimization Algorithm (HEOA), an opposition-based learning strategy is employed to uniformly initialize the population distribution, thereby enhancing the algorithm's global optimization capability. Additionally, a guidance factor strategy is introduced into the leader role during the development stage, providing clear directionality for the search process, which increases the probability of selecting optimal paths and accelerates the convergence speed. Furthermore, in the loser update strategy, an adaptive t-distribution perturbation strategy is utilized for its small mutation amplitude, which enhances the local search capability and robustness of the algorithm. Evaluations using 12 standard test functions demonstrate that these improvement strategies effectively enhance convergence precision and algorithm stability, with the IHEOA, which integrates multiple strategies, performing particularly well. Experimental comparative research on three different terrain environments and five traditional algorithms shows that the IHEOA not only exhibits excellent performance in terms of convergence speed and precision but also generates superior paths while demonstrating exceptional global optimization capability and robustness in complex environments. These results validate the significant advantages of the proposed improved algorithm in effectively addressing UAV path planning challenges.

Advanced hybrid algorithm for estimation of circularity deviation in coordinate metrology

Abstract In the field of precision mechanics such as automobiles or aeronautics, the estimation of defects in the shape of mechanical parts is a very common task, and the declaration of conformity is mainly based on the precision of this value.
This research introduces an innovative hybrid optimization methodology that enhances the precision of estimation of circularity defects. The method proposed combins the Genetic Algorithm (GA) and the Interior Point Method (IPM), this approach overcomes the limitations of traditional methods like Least Squares (LS) and Orthogonal Distance Regression (ODR), which rely on initial estimates parameters to ensure convergence. The GA-IPM hybrid eliminates the need for such initial guesses, leading to faster convergence and more accurate results.
To control a mechanical part, a cloud of points is preleved by using a Coordinate Measuring Machines (CMMs), after tratement of those datasets the estimation of circularity defects is calculated using the proposed algortihm GA-IPM. To validate our approach a comparative study is carried out according to the standard ISO 10360-6, which consists of comparing the results (substitute geometry parameters) obtained with those of National Institute of Standards and Technology (NIST) considered as reference values. Several examples have been processed, circle totally or partially measured in order to verify the robustness of the algorithm in terms of convergence and calculation precision, the circularity defect is subsequently calculated on the basis of these parameters. The comparison shows that our method estimates the parameters and the circularity defect well without needing a vector of initial estimates parameters.
Given the results obtained, this hybrid approach represents a contribution to the estimation of the circularity deviation, thus offering industries a reliable, precise method to ensure the declaration of conformity of mechanical parts.

Relaxed Positivity, η-Exponential Stabilization and l1-Gain Performance of Polynomial Discrete-Time Fuzzy System with Time-Delay and External Disturbance

The positivity constraint makes the stability for positive systems under the precise convergence decay and anti-disturbance performance quite challenging considering the current advanced control theory. Furthermore, the existence of time delay will disturb the dynamics of non-linear positive systems and even lead to a series of complex behaviours, such as oscillations and instability. With respect to the above problems, an approach of membership function-dependent positivity, η-exponential stability and l1-gain performance investigations which consider the dedicated membership function shape for the polynomial fuzzy discrete-time model (PFDM) with time-delay is proposed in this article. Firstly, we use a novel co-positive polynomial η-exponential Lyapunov–Krasovskii functional candidate to investigate the systems exponential stability under the decay η-rate and l1-gain anti-disturbance performance. Secondly, to reduce the conservativeness of conditions, a novel piecewise-polynomial membership function is used to introduce the Lagrange approximation knowledge into stability and performance analysis. Finally, the synthesized state-feedback fuzzy controller with polynomial terms guarantees these control objectives under positivity constraints. Two simulation examples validate the developed new method.

Mixed-Strategy Harris Hawk Optimization Algorithm for UAV Path Planning and Engineering Applications

This paper introduces the mixed-strategy Harris hawk optimization (MSHHO) algorithm as an enhancement to address the limitations of the conventional Harris hawk optimization (HHO) algorithm in solving complex optimization problems. HHO often faces challenges such as susceptibility to local optima, slow convergence, and inadequate precision in global solution-seeking. MSHHO integrates four innovative strategies to bolster HHO’s effectiveness in both local exploitation and global exploration. These include a positive charge repulsion strategy for diverse population initialization, a nonlinear decreasing parameter to heighten competitiveness, the introduction of Gaussian random walk, and mutual benefit-based position updates to enhance mobility and escape local optima. Empirical validation on 12 benchmark functions from CEC2005 and comparison with 10 established algorithms affirm MSHHO’s superior performance. Applications to three real-world engineering problems and UAV flight trajectory optimization further demonstrate MSHHO’s efficacy in overcoming complex optimization challenges. This study underscores MSHHO as a robust framework with enhanced global exploration capabilities, significantly improving convergence accuracy and speed in engineering applications.

Privacy-preserving and communication-efficient stochastic alternating direction method of multipliers for federated learning

Federated learning constitutes a paradigm in distributed machine learning, wherein model training unfolds through the exchange of intermediary results between a central server and federated clients. Given its decentralized nature, conventional machine learning algorithms find limited applicability in the context of federated learning models. Hence, the alternating direction method of multipliers (ADMM), tailored for distributed optimization, is leveraged for this purpose. However, despite the considerable promise of the ADMM algorithm in federated learning, it faces challenges related to computational efficiency, communication efficiency, and data security. In response to these challenges, this study proposes the privacy-preserving and communication-efficient stochastic ADMM (PPCESADMM) algorithm that enhances the computational efficiency through the stochastic optimization method, reduces communication costs through sparse communication method, and ensures the security of federated clients' data via the homomorphic encryption method. Theoretical analyses confirm the convergence of the PPCESADMM algorithm under mild conditions and establish its convergence rate as O(1/T). Experiments illustrate the superior performance of our algorithm in communication cost compared to ADMM and CEADMM algorithms, achieving reductions of 65.10% and 44.32%, respectively. Furthermore, our method surpasses classical federated learning algorithms such as FedAvg, FedAvgM, and SCAFFOLD in terms of algorithmic convergence, achieving superior convergence precision within predefined training epochs. Finally, our algorithm converges to the same results as those obtained without using homomorphic encryption, albeit at the cost of increased computation time.

Performance of PSO-GWO, VAGWO, and GWO optimization techniques for economic dispatch problem: studied case of the southeast algerian electrical network

Economic dispatch (ED) aims to identify the most cost-effective strategy for allocating power generation while meeting demand and adhering to the physical constraints of the power system. In this paper, three algorithms are proposed to solve the ED problem in power systems, including a hybrid Particle Swarm Optimization with Grey Wolf Optimizer (PSO-GWO), modified Velocity Aided Grey Wolf Optimizer (VAGWO), and Grey Wolf Optimizer (GWO). PSO is a meta-heuristic optimization technique designed to find the optimal solution to a problem by guiding the movement of particles within a defined exploration space. GWO is also a meta-heuristic optimization algorithm based on the natural behavior of grey wolves. In this paper, to enhance the performance of GWO, it is first combined with the PSO method. VAGWO is employed to refine the GWO formulation by optimizing the convergence steps. At the beginning of the iterations, the distance between the solutions (wolves) is increased to promote exploration of the search space. As the iterations progress, the step size is reduced, allowing for a more precise and efficient convergence toward the optimal solution. These algorithms will be implemented in Matlab software to minimize the fuel cost production of the following test networks: IEEE 30-bus network, Algerian 114-bus network, and Southeast Algerian network. These methods show that the PSO-GWO algorithm offers better results when compared through VAGWO and GWO.

Error estimates for the robust α-stable central limit theorem under sublinear expectation by a discrete approximation method

In this work, we develop a numerical method to study the error estimates of the α-stable central limit theorem under sublinear expectation with α∈(0,2), whose limit distribution can be characterized by a fully nonlinear integro-differential equation (PIDE). Based on the sequence of independent random variables, we propose a discrete approximation scheme for the fully nonlinear PIDE. With the help of the nonlinear stochastic analysis techniques and numerical analysis tools, we establish the error bounds for the discrete approximation scheme, which in turn provides a general error bound for the robust α-stable central limit theorem, including the integrable case α∈(1,2) as well as the non-integrable case α∈(0,1]. Finally, we provide some concrete examples to illustrate our main results and derive the precise convergence rates.

Two-layer fault diagnosis model of aircraft based on LSTM

Different component malfunctions of the aircraft may cause fault characteristics crossing easily and similar trajectory deviations, making traditional single-type diagnostic approaches to risk misidentification. To accurately ascertain the fault status based on sequential data such as flight trajectories and attitudes, this paper introduces a two-tiered fault diagnosis model leveraging long short-term memory (LSTM) neural networks. The first layer of the model discerns the fault mechanism, while the second layer pinpoints the specific fault type. Datasets encompassing four distinct actuator faults and four varying degrees of thrust drop faults (20%, 40%, 60%, and 80%,) are constructed for model training and validation. Simulation results show that employing a two-layer LSTM network enhances both training convergence and testing precision, achieving a diagnostic accuracy of 99.38%, surpassing the 96.74% accuracy of a single-layer network. Furthermore, the LSTM network's diagnostic accuracy, utilizing sequence information, significantly outperforms that of the Least Squares Classifier and the BP neural network, which rely on individual state information. Thus, the efficacy of proposed two-tiered LSTM-based fault diagnosis model in improving diagnostic accuracy and reliability in aircraft systems has been validated.

Dynamic Surface Intelligent Robust Control of Nonlinear Systems With Fixed-Time Sliding-Mode Observer.

The high tracking control precision and fast finite-time convergence for nonlinear systems is a significant challenge due to complex nonlinearity and unknown disturbances. To address this challenge, a dynamic surface intelligent robust control strategy with fixed-time sliding-mode observer (DSIRC-SMO) is proposed to improve the tracking control performance in a finite time. First, adaptive fuzzy neural network based on a predictor (P-AFNN) is designed to imitate the complex nonlinearity. In particular, the weight adaptive law is formulated by utilizing the prediction error information, which improves the accuracy of approximating the nonlinear system. Second, the fixed-time sliding-mode observer (SMO) is integrated into the dynamic surface control technique to deal with unknown disturbances and modeling errors in a fixed time. This integration allows for timely updates the dynamic surface using observation information, thereby enhancing the system's anti-interference capability. Then, the fixed-time convergence of SMO is proven. Third, the proposed DSIRC-SMO can be effectively implemented and the finite-time convergence of DSIRC-SMO is proven in detail based on the fixed-time convergence of SMO. Finally, numerical simulation and actual wastewater treatment processes simulation are conducted to validate the effectiveness of DSIRC-SMO.

Photovoltaic partial occlusion maximum power point tracking based on improved sparrow search algorithm

Abstract In scenarios of partial shading, photovoltaic array output characteristics can exhibit multiple peaks, which can cause traditional maximum power point tracking (MPPT) algorithms to get stuck in local optima. An enhanced sparrow search algorithm for MPPT is introduced to enhance the efficiency of photovoltaic systems. This improved approach utilizes Tent chaotic mapping for population initialization and incorporates an adaptive weight factor to refine convergence precision. Simulation results demonstrate that the improved sparrow search algorithm, compared to the conventional version, offers superior convergence speed and stability when applied to multi-peak MPPT scenarios.

SORM‐Enhanced Inverse Reliability Analysis for Geotechnical Multiobjective Reliability‐Based Design Optimization

ABSTRACTThe first‐order reliability method (FORM) is mostly employed in the existing geotechnical reliability‐based design (RBD) methods due to its computational simplicity and efficiency. However, the first‐order Taylor approximation of the limit state surface (LSS) may result in significant errors, especially in cases of highly nonlinear LSS characterized by substantial curvatures. Therefore, FORM‐based RBD methods require a modification of the curvatures to enhance the accuracy of the probabilistic constraints, specifically by converting the target reliability index into a more precise target failure probability. Correspondingly, reliability index‐based design is converted into failure probability‐based design. In this study, the parabolic second‐order reliability method (SORM), which avoids the Hessian calculations, is adopted to improve the accuracy of probabilistic constraints beyond what is achievable with FORM. The proposed SORM‐enhanced RBD method accounts for the curvature information of the nonlinear LSS, modifying the target reliability index to align with the exact target failure probability through the application of SORM. Moreover, by incorporating an implicit coupling function, multiobjective RBD can be effectively implemented without any additional surrogate model. Furthermore, the proposed RBD method is readily extended to reliability‐based design optimization (RBDO) through integration with an optimization strategy. The proposed RBDO method demonstrates a more precise convergence of the probabilistic constraints, surpassing the accuracy of FORM‐based RBDO methods. Notably, the proposed SORM‐enhanced RBDO method not only significantly improves accuracy but also bypasses the necessity for Hessian computation, which remains both the second‐order accuracy and first‐order efficiency. The feasibility of the proposed method is demonstrated through a mathematical example and three practical geotechnical design examples.

Robot inverse kinematics solution for center selection battle royale optimization algorithm

In order to solve the problems of high time complexity and insufficient global exploration ability of the battle royale optimization algorithm, this paper proposes an improved battle royale optimization algorithm based on chaos mapping, center selection and elite adaptive strategy. Through benchmark function testing, compared to particle swarm optimization algorithm, whale optimization algorithm, and the battle royale optimization algorithm, the improved algorithm significantly reduces time complexity and notably enhances convergence precision, speed, and stability. The improved algorithm is applied to the inverse kinematics problem of robots. The accuracy and The stability of the improved algorithm is better than those of the traditional battle royale optimization algorithm, it demonstrates superior solving precision and stability, proving its practicality and potential for development in solving robot inverse kinematics problems.

Meshless method and shifted Chebyshev polynomials for solving a class of VIEs of the third kind

The main goal of this study is to solve a class of linear and nonlinear Volterra integral equations (VIEs) of the third kind. The proposed technique estimates the solution of these equations using a technique based on MLS approximation and shifted Chebyshev polynomials. The approach is independent of the geometry of the domain and does not require any background meshes; therefore, it can be considered a meshless approach. The new method is effective and more flexible for many types of VIEs of the third kind, and its algorithm can be simply implemented on computers. The construction of a new technique for the proposed equations has been introduced. The convergence analysis is also studied. The convergence precision of the new approach is checked on classes of VIEs of the third kind, and the results validate the theoretical error estimates. Finally, numerical tests are provided to illustrate the accuracy and reliability of this approach.

Multi-strategy fusion improved Northern Goshawk optimizer is used for engineering problems and UAV path planning

Addressing the imbalance between exploration and exploitation, slow convergence, local optima Traps, and low convergence precision in the Northern Goshawk Optimizer (NGO): Introducing a Multi-Strategy Integrated Northern Goshawk Optimizer (MINGO). In response to challenges faced by the Northern Goshawk Optimizer (NGO), including issues like the imbalance between exploration and exploitation, slow convergence, susceptibility to local optima, and low convergence precision, this paper introduces an enhanced variant known as the Multi-Strategy Integrated Northern Goshawk Optimizer (MINGO). The algorithm tackles the balance between exploration and exploitation by improving exploration strategies and development approaches. It incorporates Levy flight strategies to preserve population diversity and enhance convergence precision. Additionally, to avoid getting trapped in local optima, the algorithm introduces Cauchy mutation strategies, improving its capability to escape local optima during the search process. Finally, individuals with poor fitness are eliminated using the crossover strategy of the Differential Evolution algorithm to enhance the overall population quality. To assess the performance of MINGO, this paper conducts an analysis from four perspectives: population diversity, balance between exploration and exploitation, convergence behavior, and various strategy variants. Furthermore, MINGO undergoes testing on the CEC-2017 and CEC-2022 benchmark problems. The test results, along with the Wilcoxon rank-sum test results, demonstrate that MINGO outperforms NGO and other advanced optimization algorithms in terms of overall performance. Finally, the applicability and superiority of MINGO are further validated on six real-world engineering problems and a 3D Trajectory planning for UAVs.

A Hybrid Nonlinear Whale Optimization Algorithm with Sine Cosine for Global Optimization.

The whale optimization algorithm (WOA) is constructed on a whale's bubble-net scavenging pattern and emulates encompassing prey, bubble-net devouring prey, and stochastic capturing for prey to establish the global optimal values. Nevertheless, the WOA has multiple deficiencies, such as restricted precision, sluggish convergence acceleration, insufficient population variety, easy premature convergence, and restricted operational efficiency. The sine cosine algorithm (SCA) constructed on the oscillation attributes of the cosine and sine coefficients in mathematics is a stochastic optimization methodology. The SCA upgrades population variety, amplifies the search region, and accelerates international investigation and regional extraction. Therefore, a hybrid nonlinear WOA with SCA (SCWOA) is emphasized to estimate benchmark functions and engineering designs, and the ultimate intention is to investigate reasonable solutions. Compared with other algorithms, such as BA, CapSA, MFO, MVO, SAO, MDWA, and WOA, SCWOA exemplifies a superior convergence effectiveness and greater computation profitability. The experimental results emphasize that the SCWOA not only integrates investigation and extraction to avoid premature convergence and realize the most appropriate solution but also exhibits superiority and practicability to locate greater computation precision and faster convergence speed.

A fast fixed-time backstepping control method for systems with mismatched disturbances

In this paper, a fast fixed-time backstepping control approach is developed for systems with mismatched disturbances. A novel fast fixed-time disturbance observer (FFTDO), which is convergent within fixed time regardless of initial conditions, is designed to efficiently estimate and compensate the disturbances. On the basis of FFTDO, a novel fast fixed-time backstepping control scheme is proposed, which can guarantee fast fixed-time convergence and high steady-state precision. In addition, a novel fixed-time filter is used to circumvent the problem of “explosion and complexity,” and to ensure overall fixed-time convergence. The fixed-time stability of the closed-loop system under the proposed controller is proved by the Lyapunov stability theory. The simulation results are carried out to confirm the feasibility and superiority of the proposed control strategy.

SSG-Net: A Multi-Branch Fault Diagnosis Method for Scroll Compressors Using Swin Transformer Sliding Window, Shallow ResNet, and Global Attention Mechanism (GAM).

The reliable operation of scroll compressors is crucial for the efficiency of rotating machinery and refrigeration systems. To address the need for efficient and accurate fault diagnosis in scroll compressor technology under varying operating states, diverse failure modes, and different operating conditions, a multi-branch convolutional neural network fault diagnosis method (SSG-Net) has been developed. This method is based on the Swin Transformer, the Global Attention Mechanism (GAM), and the ResNet architecture. Initially, the one-dimensional time-series signal is converted into a two-dimensional image using the Short-Time Fourier Transform, thereby enriching the feature set for deep learning analysis. Subsequently, the method integrates the window attention mechanism of the Swin Transformer, the 2D convolution of GAM attention, and the shallow ResNet's two-dimensional convolution feature extraction branch network. This integration further optimizes the feature extraction process, enhancing the accuracy of fault feature recognition and sensitivity to data variability. Consequently, by combining the global and local features extracted from these three branch networks, the model significantly improves feature representation capability and robustness. Finally, experimental results on scroll compressor datasets and the CWRU dataset demonstrate diagnostic accuracies of 97.44% and 99.78%, respectively. These results surpass existing comparative models and confirm the model's superior recognition precision and rapid convergence capabilities in complex fault environments.

Enhanced hybrid LSTM and SLAR modeling for in-depth analysis of temporal and spatial patterns in compositional data for environmental monitoring

A novel methodology for analyzing compositional data (CoDa) integrates long short-term memory (LSTM) networks with spatial lag autoregressive (SLAR) models to simultaneously capture temporal and spatial patterns. The proposed approach leverages LSTM’s strengths in handling temporal relationships and SLAR’s ability to capture spatial correlations, employing the centered log-ratio (CLR) transformation to manage CoDa’s characteristics, making it suitable for advanced analysis. The Adam optimizer ensures efficient and stable model training, enhancing convergence speed and precision. The combined approach involves preprocessing CoDa with CLR, initializing LSTM layers, performing forward passes through LSTM, integrating the SLAR model, generating outputs, post-processing data, calculating loss, and performing backpropagation. The methodology’s effectiveness is demonstrated through a case study on pollutant emissions data from a waste incineration plant, focusing on key pollutants such as Dioxins and Furans, Heavy Metals (Hg, Pb, Cd), Nitrogen Oxides (NO), Sulfur Dioxide (SO), Particulate Matter (PM), and Carbon Monoxide (CO). The LSTM network, configured with two hidden layers, dynamically adjusts learning rates for faster convergence. Integrating SLAR improves spatial pattern accounting, significantly enhancing predictive accuracy. Comparative analysis shows substantial performance metric improvements over standard LSTM models, with the LSTM-SLAR model reducing errors and explaining a higher proportion of data variability. In process safety and risk engineering, the proposed methodology enhances pollutant emission monitoring and control, enables proactive risk management, ensures regulatory compliance, and improves risk assessment accuracy, making it invaluable for dynamic risk assessment in environmental monitoring and is broadly applicable to fields requiring detailed temporal and spatial analysis, demonstrating robustness and versatility in handling complex CoDa.