Fractional Order Sequential Minimal Optimization Classification Method

Car-like mobile robots (CLMRs) are extensively utilized in various intricate scenarios owing to their exceptional maneuverability, stability, and adaptability, in which path planning is an important technical basis for their autonomous navigation. However, path planning methods are prone to inefficiently generate unsmooth paths in narrow and large-size scenes, especially considering the chassis model complexity of CLMRs with suspension. To this end, instead of traditional path planning based on an integer order model, this paper proposes fractional-order enhanced path planning using an improved Ant Colony Optimization (ACO) for CLMRs with suspension, which can obtain smooth and efficient paths in narrow and large-size scenes. On one hand, to improve the accuracy of the kinematic model construction of CLMRs with suspension, an accurate fractional-order-based kinematic modelling method is proposed, which considers the dynamic adjustment of the angle constraints. On the other hand, an improved ACO-based path planning method using fractional-order models is introduced by adopting a global multifactorial heuristic function with dynamic angle constraints, adaptive pheromone adjustment, and fractional-order state-transfer models, which avoids easily falling into a local optimum and unsmooth problem in a narrow space while increasing the search speed and success rate in large-scale scenes. Finally, the proposed method’s effectiveness is validated in both large-scale and narrow scenes, confirming its capability to handle various challenging scenarios.

Section: Fractional-order Modellingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Smooth and Efficient Path Planning for Car-like Mobile Robot Using Improved Ant Colony Optimization in Narrow and Large-Size Scenes

Li,

Jiang,

et al. 2024

“…The fractional order is a generalization of the concept of integral calculus to fractions, whose exponents can be any real number, including decimals or fractions. Fractional order calculus is an extension of integral order calculus, which can more accurately describe real systems and obtain more accurate results [34]. The introduction of fractional derivatives and integrals can better describe nonlinear changes and increase the freedom degree of mathematical models.…”

Section: Introductionmentioning

confidence: 99%

A Bearing Fault Diagnosis Method under Small Sample Conditions Based on the Fractional Order Siamese Deep Residual Shrinkage Network

Li,

Wu,

Luo

et al. 2024

A bearing fault is one of the major causes of rotating machinery faults. However, in real industrial scenarios, the harsh and complex environment makes it very difficult to collect sufficient fault data. Due to this limitation, most of the current methods cannot accurately identify the fault type in cases with limited data, so timely maintenance cannot be conducted. In order to solve this problem, a bearing fault diagnosis method based on the fractional order Siamese deep residual shrinkage network (FO-SDRSN) is proposed in this paper. After data collection, all kinds of vibration data are first converted into two-dimensional time series feature maps, and these feature maps are divided into the same or different types of fault sample pairs. Then, a Siamese network based on the deep residual shrinkage network (DRSN) is used to extract the features of the fault sample pairs, and the fault type is determined according to the features. After that, the contrastive loss function and diagnostic loss function of the sample pairs are combined, and the network parameters are continuously optimized using the fractional order momentum gradient descent method to reduce the loss function. This improves the accuracy of fault diagnosis with a small sample training dataset. Finally, four small sample datasets are used to verify the effectiveness of the proposed method. The results show that the FO-SDRSN method is superior to other advanced methods in terms of training accuracy and stability under small sample conditions.

FLRNN-FGA: Fractional-Order Lipschitz Recurrent Neural Network with Frequency-Domain Gated Attention Mechanism for Time Series Forecasting

Zhao,

Ye,

Zhu

et al. 2024

Time series forecasting has played an important role in different industries, including economics, energy, weather, and healthcare. RNN-based methods have shown promising potential due to their strong ability to model the interaction of time and variables. However, they are prone to gradient issues like gradient explosion and vanishing gradients. And the prediction accuracy is not high. To address the above issues, this paper proposes a Fractional-order Lipschitz Recurrent Neural Network with a Frequency-domain Gated Attention mechanism (FLRNN-FGA). There are three major components: the Fractional-order Lipschitz Recurrent Neural Network (FLRNN), frequency module, and gated attention mechanism. In the FLRNN, fractional-order integration is employed to describe the dynamic systems accurately. It can capture long-term dependencies and improve prediction accuracy. Lipschitz weight matrices are applied to alleviate the gradient issues. In the frequency module, temporal data are transformed into the frequency domain by Fourier transform. Frequency domain processing can reduce the computational complexity of the model. In the gated attention mechanism, the gated structure can regulate attention information transmission to reduce the number of model parameters. Extensive experimental results on five real-world benchmark datasets demonstrate the effectiveness of FLRNN-FGA compared with the state-of-the-art methods.