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Traditional grey models are integer order whitening differential models; these models are relatively effective for the prediction of regular raw data, but the prediction error of irregular series or shock series is large, and the prediction effect is not ideal.

The new model realizes the dynamic expansion and optimization of the grey Bernoulli model. Meanwhile, it also enhances the variability and self-adaptability of the model structure. And nonlinear parameters are computed by the particle swarm optimization (PSO) algorithm.

Establishing a prediction model based on the raw data from the last six years, it is verified that the prediction performance of the new model is far superior to other mainstream grey prediction models, especially for irregular sequences and oscillating sequences. Ultimately, forecasting models are constructed to calculate various energy consumption aspects in Chongqing. The findings of this study offer a valuable reference for the government in shaping energy consumption policies and optimizing the energy structure.

It is imperative to recognize its inherent limitations. Firstly, the fractional differential order of the model is restricted to 0 < a < 2, encompassing only a three-parameter model. Future investigations could delve into the development of a multi-parameter model applicable when a = 2. Secondly, this paper exclusively focuses on the model itself, neglecting the consideration of raw data preprocessing, such as smoothing operators, buffer operators and background values. Incorporating these factors could significantly enhance the model’s effectiveness, particularly in the context of medium-term or long-term predictions.

This contribution plays a constructive role in expanding the model repertoire of the grey prediction model. The utilization of the developed model for predicting total energy consumption, coal consumption, natural gas consumption, oil consumption and other energy sources from 2021 to 2022 validates the efficacy and feasibility of the innovative model.

These findings, in turn, provide valuable guidance and decision-making support for both the Chinese Government and the Chongqing Government in optimizing energy structure and formulating effective energy policies.

This research holds significant importance in enriching the theoretical framework of the grey prediction model.

The highlights of the paper are as follows:

1. A novel grey Bernoulli prediction model is proposed to improve the model’s structure.

2. Fractional derivative, fractional accumulating generation operator and Bernoulli equation are added to the new model.

3. The proposed model can achieve full compatibility with the traditional mainstream grey prediction models.

4. Energy consumption in Chongqing verifies that the performance of the new model is much better than that of the traditional grey models.

5. The research provides a reference basis for the government to formulate energy consumption policies and optimize energy structure.

A novel grey Bernoulli prediction model is proposed to improve the model’s structure.

Fractional derivative, fractional accumulating generation operator and Bernoulli equation are added to the new model.

The proposed model can achieve full compatibility with the traditional mainstream grey prediction models.

Energy consumption in Chongqing verifies that the performance of the new model is much better than that of the traditional grey models.

The research provides a reference basis for the government to formulate energy consumption policies and optimize energy structure.

The diagnosis and prediction methods used for estimating the health conditions of the bearing are of great significance in modern petrochemical industries. This paper aims to discuss the accuracy and stability of improved empirical mode decomposition (EMD) algorithm in bearing fault diagnosis.

This paper adopts the improved adaptive complementary ensemble empirical mode decomposition (ICEEMD) to process the nonlinear and nonstationary signals. Two data sets including a multistage centrifugal fan data set from the laboratory and a motor bearing data set from the Case Western Reserve University are used to perform experiments. Furthermore, the proposed fault diagnosis method, combined with intelligent methods, is evaluated by using two data sets. The proposed method achieved accuracies of 99.62% and 99.17%. Through the experiment of two data, it can be seen that the proposed algorithm has excellent performance in the accuracy and stability of diagnosis.

According to the review papers, as one of the effective decomposition methods to deal with nonlinear nonstationary signals, the method based on EMD has been widely used in bearing fault diagnosis. However, EMD is often used to figure out the nonlinear nonstationarity of fault data, but the traditional EMD is prone to modal confusion, and the white noise in signal reconstruction is difficult to eliminate.

In this paper only the top three optimal intrinsic mode functions (IMFs) are selected, but IMFs with less correlation cannot completely deny their value. Considering the actual working conditions of petrochemical units, the feasibility of this method in compound fault diagnosis needs to be studied.

Different from traditional methods, ICEEMD not only does not need human intervention and setting but also improves the extraction efficiency of feature information. Then, it is combined with a data-driven approach to complete the data preprocessing, and further carries out the fault identification and classification with the optimized convolutional neural network.

This study aims to promote the anti-disturbance and tracking accuracy performance of the servo systems, in which a modified active disturbance rejection control (MADRC) scheme is proposed.

An adaptive radial basis function (ARBF) neural network is utilized to estimate and compensate dominant friction torque disturbance, and a parallel high-gain extended state observer (PHESO) is employed to further compensate residual and other uncertain disturbances. This parallel compensation structure reduces the burden of single ESO and improves the response speed of permanent magnet synchronous motor (PMSM) to hybrid disturbances. Moreover, the sliding mode control (SMC) rate is introduced to design an adaptive update law of ARBF.

Simulation and experimental results show that as compared to conventional ADRC and SMC algorithms, the position tracking error is only 2.3% and the average estimation error of the total disturbances is only 1.4% in the proposed MADRC algorithm.

The disturbance parallel estimation structure proposed in MADRC algorithm is proved to significantly improve the performance of anti-disturbance and tracking accuracy.

This paper aims to develop a method for tuning the parameters of the active disturbance rejection controller (ADRC) for fixed-wing unmanned aerial vehicles (UAVs). The bald eagle search (BES) algorithm has been improved, and a cost function has been designed to enhance the optimization efficiency of ADRC parameters.

A six-degree-of-freedom nonlinear model for a fixed-wing UAV has been developed, and its attitude controller has been formulated using the active disturbance rejection control method. The parameters of the disturbance rejection controller have been fine-tuned using the collaborative mutual promotion bald eagle search (CMP-BES) algorithm. The pitch and roll controllers for the UAV have been individually optimized to obtain the most effective controller parameters.

Inspired by the salp swarm algorithm (SSA), the interaction among individual eagles has been incorporated into the CMP-BES algorithm, thereby enhancing the algorithm's exploration capability. The efficient and accurate optimization ability of the proposed algorithm has been demonstrated through comparative experiments with genetic algorithm, particle swarm optimization, Harris hawks optimization HHO, BES and modified bald eagle search algorithms. The algorithm's capability to solve complex optimization problems has been further proven by testing on the CEC2017 test function suite. A transitional function for fitness calculation has been introduced to accelerate the ability of the algorithm to find the optimal parameters for the ADRC controller. The tuned ADRC controller has been compared with the classical proportional-integral-derivative (PID) controller, with gust disturbances introduced to the UAV body axis. The results have shown that the tuned ADRC controller has faster response times and stronger disturbance rejection capabilities than the PID controller.

The proposed CMP-BES algorithm, combined with a fitness function composed of transition functions, can be used to optimize the ADRC controller parameters for fixed-wing UAVs more quickly and effectively. The tuned ADRC controller has exhibited excellent robustness and disturbance rejection capabilities.

The CMP-BES algorithm and transitional function have been proposed for the parameter optimization of the active disturbance rejection controller for fixed-wing UAVs.

The study aims to provide a detailed definition of Destination Cultural Reputation while also exploring its impact on tourist satisfaction through an investigation of the dynamics between these two elements. Additionally, the potential moderating role of on-site engagement in sustainable activities has been investigated, examining whether satisfaction prompts tourists to exhibit behaviors such as the intention to return and recommend the cultural destination.

To achieve these objectives, a survey and a structural equation model, based on a sample of 647 visitors to an important UNESCO World Heritage site (i.e. Urbino), have been adopted.

Findings confirm tourists’ recognition of the destination’s cultural reputation, supporting its relationship with visitor satisfaction. Additionally, tourist satisfaction is positively associated with destination loyalty. However, on-site sustainable activities negatively moderate the relationship between destination reputation and tourist satisfaction. This suggests that a favorable cultural reputation should align with quality sustainable activities in the destination to prevent tourist dissatisfaction.

The paper offers valuable practical insights for destination managers and policymakers aiming to enhance appeal and sustainability.

The study contributes to enhancing the understanding of the complex relationship between reputation, satisfaction, and loyalty in cultural destinations. In addiction it measures the reputation of tourist destination through the specific cultural dimension.