Number Of Nodes In Hidden Layer Research Articles

Improved whale optimization algorithm towards precise state-of-charge estimation of lithium-ion batteries via optimizing LSTM

Accurate state-of-charge (SOC) estimation is a crucial part of the battery management system (BMS). However, conventional estimation methods are unable to capture the extremely complex dynamic characteristics of lithium-ion batteries. Besides, manually setting the optimal hyperparameters of models has many drawbacks. To address the problems, an (improved whale optimization algorithm) IWOA- (long short-term memory) LSTM model is proposed in this work. Utilizing the whale optimization algorithm (WOA) improved with four enhancement strategies (Gaussian chaotic mapping initialization, Nonlinear weight update, Lévy flight mechanism, and Elite opposition-based learning) to optimize the number of hidden layer nodes, the learning rate, and the number of iterations of LSTM model. It not only overcomes the shortcomings of artificially setting LSTM hyperparameters but also further boosts the learning ability of the IWOA-LSTM model, making the model more suitable for SOC estimation under different scenarios. The evaluation results show that the MAE of the proposed model for SOC estimation results is lower than 0.8 % under different temperatures and dynamic conditions. Compared with SOTA models, all MAE, RMSE, and MAPE of the proposed model substantially decline. Furthermore, the R2 of the estimation results using the LG dataset in Experiment Ⅲ is 98.65 %, suggesting the applicability of the proposed model to Li-ion batteries from various manufacturers. The experimental results demonstrate the proposed IWOA-LSTM model is suitable for accurate SOC estimation.

Research on Citrus Fruit Freshness Detection Based on Near-Infrared Spectroscopy

The study developed a novel method for evaluating the freshness of citrus fruits by integrating near-infrared spectroscopy with the non-linear data processing capabilities of a BP neural network. This approach utilizes specific wavelength analysis to distinguish between fresh and non-fresh fruits effectively. Advanced pre-processing techniques are employed to remove spectral anomalies, enhancing the network’s ability to accurately identify crucial quality indicators like sugar content. Concurrently, an experiment utilizing a mathematical computing software -based BP neural network optimized the number of hidden layer nodes, identifying 61 as optimal. This configuration achieves impressive indicators, including a mean square error of 0.0025665 and a root mean square error of 49.8214. More than 1000 training iterations were performed on 100 citrus samples, and the learning rate was 80%. The model demonstrated a high accuracy rate of 97.6275%, confirming its precision and reliability in assessing citrus freshness. This synergy between advanced neural network processing and spectroscopic techniques marks a significant advancement in agricultural quality assessment, setting new standards for speed and efficiency in data processing.

Double-kernel based Bayesian approximation broad learning system with dropout

Broad learning system (BLS) is an efficient incremental learning machine algorithm. However, there are some disadvantages in such an algorithm. For example, the number of hidden layer nodes needs to be manually adjusted during the training process, meanwhile the large uncertainty will be caused by two random mappings. To solve these problems, based on the optimization ability of the kernel function, a double-kernel broad learning system (DKBLS) is proposed to eliminate the uncertainty of random mapping by using additive kernel strategy. Meanwhile, to reduce the computing costs and training time of DKBLS, a double-kernel based bayesian approximation broad learning system with dropout (Dropout-DKBLS) is further proposed. Ablation experiments show that the output accuracy of Dropout-DKBLS does not decrease even if the node is dropped. In addition, function approximation experiments show that DKBLS and Dropout-DKBLS have good robustness and can accurately predict noise data. The regression and classification experiments on multiple datasets are compared with the latest kernel-based learning methods. The comparison results show that both DKBLS and Dropout-DKBLS have good regression and classification performance. By further comparing the training time of these kernel-based learning methods, we prove that the Dropout-DKBLS can reduce the computational cost while ensuring the output accuracy.

Experimental Research and Improved Neural Network Optimization Based on the Ocean Thermal Energy Conversion Experimental Platform

With the progress of research on ocean thermal energy conversion, the stabI have checked and revised all. le operation of ocean thermal energy conversion experiments has become a problem that cannot be ignored. The control foundation for stable operation is the accurate prediction of operational performance. In order to achieve accurate prediction and optimization of the performance of the ocean thermal energy conversion experimental platform, this article analyzes the experimental parameters of the turbine based on the basic experimental data obtained from the 50 kW OTEC experimental platform. Through the selection and training of experimental data, a GA-BP-OTE (GBO) model that can automatically select the number of hidden layer nodes was established using seven input parameters. Bayesian optimization was used to complete the optimization of hyperparameters, greatly reducing the training time of the surrogate model. Analyzing the prediction results of the GBO model, it is concluded that the GBO model has better prediction accuracy and has a very low prediction error in the prediction of small temperature changes in ocean thermal energy, proving the progressiveness of the model proposed in this article. The dual-objective optimization problem of turbine grid-connected power and isentropic efficiency is solved. The results show that the change in isentropic efficiency of the permeable device is affected by the combined influence of the seven parameters selected in this study, with the mass flow rate of the working fluid having the greatest impact. The MAPE of the GBO model turbine grid-connected power is 0.24547%, the MAPE of the turbine isentropic efficiency is 0.04%, and the MAPE of the turbine speed is 0.33%. The Pareto-optimal solution for the turbine grid-connected power is 40.1792 kW, with an isentropic efficiency of 0.837439.

Prediction model of coal seam gas content based on kernel principal component analysis and IDBO-DHKELM

Abstract Accurate coal seam gas content assists in the effective prevention of coal and gas outburst accidents. To solve this problem, an IDBO-DHKELM coal seam gas content prediction model is proposed by combining improved Dung Beetle optimization algorithm (IDBO) with a deep hybrid kernel extreme learning machine (DHKELM). First, the index factors of the coupled gas content are determined according to the influence factors of coal seam gas content and the actual situation of mine production. The correlation of index factors is analyzed by SPSS 27 software via Pearson correlation coefficient matrix. Then, the principal components of the original data are extracted using the principal component analysis method (KPCA). Second, sine chaotic mapping, fusion improved sinusoidal algorithm, and fusion adaptive Gauss–Cauchy hybrid mutation perturbation are introduced to improve the Dung Beetle optimization algorithm (DBO) to enhance its global search capability. Third, IDBO is used to optimize the number of hidden layer nodes, regularization coefficient, penalty coefficient, and kernel parameter in DHKELM, which improves the prediction accuracy and further avoid the phenomenon of overfitting. Finally, the principal component extracted by KPCA is taken as the model’s input, and the gas content as the model’s output. The results are compared and analyzed with those of PSO-BPNN, GA-BPNN, PSO-SVM, and DPO-DHKELM models. The results demonstrate that the IDBO-DHKELM model’s performance is the best in each performance index. Compared with other models, the mean absolute error of test samples in the IDBO-DHKELM model is reduced by 0.402, 0.4407, 0.3554, and 0.0646, respectively. The mean absolute percentage error is decreased by 3.67%, 4.07%, 8.27%, and 6.35%, respectively. The root mean square error decreased by 0.7861, 0.7148, 0.3384, and 0.1186, respectively. The coefficient of determination (R 2) is increased by 0.1544, 0.1404, 0.0955, and 0.0396, respectively. Finally, the IDBO-DHKELM model and other models are applied to an experimental mine. The resulting IDBO-DHKELM model is the closest to the actual value, which further verifies the universality and reliability of the model. Therefore, the model is more suitable for the prediction of coal seam gas content.

An obstacle avoidance safety detection algorithm for power lines combining binocular vision technology and improved object detection

In this paper, a framework of obstacle avoidance algorithm applied to power line damage safety distance detection is constructed, and its overall architecture and key processes are described in detail. The system design covers three core modules: visual data acquisition and preliminary processing, accurate target recognition and distance measurement, and system error analysis and correction. In the visual data processing chain, we deeply analyze every step from image acquisition to preprocessing to feature extraction, aiming to enhance the adaptability of applications to complex scenes. The target recognition and distance estimation part integrates advanced technology of deep learning to improve the reliability of recognition accuracy and distance estimation. In addition, many common error sources, such as system bias, parallax discontinuity, fluctuation of illumination conditions, etc., are discussed in depth, and corresponding correction strategies are proposed to ensure the accuracy and stability of the system, which provides powerful technical support for achieving efficient and accurate safety monitoring. Specifically, by carefully adjusting the learning rate, convolution kernel size, batch size, pooling layer type, and number of hidden layer nodes, we succeeded in improving the overall accuracy from the initial average of 92.4–95%, and the error rate decreased accordingly.

The Influence of Particle Swarm Optimization‐Back Propagation Neural Network Hyperparameter Selection on the Prediction Accuracy of Converter Endpoint Temperature

The converter is a complex, high temperature, high pressure reactor with limited internal moitoring. At present, data‐driven models mainly focus on the prediction differences between algorithms, and there is relatively little analysis of the impact of different hyperparameters on prediction accuracy. Taking a 120 t converter in a Chinese steel plant as an example, this paper explores the application of particle swarm optimization‐back propagation neural network (PSO‐BP) in converter temperature prediction. First, the Pauta criterion or Box plot method was used to preprocess the data by prescreening. Subsequently, the influence of the activation function, learning rate, and number of hidden layer nodes of BP on the prediction accuracy of the endpoint temperature were explored. Then we investigated the influence of PSO parameters on the optimal result of BP initial value. Comparing the temperature prediction hit rate before and after optimization, the BP model has hit rates of 63.64%, 79.22%, and 87.45% within ±10, ±15, and ±20 °C, respectively, and the PSO‐BP model has hit rates of 68.40%, 84.85%, and 94.81%, respectively. In comparison, PSO‐BP extracts data features more accurately, has higher stability, and has better accuracy in predicting the endpoint temperature of the converter.

Predicting green tea moisture content during roasting by shape feature

This study investigated the changes in tea moisture content and shape features parameters during the roasting process of roasted green tea under different temperatures(70, 100 and 130 °C), leaf amounts (40, 70 and 100 kg), and cylinder speeds (25, 27.5 and 30 r/min), and developed a moisture content prediction model based on Random forest-Genetic algorithm-Back propagation(RF-GA-BP) neural network. Firstly, based on image processing technology, the shape parameters of tea leaves during the roasting process were automatically extracted, and the random forest algorithm was used to rank their importance to reduce the complexity of the model. Then, the activation function and the number of hidden layer nodes in the network structure were optimized. Finally, the initial weights and thresholds of the neural network were optimized using genetic algorithm to obtain the optimal parameters for constructing a moisture content prediction model during the roasting process. The results indicated that the importance of slightness was the highest, with a value of 0.865. The RF-GA-BP neural network model with mean absolute error, root mean square error, and coefficient of determination of 0.030, 0.036, and 0.915, respectively, was superior to the BP, GA-BP, and RF-BP neural network models, and could better predict the moisture content of tea during the roasting process.

The changes prediction on terrestrial water storage in typical regions of China based on neural networks and satellite gravity data

Accurate prediction of regional terrestrial water storage change (TWSA) is of great significance for water resources planning and management, and early warning of extreme climate disasters. Aiming at the problem that the conventional methods on prediction of TWSA time series are difficult to be accurate, the six typical regions are selected in China as examples, including the upper reaches of the Yangtze River (UYR), the southwest region (SWR), the Liaohe River Basin (LRB), the North China Plain (NCP), the Qinghai-Tibet Plateau (QTP), and the Pearl River Basin (PRB). The mascon product from GRACE/GRACE-FO provided by CSR is used to extract TWSA time series in six typical areas. The improved Back Propagation (BP) neural network, Long Short-Term Memory (LSTM) neural network and the latest Bidirectional LSTM (BiLSTM-attention) neural network model based on attention mechanism are proposed to predict and analyze the regional TWSA. In the experiment, the selection of the optimal model parameters such as the number of hidden layer nodes and the number of hidden units of the neural network model is tested and analyzed in detail. Meanwhile, the model prediction results are compared with the traditional least squares method and random forest (RF) prediction method. The root mean square error (RMSE), determination coefficient (R2), Nash–Sutcliffe efficiency coefficient (NSE) and mean absolute percentage error (MAPE) were used to evaluate the accuracy of the predicted results. The results show that the improved BP, LSTM and Bi-LSTM-attention neural network models all achieve higher prediction accuracy in UYR and SWR areas. RMSE is less than 2.641 cm, R2 is as high as 0.8 or more, NSE is above 0.6, and MAPE is within 0.1. Compared with the least square method, the RMSE of the predicted results from three neural network decreased by 0.998 cm, 0.700 cm and 0.7563 on average, and the R2 increased by 81.75%, 69.89% and 72% on average. Compared with RFML method, the RMSE from three neural network is reduced by 0.601 cm, 0.316 cm and 0.360, and R2 is increased by 38.20%, 24.60% and 27.06% on average. NSE and RMSE are improved to varying degrees in the above regions. It shows that the improved BP, LSTM and BiLSTM-attention model used can effectively predict TWSA. The research methods and results in this paper can provide important reference for the rational utilization of regional water resources and disaster risk assessment.

Firefly Interval Selection Combined With Extreme Learning Machine for Spectral Quantification of Complex Samples

ABSTRACTFirefly algorithm (FA) combined with extreme learning machine (ELM) is developed for spectral interval selection and quantitative analysis of complex samples. The method firstly segments the spectra into a certain number of intervals. Vectors with 1 and 0, which represent the interval selected or not, are used as the inputs of the FA. The RMSEP value predicted by ELM model is used as the fitness function of the FA. The activation function and number of hidden layer nodes of ELM, number of spectral intervals, population number, environmental absorbance, and constant of FA are optimized. The predictive performance of FA‐ELM is compared with full‐spectrum PLS, ELM, genetic algorithm‐ELM (GA‐ELM), and particle swarm optimization‐ELM (PSO‐ELM) by one ultraviolet (UV) spectrum dataset of gasoil and three near‐infrared (NIR) spectral datasets of corn, wheat, and tablet samples. The results show that FA‐ELM has a better performance compared with its competitors in predicting monoaromatics, water, wheat kernel texture, and active pharmaceutical ingredients (APIs) in gasoil, corn, wheat, and tablet samples.

Harmonic Detection Methods and Optimization Strategies for Charger in Power Grid

The charger’s operation in the power grid will cause harmonic pollution, affecting the service life of the equipment and the quality of the power grid. The harmonic characteristics and detection during the charging process are studied. The simulation model of charger is established first using MATLAB, the results of the experiment show that odd harmonics are mainly generated during charging, and the distortion rate of the current harmonics remains between 0.231 and 0.443 during the charging process. A new wavelet neural network is proposed to detect the harmonic method. Experimental results indicate that, compared with previous detection methods, this network has better detection efficiency and accuracy for harmonics. But detection result of this network is unstable and does not even converge. A new adaptive bat algorithm with improved focusing distance is presented here to optimize the wavelet neural network, which effectively solves the defect of being sensitive to the node number of hidden layer, resulting in higher detection accuracy, faster detection speed, and stable convergence. The detection error range is reduced from −0.03 to 0.02, and the number of iterations is reduced to around 1000.

Efficiency optimization methods for stochastic configuration networks

To solve the problems of the low efficiency of parameter allocation and time-consuming computation of output weights in the hidden layers of stochastic configuration networks (SCNs), an optimization method is proposed to improve the SCNs construction efficiency. Firstly, with the increase in the number of hidden layer nodes, the key parameters that determine the strictness of the supervision mechanism are reconstructed to speed up the configuration efficiency of hidden layer input weights and biases. Then, the incremental mechanism of the SCNs are combined with the QR decomposition method, and the output weights are calculated by iteratively updating the transformation matrix, thus reducing the computational complexity of training the SCNs. Finally, the proposed method is validated on four standard datasets and historical data of a municipal solid waste incineration process. The experimental results show that the proposed method improves the efficiency of SCN construction while guaranteeing the prediction accuracy of SCNs model.

Performance prediction model for desalination plants using modified grey wolf optimizer based artificial neural network approach

Desalination represents an effective method for alleviating water scarcity, applying algorithmic techniques to predict the performance of reverse osmosis (RO) desalination plants, Modified Grey Wolf Optimizer (MGWO) based Artificial Neural Networks (ANN) can predict the performance of membrane distillation (MD) equipment. Four experimental inputs are selected: feed salt concentration(35–140 g/h), feed flow rate(400–600 L/h), evaporator inlet temperature (60–80 ℃), and condenser inlet temperature (20–30 ℃). The permeate flux (L/h m2) is selected as the experimental output. Ten prediction models were proposed and compared with the existing models (ANN, WOA-ANN, and GWO-ANN). The results showed that the MGWO-ANN model-5 showed the best regression results: R2 = 99.3 %, mean square error (MSE)= 0.004. This model outperformed the existing ANN model (R2 =98.8 %, MSE=0.060), WOA-ANN model (R2 =99.1 %, MSE=0.005) and GWO-ANN model (R2 =98.9 %, MSE=0.007). Model-5 has a single hidden layer (H=1), 13 hidden nodes (n = 13), 10 search agents (SA=10), and 75 %− 20 %− 05 % dataset division. Its residual error is within acceptable limits (spanning −0.1 to 0.2). Optimizing the number of hidden layer nodes (n) and the number of search agents (SA) can improve the training efficiency and prediction accuracy of the model, and the MGWO-ANN model is capable of more accurately predicting the performance of desalination plants.

Algorithm for community security risk assessment and influencing factors analysis by back propagation neural network

This paper aims to accurately assess and effectively manage various security risks in the community and overcome the challenges faced by traditional models in handling large amounts of features and high-dimensional data. Hence, this paper utilizes the back propagation neural network (BPNN) to optimize the security risk assessment model. A key challenge of researching community security risk assessment lies in accurately identifying and predicting a range of potential security threats. These threats may encompass natural disasters, public health crises, accidents, and social security issues. The intricate interplay of these risk factors, combined with the dynamic nature of community environments, presents difficulties for traditional risk assessment methodologies to address effectively. Initially, this paper delves into the factors influencing safety incidents within communities and establishes a comprehensive system of safety risk assessment indicators. Leveraging the adaptable and generalizable nature of the BPNN model, the paper proceeds to optimize the BPNN model, enhancing the security risk assessment model through this optimization. Subsequent comparison experiments with traditional models validate the rationality and effectiveness of the proposed model, with hidden layer nodes set at various levels like 10, 15, 20, 25, 30, and 35. These traditional models include Convolutional Neural Network (CNN), Long Short-Term Memory Network (LSTM), Bidirectional Encoder Representations from Transformers (BERT), Generative Pre-trained Transformer (GPT), and eXtreme Gradient Boosting (XGBOOST). Experimental findings demonstrate that with 20 hidden layer nodes, the optimized model achieves a remarkable final recognition accuracy of 99.1 %. Moreover, the optimized model exhibits significantly lower final function loss compared to models with different node numbers. Increasing the number of hidden layer nodes may diminish the optimized model's fit and accuracy. Comparison with traditional models reveals that the average accuracy of the optimized model in community risk identification reaches 98.5 %, with a maximum accuracy of 99.6 %. This marks an improvement of 9%–11 % in recognition accuracy across various risk factors compared to traditional models. Regarding system response time and resource utilization, the optimized model exhibits a response time ranging from 100 ms to 120 ms and consistently lower resource utilization rates across all scenarios, underscoring its efficiency in community security risk assessment. In conclusion, this experiment sheds light on the underlying mechanisms and patterns of community safety risk formation, offering novel perspectives and methodologies for researching community safety risk assessment. The paper concludes by presenting recommendations and strategies for addressing community safety risks based on experimental analysis.

Performance Prediction and Optimization of Single-Piston Free Piston Expander-Linear Generator Based on Machine Learning and Genetic Algorithm

This paper proposed a single-piston free piston expander-linear generator (SFPE-LG) prototype applied to organic Rankine cycle systems. Two valve timing control strategies, namely, time control strategy (TCS) and position control strategy (PCS), were developed. Based on the experimental data, a back propagation neural network (BPNN) prediction model was established. The effects of structural parameters such as neural network layers, transfer function, training function, hidden layer nodes, and learning rate on the prediction accuracy of this BPNN model were discussed. The training and prediction accuracy of the BPNN model was verified using 5-fold cross-validation and Wilcoxon signed-rank test. Moreover, the BPNN model was integrated with a genetic algorithm to predict and optimize the maximum output power of the SFPE-LG. The results showed that the BPNN model used to predict the motion characteristics and output performance of the SFPE-LG exhibits strong learning ability and high prediction accuracy. Notably, the prediction accuracy of the BPNN model is significantly higher under the PCS compared to TCS. The effect of hidden layer nodes on mean square error (MSE) and correlation coefficient (R) is greater than that of the learning rate. When the number of hidden layer nodes exceeds 30, the BPNN model consistently achieves low MSE and high R. The optimization results showed that the SFPE-LG can obtain a maximum output power of 141.69 W under the TCS, when the working parameters are inlet pressure of 0.7 MPa, intake duration of 35 ms, load resistance of 67 Ω, and expansion duration of 104 ms, respectively.

A cooperative stochastic configuration network based on differential evolutionary sparrow search algorithm for prediction

Stochastic configuration network (SCN) is a powerful prediction model whose performance is significantly influenced by the configuration of the network parameters. To improve the prediction accuracy of the network, a cooperative stochastic configuration network (CSCN) based on a novel differential evolutionary sparrow search algorithm (DESSA), termed as DESSA-CSCN, is proposed. In the CSCN, the number of hidden layer nodes is adaptively adjusted according to the number of iterations, and the parameters of hidden nodes are cooperatively optimized by using a population-based metaheuristic algorithm. A sparse matrix is introduced to mitigate parameter overfitting caused by the increased number of hidden layer nodes. During parameter optimization, the fitness function is constructed by using the supervision mechanism of the SCN, and the DESSA is utilized as the metaheuristic algorithm to update the weights and biases. In order to verify the effectiveness of the DESSA-CSCN, several simulation experiments have been conducted. The performance of the DESSA is evaluated by the CEC2017 test suit, and the simulation results show that the DESSA exhibits better convergence accuracy and can jump out of local optima more effectively than other algorithms. The performance of the DESSA-CSCN is evaluated by 4 datasets from KEEL, and the simulation results indicate that the DESSA-CSCN achieves better prediction accuracy and faster prediction speed than other models.

Creation of Deep Learning Scenarios in the Network Teaching of Physical Education Technical Courses

The network teaching evaluation of sports professional technical courses has positive significance for the sustainable development of education. And how to establish an effective evaluation model is the key part. The research introduces the creation of in-depth learning scenarios (LS) into the network teaching of sports professional technical courses, and then constructs a new network teaching mode of sports professional technical courses. The Particle Swarm Optimization algorithm - Attention- Long Short-Term Memory network (PSO-Attention-LSTM) Chinese Emotion Classification Model (ECM) is constructed to classify the online evaluation text to realize the evaluation of online teaching. This model combines the improved PSO, Attention and LSTM classification models. The optimal number of hidden layer nodes for LSTM model is about 100, and the optimal data size for batch processing is 25. The overall error rate of online teaching teachers of male and female sports professional skill courses is 10.1%, and the overall error rate of online teaching teachers of general and advanced sports professional skill courses is 12.8%. The application effect of the creation of in-depth learning scene in the network teaching of physical education technical courses is shown. When the classification threshold is 0.6 and 0.8 respectively, the AUC of PSO-Attention-LSTM Chinese ECM is 0.821 and 0.809 respectively. The research institute has put forward that the online teaching platform of sports professional technical courses has extremely high practical application value and has been unanimously praised by network users.

An Improved Extreme Learning Machine (ELM) Algorithm for Intent Recognition of Transfemoral Amputees With Powered Knee Prosthesis.

To overcome the challenges posed by the complex structure and large parameter requirements of existing classification models, the authors propose an improved extreme learning machine (ELM) classifier for human locomotion intent recognition in this study, resulting in enhanced classification accuracy. The structure of the ELM algorithm is enhanced using the logistic regression (LR) algorithm, significantly reducing the number of hidden layer nodes. Hence, this algorithm can be adopted for real-time human locomotion intent recognition on portable devices with only 234 parameters to store. Additionally, a hybrid grey wolf optimization and slime mould algorithm (GWO-SMA) is proposed to optimize the hidden layer bias of the improved ELM classifier. Numerical results demonstrate that the proposed model successfully recognizes nine daily motion modes including low-, mid-, and fast-speed level ground walking, ramp ascent/descent, sit/stand, and stair ascent/descent. Specifically, it achieves 96.75% accuracy with 5-fold cross-validation while maintaining a real-time prediction time of only 2 ms. These promising findings highlight the potential of onboard real-time recognition of continuous locomotion modes based on our model for the high-level control of powered knee prostheses.

Real-time automatic identification methods for downhole whirling based on mechanical specific energy model of drill bit

In the drilling exploitation of hot dry rock for geothermal energy, whirling is one of the main low-efficiency conditions that affect the efficiency of Polycrystalline Diamond Compact (PDC) bit in horizontal well drilling. Realizing automatic and real-time identification with whirling is of great significance to save non-productive time and ensure drilling safety and benefit. In this paper, we first constructed a real-time drilling mechanical specific energy (MSE) model combined with while-drilling testing to reflect the real-time drilling conditions. The MSE model is used to normalize multi-source parameters. Secondly, we constructed a Back Propagation (BP) artificial neural network (ANN), and then the normalization effect verification, optimization of network parameters, and identification effect verification of whirling were carried out. The final results show that the established MSE model has a favourable effect on data normalization, which could also reduce the complexity of the required network model, and shorten the training time by 20–30 s/step. The optimal algorithm is Trainscg, whose optimal number of hidden layer nodes is 5, and the optimal maximum number of iteration steps is 1000. The established ANN model can accurately identify whirling based on MSE, the accuracy is about 0.94, and the average relative error is 1.3%. The method established in this paper provides a reference for the automatic identification of various low-efficiency conditions based on MSE.

Optimization Design of Phononic Crystals Based on BPNN‐MPA in Applied Mathematical Analysis

Traditional finite element analysis methods have the problem of expensive and unstable band structure diagram calculation when generating phononic crystals. Therefore, this study combines back propagation neural networks with ocean predator algorithms to optimize the geometric structure of phononic crystals. The results show that the coefficient of determination for the predicted bandgap width and lower bound of Model 3 is 1.00, which is better than the comparison model. However, Models 2 and 5 have poor predictive performance for bandgap width due to overfitting during actual training. Therefore, after using the ocean predator algorithm for hyperparameter adjustment, it is found that the maximum number of failures in the validation set of Model 5 is 30, the number of hidden layer nodes is 30, and after 500 experiments, the average error of the bandgap width is 5.26%, and the average error of the lower bound of the bandgap is 1.33%. The average error of the bandgap width after hyperparameter adjustment is 4.89%, and the average error of the lower bound of the bandgap is 1.21%, both of which are effectively reduced and better than the comparison model. Overall, the combination model has high computational efficiency and stability in phononic crystal optimization and can be practically applied in the design and optimization of phononic crystal geometric structures.