Review of Recent Trends in the Hybridisation of Preprocessing-Based and Parameter Optimisation-Based Hybrid Models to Forecast Univariate Streamflow

Forecasting river flow is crucial for optimal planning,management,and sustainability using freshwater resources.Many machine learning(ML)approaches have been enhanced to improve streamflow prediction.Hybrid techniques have been viewed as a viable method for enhancing the accuracy of univariate streamflow estimation when compared to standalone approaches.Current researchers have also emphasised using hybrid models to improve forecast accuracy.Accordingly,this paper conducts an updated literature review of applications of hybrid models in estimating streamflow over the last five years,summarising data preprocessing,univariate machine learning modelling strategy,advantages and disadvantages of standalone ML techniques,hybrid models,and performance metrics.This study focuses on two types of hybrid models:parameter optimisation-based hybrid models(OBH)and hybridisation of parameter optimisation-based and preprocessing-based hybridmodels(HOPH).Overall,this research supports the idea thatmeta-heuristic approaches precisely improveML techniques.It’s also one of the first efforts to comprehensively examine the efficiency of various meta-heuristic approaches(classified into four primary classes)hybridised with ML techniques.This study revealed that previous research applied swarm,evolutionary,physics,and hybrid metaheuristics with 77%,61%,12%,and 12%,respectively.Finally,there is still room for improving OBH and HOPH models by examining different data pre-processing techniques and metaheuristic algorithms.

Efficient knowledge distillation for hybrid models:A vision transformer‐convolutional neural network to convolutional neural network approach for classifying remote sensing images

In various fields,knowledge distillation(KD)techniques that combine vision transformers(ViTs)and convolutional neural networks(CNNs)as a hybrid teacher have shown remarkable results in classification.However,in the realm of remote sensing images(RSIs),existing KD research studies are not only scarce but also lack competitiveness.This issue significantly impedes the deployment of the notable advantages of ViTs and CNNs.To tackle this,the authors introduce a novel hybrid‐model KD approach named HMKD‐Net,which comprises a CNN‐ViT ensemble teacher and a CNN student.Contrary to popular opinion,the authors posit that the sparsity in RSI data distribution limits the effectiveness and efficiency of hybrid‐model knowledge transfer.As a solution,a simple yet innovative method to handle variances during the KD phase is suggested,leading to substantial enhancements in the effectiveness and efficiency of hybrid knowledge transfer.The authors assessed the performance of HMKD‐Net on three RSI datasets.The findings indicate that HMKD‐Net significantly outperforms other cuttingedge methods while maintaining a significantly smaller size.Specifically,HMKD‐Net exceeds other KD‐based methods with a maximum accuracy improvement of 22.8%across various datasets.As ablation experiments indicated,HMKD‐Net has cut down on time expenses by about 80%in the KD process.This research study validates that the hybrid‐model KD technique can be more effective and efficient if the data distribution sparsity in RSIs is well handled.

Spatial Heterogeneity Modeling Using Machine Learning Based on a Hybrid of Random Forest and Convolutional Neural Network (CNN)

Spatial heterogeneity refers to the variation or differences in characteristics or features across different locations or areas in space. Spatial data refers to information that explicitly or indirectly belongs to a particular geographic region or location, also known as geo-spatial data or geographic information. Focusing on spatial heterogeneity, we present a hybrid machine learning model combining two competitive algorithms: the Random Forest Regressor and CNN. The model is fine-tuned using cross validation for hyper-parameter adjustment and performance evaluation, ensuring robustness and generalization. Our approach integrates Global Moran’s I for examining global autocorrelation, and local Moran’s I for assessing local spatial autocorrelation in the residuals. To validate our approach, we implemented the hybrid model on a real-world dataset and compared its performance with that of the traditional machine learning models. Results indicate superior performance with an R-squared of 0.90, outperforming RF 0.84 and CNN 0.74. This study contributed to a detailed understanding of spatial variations in data considering the geographical information (Longitude & Latitude) present in the dataset. Our results, also assessed using the Root Mean Squared Error (RMSE), indicated that the hybrid yielded lower errors, showing a deviation of 53.65% from the RF model and 63.24% from the CNN model. Additionally, the global Moran’s I index was observed to be 0.10. This study underscores that the hybrid was able to predict correctly the house prices both in clusters and in dispersed areas.

Advancing Type II Diabetes Predictions with a Hybrid LSTM-XGBoost Approach

In this paper, we explore the ability of a hybrid model integrating Long Short-Term Memory (LSTM) networks and eXtreme Gradient Boosting (XGBoost) to enhance the prediction accuracy of Type II Diabetes Mellitus, which is caused by a combination of genetic, behavioral, and environmental factors. Utilizing comprehensive datasets from the Women in Data Science (WiDS) Datathon for the years 2020 and 2021, which provide a wide range of patient information required for reliable prediction. The research employs a novel approach by combining LSTM’s ability to analyze sequential data with XGBoost’s strength in handling structured datasets. To prepare this data for analysis, the methodology includes preparing it and implementing the hybrid model. The LSTM model, which excels at processing sequential data, detects temporal patterns and trends in patient history, while XGBoost, known for its classification effectiveness, converts these patterns into predictive insights. Our results demonstrate that the LSTM-XGBoost model can operate effectively with a prediction accuracy achieving 0.99. This study not only shows the usefulness of the hybrid LSTM-XGBoost model in predicting diabetes but it also provides the path for future research. This progress in machine learning applications represents a significant step forward in healthcare, with the potential to alter the treatment of chronic diseases such as diabetes and lead to better patient outcomes.

Enhancing Deep Learning Soil Moisture Forecasting Models by Integrating Physics-based Models

Accurate soil moisture(SM)prediction is critical for understanding hydrological processes.Physics-based(PB)models exhibit large uncertainties in SM predictions arising from uncertain parameterizations and insufficient representation of land-surface processes.In addition to PB models,deep learning(DL)models have been widely used in SM predictions recently.However,few pure DL models have notably high success rates due to lacking physical information.Thus,we developed hybrid models to effectively integrate the outputs of PB models into DL models to improve SM predictions.To this end,we first developed a hybrid model based on the attention mechanism to take advantage of PB models at each forecast time scale(attention model).We further built an ensemble model that combined the advantages of different hybrid schemes(ensemble model).We utilized SM forecasts from the Global Forecast System to enhance the convolutional long short-term memory(ConvLSTM)model for 1–16 days of SM predictions.The performances of the proposed hybrid models were investigated and compared with two existing hybrid models.The results showed that the attention model could leverage benefits of PB models and achieved the best predictability of drought events among the different hybrid models.Moreover,the ensemble model performed best among all hybrid models at all forecast time scales and different soil conditions.It is highlighted that the ensemble model outperformed the pure DL model over 79.5%of in situ stations for 16-day predictions.These findings suggest that our proposed hybrid models can adequately exploit the benefits of PB model outputs to aid DL models in making SM predictions.

Hybrid model for BOF oxygen blowing time prediction based on oxygen balance mechanism and deep neural network

The amount of oxygen blown into the converter is one of the key parameters for the control of the converter blowing process,which directly affects the tap-to-tap time of converter. In this study, a hybrid model based on oxygen balance mechanism (OBM) and deep neural network (DNN) was established for predicting oxygen blowing time in converter. A three-step method was utilized in the hybrid model. First, the oxygen consumption volume was predicted by the OBM model and DNN model, respectively. Second, a more accurate oxygen consumption volume was obtained by integrating the OBM model and DNN model. Finally, the converter oxygen blowing time was calculated according to the oxygen consumption volume and the oxygen supply intensity of each heat. The proposed hybrid model was verified using the actual data collected from an integrated steel plant in China, and compared with multiple linear regression model, OBM model, and neural network model including extreme learning machine, back propagation neural network, and DNN. The test results indicate that the hybrid model with a network structure of 3 hidden layer layers, 32-16-8 neurons per hidden layer, and 0.1 learning rate has the best prediction accuracy and stronger generalization ability compared with other models. The predicted hit ratio of oxygen consumption volume within the error±300 m^(3)is 96.67%;determination coefficient (R^(2)) and root mean square error (RMSE) are0.6984 and 150.03 m^(3), respectively. The oxygen blow time prediction hit ratio within the error±0.6 min is 89.50%;R2and RMSE are0.9486 and 0.3592 min, respectively. As a result, the proposed model can effectively predict the oxygen consumption volume and oxygen blowing time in the converter.

Hybrid modeling for carbon monoxide gas-phase catalytic coupling to synthesize dimethyl oxalate process

Ethylene glycol(EG)plays a pivotal role as a primary raw material in the polyester industry,and the syngas-to-EG route has become a significant technical route in production.The carbon monoxide(CO)gas-phase catalytic coupling to synthesize dimethyl oxalate(DMO)is a crucial process in the syngas-to-EG route,whereby the composition of the reactor outlet exerts influence on the ultimate quality of the EG product and the energy consumption during the subsequent separation process.However,measuring product quality in real time or establishing accurate dynamic mechanism models is challenging.To effectively model the DMO synthesis process,this study proposes a hybrid modeling strategy that integrates process mechanisms and data-driven approaches.The CO gas-phase catalytic coupling mechanism model is developed based on intrinsic kinetics and material balance,while a long short-term memory(LSTM)neural network is employed to predict the macroscopic reaction rate by leveraging temporal relationships derived from archived measurements.The proposed model is trained semi-supervised to accommodate limited-label data scenarios,leveraging historical data.By integrating these predictions with the mechanism model,the hybrid modeling approach provides reliable and interpretable forecasts of mass fractions.Empirical investigations unequivocally validate the superiority of the proposed hybrid modeling approach over conventional data-driven models(DDMs)and other hybrid modeling techniques.

HybridGAD: Identification of AI-Generated Radiology Abstracts Based on a Novel Hybrid Model with Attention Mechanism

Class Title:Radiological imaging method a comprehensive overview purpose.This GPT paper provides an overview of the different forms of radiological imaging and the potential diagnosis capabilities they offer as well as recent advances in the field.Materials and Methods:This paper provides an overview of conventional radiography digital radiography panoramic radiography computed tomography and cone-beam computed tomography.Additionally recent advances in radiological imaging are discussed such as imaging diagnosis and modern computer-aided diagnosis systems.Results:This paper details the differences between the imaging techniques the benefits of each and the current advances in the field to aid in the diagnosis of medical conditions.Conclusion:Radiological imaging is an extremely important tool in modern medicine to assist in medical diagnosis.This work provides an overview of the types of imaging techniques used the recent advances made and their potential applications.

Different El Niño Flavors and Associated Atmospheric Teleconnections as Simulated in a Hybrid Coupled Model

A previously developed hybrid coupled model(HCM)is composed of an intermediate tropical Pacific Ocean model and a global atmospheric general circulation model(AGCM),denoted as HCMAGCM.In this study,different El Niño flavors,namely the Eastern-Pacific(EP)and Central-Pacific(CP)types,and the associated global atmospheric teleconnections are examined in a 1000-yr control simulation of the HCMAGCM.The HCMAGCM indicates profoundly different characteristics among EP and CP El Niño events in terms of related oceanic and atmospheric variables in the tropical Pacific,including the amplitude and spatial patterns of sea surface temperature(SST),zonal wind stress,and precipitation anomalies.An SST budget analysis indicates that the thermocline feedback and zonal advective feedback dominantly contribute to the growth of EP and CP El Niño events,respectively.Corresponding to the shifts in the tropical rainfall and deep convection during EP and CP El Niño events,the model also reproduces the differences in the extratropical atmospheric responses during the boreal winter.In particular,the EP El Niño tends to be dominant in exciting a poleward wave train pattern to the Northern Hemisphere,while the CP El Niño tends to preferably produce a wave train similar to the Pacific North American(PNA)pattern.As a result,different climatic impacts exist in North American regions,with a warm-north and cold-south pattern during an EP El Niño and a warm-northeast and cold-southwest pattern during a CP El Niño,respectively.This modeling result highlights the importance of internal natural processes within the tropical Pacific as they relate to the genesis of ENSO diversity because the active ocean–atmosphere coupling is allowed only in the tropical Pacific within the framework of the HCMAGCM.

Enhancing Software Effort Estimation:A Hybrid Model Combining LSTM and Random Forest

Effort estimation plays a crucial role in software development projects,aiding in resource allocation,project planning,and risk management.Traditional estimation techniques often struggle to provide accurate estimates due to the complex nature of software projects.In recent years,machine learning approaches have shown promise in improving the accuracy of effort estimation models.This study proposes a hybrid model that combines Long Short-Term Memory(LSTM)and Random Forest(RF)algorithms to enhance software effort estimation.The proposed hybrid model takes advantage of the strengths of both LSTM and RF algorithms.To evaluate the performance of the hybrid model,an extensive set of software development projects is used as the experimental dataset.The experimental results demonstrate that the proposed hybrid model outperforms traditional estimation techniques in terms of accuracy and reliability.The integration of LSTM and RF enables the model to efficiently capture temporal dependencies and non-linear interactions in the software development data.The hybrid model enhances estimation accuracy,enabling project managers and stakeholders to make more precise predictions of effort needed for upcoming software projects.

Simultaneous Identification of Thermophysical Properties of Semitransparent Media Using a Hybrid Model Based on Artificial Neural Network and Evolutionary Algorithm

A hybrid identification model based on multilayer artificial neural networks(ANNs) and particle swarm optimization(PSO) algorithm is developed to improve the simultaneous identification efficiency of thermal conductivity and effective absorption coefficient of semitransparent materials.For the direct model,the spherical harmonic method and the finite volume method are used to solve the coupled conduction-radiation heat transfer problem in an absorbing,emitting,and non-scattering 2D axisymmetric gray medium in the background of laser flash method.For the identification part,firstly,the temperature field and the incident radiation field in different positions are chosen as observables.Then,a traditional identification model based on PSO algorithm is established.Finally,multilayer ANNs are built to fit and replace the direct model in the traditional identification model to speed up the identification process.The results show that compared with the traditional identification model,the time cost of the hybrid identification model is reduced by about 1 000 times.Besides,the hybrid identification model remains a high level of accuracy even with measurement errors.

A Novel Hybrid Architecture for Superior IoT Threat Detection through Real IoT Environments

As the Internet of Things(IoT)continues to expand,incorporating a vast array of devices into a digital ecosystem also increases the risk of cyber threats,necessitating robust defense mechanisms.This paper presents an innovative hybrid deep learning architecture that excels at detecting IoT threats in real-world settings.Our proposed model combines Convolutional Neural Networks(CNN),Bidirectional Long Short-Term Memory(BLSTM),Gated Recurrent Units(GRU),and Attention mechanisms into a cohesive framework.This integrated structure aims to enhance the detection and classification of complex cyber threats while accommodating the operational constraints of diverse IoT systems.We evaluated our model using the RT-IoT2022 dataset,which includes various devices,standard operations,and simulated attacks.Our research’s significance lies in the comprehensive evaluation metrics,including Cohen Kappa and Matthews Correlation Coefficient(MCC),which underscore the model’s reliability and predictive quality.Our model surpassed traditional machine learning algorithms and the state-of-the-art,achieving over 99.6%precision,recall,F1-score,False Positive Rate(FPR),Detection Time,and accuracy,effectively identifying specific threats such as Message Queuing Telemetry Transport(MQTT)Publish,Denial of Service Synchronize network packet crafting tool(DOS SYN Hping),and Network Mapper Operating System Detection(NMAP OS DETECTION).The experimental analysis reveals a significant improvement over existing detection systems,significantly enhancing IoT security paradigms.Through our experimental analysis,we have demonstrated a remarkable enhancement in comparison to existing detection systems,which significantly strength-ens the security standards of IoT.Our model effectively addresses the need for advanced,dependable,and adaptable security solutions,serving as a symbol of the power of deep learning in strengthening IoT ecosystems amidst the constantly evolving cyber threat landscape.This achievement marks a significant stride towards protecting the integrity of IoT infrastructure,ensuring operational resilience,and building privacy in this groundbreaking technology.

Locally weighted learning based hybrid intelligence models for groundwater potential mapping and modeling: A case study at Gia Lai province, Vietnam

The groundwater potential map is an important tool for a sustainable water management and land use planning,particularly for agricultural countries like Vietnam.In this article,we proposed new machine learning ensemble techniques namely AdaBoost ensemble(ABLWL),Bagging ensemble(BLWL),Multi Boost ensemble(MBLWL),Rotation Forest ensemble(RFLWL)with Locally Weighted Learning(LWL)algorithm as a base classifier to build the groundwater potential map of Gia Lai province in Vietnam.For this study,eleven conditioning factors(aspect,altitude,curvature,slope,Stream Transport Index(STI),Topographic Wetness Index(TWI),soil,geology,river density,rainfall,land-use)and 134 wells yield data was used to create training(70%)and testing(30%)datasets for the development and validation of the models.Several statistical indices were used namely Positive Predictive Value(PPV),Negative Predictive Value(NPV),Sensitivity(SST),Specificity(SPF),Accuracy(ACC),Kappa,and Receiver Operating Characteristics(ROC)curve to validate and compare performance of models.Results show that performance of all the models is good to very good(AUC:0.75 to 0.829)but the ABLWL model with AUC=0.89 is the best.All the models applied in this study can support decision-makers to streamline the management of the groundwater and to develop economy not only of specific territories but also in other regions across the world with minor changes of the input parameters.

Flow reconstructions and aerodynamic shape optimization of turbomachinery blades by POD-based hybrid models

This study presented a hybrid model method based on proper orthogonal decomposition(POD) for flow field reconstructions and aerodynamic design optimization. The POD basis modes have better description performance in a system space compared to the widely used semi-empirical basis functions because they are obtained through singular value decomposition of the system.Instead of the widely used linear regression, nonlinear regression methods are used in the function response of the coefficients of POD basis modes. Moreover, an adaptive Latin hypercube design method with improved space filling and correlation based on a multi-objective optimization approach was employed to supply the necessary samples. Prior to design optimization, the response performance of POD-based hybrid models was first investigated and validated through flow reconstructions of both single-and multiple blade rows. Then, an inverse design was performed to approach a given spanwise flow turning distribution at the outlet of a turbine blade by changing the spanwise stagger angle, based on the hybrid model method. Finally, the span wise blade sweep of a transonic compressor rotor and the spanwise stagger angle of the stator blade of a single low-speed compressor stage were modified to reduce the flow losses with the constraints of mass flow rate, total pressure ratio, and outlet flow turning.The results are presented in detail, demonstrating the good response performance of POD-based hybrid models on missing data reconstructions and the effectiveness of POD-based hybrid model method in aerodynamic design optimization.

A Hybrid Neural Network and Box-Jenkins Models for Time Series Forecasting

Time series forecasting plays a significant role in numerous applications,including but not limited to,industrial planning,water consumption,medical domains,exchange rates and consumer price index.The main problem is insufficient forecasting accuracy.The present study proposes a hybrid forecastingmethods to address this need.The proposed method includes three models.The first model is based on the autoregressive integrated moving average(ARIMA)statistical model;the second model is a back propagation neural network(BPNN)with adaptive slope and momentum parameters;and the thirdmodel is a hybridization between ARIMA and BPNN(ARIMA/BPNN)and artificial neural networks and ARIMA(ARIMA/ANN)to gain the benefits of linear and nonlinearmodeling.The forecasting models proposed in this study are used to predict the indices of the consumer price index(CPI),and predict the expected number of cancer patients in the Ibb Province in Yemen.Statistical standard measures used to evaluate the proposed method include(i)mean square error,(ii)mean absolute error,(iii)root mean square error,and(iv)mean absolute percentage error.Based on the computational results,the improvement rate of forecasting the CPI dataset was 5%,71%,and 4%for ARIMA/BPNN model,ARIMA/ANN model,and BPNN model respectively;while the result for cancer patients’dataset was 7%,200%,and 19%for ARIMA/BPNNmodel,ARIMA/ANN model,and BPNNmodel respectively.Therefore,it is obvious that the proposed method reduced the randomness degree,and the alterations affected the time series with data non-linearity.The ARIMA/ANN model outperformed each of its components when it was applied separately in terms of increasing the accuracy of forecasting and decreasing the overall errors of forecasting.

Hybrid model based on K-means++ algorithm, optimal similar day approach, and long short-term memory neural network for short-term photovoltaic power prediction

Photovoltaic(PV) power generation is characterized by randomness and intermittency due to weather changes.Consequently, large-scale PV power connections to the grid can threaten the stable operation of the power system. An effective method to resolve this problem is to accurately predict PV power. In this study, an innovative short-term hybrid prediction model(i.e., HKSL) of PV power is established. The model combines K-means++, optimal similar day approach,and long short-term memory(LSTM) network. Historical power data and meteorological factors are utilized. This model searches for the best similar day based on the results of classifying weather types. Then, the data of similar day are inputted into the LSTM network to predict PV power. The validity of the hybrid model is verified based on the datasets from a PV power station in Shandong Province, China. Four evaluation indices, mean absolute error, root mean square error(RMSE),normalized RMSE, and mean absolute deviation, are employed to assess the performance of the HKSL model. The RMSE of the proposed model compared with those of Elman, LSTM, HSE(hybrid model combining similar day approach and Elman), HSL(hybrid model combining similar day approach and LSTM), and HKSE(hybrid model combining K-means++,similar day approach, and LSTM) decreases by 66.73%, 70.22%, 65.59%, 70.51%, and 18.40%, respectively. This proves the reliability and excellent performance of the proposed hybrid model in predicting power.

FRACTALS OF HYBRID ORBITALS AND THEIR APPLICATIONS IN THE ENZYME MODELS

An enzyme is a kind of protein with catalytic activity and long chain,and its structure and shape are determined by the hybridized state of atomic orbital.The fractal dimension(D_f)is closely related to the hybridization,e.g.D_f=2ln2/ln[2(1+α/(1-α))]for the spa type, where a denotes the fraction of the s orbital in the hybridized molecular orbital.This relationship and the five fractal theorems introduced by the present paper play an important role in the investigations of the model of imitative enzyme.

Modeling and petrophysical properties of digital rock models with various pore structure types: An improved workflow

Pore structure is a crucial factor affecting the physical properties of porous materials,and understanding the mechanisms and laws of these effects is of great significance in the fields of geosciences and petroleum engineering.However,it remains a challenge to accurately understand and quantify the relationship between pore structures and effective properties.This paper improves a workflow to focus on investigating the effect of pore structure on physical properties.First,a hybrid modeling approach combining process-based and morphology-based methods is proposed to reconstruct 3D models with diverse pore structure types.Then,the characteristics and differences in pore structure in these models are compared.Finally,the varia-tion laws and pore-scale mechanisms of the influence of pore structure on physical properties(permeability and elasticity)are discussed based on the reconstructed models.The relationship models between pore structure parameters and perme-ability/elastic parameters in the grain packing model are established.The effect of pore structure evolution on permeability/elasticity and the microscopic mechanism in three types of morphology-based reconstruction models are explored.The influence degree of pore structure on elastic parameters(bulk modulus,shear modulus,P-wave velocity,and S-wave veloc-ity)is quantified,reaching 29.54%,51.40%,18.94%,and 23.18%,respectively.This work forms a workflow for exploring the relationship between pore structures and petrophysical properties at the microscopic scale,providing more ideas and references for understanding the complex physical properties in porous media.

A Novel Method in Wood Identification Based on Anatomical Image Using Hybrid Model

Nowadays,wood identification is made by experts using hand lenses,wood atlases,and field manuals which take a lot of cost and time for the training process.The quantity and species must be strictly set up,and accurate identification of the wood species must be made during exploitation to monitor trade and enforce regulations to stop illegal logging.With the development of science,wood identification should be supported with technology to enhance the perception of fairness of trade.An automatic wood identification system and a dataset of 50 commercial wood species from Asia are established,namely,wood anatomical images collected and used to train for the proposed model.In the convolutional neural network(CNN),the last layers are usually soft-max functions with dense layers.These layers contain the most parameters that affect the speed model.To reduce the number of parameters in the last layers of the CNN model and enhance the accuracy,the structure of the model should be optimized and developed.Therefore,a hybrid of convolutional neural network and random forest model(CNN-RF model)is introduced to wood identification.The accuracy’s hybrid model is more than 98%,and the processing speed is 3 times higher than the CNN model.The highest accuracy is 1.00 in some species,and the lowest is 0.92.These results show the excellent adaptability of the hybrid model in wood identification based on anatomical images.It also facilitates further investigations of wood cells and has implications for wood science.

A fast hybrid simulation approach of ion energy and angular distributions in biased inductively coupled Ar plasmas

In this work,a two-dimensional hybrid model,which consists of a bulk fluid module,a sheath module and an ion Monte-Carlo module,is developed to investigate the modulation of ion energy and angular distributions at different radial positions in a biased argon inductively coupled plasma.The results indicate that when the bias voltage amplitude increases or the bias frequency decreases,the ion energy peak separation width becomes wider.Besides,the widths of the ion energy peaks at the edge of the substrate are smaller than those at the center due to the lower plasma density there,indicating the nonuniformity of the ion energy distribution function(IEDF)along the radial direction.As the pressure increases from 1 to 10 Pa,the discrepancy of the IEDFs at different radial positions becomes more obvious,i.e.the IEDF at the radial edge is characterized by multiple low energy peaks.When a dual frequency bias source is applied,the IEDF exhibits three or four peaks,and it could be modulated efficiently by the relative phase between the two bias frequencies.The results obtained in this work could help to improve the radial uniformity of the IEDF and thus the etching process.