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Full-Text Articles in Physical Sciences and Mathematics

The Grey-Box Based Modeling Approach Research Integrating Fusion Mechanism And Data, Bin Chen, Xiaodong Wang, Rongxiao Wang, Xiaogang Qiu, Zhengqiu Zhu, Ma Liang Dec 2019

The Grey-Box Based Modeling Approach Research Integrating Fusion Mechanism And Data, Bin Chen, Xiaodong Wang, Rongxiao Wang, Xiaogang Qiu, Zhengqiu Zhu, Ma Liang

Journal of System Simulation

Abstract: With the deep understanding of world, modeling and simulation have been used to solve the problems of complex systems. The simulation models are used to model the engineering systems which follow newton laws. The modeling approach is called white-box modeling, while the black-box modeling is used to model the systems of which the internal structure and characteristics are not clear. The black-box modeling is based on statistics and data modeling. This paper discusses the deficiencies of the white-box and black-box modeling approaches first. The Grey-box based modeling approach integrating both fusion mechanism and data model is proposed. In …


Research On Extraction Method Of Time-Frequency Feature Of Fall Detection, Tianrun Wang, Su Zhong, Liu Ning, Li Chao, Guodong Fu Dec 2019

Research On Extraction Method Of Time-Frequency Feature Of Fall Detection, Tianrun Wang, Su Zhong, Liu Ning, Li Chao, Guodong Fu

Journal of System Simulation

Abstract: Aiming at the problem of features extract method for fall detection, the method using time-frequency analyze and features extraction by Fractional Fourier Transform (FRFT) has been proposed. The inertial data is measured by 15 IMU wearing on body, the features extracted after FRFT with multiple order are analyzed and compared. The difference of feature distribution of eight fall actions has been compared, and the difference of feature distribution between fall action and 4 normal actions has been compared. The feasibility of using FRFT in fall detection is proved.


Intelligent Collaborative Networking Method For Workshop Emergencies, Kong Tao, Wang Yan Dec 2019

Intelligent Collaborative Networking Method For Workshop Emergencies, Kong Tao, Wang Yan

Journal of System Simulation

Abstract: Due to the complex environment of intelligent manufacturing workshop, abnormal emergencies will cause huge security threats and economic losses to the workshop. It is difficult to transmit the abnormal event data continuously, quickly and completely in the workshop production site, and the fluctuation of abnormal event data is great with high requirements on the integrity and real-time of data transmission. In this paper, a multi-agent cooperative networking method for workshop emergencies is proposed. Mobile robots are introduced as intermediary Sink nodes for data transmission between sensor networks and the Internet. In case of emergencies, the intelligent node and cluster …


Multi-Sensor Data Fusion With Network Delays And Correlated Noises, Shankai Zhang, Zhu Cui, Su Zhong, Dai Juan Dec 2019

Multi-Sensor Data Fusion With Network Delays And Correlated Noises, Shankai Zhang, Zhu Cui, Su Zhong, Dai Juan

Journal of System Simulation

Abstract: This paper focuses on the state estimation for multi-sensor system with network delays and correlated noises. An orthogonal transformation method is applied to remove the correlations between different noises. For the problem of packet delays due to the unreliable network, a buffer with certain length is introduced to store the measurements, and the measurements are reordered using a timestamp in the buffer. Based on that, a novel sequential data fusion algorithm is proposed, by which the influence of the noise correlation and packet delays can be weakened effectively. Compared with the traditional sequential fusion method, the proposed algorithm has …


Parallel Tasks Optimization Scheduling In Cloud Manufacturing System, Chenwei Feng, Wang Yan Dec 2019

Parallel Tasks Optimization Scheduling In Cloud Manufacturing System, Chenwei Feng, Wang Yan

Journal of System Simulation

Abstract: To solve the problem of unbalanced resource requirements and low resource utilization when the same type of tasks are executed in parallel in the cloud manufacturing system, a task resource scheduling model with the goal of minimizing cost, minimizing time, maximizing reliability and optimizing quality is established. A non-dominated sorting genetic algorithm based on reference points (NSGA-III) is adopted to solve the model by combining real number matrix coding and crossover and mutation based on real number coding instead of common evolutionary strategy. And an optimal decision strategy based on combination of analytic hierarchy process and entropy value method …


Pedestrian Navigation Method Based On Uwb And Sins, Yang Yang, Li Qing Dec 2019

Pedestrian Navigation Method Based On Uwb And Sins, Yang Yang, Li Qing

Journal of System Simulation

Abstract: In view of the problem that the inertial navigation error is accumulating with time and UWB indoor is hard to continue tracking problems in complex environment, an extended Kalman filter (EKF) fusing UWB and sins pedestrian navigation is proposed.The zero speed correction algorithm is used to trigger EKF at zero speed. The sins is corrected by the velocity error measurement provided by sins and the position error measurement provided by UWB restraining error accumulation.When UWB signal is interrupted, the position of UWB output without interruption is taken as the starting position. The experiment results of SINS autonomous navigation …


Energy Efficiency Data Mining And Scheduling Optimization Of Discrete Workshop, Yugu Lin, Wang Yan Dec 2019

Energy Efficiency Data Mining And Scheduling Optimization Of Discrete Workshop, Yugu Lin, Wang Yan

Journal of System Simulation

Abstract: This paper addresses the optimization of energy consumption in discrete workshops and establishes the energy efficiency optimization model of discrete workshops. The relationship between data mining and knowledge discovery is established. Through scheduling data preprocessing and C4.5 decision tree learning algorithm, the discovery of scheduling knowledge is realized. Energy efficiency optimization calculation is achieved in discrete workshops by the combination of scheduling knowledge and improved differential evolution algorithm (IDE). By comparing with TLBO, GA and PSO, the feasibility of IDE algorithm is verified.


Research On Social Network Inference Method Based On Observation Data, Hailiang Chen, Bin Chen, Yuan Peng, Dong Jian, Chuan Ai Dec 2019

Research On Social Network Inference Method Based On Observation Data, Hailiang Chen, Bin Chen, Yuan Peng, Dong Jian, Chuan Ai

Journal of System Simulation

Abstract: Internet technology and online social networks have developed rapidly, which enables people to randomly express their opinions, ideas, emotional exchanges and economic exchanges. Inferring social networks is made possible through the observation data exchanged by people on the Internet. Through the analysis of ConNIe (Convex Network Inference) algorithm, this paper researches the effects of sparse parameter, propagation time distribution model and its parameters on the inference results of the algorithm. According to the analysis, a social network inference framework based on ConNIe algorithm is proposed. Combining the perceptron and particle swarm optimization algorithm, the ConNIe algorithm inference becomes a …


Exploration Of Soldier Morale Using Multi-Mode Simulation Approach, Yongsheng Zhang, Zhengxiang Xiong Dec 2019

Exploration Of Soldier Morale Using Multi-Mode Simulation Approach, Yongsheng Zhang, Zhengxiang Xiong

Journal of System Simulation

Abstract: Soldier morale is a complex social construction influenced by factors at multiple levels and integrates many research domains. This research seeks to explore, model, and simulate soldier morale at multiple levels of analysis. Microcosmically Agent-Based Modeling method is used to reflect the interaction among fighters and the course of affecting morale,Macrocosmically SD method is used to reflect the influence of the tactical psychology on morale and the whole war in the counter-combat process. The developed sample case scenario pertained to US security efforts against insurgency in Afghanistan in 2007. The scenario includes representation of the patrol base operations serving …


Research On Mechanical Configuration Of Automatic Container Terminals Based On Simulation Optimization Method, Shaozheng Yu, Dongshi Sun, Chen Jing, Yongchao Li Dec 2019

Research On Mechanical Configuration Of Automatic Container Terminals Based On Simulation Optimization Method, Shaozheng Yu, Dongshi Sun, Chen Jing, Yongchao Li

Journal of System Simulation

Abstract: In the study of mechanical configuration problem of automated container terminal, a system simulation model based on discrete event simulation is constructed. The key parameters and interference factors that affect the performance of the system are fully considered in the model and a mechanical scheduling algorithm interface to ensure the effectiveness of the simulation model is designed. On the premise of ensuring the reliability of the container terminal system, a cycle optimization method of mechanical configuration scheme is proposed to minimize the cost. An example is given to solve the mechanical configuration scheme of an automatic container terminal. …


Research On The Value Accessing Method For Calibrating Micro Traffic Simulation Model Parameters, Chenjing Zhou, Rong Jian, Kwok Lam Dec 2019

Research On The Value Accessing Method For Calibrating Micro Traffic Simulation Model Parameters, Chenjing Zhou, Rong Jian, Kwok Lam

Journal of System Simulation

Abstract: Parameter calibration is the precondition of the application of micro traffic simulation technology. This study focuses on the value accessing method for parameter calibration in order to further improve the parameter calibration process. The analysis of the distribution characteristics of each parameter calibration results shows that the parameters have different trends in the process of gradual iteration, and there are multiple optimal solutions for the model parameter calibration results. In this paper, the dispersion is used as the quantitative analysis index of the concentration degree of each parameter calibration result, and the parameter value of the model is determined …


Research On Source Seeking Methods Of Harmful Gas Leakage In Chemical Industry Parks, Zhao Yong, Bin Chen, Xiaodong Wang, Zhengqiu Zhu, Rongxiao Wang, Xiaogang Qiu Dec 2019

Research On Source Seeking Methods Of Harmful Gas Leakage In Chemical Industry Parks, Zhao Yong, Bin Chen, Xiaodong Wang, Zhengqiu Zhu, Rongxiao Wang, Xiaogang Qiu

Journal of System Simulation

Abstract: Chemical production safety accidents often lead to harmful gas leakage, causing serious environmental damage and casualties. Mastering the information of leaking source quickly can assist in emergency disposal decisions and reduce the harm of accidents. In this paper, Entrotaxis algorithm is used to guide the ground source seeking equipment to move to the vicinity of the leaking source quickly and autonomously in a chemical park scene, and to master the source information. According to the characteristics of the chemical industry park scene, this paper applies intermittent search module into Entrotaxis algorithm and proposes a robust and suitable algorithm (Entrotaxis-Jump …


An Lstm-Based Motion Recognition Method For Power Operation And Maintenance, Peizhen Liu, Yuxiang Jia, Shihong Xia Dec 2019

An Lstm-Based Motion Recognition Method For Power Operation And Maintenance, Peizhen Liu, Yuxiang Jia, Shihong Xia

Journal of System Simulation

Abstract: The security of power operation and maintenance has always been a subject of great social concern. In order to avoid serious consequences caused by the fault of staffs, a motion recognition method for power operation and maintenance jobs based on LSTM (Long Short-Term Memory) is proposed, which covers the whole process from data collection, data processing to motion classification and recognition, then it can recognise and supervise the behavior of staffs who are at work. In addition, a simulation experiment is conducted between the deep learning algorithm LSTM and the traditional machine learning algorithm KNN based on the newly …


The Scheduling Algorithm Of Cloud Job Based On Hopfield Neural Network, Yudong Guo, Jinping Zuo Dec 2019

The Scheduling Algorithm Of Cloud Job Based On Hopfield Neural Network, Yudong Guo, Jinping Zuo

Journal of System Simulation

Abstract: Focusing on the low efficiency of cloud job scheduling and the insufficient utility of resource, a job scheduling algorithm based on Hopfield Neural Network is proposed. In order to improve the resource scheduling ability of the system, The resource characteristics which influence the cloud job scheduling are shown. The mathematical model of resource constraints is established, and the Hopfield energy function is designed and optimized. The average utilization rate of 9 nodes is analyzed by using the standard test cases, and the performance and resource utilization of the proposed strategy are compared with three typical algorithms. …


Design Of Nonsmooth And Inversed Control Algorithm For Nonlinear Structural Vibration Control, Jianhui Wang, Wang Qing, Kemao Ma, Xiaofang Huang Dec 2019

Design Of Nonsmooth And Inversed Control Algorithm For Nonlinear Structural Vibration Control, Jianhui Wang, Wang Qing, Kemao Ma, Xiaofang Huang

Journal of System Simulation

Abstract: Considering the vibration effects of seismic waves on building with nonlinear structures, a nonsmooth and inversed control algorithm is used to suppress the vibration. It overcomes the faults of ignoring nonlinear influence in traditional approximate linearization control method and suppresses the influence of seismic waves effectively. According to Lyapunov stable theory and finite-time stability theory, the proposed control method to realize the stability of the nonlinear structural vibration is demonstrated. In the realization of the control method, the extended state observer is used to estimate the unknown disturbances. The numerical simulation is conducted for an eight-story building influenced …


Visualization Analysis Method Of Passenger Hotspot Based On Fast Density Clustering, Zihe Huang, Shangbing Gao, Zhigeng Pan, Hui Hao, Qiyu Liao, Fengfeng Zhao Dec 2019

Visualization Analysis Method Of Passenger Hotspot Based On Fast Density Clustering, Zihe Huang, Shangbing Gao, Zhigeng Pan, Hui Hao, Qiyu Liao, Fengfeng Zhao

Journal of System Simulation

Abstract: With the development of urbanized transportation, the perceptual computing plays an important role in smart cities. Aiming at the problem that the traditional density clustering algorithm cannot adapt to massive taxi GPS trajectory data and visualization, the BCS-DBSCAN (Big-Data Cluster Center Statistics Density-Based Spatial Clustering of Applications with Noise) clustering algorithm is proposed. The algorithm can segment and parallelize the trajectory data, extract the maximum density cluster, and adapt the result to the visualization model. The experimental results show that compared with other popular methods, this method has significant advantages in extracting clustering speed, accuracy and visualization of urban …


Research On Radar Signal Sorting Based On Ensemble Deep Learning, Weidong Jin, Chunli Chen Dec 2019

Research On Radar Signal Sorting Based On Ensemble Deep Learning, Weidong Jin, Chunli Chen

Journal of System Simulation

Abstract: In view of the fact it is difficult to extract the appropriate features quickly and present signal sorting method’s accuracy is low, a signal sorting method based on ensemble deep learning model is proposed. This method stacks different types of deep belief network for radar emitter signal feature learning to improve algorithm. After learning the characteristics of the radar emitter signals deeply, the posterior probability of each model is linearly integrated and learned and the final classification results are determined by the decision layer to further improve the signal recognition rate. The method is used to separate different …


Nonlinear Sliding Mode Control For Robotic Manipulator Based On Disturbance Observer, Gensuo Mi, Huaqi Liang Dec 2019

Nonlinear Sliding Mode Control For Robotic Manipulator Based On Disturbance Observer, Gensuo Mi, Huaqi Liang

Journal of System Simulation

Abstract: A nonlinear sliding mode control strategy of manipulator based on disturbance observer is designed for the characteristics of the manipulator which is sensitive to internal parameter disturbance and the external disturbance in the position tracking. According to the system dynamics model and Lyapunov stability theory, the uncertainties and external disturbances of the system are observed by disturbance observer. At the same time, the nonlinear sliding mode controller is designed and the Lyapunov function is constructed to verify the stability of the system. On this basis, the system control law and the sliding mode control law are designed to compensate …


Joint Resource Partitioning And Offloading Analysis In Heterogeneous Ultra-Dense Networks, Zhen Yan, Jiangpan Shi, Qiaoshou Liu Dec 2019

Joint Resource Partitioning And Offloading Analysis In Heterogeneous Ultra-Dense Networks, Zhen Yan, Jiangpan Shi, Qiaoshou Liu

Journal of System Simulation

Abstract: For the problem of load balancing between macro base station and small base station in heterogeneous ultra-dense networks, a general offloading framework is proposed based on the distance between users and the nearest base station. By partitioning network spectrum resource and using stochastic geometry, the expression of coverage probability and average ergodic rate of users in the fixed region and the random region are deduced on the basis of guaranteeing the quality of service of the macro users offloaded. The simulation results show that the combination of resource partitioning and offloading effectively improves the coverage probability and average ergodic …


A Review Of Modeling Human Travel And Social Contacts For Public Health Management, Duan Wei, Guo Gang, Bin Chen, Duan Hong Dec 2019

A Review Of Modeling Human Travel And Social Contacts For Public Health Management, Duan Wei, Guo Gang, Bin Chen, Duan Hong

Journal of System Simulation

Abstract: It is significant to understand the patterns of human mobility and social contacts for epidemic prevention and control. This paper analyses the regularities and the statistical properties of human behaviors at the perspective of human dynamics. Various models of human mobility and social contacts are comparatively investigated , including Brownian movement, random walks, spatial network, Motifs, bipartite graph model, gravity models, contact rate, the distribution of daily contact number, social networks, etc. The models of human behavior changes in the course of epidemic outbreak are also analyzed. The challenges of modeling human mobility and social contacts are discussed …


Survey On Modeling And Simulation Of Internet Public Opinion In China, Mingxin Zhang Dec 2019

Survey On Modeling And Simulation Of Internet Public Opinion In China, Mingxin Zhang

Journal of System Simulation

Abstract: Modeling and Simulation of Internet public opinion can analyze the causes of public opinion and its transmission path, track and predict the trend of public opinion, so as to improve the ability of public opinion guidance for its control departments. This paper reviews and analyses the existing research on Modeling and simulation of Internet public opinion. From the point of view of research directions, the current research covers many directions, mainly including the evolution mechanism of Internet public opinion and the effectiveness of guidance mechanism. From the point of view of research methods, domestic research on Internet public opinion …


Simulation Study On Aerodynamic Characteristics Of Flapping-Wing Aircraft With Multi-Stage Wing And Multiple Degree Of Freedom, Yonggang Yang, Xindong Gu Dec 2019

Simulation Study On Aerodynamic Characteristics Of Flapping-Wing Aircraft With Multi-Stage Wing And Multiple Degree Of Freedom, Yonggang Yang, Xindong Gu

Journal of System Simulation

Abstract: In the traditonal flapping-wing aircraft model, most of the wings are two-dimensional rigid wings, and the upswing and downwing processes are completely symmetrical. In order to further improve the aerodynamic characteristics of the flapping-wing aircraft, this paper uses the idea of approximate flexibility to establish the multi-stage wing to achieve the approximate flexibility effect. At the same time, the rapid return characteristic is added to prolong the down-flapping time. And a three-dimensional model of “flutter-twist-bend folding” is proposed by adding the bending-folding motion on the basis of the original movement and twisting motion. The model is imported into Xflow …


Review Of Evaluation Methods Of Contribution Rate To System Of Systems, Xiaojing Yin, Xiaofeng Hu, Rong Ming, Haiyang Liu, Yongli Yang Dec 2019

Review Of Evaluation Methods Of Contribution Rate To System Of Systems, Xiaojing Yin, Xiaofeng Hu, Rong Ming, Haiyang Liu, Yongli Yang

Journal of System Simulation

Abstract: The warfare is the encounter of system of systems (SoS). The evaluation on the contribution rate to SoS is of great importance to the development of operational SoS as a measure of the evaluating units’ contribution to SoS. In this paper the basic concept and classification of the contribution rate to operational SoS are elaborated; its connotation and nature are analyzed; and the current research status and the technical difficulties in this research field are summarized. The development trend is predicted, which provides a useful reference for relative research.


Modeling Of Capability Relations Oriented To The Evolution Of Operational System-Of-Systems, Xia Lu, Mingzhi Zhang, Jingyu Yang, Changliang Xiao Dec 2019

Modeling Of Capability Relations Oriented To The Evolution Of Operational System-Of-Systems, Xia Lu, Mingzhi Zhang, Jingyu Yang, Changliang Xiao

Journal of System Simulation

Abstract: Based on the analysis of the capability of the operational system-of-systems (OSoS) and its relationship, the capability relationship description function is constructed, and the spreading effect and emerging effect are explained. The super-network theory is used to establish the ‘entity-capability’ network model and its characteristic parameters. For measuring the emerging effect of the capability of OSoS, the capability contribution domain model and the capability emergence domain model are constructed. Taking the air defense system-of-systems evolution analysis as an example, the capability relationship model of OSoS is verified to provide a qualitative and quantitative method for constructing the evolution set …


Simulation Research On Damage Identification Of Simply Supported Beam Based On Wavelet Packet Energy Method, Xijun Liu, Xiankun Tao, Suxia Zhang Dec 2019

Simulation Research On Damage Identification Of Simply Supported Beam Based On Wavelet Packet Energy Method, Xijun Liu, Xiankun Tao, Suxia Zhang

Journal of System Simulation

Abstract: A finite element model of simply-supported beam is built by ANSYS;the displacement response of the beam is used to make wavelet packet analysis with MATLAB to get the curvature difference of WP-E (wavelet packet energy);and the studies on the effects of different parameters on damage recognition results of simple beam bridge are carried out, such as damage locations, damage level, measuring point density and speed of moving loads. For the condition of less measuring points, a method of arranging the measuring points by two steps is proposed. The normalized curvature difference of WP-E is made to study the …


Simulation Research On Operation Effect Of Vav Air-Conditioning System With Variable Water Temperature Strategy, Qinglong Meng, Zhibo Zhang, Xiong Cheng Dec 2019

Simulation Research On Operation Effect Of Vav Air-Conditioning System With Variable Water Temperature Strategy, Qinglong Meng, Zhibo Zhang, Xiong Cheng

Journal of System Simulation

Abstract: Aiming at the problem of coordinated operation between VAV (variable air volume) and variable water temperature in central air conditioning system, a TRNSYS dynamic simulation model of air conditioning system with adjustable air supply and water supply temperature is established, and the accuracy of the model is proved by experiments. By controlling the terminal air volume to simulate the effect of variable water temperature operation on the air conditioning system under different load rates, the optimal water supply temperature of the air conditioning system under different load rates is obtained, and the variable water temperature operation strategy of the …


Synthetic Aperture Ultrasonic Imaging Algorithm Based On Robust Capon Beamforming In Eigenspace, Yecai Guo, Xiaoxing Ji Dec 2019

Synthetic Aperture Ultrasonic Imaging Algorithm Based On Robust Capon Beamforming In Eigenspace, Yecai Guo, Xiaoxing Ji

Journal of System Simulation

Abstract: In order to lower the main lobe width and side lobe amplitude of SAF beams ,improve the robustness of ultrasound imaging algorithm, resolution, contrast in images, a synthetic aperture ultrasonic imaging algorithm based on robust Capon beamforming in eigenspace is proposed. Under the principle of MV, this algorithm firstly uses the Toeplitz to realize the reconstruction of the interference-noise covariance matrix and keep it nonsingular. Secondly, the vector error is constrained by the signal subspace and the elliptic constraint set in feature space. Finally, the optimal weight vector which is used to weight and image the echo data is …


Design And Simulation Analysis Of Epr Contract From The Perspective Of Government Regulation, Benhong Peng, Yuanyuan Wang, Tu Yu Dec 2019

Design And Simulation Analysis Of Epr Contract From The Perspective Of Government Regulation, Benhong Peng, Yuanyuan Wang, Tu Yu

Journal of System Simulation

Abstract: Government regulation is an important means to promote the extension of producer responsibility. Through the establishment of the agency model based on the public, the government and the producer, the situation of non-cooperation and the cooperation regulation between the public and the government respectively is modeled and analyzed, and the simulation is carried on. The study finds that the cooperation regulation is better than the non-cooperation regulation. The cooperation regulation should take into account the factors such as the risk aversion degree of the manufacturers, the uncertainty of the external environment, the cost coefficient, the comprehensive ability level, the …


Recurrent Cmacnn Control For Space Robot With Fully Flexible Arms And Elastic Base, Xiaoqin Huang, Chen Li Dec 2019

Recurrent Cmacnn Control For Space Robot With Fully Flexible Arms And Elastic Base, Xiaoqin Huang, Chen Li

Journal of System Simulation

Abstract: The trajectory tracking of elastic base and double flexible arms for a free-floating space robot system with fully flexible arms and elastic base is discussed. The elastic connection between the base and the arm is considered as a linear spring and dynamics model of the system which is regarded as a two- time scale system is derived. For the slow-varying subsystem, the recursive CMAC neural network (CMACNN) which has good dynamic characteristics is used to approximate uncertainties of dynamical equation and a recursive CMAC neural network control scheme which improves the tracking performance is designed to improve the …


Research On Topology Mapping Method For Multiscale Integration Network Emulation, Liu Yuan, Changling Qiu, Xiaofeng Wang, Jiang Min Dec 2019

Research On Topology Mapping Method For Multiscale Integration Network Emulation, Liu Yuan, Changling Qiu, Xiaofeng Wang, Jiang Min

Journal of System Simulation

Abstract: For large-scale and scalable network emulation requirements, multi-scale integration emulation based on lightweight virtualization and full virtualization is the trend. In order to take into account the advantages of both virtualizations and enhance the performance of network emulation, a topology mapping method (TMMI) is proposed for multi-scale integration network emulation. This method divides the network topology into lightweight virtualization mapping area and integration virtualization mapping area, and according to different mapping areas uses the optimized multi-level partitioning method to map the network topology reasonably. Experiments show that the proposed method can effectively balance the load and communication overhead …