Combining Ability and Heterotic Effects in Newly Developed Early Maturing and High-Yielding Maize Hybrids under Low and Recommended Nitrogen Conditions

Nitrogen (N) is a crucial nutrient vital for the growth and productivity of maize. However, excessive nitrogen application can result in numerous environmental and ecological problems, such as water pollution, biodiversity loss, and greenhouse gas emissions. Therefore, breeding maize hybrids resilient to low nitrogen conditions is crucial for sustainable agriculture, especially under low nitrogen conditions. Consequently, this study aimed to evaluate the combining ability and heterosis of maize lines, recognize promising hybrids, and study gene action controlling key traits under low and recommended N stress conditions. The half-diallel mating design hybridized seven maize inbreds, resulting in 21 F1 hybrids. These hybrids, along with two high-yielding commercial hybrids (SC10 and TWC310), were evaluated in field trials under recommended (290 kg/ha) and low N (166 kg N/ha) conditions. Significant variations were observed among assessed hybrids for all measured traits, with non-additive gene action being predominant for grain yield and its related characteristics under recommended and low N conditions. Inbred lines P105 and P106 were recognized as effective combiners for earliness, with P105 also excelling in shorter plant height and lower ear placement. In addition, P101, P102, and P104 were identified as good combiners for increasing grain yield and related attributes under low N conditions. The crosses P105 × P106 and P106 × P107 demonstrated outstanding heterotic effects for earliness, while hybrids P101 × P102 and P102 × P104 exhibited remarkable heterotic effects for grain yield low nitrogen stress conditions. These promising hybrids could be considered for commercial use after further evaluation. Strong positive correlations were found between grain yield and ear height, plant height, number of kernels per row, and 1000-grain weight, highlighting their importance for indirect selection to enhance the grain yield of maize under low N stress conditions.

Ternary Hybrid Nanofluid with First and Second Order Velocity Slips: Dual Solutions with Stability Analysis

Modeling the boundary layer flow of ternary hybrid nanofluids is important for understanding and optimizing their thermal performance,particularly in applications where enhanced heat transfer and fluid dynamics are essential.This study numerically investigates the boundary layer flow of alumina-copper-silver/water nanofluid over a permeable stretching/shrinking sheet,incorporating both first and second-order velocity slip.The mathematical model is solved in MATLAB facilitated by the bvp4c function that employs the finite difference scheme and Lobatto IIIa formula.The solver successfully generates dual solutions for the model,and further analysis is conducted to assess their stability.The findings reported that only one of the solutions is stable.For the shrinking sheet case,increasing the first-order velocity slip delays boundary layer separation and enhances heat transfer,while,when the sheet is stretched,the second-order velocity slip accelerates separation and improves heat transfer.Boundary layer separation is most likely to occur when the sheet is shrinking;however,this can be controlled by adjusting the velocity slip with the inclusion of boundary layer suction.

Multi-Objective Hybrid Sailfish Optimization Algorithm for Planetary Gearbox and Mechanical Engineering Design Optimization Problems

This paper introduces a hybrid multi-objective optimization algorithm,designated HMODESFO,which amalgamates the exploratory prowess of Differential Evolution(DE)with the rapid convergence attributes of the Sailfish Optimization(SFO)algorithm.The primary objective is to address multi-objective optimization challenges within mechanical engineering,with a specific emphasis on planetary gearbox optimization.The algorithm is equipped with the ability to dynamically select the optimal mutation operator,contingent upon an adaptive normalized population spacing parameter.The efficacy of HMODESFO has been substantiated through rigorous validation against estab-lished industry benchmarks,including a suite of Zitzler-Deb-Thiele(ZDT)and Zeb-Thiele-Laumanns-Zitzler(DTLZ)problems,where it exhibited superior performance.The outcomes underscore the algorithm’s markedly enhanced optimization capabilities relative to existing methods,particularly in tackling highly intricate multi-objective planetary gearbox optimization problems.Additionally,the performance of HMODESFO is evaluated against selected well-known mechanical engineering test problems,further accentuating its adeptness in resolving complex optimization challenges within this domain.

Sub-6GHz Assisted mmWave Hybrid Beamforming with Self-Supervised Learning

In this paper,we propose a sub-6GHz channel assisted hybrid beamforming(HBF)for mmWave system under both line-of-sight(LOS)and non-line-of-sight(NLOS)scenarios without mmWave channel estimation.Meanwhile,we resort to the selfsupervised approach to eliminate the need for labels,thus avoiding the accompanied high cost of data collection and annotation.We first construct the dense connection network(DCnet)with three modules:the feature extraction module for extracting channel characteristic from a large amount of channel data,the feature fusion module for combining multidimensional features,and the prediction module for generating the HBF matrices.Next,we establish a lightweight network architecture,named as LDnet,to reduce the number of model parameters and computational complexity.The proposed sub-6GHz assisted approach eliminates mmWave pilot resources compared to the method using mmWave channel information directly.The simulation results indicate that the proposed DCnet and LDnet can achieve the spectral efficiency that is superior to the traditional orthogonal matching pursuit(OMP)algorithm by 13.66% and 10.44% under LOS scenarios and by 32.35% and 27.75% under NLOS scenarios,respectively.Moreover,the LDnet achieves 98.52% reduction in the number of model parameters and 22.93% reduction in computational complexity compared to DCnet.

Enhancing Evapotranspiration Estimation: A Bibliometric and Systematic Review of Hybrid Neural Networks in Water Resource Management

Accurate estimation of evapotranspiration(ET)is crucial for efficient water resource management,particularly in the face of climate change and increasing water scarcity.This study performs a bibliometric analysis of 352 articles and a systematic review of 35 peer-reviewed papers,selected according to PRISMA guidelines,to evaluate the performance of Hybrid Artificial Neural Networks(HANNs)in ET estimation.The findings demonstrate that HANNs,particularly those combining Multilayer Perceptrons(MLPs),Recurrent Neural Networks(RNNs),and Convolutional Neural Networks(CNNs),are highly effective in capturing the complex nonlinear relationships and tem-poral dependencies characteristic of hydrological processes.These hybrid models,often integrated with optimization algorithms and fuzzy logic frameworks,significantly improve the predictive accuracy and generalization capabilities of ET estimation.The growing adoption of advanced evaluation metrics,such as Kling-Gupta Efficiency(KGE)and Taylor Diagrams,highlights the increasing demand for more robust performance assessments beyond traditional methods.Despite the promising results,challenges remain,particularly regarding model interpretability,computational efficiency,and data scarcity.Future research should prioritize the integration of interpretability techniques,such as attention mechanisms,Local Interpretable Model-Agnostic Explanations(LIME),and feature importance analysis,to enhance model transparency and foster stakeholder trust.Additionally,improving HANN models’scalability and computational efficiency is crucial,especially for large-scale,real-world applications.Approaches such as transfer learning,parallel processing,and hyperparameter optimization will be essential in overcoming these challenges.This study underscores the transformative potential of HANN models for precise ET estimation,particularly in water-scarce and climate-vulnerable regions.By integrating CNNs for automatic feature extraction and leveraging hybrid architectures,HANNs offer considerable advantages for optimizing water management,particularly agriculture.Addressing challenges related to interpretability and scalability will be vital to ensuring the widespread deployment and operational success of HANNs in global water resource management.

A Novel Control Strategy Based onπ-VSG for Inter-Face Converter in Hybrid Microgrid

The rapid development of new energy power generation technology and the transformation of power electronics in the core equipment of source-grid-load drives the power system towards the“double-high”development pattern of“high proportion of renewable energy”and“high proportion of power electronic equipment”.To enhance the transient performance of AC/DC hybrid microgrid(HMG)in the context of“double-high,”aπtype virtual synchronous generator(π-VSG)control strategy is applied to bidirectional interface converter(BIC)to address the issues of lacking inertia and poor disturbance immunity caused by the high penetration rate of power electronic equipment and new energy.Firstly,the virtual synchronous generator mechanical motion equations and virtual capacitance equations are used to introduce the virtual inertia control equations that consider the transient performance of HMG;based on the equations,theπ-type equivalent control model of the BIC is established.Next,the inertia power is actively transferred through the BIC according to the load fluctuation to compensate for the system’s inertia deficit.Secondly,theπ-VSG control utilizes small-signal analysis to investigate howthe fundamental parameters affect the overall stability of the HMG and incorporates power step response curves to reveal the relationship between the control’s virtual parameters and transient performance.Finally,the PSCAD/EMTDC simulation results show that theπ-VSG control effectively improves the immunity of AC frequency and DC voltage in the HMG system under the load fluctuation condition,increases the stability of the HMG system and satisfies the power-sharing control objective between the AC and DC subgrids.

Blood-based magnetohydrodynamic Casson hybrid nanofluid flow on convectively heated bi-directional porous stretching sheet with variable porosity and slip constraints

Fluid flow through porous spaces with variable porosity has wide-range applications,notably in biomedical and thermal engineering,where it plays a vital role in comprehending blood flow dynamics within cardiovascular systems,heat transfer and thermal management systems improve efficiency using porous materials with variable porosity.Keeping these important applications in view,in current study blood-based hybrid nanofluid flow has considered on a convectively heated sheet.The sheet exhibits the properties of a porous medium with variable porosity and extends in both the x and y directions.Blood has used as base fluid in which the nanoparticles of Cu and Cu O have been mixed.Thermal radiation,space-dependent,and thermal-dependent heat sources have been incorporated into the energy equation,while magnetic effects have been integrated into the momentum equations.Dimensionless variables have employed to transform the modeled equations into dimensionless form and facilitating their solution using bvp4c approach.It has concluded in this study that,both the primary and secondary velocities augmented with upsurge in variable porous factor and declined with escalation in stretching ratio,Casson,magnetic,and slip factors along x-and y-axes.Thermal distribution has grown up with upsurge in Casson factor,magnetic factor,thermal Biot number,and thermal/space-dependent heat sources while has retarded with growth in variable porous and stretching ratio factors.The findings of this investigation have been compared with the existing literature,revealing a strong agreement among present and established results that ensured the validation of the model and method used in this work.

Fully Distributed Risk-based Robust Reserve Scheduling for Bulk Hybrid AC-DC Systems

To enhance the cost-effectiveness of bulk hybrid AC-DC power systems and promote wind consumption,this paper proposes a two-stage risk-based robust reserve scheduling(RRRS)model.Different from traditional robust optimization,the proposed model applies an adjustable uncertainty set rather than a fixed one.Thereby,the operational risk is optimized together with the dispatch schedules,with a reasonable admissible region of wind power obtained correspondingly.In addition,both the operational base point and adjustment capacity of tielines are optimized in the RRRS model,which enables reserve sharing among the connected areas to handle the significant wind uncertainties.Based on the alternating direction method of multipliers(ADMM),a fully distributed framework is presented to solve the RRRS model in a distributed way.A dynamic penalty factor adjustment strategy(DPA)is also developed and applied to enhance its convergence properties.Since only limited information needs to be exchanged during the solution process,the communication burden is reduced and regional information is protected.Case studies on the 2-area 12-bus system and 3-area 354-bus system illustrate the effectiveness of the proposed model and approach.

高频链AC-DC矩阵变换器的变控制频率软开关调制策略

针对高频链AC-DC矩阵变换器的高效率要求,提出了一种变控制频率软开关调制策略。该调制策略在基于零矢量嵌入的分段同步控制策略基础上,以单控制周期平均功率不变为原则,通过改变控制周期长度,并调整一个控制周期内的电压矢量排布,优化脉冲宽度,使变换器在换流时全部开关器件的零电压开通成为可能。通过仿真分析和实验证明,采用本文提出的变控制频率调制策略,变换器在整流和逆变模式下,均可实现网侧电流三相平衡正弦,功率因数达到0.981,输出电压纹波小,最高效率达到96.9%,实现了高性能、高效率运行。

不平衡电网下AC-DC矩阵变换器的新型模型预测控制

为降低AC-DC矩阵变换器在输入不平衡条件下网侧有功功率波动,以及离散型模型预测控制中开关频率不固定的问题,提出一种新型模型预测控制方法。通过根据电网电流相位角选择有效矢量,避免了传统模型预测控制评估价值函数计算的负担。提出了一种二阶扩展复数卡尔曼滤波器,计算精度可以达到泰勒级数展开的二阶项,新型模型预测控制能够在不平衡电网系统中应用。仿真结果表明:所提控制策略在输入电压不平衡工况下,能够有效抑制网侧电流谐波,稳定系统输出的有功功率,并且表现出良好的性能。

颈椎前路Hybrid手术和颈椎后路单开门椎管扩大成形术治疗多节段脊髓型颈椎病临床疗效分析

目的:分析颈椎前路Hybrid手术和颈椎后路单开门椎管扩大成形术(EODL)治疗多节段脊髓型颈椎病的疗效,探讨多节段脊髓型颈椎病患者手术方式的选择。方法:对2017年7月—2020年7月在首都医科大学附属北京中医医院手术治疗的70例多节段脊髓型颈椎病患者进行回顾性分析,根据手术方式不同,分为前路组35例和后路组35例,前路组患者行Hybrid手术[颈椎前路椎间盘切除融合术(ACDF)联合人工颈椎间盘置换术(ACDR)],后路组患者行EODL。记录2组患者住院时间、手术时间、术中出血量和术后引流量,通过日本骨科协会(JOA)评分、JOA改善率、颈椎残障功能指数(NDI)、疼痛视觉模拟评分(VAS)和术后满意度评分进行疗效评价,统计2组患者术后并发症发生情况。结果:与后路组比较,前路组患者术中出血量、术后引流量、住院时间和手术时间均明显减少(P<0.01),术前各项评分差异无统计学意义(P>0.05)。末次随访时,与后路组比较,前路组患者JOA评分和JOA改善率明显升高(P<0.01),NDI评分和VAS评分明显降低(P<0.01)。与术前比较,末次随访时2组患者JOA评分明显升高(P<0.01),NDI和VAS评分均明显降低(P<0.01)。按术后满意度评分评价,2组患者术后满意度均较高。2组患者术后并发症发生率比较差异无统计学意义(P>0.05)。结论:颈椎前路Hybrid手术和EODL在治疗多节段脊髓型颈椎病方面均取得了较为满意的疗效。Hybrid手术具有出血量少和手术时间短等优点,临床上应根据患者实际情况选择最适宜的术式。

Study on Electromagnetic Environment of AC-DC Hybrid Transmission Lines

With the expansion of electricity demand,transmission corridors are becoming scarce.AC and DC circuits running parallel to each other and sharing the same right-of-way or even the same tower become a possible option.Due to the existence of the adjacent line,space electromagnetic field and corona of another line may be changed.Different characteristics of two line types make the electromagnetic field of transmission corridors become more complex.Hybrid line is viewed as a whole.The calculation contains surface gradient,ground level electric field,radio interference and audible noise.Interaction between the two line types is considered.The calculation results show that the interaction is mainly concentrated in the inner corridor.In the role of DC electric field,AC electric field is no longer symmetrical and ground level electric field is significantly enhanced.Under the negative DC voltage,the positive corona of the waveform is significantly strengthened,and it is inhibited under the positive DC voltage.It is better to erect the positive DC line near AC line.

Activation Redistribution Based Hybrid Asymmetric Quantization Method of Neural Networks

The demand for adopting neural networks in resource-constrained embedded devices is continuously increasing.Quantization is one of the most promising solutions to reduce computational cost and memory storage on embedded devices.In order to reduce the complexity and overhead of deploying neural networks on Integeronly hardware,most current quantization methods use a symmetric quantization mapping strategy to quantize a floating-point neural network into an integer network.However,although symmetric quantization has the advantage of easier implementation,it is sub-optimal for cases where the range could be skewed and not symmetric.This often comes at the cost of lower accuracy.This paper proposed an activation redistribution-based hybrid asymmetric quantizationmethod for neural networks.The proposedmethod takes data distribution into consideration and can resolve the contradiction between the quantization accuracy and the ease of implementation,balance the trade-off between clipping range and quantization resolution,and thus improve the accuracy of the quantized neural network.The experimental results indicate that the accuracy of the proposed method is 2.02%and 5.52%higher than the traditional symmetric quantization method for classification and detection tasks,respectively.The proposed method paves the way for computationally intensive neural network models to be deployed on devices with limited computing resources.Codes will be available on https://github.com/ycjcy/Hybrid-Asymmetric-Quantization.

基于Hybrid A^(*)算法的变压器声级巡检系统研究与设计

随着国内变电站数目逐步增加,采用固定式声级监测终端对变压器声级检测的方式已经满足不了日常检测的需求。为解决固定式声级监测终端方式成本高、维护复杂、设备利用率低等问题,该文率先提出了一种变压器声级巡检系统,并设计了最优声级巡检路径。通过场地定位传感器生成变压器场地栅格图信息,采用Hybrid A^(*)算法将场地栅格图信息生成符合国标所要求的最优声级巡检路径检测点;针对所开发的变压器声级巡检装置,采用生成的巡检路径对变压器进行声级测定作业,对测定的声级数据进行分析处理。测试结果表明,该文开发的系统与设计算法的变压器声级巡检时间、检测效率以及数据的采集准确性都优于固定式声级监测终端方式,系统完成变压器声级巡检全过程的成功率可达95%。

复杂建设环境下基于Hybrid A^(*)算法的铁路平面线形绿色优化设计

随着“双碳经济下绿色铁路”理念的兴起,将“绿色生态”融入到铁路平面线路优化已成为近年来的研究热点。本文以铁路建设成本与生态破坏成本的协同优化为目标,引入并改进了一种自动驾驶导航算法(Hybrid A^(*)算法),以适应复杂的铁路设计问题,同时考虑最小曲线半径、最大曲线半径、最短曲线长度、最短夹直线长度、缓和曲线长度等铁路线形约束。研究结果表明:(1)改进后算法以离散网格方式整合外部环境因素,实现渐进式全局探索,获取接近全局最优的铁路线路设计结果;(2)该方法在复杂外部环境约束下,无需预设水平交点位置和数量,可自动生成符合线路-环境耦合约束的优化平面线路方案。

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.

Regulatable Orthotropic 3D Hybrid Continuous Carbon Networks for Efficient Bi-Directional Thermal Conduction

Vertically oriented carbon structures constructed from low-dimen-sional carbon materials are ideal frameworks for high-performance thermal inter-face materials(TIMs).However,improving the interfacial heat-transfer efficiency of vertically oriented carbon structures is a challenging task.Herein,an orthotropic three-dimensional(3D)hybrid carbon network(VSCG)is fabricated by depositing vertically aligned carbon nanotubes(VACNTs)on the surface of a horizontally oriented graphene film(HOGF).The interfacial interaction between the VACNTs and HOGF is then optimized through an annealing strategy.After regulating the orientation structure of the VACNTs and filling the VSCG with polydimethylsi-loxane(PDMS),VSCG/PDMS composites with excellent 3D thermal conductive properties are obtained.The highest in-plane and through-plane thermal conduc-tivities of the composites are 113.61 and 24.37 W m^(-1)K^(-1),respectively.The high contact area of HOGF and good compressibility of VACNTs imbue the VSCG/PDMS composite with low thermal resistance.In addition,the interfacial heat-transfer efficiency of VSCG/PDMS composite in the TIM performance was improved by 71.3%compared to that of a state-of-the-art thermal pad.This new structural design can potentially realize high-performance TIMs that meet the need for high thermal conductivity and low contact thermal resistance in interfacial heat-transfer processes.

Ag-integrated mixed metallic Co-Fe-Ni-Mn hydroxide composite as advanced electrode for high-performance hybrid supercapacitors

Direct growth of redox-active noble metals and rational design of multifunctional electrochemical active materials play crucial roles in developing novel electrode materials for energy storage devices.In this regard,silver(Ag)has attracted great attention in the design of efficient electrodes.Inspired by the house/building process,which means electing the right land,it lays a strong foundation and building essential columns for a complex structure.Herein,we report the construction of multifaceted heterostructure cobalt-iron hydroxide(CFOH)nanowires(NWs)@nickel cobalt manganese hydroxides and/or hydrate(NCMOH)nanosheets(NSs)on the Ag-deposited nickel foam and carbon cloth(i.e.,Ag/NF and Ag/CC)substrates.Moreover,the formation and charge storage mechanism of Ag are described,and these contribute to good conductive and redox chemistry features.The switching architectural integrity of metal and redox materials on metallic frames may significantly boost charge storage and rate performance with noticeable drop in resistance.The as-fabricated Ag@CFOH@NCMOH/NF electrode delivered superior areal capacity value of 2081.9μA h cm^(-2)at 5 mA cm^(-2).Moreover,as-assembled hybrid cell based on NF(HC/NF)device exhibited remarkable areal capacity value of 1.82 mA h cm^(-2)at 5 mA cm^(-2)with excellent rate capability of 74.77%even at 70 mA cm^(-2)Furthermore,HC/NF device achieved maximum energy and power densities of 1.39 mW h cm^(-2)and 42.35 mW cm^(-2),respectively.To verify practical applicability,both devices were also tested to serve as a self-charging station for various portable electronic devices.

p-d Orbital Hybridization Engineered Single-Atom Catalyst for Electrocatalytic Ammonia Synthesis

The rational design of metal single-atom catalysts(SACs)for electrochemical nitrogen reduction reaction(NRR)is challenging.Two-dimensional metal-organic frameworks(2DMOFs)is a unique class of promising SACs.Up to now,the roles of individual metals,coordination atoms,and their synergy effect on the electroanalytic performance remain unclear.Therefore,in this work,a series of 2DMOFs with different metals and coordinating atoms are systematically investigated as electrocatalysts for ammonia synthesis using density functional theory calculations.For a specific metal,a proper metal-intermediate atoms p-d orbital hybridization interaction strength is found to be a key indicator for their NRR catalytic activities.The hybridization interaction strength can be quantitatively described with the p-/d-band center energy difference(Δd-p),which is found to be a sufficient descriptor for both the p-d hybridization strength and the NRR performance.The maximum free energy change(ΔG_(max))andΔd-p have a volcanic relationship with OsC_(4)(Se)_(4)located at the apex of the volcanic curve,showing the best NRR performance.The asymmetrical coordination environment could regulate the band structure subtly in terms of band overlap and positions.This work may shed new light on the application of orbital engineering in electrocatalytic NRR activity and especially promotes the rational design for SACs.

Ground threat prediction-based path planning of unmanned autonomous helicopter using hybrid enhanced artificial bee colony algorithm

Unmanned autonomous helicopter(UAH)path planning problem is an important component of the UAH mission planning system.Aiming to reduce the influence of non-complete ground threat information on UAH path planning,a ground threat prediction-based path planning method is proposed based on artificial bee colony(ABC)algorithm by collaborative thinking strategy.Firstly,a dynamic threat distribution probability model is developed based on the characteristics of typical ground threats.The dynamic no-fly zone of the UAH is simulated and established by calculating the distribution probability of ground threats in real time.Then,a dynamic path planning method for UAH is designed in complex environment based on the real-time prediction of ground threats.By adding the collision warning mechanism to the path planning model,the flight path could be dynamically adjusted according to changing no-fly zones.Furthermore,a hybrid enhanced ABC algorithm is proposed based on collaborative thinking strategy.The proposed algorithm applies the leader-member thinking mechanism to guide the direction of population evolution,and reduces the negative impact of local optimal solutions caused by collaborative learning update strategy,which makes the optimization performance of ABC algorithm more controllable and efficient.Finally,simulation results verify the feasibility and effectiveness of the proposed ground threat prediction path planning method.