CN114841066A - A dust particle drift trajectory model and its modeling method - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及扬尘轨迹预测技术领域,具体涉及一种扬尘颗粒物飘移轨迹模型及其建模方法。The invention relates to the technical field of dust trajectory prediction, in particular to a dust particle drift trajectory model and a modeling method thereof.
背景技术Background technique
随着城市和社会发展的速率不断加快,逐渐有越来越多的人开始关注环境和居住问题。现阶段许多发展中国家仍面临着空气污染的问题,最新的GBD(全球疾病负担)分析继续将空气污染确定为导致死亡和残疾的最重要风险因素之一。大气颗粒物是空气污染的一个组成部分,被列为早亡的第六大风险因素。As the speed of urban and social development continues to accelerate, more and more people are beginning to pay attention to environmental and residential issues. Air pollution is still a problem for many developing countries at this stage, and the latest GBD (Global Burden of Disease) analysis continues to identify air pollution as one of the most important risk factors for death and disability. Atmospheric particulate matter, a component of air pollution, is listed as the sixth-leading risk factor for premature death.
绝大部分的扬尘轨迹预测模型都是基于传统物理模型或基于神经网络,传统方法大都基于实验场研究、数值模拟研究、气象场分析研究和数据挖掘方法,这些传统的物理模型计算步骤繁琐,计算量十分庞大并且会趋于不稳定状态;基于神经网络的方法例如卷积神经网络和循环神经网络预测都有其特定的应用领域,同时也欠缺可解释性。Most of the dust trajectory prediction models are based on traditional physical models or neural networks. Most of the traditional methods are based on experimental field research, numerical simulation research, meteorological field analysis research and data mining methods. These traditional physical models have cumbersome calculation steps. The volume is very large and tends to be unstable; neural network-based methods such as convolutional neural network and recurrent neural network prediction have their specific application areas, and they also lack interpretability.
本发明引入场的概念,用编解码器结构的网络替换传统方法中速度场的计算,同时优化了对流项、扩散项、体积力项的计算。实验表明,本发明提出的扬尘轨迹预测模型较传统方法准确率和计算速度有了大幅提升,同时提高了计算的稳定性,且较神经网络的方法具有更好的通用性和可解释性。The invention introduces the concept of the field, replaces the calculation of the velocity field in the traditional method with the network of the codec structure, and optimizes the calculation of the convection term, the diffusion term and the body force term at the same time. Experiments show that the dust trajectory prediction model proposed by the present invention has greatly improved the accuracy and calculation speed compared with the traditional method, and at the same time improves the stability of calculation, and has better generality and interpretability than the neural network method.
发明内容SUMMARY OF THE INVENTION
本发明主要针对传统方法计算任务繁重、精度欠缺和扬尘运动速度场难以计算的问题,改进相关传统物理算法并结合神经网络法,提出了一种扬尘颗粒物飘移轨迹模型及其建模方法。The invention mainly aims at the problems of heavy calculation tasks, lack of precision and difficulty in calculating the velocity field of the dust movement in the traditional method, improves the relevant traditional physical algorithm and combines the neural network method, and proposes a dust particle drift trajectory model and a modeling method.
本发明的技术方案如下:The technical scheme of the present invention is as follows:
本发明使用的扬尘数据包含以下信息:设备站点的位置信息、设备编号、设备经度、纬度、设备数据状态、温度、湿度、风速、风向、PM2.5浓度、压强。The dust data used in the present invention includes the following information: location information of the equipment site, equipment number, equipment longitude, latitude, equipment data status, temperature, humidity, wind speed, wind direction, PM2.5 concentration, and pressure.
一种扬尘颗粒物飘移轨迹模型及其建模方法,其特征在于,包括如下步骤:A drift trajectory model of fugitive dust particles and a modeling method thereof, characterized in that it comprises the following steps:
1)数据预处理阶段:预处理数据;1) Data preprocessing stage: preprocessing data;
2)模型预训练阶段:根据站点设备的地理位置划分网格;2) Model pre-training stage: divide the grid according to the geographical location of the site equipment;
3)模型预训练阶段:通过模拟数据和传统物理方法进行模型预训练;3) Model pre-training stage: model pre-training through simulated data and traditional physical methods;
4)迁移学习微调阶段:使用训练好的模型预测真实的扬尘颗粒物飘移轨迹。4) Transfer learning fine-tuning stage: use the trained model to predict the real drift trajectory of dust particles.
进一步的,1)数据预处理:为提高模型预测的精度,需要开展以下数据预处理工作:Further, 1) Data preprocessing: In order to improve the accuracy of model prediction, the following data preprocessing needs to be carried out:
1.1)数据去重:通过连表查询去除设备采集过程中上传的重复数据;1.1) Data deduplication: remove the duplicate data uploaded during the device collection process by connecting table query;
1.2)风速处理:以大地经纬度为坐标轴,根据扬尘数据中的风速、风向参数计算得到风速的纵向分量u和风速的横向分量v;1.2) Wind speed processing: Take the latitude and longitude of the earth as the coordinate axis, and calculate the longitudinal component u of the wind speed and the lateral component v of the wind speed according to the wind speed and wind direction parameters in the dust data;
1.2.1)根据风向计算其与大地平面坐标轴夹角θ;1.2.1) Calculate the angle θ between it and the coordinate axis of the geodetic plane according to the wind direction;
1.2.2)计算风速V计算横向分量u和纵向分量v:1.2.2) Calculate the wind speed V Calculate the transverse component u and the longitudinal component v:
横向分量u=Vcos(θ);纵向分量v=Vsin(θ);Transverse component u=Vcos(θ); longitudinal component v=Vsin(θ);
1.3)经纬度处理:为了减少站点经纬度误差带来的影响从而提高预测结果的准确度,本发明采用高斯投影算法将普通大地坐标下(L,B)转化为高斯坐标下的(x,y);1.3) Longitude and latitude processing: In order to reduce the influence of station longitude and latitude errors and thereby improve the accuracy of the prediction results, the present invention adopts Gaussian projection algorithm to convert (L, B) under ordinary geodetic coordinates into (x, y) under Gaussian coordinates;
1.3.1)根据经纬度计算中央子午经度和带号及经度差(点到中央子午线的距离),本模型选用的是3°中央子午线,其计算过程为:1.3.1) Calculate the central meridian longitude, band number and longitude difference (the distance from the point to the central meridian) according to the latitude and longitude. The 3° central meridian is selected for this model, and the calculation process is as follows:
1.3.1.1)计算3°带n3:n3=int(L/3+0.5);1.3.1.1) Calculate the 3° band n 3 : n 3 =int(L/3+0.5);
1.3.1.2)计算3°带n3的中央子午线L0:L0=3n3;1.3.1.2) Calculate the central meridian L 0 of 3° with n 3 : L 0 =3n 3 ;
1.3.1.3)计算经度差l(站点和中央子午线的间距):l=L-L0。1.3.1.3) Calculate the longitude difference l (the distance between the station and the central meridian): l=LL 0 .
1.3.2)根据椭球的选择计算子午弧长X,本模型选取克拉索夫斯基椭球进行计算(其可以应用于54北京坐标系):1.3.2) Calculate the meridian arc length X according to the selection of the ellipsoid, and this model selects the Krasovsky ellipsoid for calculation (which can be applied to the 54 Beijing coordinate system):
X=111134.861B-16036.480 sin 2B+16.828 sin 4B-0.022 sin 6B;X=111134.861B-16036.480 sin 2B+16.828 sin 4B-0.022 sin 6B;
1.3.3)计算高斯坐标正算公式中各个参数的值,其中,B为大地纬度,t为大地维度正切值,e为椭圆偏心率,N为卯西圈曲率半径,a为椭球长半径参数:1.3.3) Calculate the value of each parameter in the positive calculation formula of Gaussian coordinates, wherein, B is the geodetic latitude, t is the tangent of the geodetic dimension, e is the eccentricity of the ellipse, N is the radius of curvature of the Maoxi circle, and a is the long radius of the ellipsoid parameter:
1.3.4)将上述计算得到的参数代入高斯坐标正算公式求高斯坐标系下的坐标(x,y):1.3.4) Substitute the parameters obtained by the above calculation into the Gaussian coordinate formula to find the coordinates (x, y) in the Gaussian coordinate system:
x=X+N sin B cos Bl2+N sin B cos3B(5-t2-9e2cos2B)l4 x=X+N sin B cos Bl 2 +N sin B cos 3 B(5-t 2 -9e 2 cos 2 B)l 4
y=N cos Bl+N cos3B(1-t2+e2cos2B)l3+N cos5B(5-18t2+t4)l5 y=N cos Bl+N cos 3 B(1-t 2 +e 2 cos 2 B)l 3 +N cos 5 B(5-18t 2 +t 4 )l 5
进一步的,2)网格处理:Further, 2) grid processing:
扬尘运动中,相邻站点在空间上的相互影响是非常紧密的,故本发明不再研究单一站点的扬尘规律,而是从整体的角度出发,通过速度场,浓度场,温度场,压强场,湿度场来研究扬尘在空间中的分布情况和变化规律。为了描述物理场,需要进一步根据站点设备的地理位置进行网格划分。In the dust movement, the spatial interaction of adjacent stations is very close, so the present invention no longer studies the dust laws of a single station, but from the overall point of view, through the velocity field, concentration field, temperature field, pressure field , humidity field to study the distribution and variation of dust in space. To describe the physics, further meshing is required based on the geographic location of the site equipment.
2.1)聚类分析:为了提高预测的准确性,在划分网格前,本发明根据站点设备的理位置进行DBScan聚类分析,得到高斯坐标下站点设备聚类簇;2.1) Cluster analysis: In order to improve the accuracy of prediction, before dividing the grid, the present invention performs DBScan cluster analysis according to the physical location of the site equipment, and obtains the site equipment cluster cluster under Gaussian coordinates;
2.2)网格划分:得到效果较好的聚类簇后,根据聚类簇内站点设备的地理位置划分均匀正方形网格;2.2) Grid division: After obtaining a cluster with better effect, divide a uniform square grid according to the geographical location of the site equipment in the cluster;
2.3)数据插值:根据设备站点间距离和扬尘数据值进行线性插分,最终将扬尘数据以速度场,浓度场,温度场,压强场,湿度场的形式保存在网格内。2.3) Data interpolation: Linear interpolation is performed according to the distance between equipment sites and the dust data value, and finally the dust data is stored in the grid in the form of velocity field, concentration field, temperature field, pressure field, and humidity field.
进一步的,3)模型预训练:Further, 3) model pre-training:
目前应用于预测扬尘颗粒物飘移轨迹的两种主流方法是基于传统物理方法的前向计算方法和基于数值模拟的神经网络方法,但这两种方法都存在一定弊端:传统物理方法的计算过于冗杂,步骤繁琐;神经网络方法缺乏可解释性且一般情况下很难获得真实的速度场作为训练标签。基此,本发明给出了一种扬尘颗粒物飘移轨迹模型及其建模方法。The two mainstream methods currently used to predict the drift trajectory of dust particles are the forward calculation method based on traditional physical methods and the neural network method based on numerical simulation, but both methods have certain drawbacks: the calculation of traditional physical methods is too complicated, The steps are cumbersome; neural network methods lack interpretability and it is generally difficult to obtain real velocity fields as training labels. Based on this, the present invention provides a drift trajectory model of fugitive dust particles and a modeling method thereof.
3.1)生成模拟数据:在划分好的网格中模拟生成T0时刻的扬尘模拟数据,其中包括扬尘的速度场,浓度场,温度场,压强场和湿度场;3.1) Generate simulation data: simulate and generate dust simulation data at time T 0 in the divided grid, including dust velocity field, concentration field, temperature field, pressure field and humidity field;
3.2)基于传统物理方法的前向计算:在模拟数据的基础上,根据传统物理方法(主要依据N-S纳维-斯托克斯方程)更新体积力项,对流项和扩散项的计算进行前向计算,得到后续时间节点T1,T2,T3,…,Tn,Tn+1的扬尘物理场增广数据集:3.2) Forward calculation based on traditional physical methods: On the basis of the simulated data, the body force term is updated according to the traditional physical method (mainly based on the NS Navier-Stokes equation), and the calculation of the convection term and diffusion term is performed forward Calculate to obtain the augmented data set of the fugitive dust physics field of the subsequent time nodes T 1 , T 2 , T 3 , ..., T n , T n+1 :
3.2.1)N-S方程:N-S纳维-斯托克斯方程(Navier-Stokes equations)是描述流体动量守恒的流体运动方程,具体公式如下所示:3.2.1) N-S equations: N-S Navier-Stokes equations (Navier-Stokes equations) are the equations of fluid motion that describe the conservation of fluid momentum. The specific formula is as follows:
其中,是流体关于速度场的物质导数。欧拉视角主要关注的是空间中的网格点,因而物质导数等于网格点上流体速度随时间的变化率与流体在速度场作用下变化率u·▽u之和。其他参数方面:ρ是流体密度;u是速度矢量;p是压力;f是单位体积流体受的外力,μ是流体粘度。in, is the material derivative of the fluid with respect to the velocity field. Euler's perspective is mainly concerned with grid points in space, so the matter derivative is equal to the rate of change of fluid velocity over time at grid points and the sum of the rate of change u·▽u of the fluid under the action of the velocity field. Other parameters: ρ is the fluid density; u is the velocity vector; p is the pressure; f is the external force per unit volume of the fluid, and μ is the fluid viscosity.
上式为流体状态的更新过程,W0代表粒子的初始状态,经过体积力项(f)计算后的状态为W1,经过对流项的计算后的得到状态W2,最后经过扩散项(μ▽2u)的计算后得到状态W3。The above formula is the update process of the fluid state, W 0 represents the initial state of the particle, the state after the calculation of the body force term (f) is W 1 , and after the convection term The state W 2 is obtained after the calculation of , and finally the state W 3 is obtained after the calculation of the diffusion term (μ▽ 2 u).
3.2.2)体积力项:体积力项的计算公式为f=ρg(g为重力加速度,ρ为流体密度)。3.2.2) Body force term: The calculation formula of the body force term is f=ρg (g is the acceleration of gravity, ρ is the fluid density).
3.2.3)对流项:在流体模拟中,对流项被自动地执行,对流的本质是流体在不同速度场作用下,相邻的网格点之间互相传递流体微团并更新网格点上的物理量值,给定一个网格点位置为(x,y),该点的物理量场值为网格点上粒子对应的速度场横向分量为u,纵向分量为v,求解1个时间步长Δt后网格点物理量场值的步骤为:3.2.3) Convective term: In fluid simulation, the convection term is automatically executed. The essence of convection is that under the action of different velocity fields, adjacent grid points transfer fluid micelles to each other and update the grid points. The physical quantity value of , given a grid point position (x, y), the physical quantity field value of this point is The transverse component of the velocity field corresponding to the particle on the grid point is u, and the longitudinal component is v. After solving one time step Δt, the physical quantity field value of the grid point is The steps are:
3.2.3.1)后向追踪1个时间步长得到粒子的网格位置(x-uΔt,y-vΔt);3.2.3.1) Track backward for 1 time step to get the grid position of the particle (x-uΔt, y-vΔt);
3.2.3.2)根据物理场网格构建Catmull-Rom样条插值函数计算得到粒子物理量场的变化均值 3.2.3.2) Construct the Catmull-Rom spline interpolation function according to the physical field grid to calculate the mean value of the change of the particle physical quantity field
3.2.3.3)最终的计算公式为: 3.2.3.3) Final The calculation formula is:
3.2.4)扩散项:扩散项的计算是流体模拟中另一个非常重要的部分。流体的扩散项的计算公式为av=μ▽2u,其中av为粒子在流体粘性力作用下的加速度,μ为流体的粘度系数。假设第n+1时刻,网格坐标(x,y)处物理量已知,现需要求解第n时刻的物理量其具体计算步骤为:3.2.4) Diffusion term: The calculation of the diffusion term is another very important part of fluid simulation. The calculation formula of the diffusion term of the fluid is a v = μ▽ 2 u, where a v is the acceleration of the particle under the action of the fluid viscous force, and μ is the viscosity coefficient of the fluid. Assuming the n+1th moment, the physical quantity at the grid coordinates (x, y) Known, now we need to solve the physical quantity at the nth time The specific calculation steps are:
3.2.4.1)建立后向欧拉方程其中Δt为时间步长;3.2.4.1) Establish the backward Euler equation where Δt is the time step;
3.2.4.2)采用中心差分法计算拉普拉斯算子:3.2.4.2) Use the central difference method to calculate the Laplace operator:
其中为网格四周的物理量,Δx为网格宽度,Δy为网格高度,本专利使用正方形网格,固有Δx=Δy;in for Physical quantities around the grid, Δx is the width of the grid, Δy is the height of the grid, this patent uses a square grid, inherent Δx=Δy;
3.2.4.3)令将常数项提出得到:3.2.4.3) Order Taking the constant term out, we get:
3.2.4.4)将其转化矩阵形式,并采用共轭梯度法求解该大规模正定稀疏矩阵。3.2.4.4) Convert it to matrix form, and use the conjugate gradient method to solve the large-scale positive definite sparse matrix.
(3.2.5)根据体积力项,对流项,扩散项更新计算得到后续时间节点T1,T2,…,Tn,Tn+1时刻的扬尘物理场数据 进而由增广数据集进行预训练。(3.2.5) According to the update and calculation of the body force term, the convection term and the diffusion term, the physical field data of the dust at the subsequent time nodes T 1 , T 2 , ..., T n , T n+1 are obtained then augmented by the dataset Do pre-training.
(3.3)预训练:将(3.2)节中通过传统物理方法计算得到的T1,T2,…,Tn,Tn+1时间节点的扬尘物理信息作为数据集输入神经网络模型U进行预训练:(3.3) Pre-training: use the dust physical information of time nodes T 1 , T 2 , ..., T n , T n+1 calculated by traditional physical methods in Section (3.2) Input the neural network model U as a dataset for pre-training:
(3.3.1)模型选取:本发明在研究扬尘数据时引入了网格和场的概念,数据集D本质上是一组表达各种物理变量场随时间变化的空间分布数据,故可以将其类比为“图像”的像素分布数据。因此,在图像分割预测领域表现优异的U-net模型相较于其他网络更加适配扬尘物理场数据,故本发明选用U-net模型作为预训练模型。(3.3.1) Model selection: the present invention introduces the concept of grid and field when studying the dust data. The data set D is essentially a set of spatial distribution data that expresses the variation of various physical variable fields with time, so it can be An analogy is the pixel distribution data of an "image". Therefore, compared with other networks, the U-net model, which has excellent performance in the field of image segmentation prediction, is more suitable for the dust physical field data. Therefore, the present invention selects the U-net model as the pre-training model.
(3.3.2)训练细节:输入通道大小为32×32×6×2,其中32×32为网格大小,6×2代表6个物理场数据(速度场横向分量,速度场纵向分量,浓度场,温度场,压强场,湿度场)和两个相邻的时间场。输出通道为32×32×3×1,其中32×32为网格大小,3×1代表预测生成的3个物理场(速度场横向分量,速度场纵向分量和浓度场)和1个时间场。(3.3.2) Training details: The input channel size is 32×32×6×2, of which 32×32 is the grid size, and 6×2 represents 6 physical field data (transverse component of velocity field, longitudinal component of velocity field, concentration field, temperature field, pressure field, humidity field) and two adjacent time fields. The output channel is 32×32×3×1, where 32×32 is the grid size, and 3×1 represents the predicted generated 3 physical fields (transverse component of velocity field, longitudinal component of velocity field and concentration field) and 1 time field .
进一步的,4)迁移学习和微调:Further, 4) transfer learning and fine-tuning:
将真实数据集输入至完成预训练的模型U,调整迭代次数(epoch)训练批次(batch-size)和损失函数(loss)得到最终的扬尘颗粒物飘移预测轨迹。Input the real data set into the pre-trained model U, and adjust the number of iterations (epoch), the training batch (batch-size) and the loss function (loss) to obtain the final predicted trajectory of dust particle drift.
(4.1)模型迁移:保留完成预训练的U-Net模型中的所有参数,将其作为真实数据集的训练模型;(4.1) Model migration: retain all the parameters in the pre-trained U-Net model and use it as the training model for the real data set;
(4.2)数据训练:输入通道大小为32×32×4×2,其中32×32为网格大小,4×2代表4个真实物理场数据(浓度场,温度场,压强场,湿度场)和两个相邻的时间场。输出通道为32×32×3×1,其中32×32为网格大小,3×1代表预测生成的3个物理场(速度场横向分量,速度场纵向分量和浓度场)和1个时间场;(4.2) Data training: the input channel size is 32×32×4×2, of which 32×32 is the grid size, and 4×2 represents 4 real physical field data (concentration field, temperature field, pressure field, humidity field) and two adjacent time fields. The output channel is 32×32×3×1, where 32×32 is the grid size, and 3×1 represents the predicted generated 3 physical fields (transverse component of velocity field, longitudinal component of velocity field and concentration field) and 1 time field ;
(4.3)模型微调:调整参数epoch的值为240,调整训练批次参数batchsize的值为8,设定L2为损失函数,训练得到最终的扬尘飘移轨迹。其中,L2损失函数即最小化平方误差(Least Square Error)函数,使用LSE的目的是最小化真实值yi和训练结果f(xi)之间差值的平方和DL2,其函数公式如下:(4.3) Model fine-tuning: adjust the value of the parameter epoch to 240, adjust the value of the training batch parameter batchsize to 8, set L2 as the loss function, and train to obtain the final dust drift trajectory. Among them, the L2 loss function is the Least Square Error function. The purpose of using LSE is to minimize the square sum of the difference between the real value yi and the training result f(x i ) D L2 , and its function formula is as follows :
本发明的有益效果如下:本发明模型较传统物理方法无论是在精确度,计算时间,还是稳定程度方面都优于传统方法,且相较于仅用神经网络的数值估算方法具有更好的通用性和更强的可解释性,因此该模型可以更广泛地适用于大部分场景。The beneficial effects of the present invention are as follows: the model of the present invention is superior to the traditional method in terms of accuracy, calculation time, and stability compared with the traditional physical method, and has better generality than the numerical estimation method only using the neural network. Therefore, the model can be more widely applicable to most scenarios.
附图说明Description of drawings
图1是本发明的整体架构图;Fig. 1 is the overall structure diagram of the present invention;
图2是本发明的高斯坐标示意图;Fig. 2 is the Gaussian coordinate schematic diagram of the present invention;
图3是本发明网格示意图;图3中每个小方格的白色色阶代表了浓度场的大小,白色色阶越高,代表该网格中的扬尘浓度越高;Fig. 3 is a grid schematic diagram of the present invention; in Fig. 3, the white color level of each small square represents the size of the concentration field, and the higher the white color level is, the higher the dust concentration in this grid is represented;
图4是本发明的半拉格朗日法示意图;Fig. 4 is the semi-Lagrangian method schematic diagram of the present invention;
图5是本发明传统方法计算得到的扬尘速度场;Fig. 5 is the dust velocity field calculated by the traditional method of the present invention;
图6是本发明传统方法计算得到的扬尘浓度场;图6中由32×32个小方格组成,每个小方格的白色色阶代表了浓度场的大小,白色色阶越高,代表该网格中的扬尘浓度越高;Fig. 6 is the dust concentration field calculated by the traditional method of the present invention; Fig. 6 is composed of 32×32 small squares, and the white color level of each small square represents the size of the concentration field. The higher the dust concentration in this grid;
图7是本发明所用的U-net网络结构示意图。FIG. 7 is a schematic diagram of the U-net network structure used in the present invention.
具体实施方式Detailed ways
以下结合说明书附图,对本发明作进一步描述。The present invention will be further described below with reference to the accompanying drawings.
参照图1-7,一种扬尘颗粒物飘移轨迹模型及其建模方法,具体步骤如下:1-7, a dust particle drift trajectory model and its modeling method, the specific steps are as follows:
1)数据预处理:1) Data preprocessing:
(1.1)去重:连表查询,筛除设备上传的重复扬尘数据;(1.1) De-duplication: query with the table to screen out the repeated dust data uploaded by the equipment;
(1.2)风速处理:(1.2) Wind speed processing:
(1.2.1)根据风向计算其与大地平面坐标轴夹角θ;(1.2.1) Calculate the angle θ between it and the coordinate axis of the geodetic plane according to the wind direction;
(1.2.2)计算风速V计算横向分量u和纵向分量v:(1.2.2) Calculate the wind speed V Calculate the transverse component u and the longitudinal component v:
横向分量u=Vcos(θ);纵向分量v=Vsin(θ)。The transverse component u=Vcos(θ); the longitudinal component v=Vsin(θ).
(1.3)将站点坐标进行高斯投影:该步骤的目标是将经纬度坐标下的(L,B)转化为高斯坐标下的(x,y),具体步骤可以参照附图2;(1.3) Gaussian projection is carried out on the site coordinates: the goal of this step is to convert (L, B) under the latitude and longitude coordinates into (x, y) under the Gaussian coordinates, and the specific steps can refer to accompanying drawing 2;
(1.3.1)根据经纬度计算中央子午经度和带号及经度差(点到中央子午线的距离),本模型选用的是3°中央子午线,其计算过程为:(1.3.1) Calculate the central meridian longitude, band number and longitude difference (the distance from the point to the central meridian) according to the latitude and longitude. The 3° central meridian is selected for this model, and the calculation process is as follows:
(1)计算3°带n3:n3=int(L/3+0.5);(1) Calculate the 3° band n 3 : n 3 =int(L/3+0.5);
(2)计算3°带n3的中央子午线L0:L0=3n3;(2) Calculate the central meridian L 0 with n 3 of 3°: L 0 =3n 3 ;
(3)计算经度差l(站点和中央子午线的间距):l=L-L0;(3) Calculate the longitude difference l (the distance between the station and the central meridian): l=LL 0 ;
(1.3.2)根据椭球的选择计算子午弧长X,本模型选取克拉索夫斯基椭球进行计算(其可以应用于54北京坐标系):(1.3.2) Calculate the meridian arc length X according to the selection of the ellipsoid. This model selects the Krasovsky ellipsoid for calculation (which can be applied to the 54 Beijing coordinate system):
X=111134.861B-16036.480 sin 2B+16.828 sin 4B-0.022 sin 6B;X=111134.861B-16036.480 sin 2B+16.828 sin 4B-0.022 sin 6B;
(1.3.3)计算高斯坐标正算公式中各个参数的值,其中,B为大地纬度,t为大地维度正切值,e为椭圆偏心率,N为卯西圈曲率半径,a为椭球长半径参数:(1.3.3) Calculate the value of each parameter in the positive calculation formula of Gaussian coordinates, where B is the geodetic latitude, t is the tangent value of the geodetic dimension, e is the eccentricity of the ellipse, N is the radius of curvature of the Maoxi circle, and a is the length of the ellipsoid Radius parameter:
(1.3.4)将上述计算得到的参数代入高斯坐标正算公式求高斯坐标系下的坐标(x,y):(1.3.4) Substitute the parameters obtained by the above calculation into the Gaussian coordinate positive formula to find the coordinates (x, y) in the Gaussian coordinate system:
x=X+N sin B cos Bl2+N sin B cos3B(5-t2-9e2cos2B)l4 x=X+N sin B cos Bl 2 +N sin B cos 3 B(5-t 2 -9e 2 cos 2 B)l 4
y=N cos Bl+N cos3B(1-t2+e2cos2B)l3+N cos5B(5-18t2+t4)l5 y=N cos Bl+N cos 3 B(1-t 2 +e 2 cos 2 B)l 3 +N cos 5 B(5-18t 2 +t 4 )l 5
2)网格处理:2) Grid processing:
(2.1)聚类分析:通过DBscan聚类算法得到聚类簇C,其步骤如下:(2.1) Cluster analysis: The cluster C is obtained through the DBscan clustering algorithm, and the steps are as follows:
(1)标记所有对象为unvisited;随机选择一个unvisited对象P;(1) Mark all objects as unvisited; randomly select an unvisited object P;
(2)如果P的ε领域至少有MinPts个对象,创建一个新簇C,并把P添加到簇C;(2) If there are at least MinPts objects in the ε field of P, create a new cluster C, and add P to the cluster C;
(3)令N为P的ε领域中的对象集合,如果P的ε领域至少有MinPts个对象,把这些对象添加到N;如果P还不是任何簇的成员,把P添加到簇C。(3) Let N be the set of objects in the ε field of P. If there are at least MinPts objects in the ε field of P, add these objects to N; if P is not yet a member of any cluster, add P to cluster C.
(2.2)线性插值得到均匀网格(网格示意图可以参照附图3):(2.2) Linear interpolation to obtain a uniform grid (see Figure 3 for a schematic diagram of the grid):
(2.2.1)根据Delaunay三角剖分算法先找出内插点四周的3个点构成(2.2.1) According to the Delaunay triangulation algorithm, first find out the composition of the three points around the interpolation point
三角形列表triangles(伪代码如下):Triangles list triangles (pseudocode below):
(2.2.2)调用griddata函数进行数据插分得到均匀网格表示的扬尘速度场,浓度场,温度场,压强场,湿度场。(2.2.2) Call the griddata function to perform data interpolation to obtain the dust velocity field, concentration field, temperature field, pressure field, and humidity field represented by a uniform grid.
3)模型预训练:3) Model pre-training:
(3.1)模拟初始数据:以2021年07月20日晚间23:00时刻的扬尘数据作为T0时刻的模拟初始数据。(3.1) Initial simulation data: Take the dust data at 23:00 on the evening of July 20, 2021 as the initial simulation data at time T 0 .
(3.2)物理传统方法前向计算:本发明在进行传统方法前向计算时主要依托的算法为纳维-斯托克斯方程(Navier-Stokes equations),简称N-S方程。(3.2) Forward calculation by traditional method of physics: The algorithm that the present invention mainly relies on when performing the forward calculation by traditional method is Navier-Stokes equations, or N-S equation for short.
(3.2.1)体积力项:更新体积力项f=ρg(g为重力加速度,ρ为密度)。(3.2.1) Body force term: update the body force term f=ρg (g is the acceleration of gravity, ρ is the density).
(3.2.2)对流项(对流过程可以参照附图4):给定一个网格点位置为(x,y),该点的物理量场值为网格点上粒子对应的速度场横向分量为u,纵向分量为v,求解1个时间步长Δt后网格点物理量场值的步骤为:(3.2.2) Convective term (refer to Figure 4 for the convection process): Given a grid point position (x, y), the physical quantity field value of this point is The lateral component of the velocity field corresponding to the particle on the grid point is u, and the vertical component is v. After solving one time step Δt, the physical quantity field value of the grid point is The steps are:
(1)后向追踪1个时间步长得到粒子的网格位置(x-uΔt,y-vΔt);(1) Track backward for 1 time step to obtain the grid position (x-uΔt, y-vΔt) of the particle;
(2)根据物理场网格构建Catmull-Rom样条插值函数计算得到粒子物理量场的变化均值 (2) Constructing the Catmull-Rom spline interpolation function according to the physical field grid to calculate the mean value of the variation of the particle physical quantity field
(3)最终的计算公式为: (3) Final The calculation formula is:
(3.2.3)扩散项:该项主要目的是求解流体的粘度项av=μ▽2u,其中av为粒子在流体粘性力作用下的加速度,μ为流体的粘度系数。假设第n+1时刻,网格坐标(x,y)处物理量已知,现需要求解第n时刻的物理量其具体计算步骤为:(3.2.3) Diffusion term: The main purpose of this project is to solve the viscosity term a v = μ▽ 2 u of the fluid, where a v is the acceleration of the particle under the action of the fluid viscous force, and μ is the viscosity coefficient of the fluid. Assuming the n+1th moment, the physical quantity at the grid coordinates (x, y) Known, now we need to solve the physical quantity at the nth time The specific calculation steps are:
(1)建立后向欧拉方程其中Δt为时间步长;(1) Establish the backward Euler equation where Δt is the time step;
(2)采用中心差分法计算拉普拉斯算子:(2) The central difference method is used to calculate the Laplace operator:
其中为网格四周的物理量,Δx为网格宽度,Δy为网格高度,本专利使用正方形网格,固有Δx=Δy;in for Physical quantities around the grid, Δx is the width of the grid, Δy is the height of the grid, this patent uses a square grid, inherent Δx=Δy;
(3)令将常数项提出得到:(3) Order Taking the constant term out, we get:
(4)将其转化矩阵形式,并采用共轭梯度法求解该大规模正定稀疏矩阵。(4) Convert it into matrix form, and use the conjugate gradient method to solve the large-scale positive definite sparse matrix.
(3.2.4)根据体积力项,对流项,扩散项,传统方法计算得到后续时间节点T1,T2,T3,…,Tn,Tn+1时刻的扬尘物理场数据 进而由增广数据集训练得到预训练模型U,增广数据集中的速度场和浓度场可以参照附图5和附图6。(3.2.4) According to the body force term, the convection term, the diffusion term, and the traditional method, the physical field data of the dust at the subsequent time nodes T 1 , T 2 , T 3 , ..., T n , T n+1 are obtained then augmented by the dataset The pre-training model U is obtained by training, and the velocity field and the concentration field in the augmented data set can be referred to Fig. 5 and Fig. 6 .
(3.3)预训练过程:(3.3) Pre-training process:
(3.3.1)网络选取:(3.3.1) Network selection:
基于扬尘飘移运动的特点(在空间上,相邻站点的扬尘数据具有强关联性),本发明在研究扬尘数据时引入了网格和场的概念,数据集D本质上是一组表达各种物理变量场随时间变化的空间分布数据,故可以将其类比为“图像”的像素分布数据。因此,在图像分割预测领域表现优异的U-net模型相较于其他网络在整体结构上更加适配扬尘物理场数据,故本发明选用U-net模型作为预训练模型(具体的U-net模型结构图可以参照附图7)。Based on the characteristics of dust drift movement (spatially, dust data of adjacent sites are strongly correlated), the present invention introduces the concept of grid and field when studying dust data. Data set D is essentially a set of expressions that express various The spatial distribution data of the physical variable field changes with time, so it can be analogized to the pixel distribution data of the "image". Therefore, the U-net model with excellent performance in the field of image segmentation prediction is more suitable for the dust physical field data in the overall structure than other networks. Therefore, the present invention selects the U-net model as the pre-training model (the specific U-net model). The structure diagram can refer to Figure 7).
(3.3.2)训练细节:(3.3.2) Training details:
(1)预训练选取了U-Net模型,参数epoch的值设定为240,参数batchsize的值设定为8,数据集的大小为2000组,训练集,测试集和验证集的比例12:3:1,回归指标选取了L2损失函数。(1) The U-Net model is selected for pre-training, the value of the parameter epoch is set to 240, the value of the parameter batchsize is set to 8, the size of the data set is 2000 groups, and the ratio of training set, test set and validation set is 12: 3:1, the regression indicator selects the L2 loss function.
(2)输入通道大小为32×32×6×2:其中32×32为网格大小,6×2代表6个物理场数据(速度场横向分量,速度场纵向分量,浓度场,温度场,压强场,湿度场)和两个相邻的时间场。输出通道为32×32×3×1:其中32×32为网格大小,3×1代表预测生成的3个物理场(速度场横向分量,速度场纵向分量和浓度场)和1个时间场。(2) The input channel size is 32×32×6×2: 32×32 is the grid size, 6×2 represents 6 physical field data (transverse component of velocity field, longitudinal component of velocity field, concentration field, temperature field, pressure field, humidity field) and two adjacent time fields. The output channel is 32×32×3×1: 32×32 is the grid size, and 3×1 represents the predicted generated 3 physical fields (transverse component of velocity field, longitudinal component of velocity field and concentration field) and 1 time field .
4)模型迁移与微调:4) Model migration and fine-tuning:
(4.1)模型迁移:保留完成预训练的U-Net模型中的所有参数,将其作为真实数据集的训练模型;(4.1) Model migration: retain all the parameters in the pre-trained U-Net model and use it as the training model for the real data set;
(4.2)数据训练:输入通道大小为32×32×4×2,其中32×32为网格大小,4×2代表4个真实物理场数据(浓度场,温度场,压强场,湿度场)和两个相邻的时间场。输出通道为32×32×3×1,其中32×32为网格大小,3×1代表预测生成的3个物理场(速度场横向分量,速度场纵向分量和浓度场)和1个时间场;(4.2) Data training: the input channel size is 32×32×4×2, of which 32×32 is the grid size, and 4×2 represents 4 real physical field data (concentration field, temperature field, pressure field, humidity field) and two adjacent time fields. The output channel is 32×32×3×1, where 32×32 is the grid size, and 3×1 represents the predicted generated 3 physical fields (transverse component of velocity field, longitudinal component of velocity field and concentration field) and 1 time field ;
(4.3)模型微调:调整参数epoch的值为240,调整训练批次参数batchsize的值为8,设定L2为损失函数,训练得到最终的扬尘飘移轨迹。其中,L2损失函数即最小化平方误差(Least Square Error)函数,使用LSE的目的是最小化真实值yi和训练结果f(xi)之间差值的平方和DL2,其函数公式如下:(4.3) Model fine-tuning: adjust the value of the parameter epoch to 240, adjust the value of the training batch parameter batchsize to 8, set L2 as the loss function, and train to obtain the final dust drift trajectory. Among them, the L2 loss function is the Least Square Error function. The purpose of using LSE is to minimize the square sum of the difference between the real value yi and the training result f(x i ) D L2 , and its function formula is as follows :
本发明针对传统方法计算量过大、精度与稳定性较差,神经网络方法又缺乏可解释性的问题,本发明结合编解码器神经网络和经过优化的传统方法,提出了一种扬尘颗粒物飘移轨迹模型及其建模方法。Aiming at the problems that the traditional method has too large amount of calculation, poor accuracy and stability, and the neural network method lacks interpretability, the present invention combines the codec neural network and the optimized traditional method, and proposes a dust particle drift. Trajectory model and its modeling method.
本说明书实施例所述的内容仅仅是对发明构思的实现形式的列举,本发明的保护范围不应当被视为仅限于实施例所陈述的具体形式,本发明的保护范围也及于本领域技术人员根据本发明构思所能够想到的等同技术手段。The content described in the embodiments of the present specification is only an enumeration of the realization forms of the inventive concept, and the protection scope of the present invention should not be regarded as limited to the specific forms stated in the embodiments, and the protection scope of the present invention also extends to those skilled in the art. Equivalent technical means that can be conceived by a person based on the inventive concept.
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