A ballistic wind identification method based on multi-source information fusion

Abstract

This invention is a multi-source fusion method for ballistic wind identification. It includes the following steps: (1) constructing a wind field model I using the thermal wind formula; (2) analyzing historical data using SPSS to construct a wind field model II; (3) constructing a wind field model III based on Extreme Learning Machine (ELM) using a data-driven approach; (4) using the wind direction and speed data obtained from the wind field models in steps (1) to (3), along with the actual wind direction and speed, as a new dataset, performing normalization preprocessing, and then proceeding to step (5); (5) based on the Stacking concept, using a recurrent neural network (ELM) to learn the multi-source data preprocessed in step (4), establishing the final wind field model, and identifying ballistic wind. This invention is low-cost, and the multi-model fusion approach effectively avoids the impact of noise in historical data on identification accuracy. The obtained meteorological wind data is more suitable for artillery operations in both the time and spatial domains.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of exterior ballistics, and particularly relates to a ballistic wind identification method based on multi-information source fusion. BACKGROUND

[0002] In the case of ignoring muzzle disturbance, the wind direction and wind speed have become the primary factors affecting the range and accuracy of artillery (accounting for 70%). At present, the main means for obtaining wind direction and wind speed in actual engineering are physical measurement means represented by sounding balloons and wind profile radars. The above-mentioned physical measurement means are low in timeliness, limited in use, high in cost, and the detection position cannot cover the whole trajectory area, which cannot meet the requirements of future war operations. With the development of meteorology, statistics and artificial intelligence technologies, constructing a wind field model has become the mainstream technical means for quickly and accurately obtaining wind direction and wind speed. According to different modeling principles, the wind field modeling methods can be roughly divided into atmospheric dynamics numerical method, statistical modeling method and data-driven method.

[0003] The atmospheric dynamics numerical method constructs a physical model of wind speed and direction through time and space integration of mass, momentum, heat, water vapor and aerosol conservation equations. Although it can efficiently simulate the change of wind field, the model is established based on a large number of assumptions and has high computational complexity. The statistical modeling method is based on historical meteorological data to fit the change law of wind direction and wind speed with time and space. The wind field model obtained by this method reflects the change law of average direction and average wind speed, and due to the error caused by statistics itself, the historical meteorological data is not fully applied. The data-driven method is based on the good generalization performance of neural network to construct a mapping relationship and realize wind field prediction, but the prediction accuracy of this method is too dependent on the sample quantity and quality.

[0004] From the perspective of research content, the existing modeling methods mainly focus on the change law of wind field in the time domain. However, in actual combat, the flight time of artillery is short and the spatial span is large, and the time interval span of the existing wind field model is too large for artillery operations. From the perspective of model quantity, at present, a single model is mainly used to predict the wind field, and the single model is sensitive to the distribution and characteristics of data and is easily affected by data noise and outliers. From the perspective of the type of data used, the wind direction and wind speed in the whole trajectory range have both vertical spatial distribution characteristics under different atmospheric boundary layer types and time sequence change characteristics, while the existing researches mainly use other meteorological data to predict the change of wind field, which is not closely combined with the characteristics of artillery. SUMMARY

[0005] The purpose of the present application is to provide a ballistic wind identification method based on multi-information source fusion, which provides a fast, accurate and low-cost way to obtain wind direction and wind speed for artillery operations.

[0006] The technical scheme for achieving the object of the present application is a multi-information source fusion ballistic wind identification method, comprising the following steps:

[0007] Step (1): constructing a wind field model I by using a thermal wind formula;

[0008] Step (2): constructing a wind field model II by using SPSS to analyze historical data;

[0009] Step (3): constructing a wind field model III by using a data-driven method based on an extreme learning machine (ELM);

[0010] Step (4): taking the wind direction and wind speed data obtained from the wind field models of steps (1)-(3) and the real wind direction and wind speed as new data sets, performing normalization preprocessing, and then entering step (5);

[0011] Step (5): according to the Stacking idea, using a recurrent neural network (Elman) to learn the multi-information source data preprocessed in step (4) to establish a final wind field model and identify the ballistic wind.

[0012] Further, the wind field model I established in step (1) comprises a wind speed model I and a wind direction model I;

[0013] The wind speed model I is as follows:

[0014]

[0015] where u is the wind speed, h is the height, h1 is the sea level height, u1 is the wind speed at sea level, z0 is the roughness parameter, u g is the zonal wind speed, v g is the radial wind speed, f is the geostrophic parameter, k1 is the turbulence coefficient, ω is the geostrophic angular velocity, Λ is the local dimension, f * is the potential;

[0016] The wind direction model I is as follows:

[0017] In the near-surface layer of 100 m: the wind direction is consistent with the average wind speed

[0018] In the upper boundary layer of 100-1500 m:

[0019]

[0020] In the free atmosphere layer of 1500-20000 m:

[0021]

[0022] where ψ is the wind direction,

[0023] Further, step (2) historical meteorological data preprocessing: selecting the target point historical n days of meteorological wind data, obtaining the average value of wind direction and wind speed data, and obtaining the wind direction and wind speed change curve; according to the concave and convex points on the wind direction and wind speed change curve, using SPSS segmented fitting, a wind direction and wind speed model is constructed;

[0024] The wind speed model II is as follows:

[0025]

[0026] The wind direction model II is as follows:

[0027]

[0028] Further, step (3) of constructing the wind field model III:

[0029] When N groups of training samples are given For the ELM with the model structure I-L-O, wherein I, L and O are the number of input layer, hidden layer and output layer neurons respectively, and the activation function is h(x), the output of the ELM is:

[0030]

[0031]

[0032]

[0033]

[0034] wherein is the connection weight matrix of the hidden layer and the output layer, H L×N is the hidden layer output matrix, and b L×N are the randomly generated structure parameter matrices;

[0035] The optimal is obtained through training, so that the network output is as close as possible to the actual output, i.e.

[0036]

[0037] Based on the least square criterion, the connection weight matrix

[0038]

[0039] In the formula, is the Moor-Penrose generalized inverse matrix of H L×N .

[0040] Further, step (3) specifically comprises the following steps:

[0041] Step (31): Data normalization processing: using min-max normalization formula to preprocess data:

[0042]

[0043] where r * is the normalized data, r min is the minimum value of the data, and r max is the data;

[0044] Step (32): Constructing an ELM network model: determining the number of input layer neurons I, the number of output layer neurons O, the number of hidden layer neurons L, and the activation function h(x):

[0045] The number of input layer neurons I

[0046] ELM is used to construct the mapping relationship between ballistic data and meteorological wind, and the input layer neurons are used to record the ballistic data, which includes the range x, elevation y, deflection z, and the corresponding velocity components v x ,v y ,v z and the velocity azimuth v θ ; therefore, the number of ELM input layer neurons I = 7;

[0047] The number of output layer neurons O

[0048] The ELM output layer is used to output the required ballistic wind data: wind speed u and wind direction ψ, so the number of ELM output layer neurons O = 2;

[0049] The number of hidden layer neurons L

[0050] The exponential growth strategy is combined with the dichotomy method, and the value range of L is [L min , L max ] = [2 j-1 , 2 j ]; the dichotomy method continuously narrows the interval range until the final number of hidden layer neurons L is determined;

[0051] The activation function h(x)

[0052] After normalization processing, the ballistic data is mapped to the interval [0, 1], and the Sigmoid function is selected as the activation function, and the expression of the Sigmoid function is as follows:

[0053]

[0054] Further, the Elman neural network in step (5) is composed of an input layer, a hidden layer, a connection layer and an output layer; the signal is connected to the connection layer after passing through the hidden layer, which is used to memorize the output value of the hidden layer unit at previous time, and the node numbers of the input layer, the hidden layer, the connection layer and the output layer are respectively R, G, G and M, and the nonlinear state expression of the Elman neural network is described as:

[0055] x(t) = f(ω1x c (t) + ω2p(t-1))

[0056] x c (t) = x(t-1)

[0057] y t = g(ω3x(t))

[0058] In the formula:

[0059] t - the t time; x(t) - the output of the hidden layer;

[0060] p - the input of the input layer; x c (t) - the output of the connection layer;

[0061] ω1 - the weight value from the connection layer to the hidden layer; y(t) - the output of the output layer;

[0062] ω2 - the weight value from the input layer to the hidden layer; g(x) - the transfer function of the output layer;

[0063] ω3 - the weight value from the hidden layer to the output layer; f(x) - the activation function of the hidden layer.

[0064] Further, the value of the input layer neuron number R in the Elman neural network in step (5) is the corresponding dimension of the data, R = 3; the output layer neuron of the Elman is used to output the final result, M = 1; the hidden layer / connection layer neuron number G is determined by combining the exponential growth strategy and the bisection method; and the activation function f(x) adopts the Sigmoid function.

[0065] Further, the Elman neural network adopts the error index function E to calculate the error function of the data preprocessed in step (4); the network weight of the Elman neural network is updated, and after the update, whether the training stop condition is met is judged, and the specific is:

[0066] The error index function E is:

[0067]

[0068] Let Then:

[0069]

[0070] The partial derivative of the function E with respect to the weight ω3 is obtained as follows:

[0071]

[0072] Let Then

[0073]

[0074] The partial derivative of the function E with respect to the weight ω1 is obtained as follows:

[0075]

[0076] Wherein:

[0077]

[0078] In the case of not taking the dependence of x c (t) on the weight ω 1jl is:

[0079]

[0080] According to the theory of gradient descent, the correction of each weight is

[0081]

[0082]

[0083]

[0084] Wherein, η1, η2, η3 respectively represent the learning step of the weight ω1, ω2, ω3.

[0085] Compared with the prior art, the present application has the following advantages:

[0086] The present application combines aerodynamics, statistics and exterior ballistics, and proposes a trajectory wind identification method of multiple information sources; the method has low cost, can effectively avoid the influence of noise in historical data on identification accuracy by using a multi-model integration method, and the obtained meteorological wind data is more suitable for artillery combat in time domain and space domain. BRIEF DESCRIPTION OF DRAWINGS

[0087] Figure 1 The figure is a flowchart of the trajectory wind identification method of the present application.

[0088] Figure 2 The figure is a wind speed data diagram used in the present application.

[0089] Figure 3 The figure is a wind direction data diagram used in the present application.

[0090] Figure 4 Network structure diagram of ELM in the present application

[0091] Figure 5 Flow chart of the implicit layer determination method based on dichotomy and exponential growth strategy adopted in the present application

[0092] Figure 6 Network structure diagram of Elman in the present application

[0093] Figure 7 Workflow diagram of Elman in the present application

[0094] Figure 8 Wind speed identification result diagram of the present application.

[0095] Figure 9 Wind direction identification result diagram of the present application DETAILED DESCRIPTION

[0096] The present application will be further described in detail below with reference to the accompanying drawings.

[0097] The multi-information source fusion ballistic wind identification method of the present application comprises the following steps:

[0098] Step 1, constructing a wind field model I by using a thermal wind formula;

[0099] Step 1.1 wind speed model I

[0100]

[0101] wherein u is the wind speed, h is the height, h1 is the sea level height, u1 is the wind speed at sea level, z0 is the roughness parameter, u g is the zonal wind speed, v g is the radial wind speed, f is the geostrophic parameter, k1 is the turbulence coefficient, ω is the geostrophic angular velocity, Λ is the local dimension, f * is the potential.

[0102] Step 1.2 wind direction model I

[0103] Near-surface layer (within 100m): the wind direction is consistent with the average wind speed

[0104] Upper boundary layer (100m-1500m):

[0105]

[0106] Free atmosphere layer (1500m-20000m):

[0107]

[0108] wherein ψ is the wind direction,

[0109] Step 2, analyze historical data using SPSS to build wind field model II;

[0110] Step 2.1 historical weather data preprocessing: select the target point historical 120 days within the meteorological wind data, get the average value of wind direction, wind speed data, specific wind direction and wind speed change curve as shown in Figure 2 Figure 3 .

[0111] Step 2.2 according to Figure 2 、 Figure 3 concave and convex points, using SPSS piecewise fitting, build wind direction and wind speed model as follows

[0112] Wind speed model II:

[0113]

[0114] Wind direction model II:

[0115]

[0116] Step 3, using data-driven method, based on extreme leaning machine (ELM) to build wind field model III;

[0117] When given N groups of training samples For the model structure I-L-O (I, L, O are the number of input layer, hidden layer and output layer neurons respectively), the activation function is h(x), the output of ELM at this time:

[0118]

[0119]

[0120]

[0121]

[0122] Where is the connection weight matrix between the hidden layer and the output layer, H L×N is the hidden layer output matrix, and b L×N are the structure parameter matrix generated randomly;

[0123] Through training, the optimal is obtained, so that the network output is as close as possible to the actual output, that is

[0124]

[0125] The connection weight matrix between the hidden layer and the output layer is determined based on a least square criterion

[0126]

[0127] wherein is H L×N is the Moore-Penrose generalized inverse matrix.

[0128] Step 3.1 data normalization processing: the ballistic data and the meteorological data have different dimensions, in order to eliminate the influence of the dimension of the index, the min-max normalization formula is used to preprocess the data

[0129]

[0130] wherein r * is the normalized data, r min is the minimum value of the data, r max is the maximum value of the data

[0131] Step 3.2 constructing an ELM network model Figure 4 ): as a single hidden layer feedforward neural network, when constructing the network model of the ELM, the number of input layer neurons I, the number of output layer neurons O, the number of hidden layer neurons L and the activation function h(x) need to be determined

[0132] 1) the number of input layer neurons I

[0133] In the application, the ELM is used to construct the mapping relationship between the ballistic data and the meteorological wind, the input layer neurons are used to record the ballistic data, and the ballistic data include the firing range x, the elevation y, the side deviation z and the velocity component v x ,v y ,v z and the velocity azimuth v θ in the corresponding direction. Therefore, the number of ELM input layer neurons I = 7.

[0134] 2) the number of output layer neurons O

[0135] The ELM output layer is used to output the ballistic wind data required to be identified in the application: the wind speed u and the wind direction ψ, therefore, the number of ELM output layer neurons O = 2.

[0136] 3) the number of hidden layer neurons L

[0137] Selecting a suitable number of hidden layer neurons L can effectively improve the generalization ability of the model. In the application, the exponential growth strategy and the dichotomy method are combined to determine the number of hidden layer neurons L. The value range of L is [L min ,L max ] = [2j-1 ,2 j The binary search method continuously narrows down the interval until the final number L of hidden layer neurons is determined. The method for determining the number of hidden layer nodes is as follows: Figure 5 As shown. Where floor(·) represents the floor function, Error max This represents the maximum permissible error.

[0138] 4) Activation function h(x)

[0139] Activation functions introduce nonlinear characteristics into the network, allowing it to approximate any other nonlinear function. Ballistic data, after min-max normalization, is mapped to the [0,1] interval. Within this interval, the Sigmoid function exhibits good nonlinear characteristics, therefore it is chosen as the activation function. Furthermore, since the structural parameters of the ELM do not require adjustment based on gradient descent, using the Sigmoid function as the activation function does not result in the gradient vanishing problem. The expression for the Sigmoid function is as follows:

[0140]

[0141] Step 4: Take the wind direction and wind speed data obtained in Steps 1 to 3 above, as well as the actual wind direction and wind speed, as a new dataset. After preprocessing using formula (12), proceed to Step 5.

[0142] Step 5: Based on the Stacking concept, use the Elman recurrent neural network to learn the multi-source data from Step 4, establish the final wind field model, and identify ballistic winds.

[0143] The Elman neural network consists of four parts: input layer, hidden layer, sublayer, and output layer (structure diagram shown below). Figure 6 (As shown). After passing through the hidden layer, the signal is not transmitted back to the input, but is connected to the receiving layer to remember the output value of the hidden layer unit at a previous time. This internal feedback learning and memory mode increases the network's adaptive time-varying characteristics and its ability to reflect dynamic processes. Let the number of nodes in the input layer, hidden layer, receiving layer, and output layer be R, G, G, and M, respectively. Then, the nonlinear state expression of the Elman neural network can be described as:

[0144] x(t)=f(ω1x c (t)+ω2p(t-1)) (14)

[0145] x c (t)=x(t-1) (15)

[0146] y t =g(ω3x(t)) (16)

[0147] where:

[0148] t - time t; x(t) - output of hidden layer;

[0149] p - input layer input; x c (t) - output of hidden layer;

[0150] ω1 - weight from hidden layer to output layer; y(t) - output of output layer;

[0151] ω2 - weight from input layer to hidden layer; g(x) - transfer function of output layer; ω3 - weight from hidden layer to output layer; f(x) - activation function of hidden layer. Then the error index function E is:

[0152]

[0153] Let Then:

[0154]

[0155] The partial derivative of the function E with respect to the weight ω3 is:

[0156]

[0157] Let Then:

[0158]

[0159] The partial derivative of the function E with respect to ω1 is:

[0160]

[0161] where:

[0162]

[0163] Without considering the dependence of x c (t) on the weight ω 1jl , then:

[0164]

[0165] According to the theory of gradient descent, the correction of each weight is

[0166]

[0167]

[0168]

[0169] η1, η2, η3 respectively represent the learning step of the weight ω1, ω2, ω3.

[0170] The workflow diagram of Elman is shown in Figure 7 .

[0171] Step 5.1: Constructing the Elman network model: when constructing the Elman network model, the number of input layer neurons R, the number of output layer neurons M, the number of hidden layer neurons G, the number of carry layer neurons G and the activation function f(x) need to be determined.

[0172] 1) The number of input layer neurons R

[0173] In the present application, the Elman input layer neurons are used to receive the data in step 4, so the value of R is the corresponding dimension of the data, that is, R = 3;

[0174] 2) The number of output layer neurons M

[0175] The Elman output layer neurons are used to output the final result, so M = 1;

[0176] 3) The number of hidden layer / carry layer neurons G

[0177] The determination method of the number of hidden layer / carry layer neurons is the same as step 3.2 3)

[0178] 5) The activation function f(x)

[0179] The selection method of the activation function is the same as step 3.2 4)

[0180] Step 5.2: Calculate the error function: calculate the error function according to formula (17) for the data given in step 4;

[0181] Step 5.3: Update the network weight: update the network weight according to formula (25)-(27);

[0182] Step 5.4: Determine whether the training stop condition is met, if yes, go to step 5.5, if not, return to step 5.2;

[0183] Step 5.6: Data test: randomly sample data for testing to verify the generalization performance of the model; (this step is optional);

[0184] Step 5.7: Experimental test: given a target point trajectory data, the predicted wind direction and wind speed change curve is obtained by using the model, and compared with the real wind direction and wind speed curve. (Details are shown in Figure 8 、 9 .

Claims

1. A method for ballistic wind identification by multi-information source fusion, characterized in that, Comprising the following steps: Step (1): Constructing wind field model I by using thermal wind equation; Step (2): Constructing wind field model II by using SPSS to analyze historical data; historical meteorological data preprocessing: selecting target point historical n-day meteorological wind data, obtaining wind direction and wind speed data average value, obtaining wind direction and wind speed change curve; according to the concave and convex points on the wind direction and wind speed change curve, using SPSS piecewise fitting, constructing wind direction and wind speed model: Wind speed model II is as follows: Wind direction model II is as follows: Wherein, u(2) is the wind speed obtained by wind speed model II, h is the altitude, and ψ(2) is the wind direction obtained by wind speed model II; Step (3): Constructing wind field model III by using data-driven method based on extreme learning machine ELM; Step (4): Taking the wind direction and wind speed data obtained by the wind field models in steps (1)-(3) and the real wind direction and wind speed as new data set, performing normalization preprocessing, and then entering step (5); Step (5): According to the Stacking idea, using recursive neural network Elman to learn the multi-information source data preprocessed in step (4), establishing the final wind field model, and identifying the trajectory wind direction and wind speed.

2. The method of claim 1, wherein, The wind field model I established in step (1) includes wind speed model I and wind direction model I; Wind speed model I is as follows: where u(l) is the wind speed from wind speed model I, hi is the sea level height, ui is the wind speed at sea level, z0 is the roughness parameter, u g (1) is the zonal wind speed from wind speed model I, v g (1) is the radial wind speed from wind speed model I, f is the geostrophic parameter, k1 is the turbulence coefficient, ω is the geostrophic angular velocity, and Λ is the local dimension; Wind direction model I is as follows: In the near-surface layer 100m: the wind direction is consistent with the average wind speed In the upper boundary layer 100m-1500m: In the free atmosphere layer 1500m-20000m: where ψ(1) is the wind direction obtained from the wind speed model I, 3. The method of claim 2, wherein, The wind field model III constructed in step (3) is as follows: When N groups of training samples are given For the ELM with the model structure I-L-O, where I, L, O are the numbers of neurons in the input layer, hidden layer and output layer respectively, and the activation function is z(·), the output of the ELM is wherein is a matrix of connection weights of the hidden layer to the output layer, H L×N is a matrix of hidden layer outputs, and b L×N is a randomly generated matrix of structure parameters; The optimal model is obtained by training The network output is close to the actual output, that is: Based on the least square criterion, the connection weight matrix of the hidden layer and the output layer wherein is H L×N Moor-Penrose generalized inverse matrix.

4. The method of claim 3, wherein, Step (3) specifically includes the following steps: Step (31): Data normalization processing: preprocessing data by using min-max normalization formula: Wherein, r is the original data before normalization, r * is the data after normalization, r min is the minimum value of data, r max is the maximum value of data; Step (32): Constructing ELM network model: determining the number of input layer neurons I, the number of output layer neurons O, the number of hidden layer neurons L and the activation function z(·): Number of input layer neurons I ELM is used to build the mapping relationship between ballistic data and meteorological wind, the input layer neurons are used to record ballistic data, which contains the range x p , the elevation y p , the side deviation z p , and the velocity components v x , v y , v z and the velocity azimuth v θ ; therefore, the number of ELM input layer neurons I = 7; Number of output layer neurons O The ELM output layer is used for outputting the trajectory wind data to be identified: wind speed u and wind direction ψ, so the number of ELM output layer neurons O=2; Number of hidden layer neurons L The exponential growth strategy is combined with dichotomy, and the value range of L is [L min , L max ] = [2 J-1 , 2 J ], where J is a power coefficient; dichotomy is used to continuously reduce the interval range until the final number of hidden layer neurons L is determined; Activation function z(·) After normalization processing, the trajectory data is mapped to the interval [0,1], and the Sigmoid function is selected as the activation function, and the expression of the Sigmoid function is as follows:

5. The method of claim 4, wherein, The Elman neural network in step (5) is composed of input layer, hidden layer, connection layer and output layer; the signal is connected to the connection layer after passing through the hidden layer, which is used to remember the output value of the hidden layer unit at previous time, and the node numbers of the input layer, hidden layer, connection layer and output layer are R, G, G and M respectively, then the nonlinear state expression of the Elman neural network is described as: x h (t) = f(ω1x c (t) + ω2p(t - 1)) x c (t) = x h (t-1) y d (t) = g(ω3x h (t)) In the formula: t - time t; x h (t) - output of the hidden layer p(t) - input layer input at time t; x c (t) - output of the hidden layer; ω1— weights from the hidden layer to the output layer; y d (t) — output of the output layer ω2-input layer to hidden layer weight; g(·)-output layer transfer function; ω3-hidden layer to output layer weight; f(·)-hidden layer activation function.

6. The method of claim 5, wherein, The value of the input layer neuron number R in the Elman neural network in step (5) is the corresponding dimension of the data, R=3; the output layer neuron of the Elman is used for outputting the final result, M=1; the number of hidden layer / neuron layer neurons G is determined by combining exponential growth strategy and bisection method; and the activation function f(·) adopts a Sigmoid function.

7. The method of claim 6, wherein, The Elman neural network is used to calculate the error function of the data preprocessed in step (4) by using an error index function E; the network weight of the Elman neural network is updated, and after the update, it is judged whether the training stop condition is met, and the specific condition is: The error index function E is: wherein is the partial derivative symbol; Let Then: The partial derivative of the function E with respect to the weight ω2 is: Let then The partial derivative of the function E with respect to ω1 is: Wherein: Without considering the output x of the receiving layer c (t) for ω 1jl In the case of dependency, then: According to the theory of gradient descent, the weight correction amount is Wherein, η1, η2, η3 respectively represent the learning step of the weight ω1 from the neuron layer to the hidden layer, the weight ω2 from the input layer to the hidden layer and the weight ω3 from the hidden layer to the output layer.

Images