CN112731439A - Direct calculation method for rough surface light scattering field - Google Patents
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Abstract
The invention relates to the technical field of laser radars, in particular to a direct calculation method of a rough surface light scattering field, which comprises the following steps: s1: obtaining a plurality of groups of simulation data E (r) of the scattering field corresponding to the rough surface under a plurality of groups of parameter set values according to a kirchhoff approximation algorithm; s2: determining the number of data input ports corresponding to the model according to the parameters in the S1, and constructing a deep learning frame model; s3: selecting a parameter set value corresponding to the partial parameter group in the S1 and corresponding scattered field data for training the deep learning frame model in the S2 to obtain a deep learning frame model after training; s4: and selecting a parameter set value corresponding to the other partial parameter group in the S1 to verify the deep learning frame model trained in the S3, and calculating the rough surface light scattering field after the verification is finished.
Description
Technical Field
The invention relates to the technical field of laser radars, in particular to a direct calculation method for a rough surface light scattering field.
Background
The target detection and identification has important application prospects in many fields, and as a classic and widely-applied target detection and identification technology, the laser radar realizes accurate measurement of target distance based on echo signals, and has the advantages of simple system, wide detection range, high signal-to-noise ratio, small influence by the outside and the like, so that the laser radar is widely applied to military fields (such as terminal-sensitive ammunition, target detection and the like) and civil fields (such as remote sensing, unmanned driving and the like). However, such basic detection can only achieve quantitative distance detection of targets, and although it can identify targets and estimate their motion trajectories according to range profiles, such target detection identification methods that can only extract information according to shapes often lose a large amount of target features, such as target materials, target surface characteristics, etc., resulting in difficulty in distinguishing real targets from disguised targets, thereby limiting the application prospects of laser detection.
In consideration of the important role and value of scattered field analysis in target detection and identification, the development of research on the scattered field of the rough surface can provide important research basis for application research of future scattering detection in military and civil fields based on application reference, and in random rough surface scattering calculation, no matter a classical MoM and KA method, or a scattering calculation method such as a perturbation method, a geometric optics method and a small slope approximation method, stable scattered field full-angle spatial distribution is obtained and depends on ensemble average calculation, namely, a large number of scattered fields of the generated random rough surface are calculated at first, and then the scattered field distribution is averaged, so that the scattered field full-angle spatial distribution corresponding to the characteristic random rough surface parameter is obtained.
Although the problem of random fluctuation of the spatial scattered field is solved by ensemble averaging, the scattered field of a large number of random rough surfaces needs to be calculated, the calculation load is heavy, and the calculation time is long; in addition, due to the limitation of the number of samples to be calculated, the distribution of the optical scattered field obtained by ensemble averaging still has a part of fluctuation noise, thereby limiting the application range of these random rough surface optical scattered field calculation methods depending on ensemble averaging, resulting in low calculation efficiency.
Therefore, the invention provides a direct calculation method of a rough surface light scattering field, which solves the problems.
Disclosure of Invention
The embodiment of the invention provides a direct calculation method of a rough surface light scattering field, which can solve the problems in the prior art.
The invention provides a method for directly calculating a rough surface light scattering field, which comprises the following steps:
s1: obtaining a plurality of groups of simulation data E (r) of the scattering field corresponding to the rough surface under a plurality of groups of parameter set values according to a kirchhoff approximation algorithm, wherein each group of parameters comprises root-mean-square height, correlation length, refractive index, incidence angle and incident light wave;
s2: determining the number of data input ports corresponding to the model according to the parameters in the S1, and constructing a deep learning frame model;
s3: selecting a parameter set value corresponding to the partial parameter group in the S1 and corresponding scattered field data for training the deep learning frame model in the S2 to obtain a deep learning frame model after training;
s4: and selecting a parameter set value corresponding to the other partial parameter group in the step S1 to verify the deep learning frame model trained in the step S3, and calculating the rough surface light scattering field after the verification is finished.
Preferably, the step of calculating the scattered field data in S1 is:
S11：
the rough surface height is calculated according to equation (1):
wherein x isnWhere N Δ x (N ═ N/2+1, …, N/2) is the nth sample point, F (k)j) As a function of surface relief f (x)n) Fourier transform of (a) when j>0, F (k)j)＝F(k-j) Wherein the wave number k j2 pi j/L, Δ k is the wavenumber difference, N (0, 1) is a gaussian distribution random number, and s (kj) is the gaussian distribution power spectral density;
where δ is the root mean square height of the surface and T is the surface correlation length.
Given the relevant parameters in the formula, the rough surface height function F (k) can be passedj) Obtaining one-dimensional distribution of the rough surface in an XZ coordinate system, wherein any point on the rough surface is represented as r';
S12：
a scattered field integral equation obtained by using a wave equation, as shown in formula (3):
the random rough surface height S is in a limited region V, the radius of a spherical surface SR is R, the random rough surface height S and the rough surface form a region V, R is any point in the region V, R' is any point on the rough surface, and n is a unit normal vector;
the simulation data of the scattered field was calculated according to equation (4):
wherein E (r) is simulation data of the spatial scattering field, r is a position vector of a point in space, r 'is a position vector of a point on the rough surface, n is a normal vector of a surface element of the rough surface, E (r') is a surface field of a point on the rough surface, G (r, r ') is a Green function, and ds' is a surface element surface area;
s13: generating rough surfaces with multiple groups of parameters according to the rough surface height function in the S11, and calculating simulation data of the surface space scattering field of each group of parameters by using a Sterlon-Cwland equation in the S12 to obtain the scattering field simulation data of the rough surfaces with multiple groups of parameters.
Preferably, the construction step of the deep learning framework model in S2:
s21: firstly, determining the number of data input ports corresponding to the model according to the type of the input data in S1;
wherein, the output data of the model is the intensity distribution of the rough surface scattering field;
s22: constructing a deep learning framework model based on a deep neural network, wherein the deep neural network selects a fully-connected neural network, and the fully-connected neural network comprises a plurality of hidden layers;
the vector of the neurons of each hidden layer in the network is calculated according to the following equation (5):
y＝W·x+b (5)
w is a weight matrix, x is a vector formed by the neurons of the last hidden layer neural network, and an offset vector b
Equation (6) is the activation function of the neural network:
f(x)＝max(0，x) (6)
when the input signal x is less than 0, the function value f (x) is 0; when x is greater than 0, the function value f (x) is x;
when the function value is less than 0, the function is in a suppressed state, and when the function value is greater than 0, the gradient is constantly equal to 1, so that the right saturation phenomenon cannot occur, and the requirement for establishing a rough surface scattered field distribution calculation model is met;
calculating a loss function value E according to equation (7)MSE：
Wherein, ypPrediction data of scattered fields, and E (r) simulation data of the scattered fields;
and evaluating the model by using a loss function value, selecting Adam as an optimizer of the neural network model, and comprehensively considering the first moment estimation and the second moment estimation of the gradient by combining the advantages of two optimization algorithms of AdaGrad and RMSProp to calculate the updating step length.
Preferably, the training step of the deep learning framework model in S3 is:
s31: dividing the simulation data E (r) calculated in the S13 into training set data and testing set data according to the ratio of 8: 2;
s32: initializing a weight matrix W and a bias vector b of all hidden layer neurons in the model;
s33: inputting training set data into a model in batches to calculate a network output value and a network output error;
s34: and optimizing the loss function by using an Adam optimizer to obtain a multilayer network weight matrix W, entering next learning, stopping learning after reaching a specified learning frequency or meeting the condition of a loss function value, and obtaining a model which is qualified in training and a training error value after the model is converged.
Preferably, the validity of the model verifies:
s41: inputting the test set data in S31 into the deep learning framework model trained in S3, and outputting the prediction data y of the scattered fieldp；
S42: simulation data E (r) of scattered field obtained by using kirchhoff approximation algorithm in S1 and prediction data y obtained in S41pCarry out the loss function value EMSECalculating if loss function value EMSEAnd if the error value is less than 105% of the training error value in the S3, the model training effect is good, otherwise, the model training effect is poor, and the step returns to S2 to modify the model structure and train the modified model again.
Compared with the prior art, the invention has the advantages that:
the method has the advantages of self-learning and self-adaption, has good robustness in the aspect of parameter fitting, does not depend on ensemble average calculation compared with a classical KA method and a moment method, and greatly improves the calculation speed and the calculation efficiency.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a method for directly calculating a scattering field on a metallic iron surface according to the present invention;
FIG. 2 is a graph showing the decrease in the value of the loss function of metallic iron according to the present invention;
FIG. 3 is a graph showing the fitting effect of metallic iron at an incident angle of 10 ° in the embodiment of the present invention;
FIG. 4 is a graph showing the fitting effect of metallic iron at an incident angle of 20 ° in an embodiment of the present invention;
FIG. 5 is a graph showing the fitting effect of metallic iron at an incident angle of 30 ° in an embodiment of the present invention;
fig. 6 is a graph showing the fitting effect of the metallic iron at an incident angle of 40 ° in the example of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to fig. 1 to 6 in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A metallic iron surface was selected as the calculation object at an incident light wavelength λ of 0.6328 μm, a root mean square height of 0.6 λ, and a surface correlation length of 6 λ, and the refractive index of iron at this wavelength was 2.85+3.36 i.
The invention provides a method for directly calculating a rough surface light scattering field, which comprises the following steps: the method comprises the following steps:
s1: obtaining a plurality of groups of simulation data E (r) of the scattering field corresponding to the rough surface under a plurality of groups of parameter set values according to a kirchhoff approximation algorithm, wherein each group of parameters comprises root-mean-square height, correlation length, refractive index, incidence angle and incident light wave; s2: determining the number of data input ports corresponding to the model according to the parameters in the S1, and constructing a deep learning frame model; s3: selecting a parameter set value corresponding to the partial parameter group in the S1 and corresponding scattered field data for training the deep learning frame model in the S2 to obtain a deep learning frame model after training; s4: and selecting a parameter set value corresponding to the other partial parameter group in the step S1 to verify the deep learning frame model trained in the step S3, and calculating the rough surface light scattering field after the verification is finished.
The input of the model comprises the previously determined random rough surface characteristic parameters influencing the final scattered field distribution, wherein the rough surface characteristic parameters comprise refractive index, root mean square height, correlation length, incidence pitch angle theta i, scattering pitch angle theta s and incident light wavelength lambda
Further, the step of calculating the scattered field data in S1 is:
s11: and performing frequency domain filtering on the power spectrum function according to the required surface parameters to obtain a rough surface height function:
wherein x isnWhere N Δ x (N ═ N/2+1, …, N/2) is the nth sample point, F (k)j) As a function of surface relief f (x)n) Fourier transform of (a) when j>0, F (k)j)＝F(k-j) Wherein the wave number k j2 pi j/L, Δ k is the wavenumber difference, N (0, 1) is the gaussian distribution random number, and s (kj) is the gaussian distribution power spectral density.
Where δ is the root mean square height of the surface and T is the surface correlation length.
Given the relevant parameters in the formula, the rough surface height function F (k) can be passedj) One-dimensional distribution of the rough surface in the XZ coordinate system is obtained, and any point on the rough surface is represented as r'.
S12：
According to the vector Green theorem, the integral equation of the scattering field as shown in the formula (3) can be obtained by utilizing the wave equation:
the random rough surface height S is in a limited region V, the radius of the spherical surface SR is R, the random rough surface height S and the rough surface form a region V, R is any point in the region V, R' is any point on the rough surface, and n is a unit normal vector.
Further expanding by utilizing a kirchhoff-helmholtz integral formula to obtain a stewarton-zhulan equation, and calculating simulation data of the scattering field according to the formula (4):
where E (r) is simulation data of the spatial fringe field, r is a position vector of a point (i.e., an observation point) in space, r ' is a position vector of a point on the rough surface, n is a surface bin normal vector of the rough surface, E (r ') is a surface field of a point on the rough surface, G (r, r ') is a green's function, and ds ' is a surface bin surface area.
S13: and generating rough surfaces with multiple groups of parameters according to a rough surface height function in S11 by using different parameters such as multiple root mean square heights, multiple correlation lengths, multiple refractive indexes, multiple incidence angles and multiple incident light wavelengths, and calculating simulation data of the surface space scattering field of each group of parameters by using a Stewarton-Zealand composition equation in S12 to obtain simulation data of the scattering of the rough surfaces under multiple groups of parameters.
Further, the construction step of the deep learning framework model in S2:
s21, firstly, determining the number of data input ports corresponding to the model according to the type of the input data in S1;
wherein, the output data of the model is the intensity distribution of the rough surface scattered field.
S22, constructing a deep learning framework model based on a deep neural network, wherein the deep neural network selects a fully-connected neural network, and the fully-connected neural network comprises a plurality of hidden layers;
the vector of the neurons of each hidden layer in the network is calculated according to the following equation (5):
y＝W·x+b (5)
w is a weight matrix, x is a vector formed by the neurons of the last hidden layer neural network, and an offset vector b
Using equation (6) as the activation function of the neural network:
f(x)＝max(0，x) (6)
when the input signal x is less than 0, the function value f (x) is 0; when x is greater than 0, the function value f (x) is x.
When the function value is less than 0, the function is in a suppressed state, and when the function value is greater than 0, the gradient is constantly equal to 1, so that the right saturation phenomenon cannot occur, and the requirement for establishing a rough surface scattered field distribution calculation model is met;
calculating a loss function value E according to equation (7)MSE：
Wherein, ypPrediction data of scattered fields, and E (r) simulation data of the scattered fields;
the model can be evaluated using the loss function values. And simultaneously selecting Adam as an optimizer of the neural network model, and combining the advantages of two optimization algorithms of AdaGrad and RMSProp by the Adam optimizer, comprehensively considering the first moment estimation and the second moment estimation of the gradient and calculating the updating step length.
Further, the training step of the deep learning framework model in S3 is:
s31: dividing the simulation data E (r) calculated in the S13 into training set data and testing set data according to the ratio of 8: 2; s32: initializing a weight matrix W and a bias vector b of all hidden layer neurons in the model; s33: inputting training set data into a model in batches to calculate a network output value and a network output error; s34: and optimizing the loss function by using an Adam optimizer to obtain a multilayer network weight matrix W, entering next learning, stopping learning after reaching a specified learning frequency or meeting the condition of a loss function value, and obtaining a model which is qualified in training and a training error value after the model is converged.
The model is evaluated by using a loss function value, and simultaneously Adam is selected as an optimizer of the neural network model, and the Adam optimizer comprehensively considers the first moment estimation and the second moment estimation of the gradient by combining the advantages of two optimization algorithms of AdaGrad and RMSProp, and calculates the updating step length.
Further, the validity of the model is verified:
s41: inputting the test set data in S31 into the deep learning framework model trained in S3, and outputting the prediction data y of the scattered fieldp；
S42: simulation data E (r) of scattered field obtained by using kirchhoff approximation algorithm in S1 and prediction data y obtained in S41pCarry out the loss function value EMSECalculating if loss function value EMSEAnd if the error value is less than 105% of the training error value in the S3, the model training effect is good, otherwise, the model training effect is poor, and the step returns to S2 to modify the model structure and train the modified model again.
Fig. 2 is a variation curve of a loss function in a training process, each point on the curve represents an error magnitude in the current iteration times, which reflects a learning process of a neural network, and because samples selected in each batch of training are different, a loss function value fluctuates in an early stage of model training, but can be effectively converged along with the training, thereby embodying the effectiveness and excellent learning ability of the model.
Wherein figures 3 to 6 show a comparison of kirchhoff approximation calculation data for iron as a material with neural network modeling data. Contrast images at an incident light wavelength λ of 0.6328 μm, a root mean square height of 0.6 λ, a surface correlation length of 6 λ, incident angles of 10 °, 20 °, 30 °, 40 °, and an azimuth angle of 0 °, respectively. It can be seen that the peak value of the curve of the raw data calculated by kirchhoff approximation in fig. 3 to fig. 6 changes with the scattering angle, and the curve fitted by the neural network model is substantially consistent with the raw data, which indicates that the deep neural network has a good effect on describing the material iron, and can accurately describe the optical scattering property of the material iron.
In conclusion, the method has the advantages of self-learning and self-adaption, has good robustness in the aspect of parameter fitting, does not depend on ensemble average calculation compared with a classical KA method and a moment method, greatly improves the calculation speed and the calculation efficiency, and is simple and worthy of popularization.
Having described preferred embodiments of the invention, further alterations and modifications may be effected to these embodiments by those skilled in the art once apprised of the basic inventive concept, and it is therefore intended that the appended claims be interpreted to include preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (5)
1. A method for directly calculating a rough surface light scattering field, comprising the steps of:
s1: obtaining a plurality of groups of simulation data E (r) of the scattering field corresponding to the rough surface under a plurality of groups of parameter set values according to a kirchhoff approximation algorithm, wherein each group of parameters comprises root-mean-square height, correlation length, refractive index, incident angle and incident light wavelength;
s2: determining the number of data input ports corresponding to the model according to the parameters in the S1, and constructing a deep learning frame model;
s3: selecting a parameter set value corresponding to the partial parameter group in the S1 and corresponding scattered field data for training the deep learning frame model in the S2 to obtain a deep learning frame model after training;
s4: and selecting a parameter set value corresponding to the other partial parameter group in the step S1 to verify the deep learning frame model trained in the step S3, and calculating the rough surface light scattering field after the verification is finished.
2. The method of directly calculating a rough surface light scattering field according to claim 1, wherein the step of calculating the scattering field data in S1 is:
S11：
the rough surface height is calculated according to equation (1):
wherein x isnWhere N Δ x (N ═ N/2+1, …, N/2) is the nth sample point, F (k)j) As a function of surface relief f (x)n) Fourier transform of (a) when j>0, F (k)j)＝F(k-j) Wherein the wave number kj2 pi j/L, Δ k is the wavenumber difference, N (0, 1) is a gaussian distribution random number, and s (kj) is the gaussian distribution power spectral density;
where δ is the root mean square height of the surface and T is the surface correlation length.
Given the relevant parameters in the formula, the rough surface height function F (k) can be passedj) Obtaining one-dimensional distribution of the rough surface in an XZ coordinate system, wherein any point on the rough surface is represented as r';
S12：
a scattered field integral equation obtained by using a wave equation, as shown in formula (3):
the random rough surface height S is in a limited region V, the radius of a spherical surface SR is R, the random rough surface height S and the rough surface form a region V, R is any point in the region V, R' is any point on the rough surface, and n is a unit normal vector;
the simulation data of the scattered field was calculated according to equation (4):
wherein E (r) is simulation data of the spatial scattering field, r is a position vector of a point in space, r 'is a position vector of a point on the rough surface, n is a normal vector of a surface element of the rough surface, E (r') is a surface field of a point on the rough surface, G (r, r ') is a Green function, and ds' is a surface element surface area;
s13: generating rough surfaces with multiple groups of parameters according to the rough surface height function in the S11, and calculating simulation data of the surface space scattering field of each group of parameters by using a Sterlon-Cwland equation in the S12 to obtain the scattering field simulation data of the rough surfaces with multiple groups of parameters.
3. The method for directly calculating the rough surface light scattering field according to claim 2, wherein the step of constructing the deep learning framework model in S2 comprises:
s21: firstly, determining the number of data input ports corresponding to the model according to the type of the input data in S1;
wherein, the output data of the model is the intensity distribution of the rough surface scattering field;
s22: constructing a deep learning framework model based on a deep neural network, wherein the deep neural network selects a fully-connected neural network, and the fully-connected neural network comprises a plurality of hidden layers;
the vector of the neurons of each hidden layer in the network is calculated according to the following equation (5):
y＝W·x+b (5)
w is a weight matrix, x is a vector formed by the neurons of the last hidden layer neural network, and an offset vector b
Equation (6) is the activation function of the neural network:
f(x)＝max(0，x) (6)
when the input signal x is less than 0, the function value f (x) is 0; when x is greater than 0, the function value f (x) is x;
when the function value is less than 0, the function is in a suppressed state, and when the function value is greater than 0, the gradient is constantly equal to 1, so that the right saturation phenomenon cannot occur, and the requirement for establishing a rough surface scattered field distribution calculation model is met;
calculating a loss function value E according to equation (7)MSE：
Wherein, ypPrediction data of scattered fields, and E (r) simulation data of the scattered fields;
and evaluating the model by using a loss function value, selecting Adam as an optimizer of the neural network model, and comprehensively considering the first moment estimation and the second moment estimation of the gradient by combining the advantages of two optimization algorithms of AdaGrad and RMSProp to calculate the updating step length.
4. The method for directly calculating the rough surface light scattering field according to claim 1, wherein the training step of the deep learning framework model in S3 comprises:
s31: dividing the simulation data E (r) calculated in the S13 into training set data and testing set data according to the ratio of 8: 2;
s32: initializing a weight matrix W and a bias vector b of all hidden layer neurons in the model;
s33: inputting training set data into a model in batches to calculate a network output value and a network output error;
s34: and optimizing the loss function by using an Adam optimizer to obtain a multilayer network weight matrix W, entering next learning, stopping learning after reaching a specified learning frequency or meeting the condition of a loss function value, and obtaining a model which is qualified in training and a training error value after the model is converged.
5. The method of claim 4, wherein the validation of the model comprises:
s41: inputting the test set data in S31 into the deep learning framework model trained in S3, and outputting the prediction data y of the scattered fieldp；
S42: simulation data E (r) of scattered field obtained by using kirchhoff approximation algorithm in S1 and prediction data y obtained in S41pCarry out the loss function value EMSECalculating if loss function value EMSEAnd if the error value is less than 105% of the training error value in the S3, the model training effect is good, otherwise, the model training effect is poor, and the step returns to S2 to modify the model structure and train the modified model again.
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