CN107844870A - Heavy metal content in soil Forecasting Methodology based on Elman neural network models - Google Patents

Heavy metal content in soil Forecasting Methodology based on Elman neural network models Download PDF

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CN107844870A
CN107844870A CN201711281809.6A CN201711281809A CN107844870A CN 107844870 A CN107844870 A CN 107844870A CN 201711281809 A CN201711281809 A CN 201711281809A CN 107844870 A CN107844870 A CN 107844870A
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mrow
msub
layer
msubsup
soil
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CN107844870B (en
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王儒敬
贾秀芳
谢成军
李伟
鲁翠萍
胡海瀛
王雪
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Hefei Institutes of Physical Science of CAS
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/044—Recurrent networks, e.g. Hopfield networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/048—Activation functions
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/02—Agriculture; Fishing; Mining

Abstract

The present invention relates to the heavy metal content in soil Forecasting Methodology based on Elman neural network models, solves do not consider the defects of transference of the heavy metal in soil causes to be difficult to Accurate Prediction heavy metal content in soil compared with prior art.The present invention comprises the following steps：The acquisition and pretreatment of sample data；Construct the Elman Neural Network Prediction models based on storehouse autoencoder network；Unsupervised training is carried out to the Elman Neural Network Predictions model based on storehouse autoencoder network；Elman Neural Network Predictions model based on storehouse autoencoder network carries out Training；The forecast analysis of heavy metal content in soil.The present invention ensure that the precision that heavy metals in soil is predicted using heavy metal content in soil migration characteristic is taken into full account and modified Delphi approach model carries out analysis prediction.

Description

Heavy metal content in soil Forecasting Methodology based on Elman neural network models
Technical field
The present invention relates to soil data analysis technical field, the soil specifically based on Elman neural network models Content of beary metal Forecasting Methodology.
Background technology
Heavy metal pollution of soil problem has turned into the great agricultural ecological environment of China's extensive concern, to modern agriculture Sustainable development, Agriculture Ecological Environment Security and agricultural product quality and safety with social economy constitute serious threat.More than ten years Scientific research and substantial amounts of it was verified that due to the particularity of China's agroecological environment, indiscriminately imitate foreign technology and theory Can not solve great environmental and problem in science that China's agriculture field is faced conscientiously, it is difficult to effectively contain agricultural environment pollution Increasingly the developing state aggravated.
Domestic existing heavy metal-polluted soil detection method is mainly spot sampling, lab analysis, although the detection method energy Accurate content of beary metal is obtained, but sample pre-treatments are relatively complicated, detection cycle is long, need to expend substantial amounts of manpower and materials, It is likely to result in secondary pollution.Because China's area is big, made a concrete analysis of to be acquired great amount of samples, it is difficult to Realize the quick detection of the automating of heavy metal in soil composition, intelligent, synthesization and precision.
LIBS method (LIBS) have almost without sample pretreatment, can simultaneously multiple element is divided Analysis, the features such as detection time is short, suitable for the quick detection of heavy metal in soil.And found in actual analysis, it is substantial amounts of high There is migration problem in the dimension heavy metal such as soil sample and arsenic in soil, cadmium, lead, if heavy metal can not be taken into full account in soil in time Transference in earth, then it can not accurately realize the Accurate Prediction of heavy metal content in soil.
Therefore, how to realize that the preparation of heavy metal content in soil is predicted using LIBS technologies and have become the skill for being badly in need of solution Art problem.
The content of the invention
The invention aims to solve not considering that transference of the heavy metal in soil causes difficulty in the prior art A kind of the defects of with Accurate Prediction heavy metal content in soil, there is provided heavy metal content in soil based on Elman neural network models Forecasting Methodology solves the above problems.
To achieve these goals, technical scheme is as follows：
Heavy metal content in soil Forecasting Methodology based on Elman neural network models, comprises the following steps：
The acquisition and pretreatment of sample data, the soil sample of collection is divided into training sample and test sample, utilized The spectroscopic data of soil forms training data in LIBS technical limit spacing training samples, and training data is divided into label data and without mark Sign data；
Construct the Elman Neural Network Prediction models based on storehouse autoencoder network；
Unsupervised training is carried out to the Elman Neural Network Predictions model based on storehouse autoencoder network, utilizes nothing Label data carries out nothing to the storehouse autoencoder network of the Elman Neural Network Prediction models based on storehouse autoencoder network Supervised training；
Elman Neural Network Predictions model based on storehouse autoencoder network carries out Training, will train sample This label data is input in the storehouse autoencoder network after training and carries out feature extraction, will extract what is pre-processed after feature Elman neural network prediction point of the historical data of the label data and heavy metal content in soil input based on storehouse autoencoder network Model is analysed, Training is carried out to Elman Neural Network Predictions model；
The forecast analysis of heavy metal content in soil, by the LIBS light of the historical data of heavy metal content in soil and test sample Input in the Elman Neural Network Prediction models based on storehouse autoencoder network, completed to test specimens after Spectrum data processing The dynamic analysis prediction of this heavy metal content in soil.
The construction includes following step based on storehouse autoencoder network modified Delphi approach forecast analysis model Suddenly：
Structure includes the storehouse autoencoder network of encoder and decoder, and storehouse autoencoder network includes multilayer neural network Model, it is followed successively by one layer of input layer, multilayer hidden layer, one layer of output layer；
Elman neutral nets are built, Elman neutral nets include input layer, hidden layer successively, node layer is anti-as exporting The undertaking layer of feedback and the output layer for possessing Dynamic Recurrent Neural Network model；
Using the input without label data as storehouse autoencoder network first layer input layer of training sample, storehouse own coding Input of the output of network first tier input layer as second layer hidden layer, the output of last layer hidden layer are hidden as next layer The input of layer, the input of the output of last layer of hidden layer as output layer, storehouse autoencoder network first layer input layer it is hidden Layer unit is n1, second layer hidden layer Hidden unit be n2, third layer hidden layer Hidden unit be n3, X layer hidden layer Hidden unit is nx, last layer of output layer Hidden unit be nt；
Using the sign output data of last layer of output layer of storehouse autoencoder network as Elman neural network input layers Input；
Storehouse autoencoder network and Elman neutral nets are stacked to form the Elman neutral nets based on storehouse own coding Model.
The described pair of Elman Neural Network Predictions model based on storehouse autoencoder network, which carries out unsupervised training, to be included Following steps：
Obtain without label data X={ x1,x2,...,xr, by xi∈Rn×1I-th of input as storehouse autoencoder network Vector, it is input to the encoder with d neuron；Encoder obtains encoding z by nonlinear activation function fi∈Rd×1, its Calculation expression is as follows：
zi=sf(Wxi+b1),
Wherein, W ∈ Rd×nIt is weight matrix, b1∈Rd×1It is coding layer bias vector；
By ziDecoder is input to, obtains decoded resultIts calculation expression is as follows：
Wherein, sgFor the activation primitive of decoder,WT∈Rn×dIt is weight matrix W device, b2∈Rn×1It is Decoding layer bias vector；
Reconstructed by minimizingWith original input data xi, between error cost carry out feature extraction, using under gradient The weights of drop method renewal training between layersObtain extracted feature so thatBetween Error reaches minimum value, and its cost function is as follows：
The Elman Neural Network Predictions model based on storehouse autoencoder network carry out Training include with Lower step：
The label data of training sample is input in the storehouse autoencoder network after training and carries out feature extraction；
Obtain the historical data of heavy metal content in soil；
Elman Neural Network Prediction model definitions is as follows：
Wherein, k is the frequency of training of Elman neutral nets, and y is output vector, and x is hidden neuron output vector, and u is Input vector, ycFor the previous moment output valve fed back of memory output layer unit, 0≤α≤1 be from connection feedback oscillator because Son, W3、W2、W1Respectively hidden layer to output layer, accept layer to output layer, the connection weight matrix of input layer to hidden layer, f () and g () are respectively to hide the Nonlinear Vector function that the excitation function of layer unit and output layer unit is formed；
The parameter of Elman Neural Network Prediction models is adjusted,
If the actual output of kth time is
Error extension function is
E (k) is calculated respectively to weights W3、W2、W1Partial derivative and be 0, it is pre- to obtain modified Delphi approach Survey analysis model training method；
Connection weight W by E (k) to hidden layer to output layer3Local derviation is sought, it is calculated as follows：
Wherein,
Order
Connection weight W by E (k) to hidden layer to output layer2Local derviation is sought, it is calculated as follows：
Do not consider yc,i(k) it is rightDependence,
Connection weight W by E (k) to hidden layer to output layer1Local derviation is sought, it is calculated as follows：
Label data after extraction feature and the historical data of heavy metal content in soil are inputted into Elman neural network predictions Analysis model carries out parameter adjustment, and Elman Neural Network Prediction models are trained.
The forecast analysis of the heavy metal content in soil comprises the following steps：
The LIBS spectroscopic datas of test sample are input to storehouse autoencoder network and carry out feature extraction；
Preprocessed data after extraction feature and the historical data of content of beary metal are input to and improve Elman nerve nets In network model, the analysis prediction to test sample heavy metal content in soil is carried out.
Beneficial effect
The heavy metal content in soil Forecasting Methodology based on Elman neural network models of the present invention, compared with prior art Using heavy metal content in soil migration characteristic is taken into full account and modified Delphi approach model carries out analysis prediction, ensure The precision of heavy metals in soil prediction.
The present invention carries out feature extraction using storehouse autoencoder network to the soil spectrum data obtained by LIBS technologies； Using the historical data of characteristic, heavy metal content in soil data and content of beary metal as modified Delphi approach The input of model, the forecast model of heavy metal content in soil is constructed, it is special to take full advantage of the dynamic that Elman neutral nets have Property, effectively solve the prediction challenge that heavy metal in soil content is migrated and changed over time.
When having too many characteristic variable input in order to avoid Elman neutral nets, the convergence of network is hindered, influences prediction essence Degree, spy extract the feature of key using storehouse autoencoder network from substantial amounts of characteristic variable.In view of heavy metal in soil Content is migrated and changed over time, to improve the accuracy of forecast model, utilizes modified Delphi approach dynamic model Instead of traditional BP forecast models, Elman neural network dynamics model has been carried out based on history heavy metal in soil content The element of data incorporates.The present invention has precision of prediction height, the fireballing feature of predicated response.
Brief description of the drawings
Fig. 1 is the method precedence diagram of the present invention.
Embodiment
The effect of to make to architectural feature of the invention and being reached, has a better understanding and awareness, to preferable Embodiment and accompanying drawing coordinate detailed description, are described as follows：
As shown in figure 1, the heavy metal content in soil Forecasting Methodology of the present invention based on Elman neural network models, Comprise the following steps：
The first step, the acquisition and pretreatment of sample data.The soil sample of collection is divided into training sample and test specimens This, training data is formed using the spectroscopic data of soil in LIBS technical limit spacing training samples.Examined using traditional chemical method The content of beary metal for determining training data is surveyed, label data is classified as, training data is divided into label data and without number of tags According to.
After impurity elimination, air-drying and handle, grind, sieve, weigh, the process such as number, it is close to pack progress for the soil of collection Envelope preserves；Cylindrical pedotheque in uniform thickness is fabricated to using tablet press machine；Pedotheque surface is acted on using laser, Pedotheque on surface forms one layer of heating region after being excited, and with spectrometer collection plasma signal, obtains soil The characteristic spectral line of various elements in sample, i.e. spectroscopic data are collected.
Second step, construct the Elman Neural Network Prediction models based on storehouse autoencoder network.
Here, considering dynamic characteristic specific to Elman neutral nets, preferably can contain applied to heavy metal-polluted soil Amount migration, it is special that traditional BP neural network is replaced with Elman neutral nets.But in Elman neutral nets, if input feature vector Variable is larger, then can influence convergence rate, or even influence prediction result.Therefore, it is self-editing that storehouse is added in Elman neutral nets Code network so that the dimension-reduction treatment of storehouse autoencoder network is all passed through in the prediction of Elman neutral nets, to make full use of While Elman neural network dynamic characteristics, it is pre- to it also avoid the excessive influence on the contrary of operand caused by Elman neutral nets The problem of surveying result.It is comprised the following steps that：
(1) structure includes the storehouse autoencoder network of encoder and decoder, storehouse autoencoder network bag in a traditional way Multilayer neural network model is included, is followed successively by one layer of input layer, multilayer hidden layer, one layer of output layer, as input layer, first layer is hidden Hide layer, second layer hidden layer, third layer hidden layer, n-th layer hidden layer, the structure of output layer.
(2) Elman neutral nets are built, Elman neutral nets include input layer, hidden layer, as output layer section successively The undertaking layer of point feedback and the output layer for possessing Dynamic Recurrent Neural Network model.
(3) using the input without label data as storehouse autoencoder network first layer input layer of training sample, the second layer Input of the output of hidden layer as third layer hidden layer, the input exported as the 4th layer of hidden layer of third layer hidden layer, By that analogy, input of the output of last layer of hidden layer as last layer of output layer.Storehouse autoencoder network first layer is defeated The Hidden unit for entering layer is n1, second layer hidden layer Hidden unit be n2, third layer hidden layer Hidden unit be n3, X layer The Hidden unit of hidden layer is nx, last layer of output layer Hidden unit be nt。
(4) inputted the sign output data of last layer of output layer of storehouse autoencoder network as Elman neutral nets The input of layer, i.e. input of the feature after the extraction of storehouse autoencoder network as Elman neutral nets.
(5) storehouse autoencoder network and Elman neutral nets are stacked to form the Elman nerve nets based on storehouse own coding Network model.
3rd step, unsupervised training is carried out to the Elman Neural Network Predictions model based on storehouse autoencoder network. Utilize the storehouse autoencoder network without label data to the Elman Neural Network Prediction models based on storehouse autoencoder network Carry out unsupervised training.By to high dimensional data carry out feature extraction to realize dimensionality reduction, so as to using feature new after dimensionality reduction come Characterize initial data so that carry out data prediction before structure Elman models, reduce the complexity in time and space.It has Body step is as follows：
(1) obtain without label data X={ x1,x2,...,xr, by xi∈Rn×1I-th as storehouse autoencoder network Input vector, it is input to the encoder with d neuron.
Encoder obtains encoding z by nonlinear activation function fi∈Rd×1, its calculation expression is as follows：
zi=sf(Wxi+b1),
Wherein, W ∈ Rd×nIt is weight matrix, b1∈Rd×1It is coding layer bias vector.
(2) by ziDecoder is input to, obtains decoded resultIts calculation expression is as follows：
Wherein, sgFor the activation primitive of decoder,WT∈Rn×dIt is weight matrix W device, b2∈Rn×1It is Decoding layer bias vector.
(3) reconstructed by minimizingWith original input data xi, between error cost carry out feature extraction, using ladder Spend the weights of descent method renewal training between layersObtain extracted feature so thatIt Between error reach minimum value, its cost function is as follows：
4th step, the Elman Neural Network Predictions model based on storehouse autoencoder network carry out Training.
The label data of training sample is input in the storehouse autoencoder network after training and carries out feature extraction, will have been carried The input of the historical data of the label data pre-processed after feature and heavy metal content in soil is taken based on storehouse autoencoder network Elman Neural Network Prediction models, Training is carried out to Elman Neural Network Predictions model.It is specifically walked It is rapid as follows：
(1) label data of training sample is input in the storehouse autoencoder network after training and carries out feature extraction；
(2) historical data of heavy metal content in soil is obtained, here, the historical data of heavy metal content in soil is used to be directed to The migration characteristic of heavy metal-polluted soil carries out analysis use, and the data have splendid approximation capability to the accuracy of data prediction.
(3) it is Elman Neural Network Prediction model definitions is as follows：
Wherein, k is the frequency of training of Elman neutral nets, and y is output vector, and x is hidden neuron output vector, and u is Input vector, ycFor the previous moment output valve fed back of memory output layer unit, 0≤α≤1 be from connection feedback oscillator because Son, W3、W2、W1Respectively hidden layer to output layer, accept layer to output layer, the connection weight matrix of input layer to hidden layer, f () and g () are respectively to hide the Nonlinear Vector function that the excitation function of layer unit and output layer unit is formed.
For the migration characteristic of heavy metal-polluted soil, following traditional Elman Neural Network Predictions model is carried out It is correspondingly improved,
The migration characteristic problem according to specific to heavy metal content in soil, by the x in above formulac(hide layer unit to be fed back Previous moment output valve) replace with yc(the previous moment output valve that memory output layer unit is fed back), therefore, after improvement The output vector y (k) of Elman neural network models is anti-dependent on hidden neuron output vector x and memory output layer unit institute The previous moment output vector y of feedbackc。
(4) parameter of Elman Neural Network Prediction models is adjusted.Calculated and joined using traditional gradient descent method Several methods, but because Elman Neural Network Prediction models are correspondingly improved, then it is obtained a result just different, The derivation for new Elman Neural Network Predictions model parameter adjustment is provided herein.
If the actual output of kth time is
Error extension function is
E (k) is calculated respectively to weights W3、W2、W1Partial derivative and be 0, it is pre- to obtain modified Delphi approach Survey analysis model training method.
A, the connection weight W by E (k) to hidden layer to output layer3Local derviation is sought, it is calculated as follows：
Wherein,
Order
B, the connection weight W by E (k) to hidden layer to output layer2Local derviation is sought, it is calculated as follows：
Do not consider yc,i(k) it is rightDependence,
C, the connection weight W by E (k) to hidden layer to output layer1Local derviation is sought, it is calculated as follows：
(5) label data after extraction feature and the historical data of heavy metal content in soil are inputted into Elman neutral nets Forecast analysis model carries out parameter adjustment, Elman Neural Network Prediction models is trained so that Elman nerve nets Network forecast analysis model has analysis predictive ability.
5th step, the forecast analysis of heavy metal content in soil.By the historical data of content of beary metal and test sample The Elman Neural Network Prediction models based on storehouse autoencoder network are inputted after the processing of LIBS spectroscopic datas, are completed to surveying The dynamic analysis prediction of this heavy metal content in soil of sample, so as to analyze the difference between actual result and prediction result, evaluation The quality of improved model.It is comprised the following steps that：
(1) the LIBS spectroscopic datas of test sample are input to storehouse autoencoder network and carry out feature extraction.
(2) preprocessed data after extraction feature and the historical data of content of beary metal are input to and improve Elman god Analysis through in network model, carrying out to test sample heavy metal content in soil is predicted.
This method is built in using Elman neural network models with reference to historical data to forecast analysis model, from And existing soil sample is precisely predicted.Because the migration characteristic of heavy metal content in soil is to the dependence of historical data, Using historical data as the part in model in Elman neural network models, the theoretical method of science and rigorous has been used Logical thinking.
General principle, principal character and the advantages of the present invention of the present invention has been shown and described above.The technology of the industry For personnel it should be appreciated that the present invention is not limited to the above embodiments, that described in above-described embodiment and specification is the present invention Principle, various changes and modifications of the present invention are possible without departing from the spirit and scope of the present invention, these change and Improvement is both fallen within the range of claimed invention.The protection domain of application claims by appended claims and its Equivalent defines.

Claims (5)

1. a kind of heavy metal content in soil Forecasting Methodology based on Elman neural network models, it is characterised in that including following step Suddenly：
11) acquisition and pretreatment of sample data, the soil sample of collection is divided into training sample and test sample, utilized The spectroscopic data of soil forms training data in LIBS technical limit spacing training samples, and training data is divided into label data and without mark Sign data；
12) the Elman Neural Network Prediction models based on storehouse autoencoder network are constructed；
13) unsupervised training is carried out to the Elman Neural Network Predictions model based on storehouse autoencoder network, using without mark Data are signed to carry out without prison the storehouse autoencoder network of the Elman Neural Network Prediction models based on storehouse autoencoder network Supervise and instruct white silk；
14) the Elman Neural Network Predictions model based on storehouse autoencoder network carries out Training, by training sample Label data be input in the storehouse autoencoder network after training and carry out feature extraction, the mark that is pre-processed after feature will have been extracted Sign Elman Neural Network Prediction of the historical data input based on storehouse autoencoder network of data and heavy metal content in soil Model, Training is carried out to Elman Neural Network Predictions model；
15) forecast analysis of heavy metal content in soil, by the LIBS light of the historical data of heavy metal content in soil and test sample Input in the Elman Neural Network Prediction models based on storehouse autoencoder network, completed to test specimens after Spectrum data processing The dynamic analysis prediction of this heavy metal content in soil.
2. the heavy metal content in soil Forecasting Methodology according to claim 1 based on Elman neural network models, its feature It is, the construction is comprised the following steps based on storehouse autoencoder network modified Delphi approach forecast analysis model：
21) structure includes the storehouse autoencoder network of encoder and decoder, and storehouse autoencoder network includes multilayer neural network Model, it is followed successively by one layer of input layer, multilayer hidden layer, one layer of output layer；
22) Elman neutral nets are built, Elman neutral nets include input layer, hidden layer successively, node layer is anti-as exporting The undertaking layer of feedback and the output layer for possessing Dynamic Recurrent Neural Network model；
23) using the input without label data as storehouse autoencoder network first layer input layer of training sample, storehouse own coding Input of the output of network first tier input layer as second layer hidden layer, the output of last layer hidden layer are hidden as next layer The input of layer, the input of the output of last layer of hidden layer as output layer, storehouse autoencoder network first layer input layer it is hidden Layer unit is n1, second layer hidden layer Hidden unit be n2, third layer hidden layer Hidden unit be n3, X layer hidden layer Hidden unit is nx, last layer of output layer Hidden unit be nt；
24) using the sign output data of last layer of output layer of storehouse autoencoder network as Elman neural network input layers Input；
25) storehouse autoencoder network and Elman neutral nets are stacked to the Elman neutral net moulds to be formed based on storehouse own coding Type.
3. the heavy metal content in soil Forecasting Methodology according to claim 1 based on Elman neural network models, its feature Be, described pair of Elman Neural Network Predictions model based on storehouse autoencoder network carry out unsupervised training include with Lower step：
31) obtain without label data X={ x1,x2,...,xr, by xi∈Rn×1I-th of input as storehouse autoencoder network Vector, it is input to the encoder with d neuron；Encoder obtains encoding z by nonlinear activation function fi∈Rd×1, its Calculation expression is as follows：
zi=sf(Wxi+b1),
Wherein, W ∈ Rd×nIt is weight matrix, b1∈Rd×1It is coding layer bias vector；
32) by ziDecoder is input to, obtains decoded resultIts calculation expression is as follows：
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>s</mi> <mi>g</mi> </msub> <mrow> <mo>(</mo> <mover> <mi>W</mi> <mo>^</mo> </mover> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
Wherein, sgFor the activation primitive of decoder,WT∈Rn×dIt is weight matrix W device, b2∈Rn×1It is decoding Layer bias vector；
33) reconstructed by minimizingWith original input data xi, between error cost carry out feature extraction, using under gradient The weights of drop method renewal training between layersObtain extracted feature so thatBetween mistake Difference reaches minimum value, and its cost function is as follows：
<mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>W</mi> <mo>,</mo> <mover> <mi>W</mi> <mo>^</mo> </mover> <mo>,</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mi>g</mi> </msub> <mrow> <mo>(</mo> <mover> <mi>W</mi> <mo>^</mo> </mover> <msub> <mi>s</mi> <mi>f</mi> </msub> <mo>(</mo> <mrow> <msub> <mi>Wx</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>.</mo> </mrow>
4. the heavy metal content in soil Forecasting Methodology according to claim 1 based on Elman neural network models, its feature It is, the Elman Neural Network Predictions model based on storehouse autoencoder network carries out Training including following Step：
41) label data of training sample is input in the storehouse autoencoder network after training and carries out feature extraction；
42) historical data of heavy metal content in soil is obtained；
43) it is Elman Neural Network Prediction model definitions is as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <msup> <mi>W</mi> <mn>3</mn> </msup> <mi>x</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>+</mo> <msup> <mi>W</mi> <mn>2</mn> </msup> <msub> <mi>y</mi> <mi>c</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <msup> <mi>W</mi> <mn>1</mn> </msup> <mi>u</mi> <mo>(</mo> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;alpha;y</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>
Wherein, k is the frequency of training of Elman neutral nets, and y is output vector, and x is hidden neuron output vector, and u is input Vector, ycThe previous moment output valve fed back for memory output layer unit, 0≤α≤1 are from the connection feedback oscillator factor, W3、 W2、W1Respectively hidden layer to output layer, accept layer to output layer, the connection weight matrix of input layer to hidden layer, f () and g () is respectively to hide the Nonlinear Vector function that the excitation function of layer unit and output layer unit is formed；
44) parameter of Elman Neural Network Prediction models is adjusted,
If the actual output of kth time is
Error extension function is
E (k) is calculated respectively to weights W3、W2、W1Partial derivative and be 0, obtain modified Delphi approach prediction point Analyse model training method；
441) the connection weight W by E (k) to hidden layer to output layer3Local derviation is sought, it is calculated as follows：
<mrow> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>E</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msubsup> <mi>g</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mo>&amp;CenterDot;</mo> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>r</mi> </munderover> <msubsup> <mi>W</mi> <mrow> <mi>j</mi> <mi>q</mi> </mrow> <mn>2</mn> </msubsup> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msubsup> <mi>&amp;delta;</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>r</mi> </munderover> <msubsup> <mi>W</mi> <mrow> <mi>j</mi> <mi>q</mi> </mrow> <mn>2</mn> </msubsup> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>n</mi> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
Wherein,
Order
442) the connection weight W by E (k) to hidden layer to output layer2Local derviation is sought, it is calculated as follows：
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>E</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>l</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>l</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> </mrow>
Do not consider yc,i(k) it is rightDependence,
<mrow> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>l</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>=</mo> <mi>&amp;alpha;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>l</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <msubsup> <mi>g</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mo>&amp;CenterDot;</mo> <mo>)</mo> </mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>l</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>n</mi> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
443) the connection weight W by E (k) to hidden layer to output layer1Local derviation is sought, it is calculated as follows：
<mrow> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>E</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>j</mi> <mi>q</mi> </mrow> <mn>1</mn> </msubsup> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msubsup> <mi>W</mi> <mrow> <mi>j</mi> <mi>q</mi> </mrow> <mn>1</mn> </msubsup> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>-</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <msubsup> <mi>g</mi> <mi>i</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mo>&amp;CenterDot;</mo> <mo>)</mo> </mrow> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> <msubsup> <mi>f</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mo>&amp;CenterDot;</mo> <mo>)</mo> </mrow> <msub> <mi>u</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msubsup> <mi>&amp;delta;</mi> <mi>i</mi> <mn>0</mn> </msubsup> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> <msubsup> <mi>f</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mo>&amp;CenterDot;</mo> <mo>)</mo> </mrow> <msub> <mi>u</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>n</mi> <mo>,</mo> <mi>q</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>r</mi> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
45) label data after extraction feature and the historical data of heavy metal content in soil are inputted into Elman neural network predictions Analysis model carries out parameter adjustment, and Elman Neural Network Prediction models are trained.
5. the heavy metal content in soil Forecasting Methodology according to claim 1 based on Elman neural network models, its feature It is, the forecast analysis of the heavy metal content in soil comprises the following steps：
51) the LIBS spectroscopic datas of test sample are input to storehouse autoencoder network and carry out feature extraction；
52) preprocessed data after extraction feature and the historical data of content of beary metal are input to and improve Elman nerve nets In network model, the analysis prediction to test sample heavy metal content in soil is carried out.
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