CN113077039A - Task-driven RBF neural network-based water outlet total nitrogen TN soft measurement method - Google Patents

Task-driven RBF neural network-based water outlet total nitrogen TN soft measurement method Download PDF

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CN113077039A
CN113077039A CN202110304217.1A CN202110304217A CN113077039A CN 113077039 A CN113077039 A CN 113077039A CN 202110304217 A CN202110304217 A CN 202110304217A CN 113077039 A CN113077039 A CN 113077039A
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蒙西
张寅�
乔俊飞
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Abstract

The invention discloses a water outlet total nitrogen TN soft measurement method based on a task-driven RBF neural network, wherein a water outlet total nitrogen soft measurement model is established based on a task-driven radial basis function neural network, so that the real-time accurate acquisition of the water outlet total nitrogen concentration is realized; firstly, determining characteristic variables related to the effluent TN by combining mechanism knowledge and mutual information analysis; and then, organically combining a second-order learning algorithm and a self-adaptive structure adding and deleting algorithm, driving the RBF neural network by a self-adaptive design task, establishing a soft measurement model of total nitrogen TN of the effluent of the municipal sewage treatment, realizing real-time detection of the total nitrogen TN of the effluent, and solving the problem that the total nitrogen TN of the effluent of the municipal sewage treatment is difficult to accurately measure in real time.

Description

Task-driven RBF neural network-based water outlet total nitrogen TN soft measurement method
Technical Field
The invention belongs to the field of sewage treatment, and particularly relates to a soft measurement method for total nitrogen TN of effluent based on a task-driven RBF neural network.
Background
The urban sewage is a stable fresh water resource, the recycling of the urban sewage can reduce the social demand on natural water and reduce the pollution to the water environment, and the urban sewage is an effective way for realizing the continuous utilization and virtuous cycle of the fresh water resource. Therefore, with the national emphasis on the environmental and water resource management problem and the great demand of the urban development on fresh water resources, the treatment of urban sewage has become an important way for sewage recovery, sustainable reuse and water environmental protection. Nitrogen is a main pollutant index in urban sewage treatment, and nitrogen-containing water quality indexes such as ammonia nitrogen, total nitrogen and the like do not reach the standard, so that the problem of eutrophication of water is caused, and the ecological environment of the water is seriously damaged. However, the influence factors of total nitrogen TN in the effluent of the sewage treatment process are various, and the relationship among the influence factors is complex, so that the real-time measurement is difficult, and the stable operation of the sewage treatment process is seriously influenced. The soft measurement method for total nitrogen TN of effluent based on the task-driven RBF neural network is beneficial to the safe and stable operation of the municipal sewage treatment process and the improvement of the denitrification efficiency of the municipal sewage treatment plant, and has obvious economic benefit, environmental benefit and social benefit.
The sewage treatment process is a complex biochemical reaction process, and some important parameters in the sewage treatment process are difficult to accurately measure due to the limitation of measurement technology. At present, most municipal sewage treatment plants in China still adopt a manual sampling assay method to detect nitrogen-containing compounds in water. When the nitrogen content in water is measured by a manual sampling assay method, links such as sampling, assay, feedback and the like need to be carried out, the steps are complicated, the measurement period is long, and great time lag exists. On the other hand, factors such as temperature, time, reagents and manual operation all affect the accuracy of the measurement result. With the development of industry and automation, domestic and foreign enterprises begin to research and develop detection equipment or instruments to replace manual operation, and although automatic instruments and meters liberate inspectors from complicated sampling, inspection and testing steps, the detection principle of nitrogen content is not fundamentally changed, corresponding chemical reagents are still required to be selected as assistance, and the accuracy and the universality of the instruments and meters are limited. Nitrogen-containing water quality detection equipment is generally expensive and difficult to maintain, and corrosion and damage to instruments and meters can be caused even if the equipment is in a severe working environment for a long time. Therefore, the research on a new measuring method and the real-time detection problem of the total nitrogen TN of the effluent have important practical significance.
With the development of control theory and intelligent science, the soft measurement technology for analyzing and researching variables to be tested by means of key characteristic variables is widely concerned by academic and industrial fields, and the research hotspot soft measurement which becomes the field of process on-line detection is to establish a mapping relation between variables easy to be tested and variables to be tested which are difficult to be directly measured, namely a soft measurement model, based on mechanism analysis or data, and then realize the prediction of the variables to be tested by a mathematical calculation or estimation method. In recent years, soft measurement technology is widely applied to characteristic modeling of water quality parameters in a sewage treatment process, and a method using a neural network as a soft measurement tool is researched most actively. The invention provides a soft measurement method based on a task-driven RBF neural network. From the organization of network structures through neuronal growth and pruning. On one hand, each addition of an RBF neuron is to compensate a larger residual error and improve learning ability. On the other hand, the process of pruning is to avoid structural redundancy without losing learning ability. Meanwhile, a second-order algorithm is adopted to optimize all parameters so as to improve the learning performance. The method can realize real-time detection of the total nitrogen of the effluent, improve the TN measurement quality of the total nitrogen of the effluent and the monitoring capability of the sewage treatment process, and has wide application prospect and important practical significance.
Disclosure of Invention
Aiming at the defects of the existing method, the invention provides a task-driven Radial Basis Function (RBF) neural network-based total nitrogen TN soft measurement method, which is based on mutual information theory and expert knowledge, analyzes and summarizes easily-measured auxiliary variables closely related to total nitrogen TN, determines the input quantity of a neural network model, designs a network structure based on a self-organization method, establishes a soft measurement model of the total nitrogen TN, realizes the real-time detection of the effluent total nitrogen TN, and solves the problem that the effluent total nitrogen TN of sewage treatment is difficult to measure.
The invention adopts the following technical scheme and implementation steps:
(1) determining input and output variables of the effluent total nitrogen TN: selecting characteristic variables of the soft measurement model into selection of main variables and selection of auxiliary variables, taking total nitrogen TN (total nitrogen) concentration of effluent as the main variables, analyzing the correlation between key water quality parameters and other related variables by utilizing mutual information, and determiningSetting the water inlet temperature, the water outlet temperature and the ammonia nitrogen NH in the water outlet4N, total nitrogen TN of the inlet water, total phosphorus TP of the inlet water and suspended matter concentration are auxiliary variables;
(2) designing a soft measurement model for intelligent detection of total nitrogen TN of effluent: establishing a soft measurement model of the total nitrogen TN of the effluent by utilizing a task-driven RBF neural network, wherein the task-driven RBF neural network comprises an input layer, a hidden layer and an output layer; at the initial moment, the structure of the neural network is a connection mode of 6-0-1, an input layer has 6 neurons, a hidden layer has no neurons, an output layer has 1 neuron, and an input vector of the neural network is expressed as x ═ x (x-1)1,x2,...,x6)T，x1,x2,x3,x4,x5,x6Respectively representing the water inlet temperature, the water outlet ammonia nitrogen, the water inlet total phosphorus and the suspended solid concentration of the mixed solution; the output of the output layer is the value of total nitrogen TN of the effluent, and the number of neurons of the output layer is 1; at time t, the output vector of the neural network is represented as y (t), and the calculation method is as follows:
inputting a layer: this layer consists of 6 neurons, each with an output of:
ui(t)＝xi(t) (1)
wherein u isi(t) is the output of the ith neuron at time t, i ═ 1,2, …, 6;
② hidden layer: the hidden layer consists of J neurons, the output of each neuron being:
Figure BDA0002987449540000031
wherein phij(xi) Representing the ith input vector xiCorresponding output of the jth hidden layer neuron upon entering the network, cjIs the central vector of the jth hidden layer neuron, δjIs the width value of the jth hidden layer neuron;
output layer: the output of the output layer is:
Figure BDA0002987449540000032
wherein y (i) is the ith input vector xiCorresponding output on entry into the network, wjiThe connection weights, phi, for the j hidden layer neurons to the output neuronjThe transfer functions for the j hidden layer neurons.
The error of the task-driven RBF neural network is defined as follows:
Figure BDA0002987449540000033
wherein, yd(t) the expected output of the RBF neural network driven by the task at the time t, y (t) the actual output of the RBF neural network driven by the task at the time t, and p is the number of training samples;
(3) the training task driving RBF neural network specifically comprises the following steps:
firstly, at the initial moment, the number of neurons in a hidden layer of the network is 0;
searching a sample with the maximum absolute expected output value, and adding a first neuron;
at the initial moment, the number of the hidden layer neurons is set to be 0, and the data sample corresponding to the maximum absolute residual error of the current network is the sample k with the maximum absolute expected output1：
k1＝argmax[||yd1||,||yd2||,...,||ydp||,...||ydP||] (5)
Wherein P represents the number of training samples, ydpRepresenting the expected output of the p-th sample. Thus, adding the first RBF neuron sets the following:
Figure BDA0002987449540000034
Figure BDA0002987449540000035
σ1＝1 (8)
thirdly, adjusting the network parameters by using an improved second-order algorithm, wherein the method comprises the following steps:
Ψ(t+1)＝Ψ(t)-(H(t)+λI(t))-1Ω(t) (9)
h is a Hessian-like matrix, lambda is a learning rate parameter with a value of a normal number, I is an identity matrix, omega is a gradient vector, and psi refers to all parameters;
Ψ(t)＝[c1(t),c2(t),...,cl(t),σ1(t),σ2(t),...,σl(t),w1(t),w2(t),...,wl(t)] (10)
to reduce computational complexity, the hessian-like matrix is converted to a sum of a plurality of hessian-like submatrices. Similarly, the calculation of the gradient vector Ω may be converted to a summation of the gradient sub-vectors:
Figure BDA0002987449540000041
Figure BDA0002987449540000042
wherein the sub-hessian matrix and the sub-gradient vectors can be calculated by:
Figure BDA0002987449540000043
Figure BDA0002987449540000044
jacobian vector jp(t) is calculated as follows:
Figure BDA0002987449540000045
wherein, l is the number of hidden layer neurons, N is the dimension of the input vector, and by utilizing the differential chain rule, the row elements of the Jacobian matrix in the above formula can be written as:
Figure BDA0002987449540000046
Figure BDA0002987449540000047
Figure BDA0002987449540000048
fourthly, calculating the instantaneous residual vector of the network, finding out the position of the residual peak point, adding a neuron at the position, and then adjusting the network parameters by using an improved second-order algorithm;
at time t, for all training set samples, the residual vectors are calculated as follows:
e(t)＝[e1(t),e2(t),...,ep(t),...eP(t)]T (19)
the residual value of the p-th sample is calculated as follows:
ep(t)＝ydp-yp(t) (20)
wherein, ydpAnd yp(t)The expected output of the p sample and the actual output at the time t are respectively;
searching the position of the current residual peak point:
kt＝argmax||e(t)|| (21)
the current network pair k may be consideredtThe learning ability of each sample is not enough, so an RBF neuron needs to be added to learn the current sample, and the center vector and the output weight of the newly added neuron are set as follows:
Figure BDA0002987449540000051
Figure BDA0002987449540000052
if the two RBF neurons are close in distance and have larger radial action ranges, the same action is easy to generate, and further the redundancy on a network structure is caused, in order to avoid the problem of structural redundancy, the existing RBF neurons are expected to have smaller influence on the current newly-added neurons, so the following setting is made, and when the following relations are met, the existing neurons have smaller influence on the newly-added neurons:
Figure BDA0002987449540000053
cmin＝argmin(dist(ct,cj≠t)) (25)
thus, the following relationship can be obtained:
σt≤0.7||ct-cmin|| (26)
at present, during the experiment, sigma is usually takent＝0.7||ct-cmin||
If the number of RBF neurons reaches JmaxOr training error up to E0If yes, storing the current mean square error MSE _0, and entering the step (c), otherwise repeating the step (c) and the step (c). The calculation formula of MSE is as follows:
Figure BDA0002987449540000054
sixthly, calculating the significance indexes of neurons of all hidden layers, deleting the neurons with the lowest significance, and adjusting network parameters by using an improved second-order learning algorithm to obtain the mean square error MSE _1 of the pruned network;
the calculation method for defining the neuron significance index is as follows:
Figure BDA0002987449540000055
wherein, wjThe connection weight value from the jth neuron to the output neuron;
comparing the error MSE _1 after deleting the neurons with the error MSE _0 before deleting the neurons, and if the current MSE _1 is smaller than or equal to the MSE _0, turning to the step (IV) to continue the pruning process; otherwise, the structure before pruning is recovered, and the construction of the task-driven self-adaptive RBF neural network is completed;
(4) predicting the concentration of total nitrogen TN in the effluent;
and taking the test sample data as the input of the trained task-driven self-adaptive RBF neural network, wherein the output of the neural network is the prediction result of the total nitrogen TN concentration of the effluent.
Compared with the prior art, the invention has the following obvious advantages and beneficial effects:
1. according to the characteristic that the radial basis function neural network has good nonlinear mapping capability, aiming at the defects of the total nitrogen measurement of the effluent in the current sewage treatment process, the task-driven adaptive radial basis function neural network is adopted to realize the nonlinear mapping between the auxiliary variable and the total nitrogen TN, a soft measurement model of the total nitrogen of the effluent in the sewage treatment process is established, the soft measurement of the total nitrogen TN of the effluent is realized, and the method has the characteristics of good real-time performance, good stability, high precision and the like;
2. the invention is based on the interaction of the structure construction and the parameter adjustment of the task-driven self-adaptive RBF neural network, and can design the RBF neural network with simple structure and good generalization performance according to the task to be solved.
Drawings
FIG. 1 is a radial basis neural network topology of the present invention;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a graph of the radial basis function neural network test results of the present invention;
FIG. 4 is a radial basis function neural network test error map of the present invention.
Detailed Description
The invention selects 6 related variables to carry out soft measurement on total nitrogen TN of effluent of sewage treatment: water inlet temperature, water outlet temperature and water outlet ammonia nitrogen NH4N, total nitrogen TN, total phosphorus TP, suspended matterConcentration; according to the embodiment of the invention, water quality analysis data of a certain Beijing sewage treatment plant is adopted, 360 samples are used together to design and evaluate a prediction model after pretreatment, 270 groups of samples are used as training samples, and the other 90 groups of samples are used as test samples. In the experiment, the data needs to be normalized, and all input data are normalized to [ -1,1 [ -1 [ ]]All output data are normalized to [0,1 ]]. The invention adopts the following technical scheme and implementation steps:
a soft measurement model of total nitrogen TN of effluent is established by utilizing a task-driven adaptive RBF neural network, and the soft measurement model comprises the following steps:
(1) determining input and output variables of the effluent total nitrogen TN: selecting characteristic variables of the soft measurement model into selection of main variables and selection of auxiliary variables, taking the concentration of total nitrogen TN of the effluent as the main variable, analyzing the correlation between the total nitrogen TN of the effluent and other related variables by utilizing mutual information, and determining the water inlet temperature, the water outlet temperature and the ammonia nitrogen NH of the effluent4N, total nitrogen TN of the inlet water, total phosphorus TP of the inlet water and suspended matter concentration are auxiliary variables;
(2) designing a soft measurement model for intelligent detection of total nitrogen TN of effluent: and establishing a soft measurement model of the total nitrogen TN of the effluent by utilizing a task-driven self-adaptive RBF neural network. The task-driven self-adaptive RBF neural network comprises an input layer, a hidden layer and an output layer. At the initial moment, the structure of the neural network is a connection mode of 6-0-1, an input layer has 6 neurons, a hidden layer has no neurons, an output layer has 1 neuron, and an input vector of the neural network is expressed as x ═ x (x-1)1,x2,...,x6)T，x1,x2,x3,x4,x5,x6Respectively representing the water inlet temperature, the water outlet ammonia nitrogen, the water inlet total phosphorus and the suspended solid concentration of the mixed solution; the output of the output layer is the value of total nitrogen TN of the effluent, and the number of neurons of the output layer is 1; at time t, the output vector of the neural network is represented as y (t), and the calculation method is as follows:
inputting a layer: this layer consists of 6 neurons, each with an output of:
ui(t)＝xi(t) (29)
wherein u isi(t) is the output of the ith neuron at time t, i ═ 1,2, …, 6;
② hidden layer: the hidden layer consists of J neurons, the output of each neuron being:
Figure BDA0002987449540000071
wherein phij(xi) Representing the ith input vector xiCorresponding output of jth RBF neuron upon entering network, cjIs the central vector of the jth RBF neuron, δjThe width value of the jth RBF neuron;
output layer: the output of the output layer is:
Figure BDA0002987449540000072
wherein y (i) is the ith input vector xiCorresponding output on entry into the network, wjiIs the connection weight of the jth RBF neuron to the output node, phijA transfer function for the jth RBF neuron;
the error of the task-driven RBF neural network is defined as follows:
Figure BDA0002987449540000073
wherein, yd(t) the expected output of the RBF neural network is driven by the task at the moment t, y (t) the actual output of the RBF neural network is driven by the task at the moment t, and P is the number of training samples;
(3) the training task driving RBF neural network specifically comprises the following steps:
firstly, at the initial moment, the number of neurons in a hidden layer of the network is 0;
searching a sample with the maximum absolute expected output value, and adding a first neuron;
initial time, number of hidden layer neuron is 0, and maximum absolute residual error of current network corresponds toThe data sample is the sample k with the maximum absolute expected output1：
k1＝argmax[||yd1||,||yd2||,...,||ydp||,...||ydP||] (33)
Wherein P represents the number of training samples, ydpRepresenting the expected output of the p-th sample. Thus, adding the first RBF neuron sets the following:
Figure BDA0002987449540000081
Figure BDA0002987449540000082
σ1＝1 (36)
thirdly, adjusting the network parameters by using an improved second-order algorithm, wherein the method comprises the following steps:
Ψ(t+1)＝Ψ(t)-(H(t)+λI(t))-1Ω(t) (37)
h is a Hessian-like matrix, lambda is a learning rate parameter with a value of a normal number, I is an identity matrix, omega is a gradient vector, and psi refers to all parameters;
Ψ(t)＝[c1(t),c2(t),...,cl(t),σ1(t),σ2(t),...,σl(t),w1(t),w2(t),...,wl(t)] (38)
to reduce computational complexity, the hessian-like matrix is converted to a sum of a plurality of hessian-like submatrices. Similarly, the calculation of the gradient vector Ω may be converted to a summation of the gradient sub-vectors:
Figure BDA0002987449540000083
Figure BDA0002987449540000084
wherein the sub-hessian matrix and the sub-gradient vectors can be calculated by:
Figure BDA0002987449540000085
Figure BDA0002987449540000086
jacobian vector jp(t) is calculated as follows:
Figure BDA0002987449540000087
wherein, l is the number of neurons in the hidden layer, N is the dimension of the input vector, and the Jacobian matrix row elements in the above formula can be written as:
Figure BDA0002987449540000088
Figure BDA0002987449540000091
Figure BDA0002987449540000092
fourthly, calculating the instantaneous residual vector of the network, finding out the position of the residual peak point, adding a neuron at the position, and then adjusting the network parameters by using an improved second-order algorithm;
at time t, for all training set samples, the residual vectors are calculated as follows:
e(t)＝[e1(t),e2(t),...,ep(t),...eP(t)]T (47)
the residual value of the p-th sample is calculated as follows:
ep(t)＝ydp-yp(t) (48)
wherein, ydpAnd yp(t)The expected output of the p sample and the actual output at the time t are respectively;
searching the position of the current residual peak point:
kt＝argmax||e(t)|| (49)
the current network pair k may be consideredtThe learning ability of individual samples is not sufficient. Therefore, an RBF neuron needs to be added to learn the current sample, and the center vector and the output weight of the newly added neuron are set as follows:
Figure BDA0002987449540000093
Figure BDA0002987449540000094
if the two RBF neurons are close in distance and have larger radial action ranges, the same action is easy to generate, and further the redundancy on a network structure is caused, in order to avoid the problem of structural redundancy, the existing RBF neurons are expected to have smaller influence on the current newly-added neurons, so the following setting is made, and when the following relations are met, the existing neurons have smaller influence on the newly-added neurons:
Figure BDA0002987449540000095
cmin＝argmin(dist(ct,cj≠t)) (53)
thus, the following relationship can be obtained:
σt≤0.7||ct-cmin|| (54)
at present, during the experiment, sigma is usually takent＝0.7||ct-cmin||
If the number of RBF neurons reaches JmaxOr training error up to E0Then the current mean square error is storedMSE _0, and entering the step (c), otherwise repeating the step (c) and the step (c), wherein the MSE calculation formula is as follows:
Figure BDA0002987449540000101
sixthly, calculating the significance indexes of neurons of all hidden layers, deleting the neurons with the lowest significance, and adjusting network parameters by using an improved second-order learning algorithm to obtain the mean square error MSE _1 of the pruned network;
the calculation method for defining the neuron significance index is as follows:
Figure BDA0002987449540000102
wherein, wjThe connection weight value from the jth neuron to the output neuron;
comparing the error MSE _1 after deleting the neurons with the error MSE _0 before deleting the neurons, and if the current MSE _1 is smaller than or equal to the MSE _0, turning to the step (IV) to continue the pruning process; otherwise, the structure before pruning is recovered, and the task drives the RBF neural network to be constructed;
(4) predicting the concentration of total nitrogen TN in the effluent;
the test result of the total nitrogen TN soft measurement method is shown in FIG. 3, and the X axis: number of samples tested, in units of units per sample, Y-axis: the unit of the output value of the total nitrogen TN of the effluent is milligram/liter, the blue line is the actual output value of the total nitrogen TN of the effluent, and the red line is the predicted value of the task-driven RBF neural network; the error between the actual output and the test output of the total nitrogen TN concentration of the effluent is shown in FIG. 4, and the X axis: number of samples tested, in units of units per sample, Y-axis: the error of the prediction of total nitrogen TN of the effluent is milligram/liter.
It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that modifications and variations can be made without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A soft measurement method for total nitrogen TN (total nitrogen) of effluent based on a task-driven RBF (radial basis function) neural network is characterized by comprising the following steps of:
step 1, determining input and output variables of water outlet total nitrogen TN soft measurement model
According to actual data obtained by a sewage treatment plant, the correlation between total nitrogen TN of the effluent and other related variables is analyzed by utilizing mutual information, and the water inlet temperature, the water outlet temperature and the ammonia nitrogen NH of the effluent are determined4N, total nitrogen TN of the inlet water, total phosphorus TP of the inlet water and suspended matter concentration are auxiliary variables;
step 2, constructing a soft measurement model for intelligent detection of total nitrogen TN of effluent:
establishing a soft measurement model of total nitrogen TN (total nitrogen) of effluent by utilizing a task-driven RBF (radial basis function) neural network, wherein the task-driven self-adaptive RBF neural network comprises the following steps: an input layer, a hidden layer and an output layer; at the initial moment, the structure of the neural network is a connection mode of 6-0-1, an input layer has 6 neurons, a hidden layer has no neurons, an output layer has 1 neuron, and an input vector of the neural network is expressed as x ═ x (x-1)1,x2,...,x6)T，x1,x2,x3,x4,x5,x6Respectively representing the water inlet temperature, the water outlet ammonia nitrogen, the water inlet total phosphorus and the suspended solid concentration of the mixed solution; the output of the output layer is the value of total nitrogen TN of the effluent, and the number of neurons of the output layer is 1;
step 3, driving the RBF neural network by the training task;
and 4, taking the test sample data as the input of the trained task driving self-adaptive RBF neural network, wherein the output of the neural network is the prediction result of the total nitrogen TN concentration of the effluent.
2. The task-driven RBF neural network-based water outlet total nitrogen TN soft measurement method according to claim 1, characterized in that in step 2, at the time t, the output vector of the neural network is represented as y (t), and the calculation method is as follows:
inputting a layer: this layer consists of 6 neurons, each with an output of:
ui(t)＝xi(t) (1)
wherein u isi(t) is the output of the ith neuron at time t, i ═ 1,2, …, 6;
② hidden layer: the hidden layer consists of J neurons, the output of each neuron being:
Figure FDA0002987449530000011
wherein phij(xi) Representing the ith input vector xiCorresponding output of the jth hidden node upon entering the network, cjIs the central vector of the jth hidden node, deltajThe width value of the jth hidden node;
output layer: the output of the output layer is:
Figure FDA0002987449530000021
wherein y (i) is the ith input vector xiCorresponding output on entry into the network, wjiThe connection weight, phi, of the jth hidden layer neuron to the output neuronjFor the transfer function of the jth hidden layer neuron,
the error of the task-driven self-adaptive RBF neural network is defined as follows:
Figure FDA0002987449530000022
wherein, ydAnd (t) is the expected output of the task-driven adaptive RBF neural network at the time t, y (t) is the actual output of the task-driven adaptive RBF neural network at the time t, and p is the number of training samples.
3. The task-driven RBF neural network-based water outlet total nitrogen TN soft measurement method according to claim 1, characterized in that the step 3 specifically comprises:
firstly, at the initial moment, the number of neurons in a hidden layer of the network is 0;
second, find the sample with the largest absolute expected output value, add the first neuron,
at the initial moment, the number of the hidden layer neurons is set to be 0, and the data sample corresponding to the maximum absolute residual error of the current network is the sample k with the maximum absolute expected output1:
k1＝arg max[||yd1||,||yd2||,...,||ydp||,...||ydP||] (5)
Wherein P represents the number of training samples, ydpRepresenting the desired output of the p-th sample, adding the first RBF neuron sets as follows:
Figure FDA0002987449530000023
Figure FDA0002987449530000024
σ1＝1 (8)
thirdly, adjusting the network parameters by using an improved second-order algorithm, wherein the method comprises the following steps:
Ψ(t+1)＝Ψ(t)-(H(t)+λI(t))-1Ω(t). (9)
wherein H is a Hessian-like matrix, λ is a learning rate parameter whose value is a normal number, I is an identity matrix, and Ω
For the gradient vector, Ψ denotes all parameters,
Ψ(t)＝[c1(t),c2(t),...,cl(t),σ1(t),σ2(t),...,σl(t),w1(t),w2(t),...,wl(t)] (10)
converting the hessian-like matrix into a sum of a plurality of hessian-like sub-matrices, and calculating the gradient vector Ω may be converted into a sum of gradient sub-vectors, as shown in the following equation:
Figure FDA0002987449530000031
Figure FDA0002987449530000032
wherein the sub-hessian matrix and the sub-gradient vectors can be calculated by:
Figure FDA0002987449530000033
Figure FDA0002987449530000034
jacobian vector jp(t) is calculated as follows:
Figure FDA0002987449530000035
wherein, l is the number of neurons in the hidden layer, N is the dimension of the input vector, and the Jacobian matrix row elements in the above formula can be written as:
Figure FDA0002987449530000036
Figure FDA0002987449530000037
Figure FDA0002987449530000038
fourthly, calculating the instantaneous residual vector of the network, finding out the position of the peak point of the residual, adding a neuron at the position, then adjusting the network parameters by using an improved second-order algorithm,
at time t, for all training set samples, the residual vectors are calculated as follows:
e(t)＝[e1(t),e2(t),...,ep(t),...eP(t)]T (19)
the residual value of the p-th sample is calculated as follows:
ep(t)＝ydp-yp(t) (20)
wherein, ydpAnd yp(t)The expected output of the p sample and the actual output at the time t are respectively; searching the position of the current residual peak point:
kt＝arg max||e(t)|| (21)
the current network pair k may be consideredtThe learning ability of each sample is not enough, an RBF neuron is added to learn the current sample, and the center vector and the output weight of the newly added neuron are set as follows:
Figure FDA0002987449530000041
Figure FDA0002987449530000042
when the following relation is satisfied, the influence of the existing neurons on the newly added neurons is small:
Figure FDA0002987449530000043
cmin＝arg min(dist(ct,cj≠t)) (25)
thus, the following relationship can be obtained:
σt≤0.7||ct-cmin|| (26)
at present, during the experiment, sigma is usually takent＝0.7||ct-cmin||；
If the number of RBF neurons reaches JmaxOr training error up to E0If yes, storing the current mean square error MSE _0, and entering the step C, otherwise repeating the step C and the step C, wherein the MSE has the following calculation formula:
Figure FDA0002987449530000044
sixthly, calculating the significance indexes of neurons in all hidden layers, deleting the neurons with the lowest significance, adjusting network parameters by using an improved second-order learning algorithm to obtain the mean square error MSE _1 of the pruned network,
the calculation method for defining the neuron significance index is as follows:
Figure FDA0002987449530000045
wherein, wjThe connection weight value from the jth neuron to the output neuron;
comparing the error MSE _1 after deleting the neurons with the error MSE _0 before deleting the neurons, and if the current MSE _1 is smaller than or equal to the MSE _0, turning to the step (IV) to continue the pruning process; otherwise, the structure before pruning is recovered, and the construction of the task-driven self-adaptive RBF neural network is completed.
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