CN113311035A - Effluent total phosphorus prediction method based on width learning network - Google Patents

Effluent total phosphorus prediction method based on width learning network Download PDF

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CN113311035A
CN113311035A CN202110535042.5A CN202110535042A CN113311035A CN 113311035 A CN113311035 A CN 113311035A CN 202110535042 A CN202110535042 A CN 202110535042A CN 113311035 A CN113311035 A CN 113311035A
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韩红桂
李泓颉
刘峥
乔俊飞
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Beijing University of Technology
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Abstract

Aiming at the problem that the total phosphorus in the effluent is difficult to detect on line in the sewage treatment process, an effluent total phosphorus prediction model based on a width learning network is designed, and a gradient descent algorithm is adopted to perform on-line adjustment on model parameters to establish an accurate effluent total phosphorus prediction model; applying the designed prediction model to an actual sewage treatment process; the experimental results show that: the prediction model based on the width learning network not only can realize the online detection of the total phosphorus in the effluent of the sewage treatment process, but also has higher detection precision.

Description

Effluent total phosphorus prediction method based on width learning network
Technical Field
The invention provides a prediction method based on a width learning network. Firstly, analyzing the operation data of the sewage treatment process by using a partial least square method, and screening out process variables with strong correlation with total phosphorus in effluent; secondly, a prediction method based on a width learning network is designed, and the model parameters are adjusted on line by adopting a gradient descent algorithm, so that the precision of the prediction method is improved; and finally, applying the designed prediction method to the actual sewage treatment process. The experimental results show that: the prediction method based on the width learning network not only can realize the on-line detection of the total phosphorus in the effluent of the sewage treatment process, but also has higher detection precision, and belongs to the field of water treatment.
Background
The sewage is a stable fresh water resource, and the regeneration and the utilization of the sewage can meet the requirements on natural water and reduce the pollution to the ecological environment. Therefore, implementing sewage treatment has become the most effective way to realize water resource recycling.
The accurate online prediction of the total phosphorus concentration of the effluent in the sewage treatment is an important problem faced by the current sewage treatment plant. At present, the method for detecting the phosphorus content in a water plant is mainly based on an ammonium molybdate spectrophotometry, and the method can realize relatively accurate detection precision. However, the sewage treatment process is a complex and variable system, and has the characteristics of nonlinearity, time-varying property, interference and the like, and the detection method cannot meet the requirement of real-time detection, so that accurate prediction by using an intelligent means is the current research focus. The width learning network has the learning capability of the neural network and the dual advantages of a plane network structure, so that the method is very suitable for quickly and accurately predicting the total phosphorus of the effluent of sewage treatment.
The invention designs a soft measurement method based on a width learning network, which comprises the steps of firstly, analyzing operation data of a sewage treatment process by using a partial least square method, and screening out process variables with strong correlation with total phosphorus in effluent; secondly, designing a soft measurement method based on a width learning network, and adopting a gradient descent algorithm to perform online adjustment on model parameters, so that the precision of the soft measurement method is improved; and finally, applying the designed soft measurement method to the actual sewage treatment process. The experimental results show that: the soft measurement method based on the width learning network not only can realize the on-line detection of the total phosphorus in the effluent of the sewage treatment process, but also has higher detection precision.
Disclosure of Invention
The invention obtains a water yielding total phosphorus prediction method based on a width learning network, and the method firstly uses a partial least square method to carry out correlation analysis and extract auxiliary variables; secondly, a width learning effluent total phosphorus prediction model is constructed, and model parameters are adjusted on line by using a gradient descent algorithm, so that the precision of the soft measurement method is improved; the real-time accurate prediction of the total phosphorus in the effluent is realized.
The invention adopts the following technical scheme and implementation steps:
1. a method for predicting total phosphorus in effluent based on a width learning network is characterized by comprising the following steps: determining input and output variables of a total phosphorus prediction model of effluent, establishing a width learning effluent total phosphorus prediction model, and adjusting parameters of the width learning effluent total phosphorus prediction model, wherein the method comprises the following steps:
(1) determining input and output variables of effluent total phosphorus prediction model
Calculating an independent variable regression coefficient by using a partial least square method and according to the relation between each variable and the total phosphorus in the effluent, screening auxiliary variables, and finally determining 6 auxiliary variables: the method comprises the following steps of (1) feeding water pH value, feeding water chemical oxygen demand, oxidation-reduction potential of the middle section of an anaerobic zone, oxidation-reduction potential of the front end of an anoxic zone, suspended solids of mixed liquor at the tail end of the anoxic zone and dissolved oxygen of a second aerobic zone; the output variable is the total phosphorus concentration of the effluent; dividing all sample data into two groups, wherein the first group comprises H training samples, H is an integer and belongs to [3000,3400], the second group comprises R test samples, R is an integer and belongs to [800,900 ];
(2) establishing a width learning effluent total phosphorus prediction model
The breadth learning network structure has four layers: an input layer, a feature layer, an enhancement layer and an output layer; the construction of the prediction model based on the width learning network is divided into four steps: processing variables and inputting the variables into a network, constructing characteristic neurons in width learning, constructing enhanced neurons, and updating weights from the characteristic neurons and the enhanced neurons to output neurons; determining the number of input neurons of a width learning network for predicting total phosphorus in effluent to be 6, the number of characteristic neuron groups to be N, N being an integer, N being an element [10,30 ]]The number of the enhanced neuron groups is M, M is an integer, and M belongs to [20,50 ]]The number of output neurons is 1, and a training sample is used for training a width learning network; the 6 auxiliary variables selected as network inputs may be denoted as x (t) ═ x1(t),x2(t),x3(t),x4(t),x5(t),x6(t)]Where t is 1,2, …, H is the number of samples, x1(t) ispH value of inlet water in the tth sample, x2(t) is the chemical oxygen demand of the influent water in the tth sample, x3(t) is the oxidation-reduction potential of the middle section of the anaerobic zone in the tth sample, x4(t) is the oxidation-reduction potential of the front end of the anoxic zone in the tth sample, x5(t) the concentration of suspended solids in the mixed liquor at the end of the anoxic zone in the tth sample, x6(t) the concentration of dissolved oxygen in the aerobic zone in the tth sample; an input layer: the input layer consists of 6 neurons, and the output of each input neuron can be expressed as:
ue(t)＝xe(t),e＝1,2,...,6 (1)
wherein x ise(t) is the input value of the e-th neuron of the input layer, ue(t) is the output value of the e-th neuron of the input layer;
characteristic layer: the characteristic layer is composed of N groups of neurons, and the characteristic neuron Z (t) is [ Z1(t),Z2(t),…,ZN(t)]The output of each set of characteristic neurons can be expressed as:
Figure BDA0003069483540000031
wherein Z isi(t) is the output value of the i-th group of neurons in the feature layer, Wei(t) is the weight between the e-th input neuron and the i-th set of characteristic neurons, βei(t) is the deviation term between the e-th input neuron and the i-th group of characteristic neurons, βeiEach element in the (t) matrix belongs to (0, 1)]，
Figure BDA0003069483540000032
As a function of the activation of the network,
Figure BDA0003069483540000033
enhancement layer: the enhancement layer consists of M groups of neurons, enhancing the neurons H (t) ═ H1(t),H2(t),...,HM(t)]The output of each set of augmented neurons may be expressed as:
Figure BDA0003069483540000034
wherein Hj(t) is the output value of the j-th group of neurons of the enhancement layer, Wij(t) is the weight between the i-th group of characteristic neurons and the j-th group of enhanced neurons, βij(t) is the deviation term between the i-th group of characteristic neurons and the j-th group of enhanced neurons, βijEach element in the (t) matrix belongs to (0, 1)]；
An output layer: the output layer consists of 1 neuron, and the output of the output neuron can be expressed as:
Figure BDA0003069483540000035
Q(t)＝[Z(t)|H(t)]＝[Z1(t),...,ZN(t) H1(t),...,HM(t)] (5)
wherein the content of the first and second substances,
Figure BDA0003069483540000036
for the output value of the width learning network, w (t) ═ w1(t),w2(t),…,wN(t),w1 *(t),w2 *(t),…,wM *(t)]TIs the network weight, wi(t) is the weight between the ith set of signature neurons and the output neuron, wj *(t) weights between the j-th group of enhanced neurons and output neurons;
(3) width learning effluent total phosphorus prediction model parameter adjustment
Initializing a width learning network:
let the current iteration number t be 1, the network parameter wi(1)，wj *(1)，Wei(1) And Wij(1) Can be expressed as:
Figure BDA0003069483540000037
Figure BDA0003069483540000038
Figure BDA0003069483540000039
Figure BDA00030694835400000310
wherein, wi(1) Each element in the matrix belongs to (0, 0.9)]，wi k(1) Is the weight between the kth characteristic neuron in the ith group of characteristic neurons and the output neuron, k is an integer, and k is an element [20,50 ]]；wj *(1) Each element in the matrix belongs to (0, 0.18)]，wj q(1) For the weight between the qth enhanced neuron in the jth group of enhanced neurons and the output neuron, q is an integer, q is [20,50 ]]；Wei(1) Each element in the matrix belongs to (0, 1)]，wei k(1) Is the weight between the e input neuron and the k characteristic neuron in the i characteristic neuron; wij(1) Each element in the matrix belongs to (0, 0.2)]，wij kq(1) Weighting between the kth signature neuron in the ith group of signature neurons and the qth enhancement neuron in the jth group of enhancement neurons;
updating the network weight by using a gradient descent algorithm:
the weight update formula can be expressed as:
Figure BDA0003069483540000041
Figure BDA0003069483540000042
wherein, e (t) is an error between the output value of the width learning network and the true value, η is a learning rate, η is 0.03, and y (t) is a true value of total phosphorus in the effluent;
increasing 1 for the iteration times t; if t is less than H, returning to the second step; if t is larger than or equal to H, stopping calculation and finishing training;
(4) effluent total phosphorus prediction
Learning an effluent total phosphorus prediction model by using the trained width, using the influent acid-base number value, the influent chemical oxygen demand, the oxidation-reduction potential of the middle section of the anaerobic zone, the oxidation-reduction potential of the front end of the anoxic zone, the suspended solids of the mixed liquor at the tail end of the anoxic zone and the dissolved oxygen of the aerobic zone of the test sample as input variables of the model to obtain an effluent total phosphorus prediction value of the model, and carrying out inverse normalization on the model effluent total phosphorus prediction value to obtain an actual effluent total phosphorus concentration value.
The invention is mainly characterized in that:
(1) aiming at the problems that the period of detecting the total phosphorus in the effluent by using a chemical experiment means is long and the price is high in the current sewage treatment, a sewage detection soft measurement model based on a width learning network is established, and the problem of detecting the concentration of the total phosphorus in the effluent in real time is solved;
(2) aiming at the problems of low detection precision and poor real-time performance of the total phosphorus in the effluent of the traditional neural network, the invention provides the width learning network which has good approximation capability, high detection precision and high speed.
Drawings
FIG. 1 is a diagram of a breadth learning network used in the present invention;
FIG. 2 is a graph of the total phosphorus training effect of effluent from the prediction method of the present invention, where the black line represents the true value, the red line represents the width learning network result, the blue line represents the convolutional neural network result, and the green line represents the residual neural network result;
FIG. 3 is a graph of the effluent total phosphorus test results of the prediction method of the present invention, where the black line represents the true value, the red line represents the width learning network result, the blue line represents the convolutional neural network result, and the green line represents the residual neural network result;
FIG. 4 is a graph of the total phosphorus training error in effluent for the prediction method of the present invention, where the red line represents the width learning network training error, the blue line represents the convolutional neural network training error, and the green line represents the residual neural network training error;
FIG. 5 is a graph of the total phosphorus test error in effluent for the prediction method of the present invention, where the red line represents the width learning network training error, the blue line represents the convolutional neural network training error, and the green line represents the residual neural network training error;
Detailed Description
The experimental data come from 2020 data of a certain sewage treatment plant, and 6 input variables of pH value of a water inlet chamber, chemical oxygen demand of the water inlet chamber, oxidation-reduction potential of a middle section of an anaerobic zone, oxidation-reduction potential of a front end of an anoxic zone, suspended solid of mixed liquor at the tail end of the anoxic zone and dissolved oxygen of a second aerobic zone are used; the output variable is the total phosphorus concentration of the effluent; all sample data were divided into two groups, one was the training set, there were 3336 groups of samples, one was the test set, and there were 834 groups of samples.
The invention adopts the following technical scheme and implementation steps:
1. a method for predicting total phosphorus in effluent based on a width learning network is characterized by comprising the following steps: determining input and output variables of a total phosphorus prediction model of effluent, establishing a width learning effluent total phosphorus prediction model, and adjusting parameters of the width learning effluent total phosphorus prediction model, wherein the method comprises the following steps:
(1) determining input and output variables of effluent total phosphorus prediction model
Calculating an independent variable regression coefficient by using a partial least square method and according to the relation between each variable and the total phosphorus in the effluent, screening auxiliary variables, and finally determining 6 auxiliary variables: the method comprises the following steps of (1) feeding water pH value, feeding water chemical oxygen demand, oxidation-reduction potential of the middle section of an anaerobic zone, oxidation-reduction potential of the front end of an anoxic zone, suspended solids of mixed liquor at the tail end of the anoxic zone and dissolved oxygen of a second aerobic zone; the output variable is the total phosphorus concentration of the effluent; dividing all sample data into two groups, wherein the first group comprises H training samples, H is an integer and belongs to [3000,3400], the second group comprises R test samples, R is an integer and belongs to [800,900 ];
(2) establishing a width learning effluent total phosphorus prediction model
The breadth learning network structure has four layers: an input layer, a feature layer, an enhancement layer and an output layer; the construction of the prediction model based on the width learning network is divided into four steps: processing variables and inputting the variables into a network, constructing characteristic neurons in width learning, constructing enhanced neurons, and updating weights from the characteristic neurons and the enhanced neurons to output neurons; determining the number of input neurons of a width learning network for predicting total phosphorus in effluent to be 6, the number of characteristic neuron groups to be N, N being an integer, N being an element [10,30 ]]The number of the enhanced neuron groups is M, M is an integer, and M belongs to [20,50 ]]The number of output neurons is 1, and a training sample is used for training a width learning network; the 6 auxiliary variables selected as network inputs may be denoted as x (t) ═ x1(t),x2(t),x3(t),x4(t),x5(t),x6(t)]Where t is 1,2, …, H is the number of samples, x1(t) is the pH of the feed water in the tth sample, x2(t) is the chemical oxygen demand of the influent water in the tth sample, x3(t) is the oxidation-reduction potential of the middle section of the anaerobic zone in the tth sample, x4(t) is the oxidation-reduction potential of the front end of the anoxic zone in the tth sample, x5(t) the concentration of suspended solids in the mixed liquor at the end of the anoxic zone in the tth sample, x6(t) the concentration of dissolved oxygen in the aerobic zone in the tth sample; an input layer: the input layer consists of 6 neurons, and the output of each input neuron can be expressed as:
ue(t)＝xe(t),e＝1,2,...,6 (1)
wherein x ise(t) is the input value of the e-th neuron of the input layer, ue(t) is the output value of the e-th neuron of the input layer;
characteristic layer: the characteristic layer is composed of N groups of neurons, and the characteristic neuron Z (t) is [ Z1(t),Z2(t),…,ZN(t)]The output of each set of characteristic neurons can be expressed as:
Figure BDA0003069483540000061
wherein Z isi(t) output of i-th group of neurons in feature layerValue, Wei(t) is the weight between the e-th input neuron and the i-th set of characteristic neurons, βei(t) is the deviation term between the e-th input neuron and the i-th group of characteristic neurons, βeiEach element in the (t) matrix belongs to (0, 1)]，
Figure BDA0003069483540000062
As a function of the activation of the network,
Figure BDA0003069483540000063
enhancement layer: the enhancement layer consists of M groups of neurons, enhancing the neurons H (t) ═ H1(t),H2(t),...,HM(t)]The output of each set of augmented neurons may be expressed as:
Figure BDA0003069483540000064
wherein Hj(t) is the output value of the j-th group of neurons of the enhancement layer, Wij(t) is the weight between the i-th group of characteristic neurons and the j-th group of enhanced neurons, βij(t) is the deviation term between the i-th group of characteristic neurons and the j-th group of enhanced neurons, βijEach element in the (t) matrix belongs to (0, 1)]；
An output layer: the output layer consists of 1 neuron, and the output of the output neuron can be expressed as:
Figure BDA0003069483540000071
Q(t)＝[Z(t)|H(t)]＝[Z1(t),...,ZN(t) H1(t),...,HM(t)] (5)
wherein the content of the first and second substances,
Figure BDA0003069483540000072
for the output value of the width learning network, w (t) ═ w1(t),w2(t),…,wN(t),w1 *(t),w2 *(t),…,wM *(t)]TIs the network weight, wi(t) is the weight between the ith set of signature neurons and the output neuron, wj *(t) weights between the j-th group of enhanced neurons and output neurons;
(3) width learning effluent total phosphorus prediction model parameter adjustment
Initializing a width learning network:
let the current iteration number t be 1, the network parameter wi(1)，wj *(1)，Wei(1) And Wij(1) Can be expressed as:
Figure BDA0003069483540000073
Figure BDA0003069483540000074
Figure BDA0003069483540000075
Figure BDA0003069483540000076
wherein, wi(1) Each element in the matrix belongs to (0, 0.9)]，wi k(1) Is the weight between the kth characteristic neuron in the ith group of characteristic neurons and the output neuron, k is an integer, and k is an element [20,50 ]]；wj *(1) Each element in the matrix belongs to (0, 0.18)]，wj q(1) For the weight between the qth enhanced neuron in the jth group of enhanced neurons and the output neuron, q is an integer, q is [20,50 ]]；Wei(1) Each element in the matrix belongs to (0, 1)]，wei k(1) Is the weight between the e input neuron and the k characteristic neuron in the i characteristic neuron; wij(1) Each element in the matrix belongs to (0, 0.2)]，wij kq(1) Weighting between the kth signature neuron in the ith group of signature neurons and the qth enhancement neuron in the jth group of enhancement neurons;
updating the network weight by using a gradient descent algorithm:
the weight update formula can be expressed as:
Figure BDA0003069483540000077
Figure BDA0003069483540000081
wherein, e (t) is an error between the output value of the width learning network and the true value, η is a learning rate, η is 0.03, and y (t) is a true value of total phosphorus in the effluent;
increasing 1 for the iteration times t; if t is less than H, returning to the second step; if t is larger than or equal to H, stopping calculation and finishing training;
(4) effluent total phosphorus prediction
Learning an effluent total phosphorus prediction model by using the trained width, using the influent acid-base number value, the influent chemical oxygen demand, the oxidation-reduction potential of the middle section of the anaerobic zone, the oxidation-reduction potential of the front end of the anoxic zone, the suspended solids of the mixed liquor at the tail end of the anoxic zone and the dissolved oxygen of the aerobic zone of the test sample as input variables of the model to obtain an effluent total phosphorus prediction value of the model, and carrying out inverse normalization on the model effluent total phosphorus prediction value to obtain an actual effluent total phosphorus concentration value.
The training result of the intelligent detection method for the total phosphorus concentration of the effluent is shown in figure 1, and the X axis: number of training samples, Y-axis: the output value of the total phosphorus training of the effluent water is shown, a black line represents a true value, a red line represents a width learning network result, a blue line represents a convolution neural network result, and a green line represents a residual error neural network result;
the test results of the total phosphorus concentration of the effluent are shown in figure 2, and the X axis: number of test samples, Y-axis: the output value of the total phosphorus prediction is output, a black line represents a true value, a red line represents a width learning network result, a blue line represents a convolution neural network result, and a green line represents a residual neural network result;
the output error of the total phosphorus concentration training of the effluent is shown in figure 3, and the X axis: number of training sample sets, Y-axis: the output error of the total phosphorus training of effluent water is shown by a red line, the training error of a width learning network is shown by a blue line, the training error of a convolution neural network is shown by a blue line, and the training error of a residual neural network is shown by a green line;
the output error of the test of the total phosphorus concentration of the effluent is shown in figure 4, and the X axis: number of test sample sets, Y-axis: the water total phosphorus prediction error is shown, a red line shows a width learning network training error, a blue line shows a convolutional neural network training error, and a green line shows a residual neural network training error; the experimental result shows the effectiveness of the water yielding total phosphorus prediction method based on the width learning network.
Actual data:
TABLE 1 pH of the influent
6.11 6.11 6.11 6.1 6.11 6.1 6.1 6.11 6.11 6.11
6.11 6.1 6.1 6.11 6.1 6.11 6.1 6.1 6.1 6.11
6.1 6.09 6.09 6.1 6.1 6.07 6.1 6.1 6.1 6.09
6.1 6.1 6.09 6.08 6.07 6.09 6.09 6.09 6.09 6.1
6.11 6.1 6.1 6.11 6.11 6.11 6.11 6.11 6.11 6.1
…
…
6.09 6.11 6.13 6.16 6.18 6.21 6.21 6.21 6.21 6.22
6.23 6.23 6.24 6.24 6.25 6.25 6.26 6.26 6.26 6.26
6.26 6.26 6.24 6.24 6.24 6.24 6.16 6.11 6.15 6.17
6.17 6.18 6.18 6.19 6.2 6.2 6.20 6.21 6.21 6.21
6.2 6.2 6.2 6.2 6.2 6.2 6.2 6.19 6.2 6.2
TABLE 2. influent chemical oxygen demand values
261.37 261.25 266.98 266.98 267.11 266.98 279.31 279.31 279.44 285.16
285.16 285.04 267.16 285.31 285.19 291.31 291.31 472.19 291.31 472.31
291.31 291.31 266.29 266.41 266.29 266.29 266.28 255.29 255.51 255.51
255.64 255.64 256.64 256.64 256.51 266.51 266.04 266.04 249.16 249.16
249.16 249.16 249.16 249.16 255.45 255.45 255.45 255.51 255.51 255.51
…
…
435.32 435.32 435.32 435.32 435.32 435.32 435.32 435.32 435.32 435.32
435.32 435.32 435.32 435.32 435.32 435.32 435.32 435.32 435.32 435.32
435.32 435.32 435.32 435.32 435.2 435.32 435.32 435.32 435.32 435.32
471.65 471.65 471.65 471.65 471.65 471.65 471.65 471.78 471.44 471.57
471.57 471.57 47157 471.45 471.04 471.04 471.16 471.16 471.04 471.04
TABLE 3 Oxidation-reduction potential of the middle section of the anaerobic zone
Figure BDA0003069483540000091
Figure BDA0003069483540000101
TABLE 4 Oxidation-reduction potential at front end of anoxic zone
-68.79 -62.41 -57.35 -52.81 -44.14 -38.86 -24.49 -17.09 -20.50 -20.82
-17.17 -15.10 -12.69 -13.71 -8.29 -0.30 -1.11 -1.03 0.03 -1.74
10.74 6.54 4.23 -3.28 -5.64 -6.74 -7.11 -5.01 -6.56 -5.23
-5.54 -6.38 -7.03 -5.95 -5.7 -4.64 -5.34 -2.54 -3.79 -3.15
-4.23 -5.34 -6.7 -7.05 -3.68 -4.05 -11.31 -9.7 -10.25 -18.1
…
…
-3.2 -1.44 -3.73 -3.52 -3.07 -3.42 -3.93 -0.53 -0.87 -0.55
2.67 1.93 0.59 -1.18 2.85 4.72 3.6 -16.28 -40.91 -51.06
-58.48 -83.82 -104.65 -120.55 -130.46 -136.29 -138.72 -140.75 -141.08 -141.1
-139.39 -138.67 -138.06 -137.61 -137.37 -139.73 -141.06 -143.47 -142.81 -24.93
-19.81 -17.2 -16.26 -13.86 -14.82 -5.78 -1.38 -0.4 0 -0.53
TABLE 5 concentration of suspended solids (mg/L) in the end of anoxic zone
Figure BDA0003069483540000102
Figure BDA0003069483540000111
TABLE 6 dissolved oxygen concentration (mg/L) in the second aerobic zone
1.73 1.73 1.82 1.91 1.97 2.01 1.93 1.96 1.81 1.91
1.87 1.84 1.86 1.83 1.87 1.76 1.88 1.88 2.00 1.99
1.97 1.98 2.05 2.03 2.03 2.13 2.22 2.22 2.13 2.22
2.47 2.71 2.66 1.56 2.12 1.38 1.39 1.06 1.11 1.02
0.62 0.65 0.79 1.94 2.07 0.56 0.71 0.68 0.65 0.68
…
…
0.61 0.69 0.71 0.64 0.83 0.67 0.73 0.71 0.73 0.78
0.83 0.67 0.81 0.76 0.87 0.77 0.78 0.74 0.5 0.4
0.38 0.38 0.39 0.38 0.4 0.38 0.37 0.39 0.38 0.4
0.39 0.39 0.38 0.38 0.39 0.38 0.41 0.39 0.39 0.4
0.38 0.43 0.47 0.56 0.53 0.56 0.89 0.95 0.96 1.29
TABLE 7 Total phosphorus concentration value (mg/L) of effluent
Figure BDA0003069483540000112
Figure BDA0003069483540000121

Claims (1)

1. A method for predicting total phosphorus in effluent based on a width learning network is characterized by comprising the following steps: determining input and output variables of a total phosphorus prediction model of effluent, establishing a width learning effluent total phosphorus prediction model, and adjusting parameters of the width learning effluent total phosphorus prediction model, wherein the method comprises the following steps:
(1) determining input and output variables of effluent total phosphorus prediction model
Calculating an independent variable regression coefficient by using a partial least square method and according to the relation between each variable and the total phosphorus in the effluent, screening auxiliary variables, and finally determining 6 auxiliary variables: the method comprises the following steps of (1) feeding water pH value, feeding water chemical oxygen demand, oxidation-reduction potential of the middle section of an anaerobic zone, oxidation-reduction potential of the front end of an anoxic zone, suspended solids of mixed liquor at the tail end of the anoxic zone and dissolved oxygen of a second aerobic zone; the output variable is the total phosphorus concentration of the effluent; dividing all sample data into two groups, wherein the first group comprises H training samples, H is an integer and belongs to [3000,3400], the second group comprises R test samples, R is an integer and belongs to [800,900 ];
(2) establishing a width learning effluent total phosphorus prediction model
The breadth learning network structure has four layers: an input layer, a feature layer, an enhancement layer and an output layer; the construction of the prediction model based on the width learning network is divided into four steps: processing variables and inputting the variables into a network, constructing characteristic neurons in width learning, constructing enhanced neurons, and updating weights from the characteristic neurons and the enhanced neurons to output neurons; determining breadth learning for predicting total phosphorus in effluentThe number of the network input neurons is 6, the number of the characteristic neuron groups is N, N is an integer, and N belongs to [10,30 ]]The number of the enhanced neuron groups is M, M is an integer, and M belongs to [20,50 ]]The number of output neurons is 1, and a training sample is used for training a width learning network; the 6 auxiliary variables selected as network inputs may be denoted as x (t) ═ x1(t),x2(t),x3(t),x4(t),x5(t),x6(t)]Where t is 1,2, …, H is the number of samples, x1(t) is the pH of the feed water in the tth sample, x2(t) is the chemical oxygen demand of the influent water in the tth sample, x3(t) is the oxidation-reduction potential of the middle section of the anaerobic zone in the tth sample, x4(t) is the oxidation-reduction potential of the front end of the anoxic zone in the tth sample, x5(t) the concentration of suspended solids in the mixed liquor at the end of the anoxic zone in the tth sample, x6(t) the concentration of dissolved oxygen in the aerobic zone in the tth sample; an input layer: the input layer consists of 6 neurons, and the output of each input neuron can be expressed as:
ue(t)＝xe(t),e＝1,2,...,6 (1)
wherein x ise(t) is the input value of the e-th neuron of the input layer, ue(t) is the output value of the e-th neuron of the input layer;
characteristic layer: the characteristic layer is composed of N groups of neurons, and the characteristic neuron Z (t) is [ Z1(t),Z2(t),…,ZN(t)]The output of each set of characteristic neurons can be expressed as:
Figure FDA0003069483530000011
wherein Z isi(t) is the output value of the i-th group of neurons in the feature layer, Wei(t) is the weight between the e-th input neuron and the i-th set of characteristic neurons, βei(t) is the deviation term between the e-th input neuron and the i-th group of characteristic neurons, βeiEach element in the (t) matrix belongs to (0, 1)]，
Figure FDA0003069483530000021
As a function of the activation of the network,
Figure FDA0003069483530000022
enhancement layer: the enhancement layer consists of M groups of neurons, enhancing the neurons H (t) ═ H1(t),H2(t),...,HM(t)]The output of each set of augmented neurons may be expressed as:
Figure FDA0003069483530000023
wherein Hj(t) is the output value of the j-th group of neurons of the enhancement layer, Wij(t) is the weight between the i-th group of characteristic neurons and the j-th group of enhanced neurons, βij(t) is the deviation term between the i-th group of characteristic neurons and the j-th group of enhanced neurons, βijEach element in the (t) matrix belongs to (0, 1)]；
An output layer: the output layer consists of 1 neuron, and the output of the output neuron can be expressed as:
Figure FDA0003069483530000024
Q(t)＝[Z(t)|H(t)]＝[Z1(t),...,ZN(t)H1(t),...,HM(t)] (5)
wherein the content of the first and second substances,
Figure FDA0003069483530000025
for the output value of the width learning network, w (t) ═ w1(t),w2(t),…,wN(t),w1 *(t),w2 *(t),…,wM *(t)]TIs the network weight, wi(t) is the weight between the ith set of signature neurons and the output neuron, wj *(t) weights between the j-th group of enhanced neurons and output neurons;
(3) width learning effluent total phosphorus prediction model parameter adjustment
Initializing a width learning network:
let the current iteration number t be 1, the network parameter wi(1)，wj *(1)，Wei(1) And Wij(1) Can be expressed as:
Figure FDA0003069483530000026
Figure FDA0003069483530000027
Figure FDA0003069483530000028
Figure FDA0003069483530000029
wherein, wi(1) Each element in the matrix belongs to (0, 0.9)]，
Figure FDA00030694835300000210
Is the weight between the kth characteristic neuron in the ith group of characteristic neurons and the output neuron, k is an integer, and k is an element [20,50 ]]；wj *(1) Each element in the matrix belongs to (0, 0.18)]，
Figure FDA0003069483530000031
For the weight between the qth enhanced neuron in the jth group of enhanced neurons and the output neuron, q is an integer, q is [20,50 ]]；Wei(1) Each element in the matrix belongs to (0, 1)]，
Figure FDA0003069483530000032
For the e-th input neuron and the i-th groupWeights between kth ones of the feature neurons; wij(1) Each element in the matrix belongs to (0, 0.2)]，
Figure FDA0003069483530000033
Weighting between the kth signature neuron in the ith group of signature neurons and the qth enhancement neuron in the jth group of enhancement neurons;
updating the network weight by using a gradient descent algorithm:
the weight update formula can be expressed as:
Figure FDA0003069483530000034
Figure FDA0003069483530000035
wherein, e (t) is an error between the output value of the width learning network and the true value, η is a learning rate, η is 0.03, and y (t) is a true value of total phosphorus in the effluent;
increasing 1 for the iteration times t; if t is less than H, returning to the second step; if t is larger than or equal to H, stopping calculation and finishing training;
(4) effluent total phosphorus prediction
Learning an effluent total phosphorus prediction model by using the trained width, using the influent acid-base number value, the influent chemical oxygen demand, the oxidation-reduction potential of the middle section of the anaerobic zone, the oxidation-reduction potential of the front end of the anoxic zone, the suspended solids of the mixed liquor at the tail end of the anoxic zone and the dissolved oxygen of the aerobic zone of the test sample as input variables of the model to obtain an effluent total phosphorus prediction value of the model, and carrying out inverse normalization on the model effluent total phosphorus prediction value to obtain an actual effluent total phosphorus concentration value.
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