CN112485394A - Water quality soft measurement method based on sparse self-coding and extreme learning machine - Google Patents

Water quality soft measurement method based on sparse self-coding and extreme learning machine Download PDF

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CN112485394A
CN112485394A CN202011249258.7A CN202011249258A CN112485394A CN 112485394 A CN112485394 A CN 112485394A CN 202011249258 A CN202011249258 A CN 202011249258A CN 112485394 A CN112485394 A CN 112485394A
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杨秦敏
曹伟伟
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Abstract

The invention discloses a water quality soft measurement method based on sparse self-coding and an extreme learning machine, which combines the sparse self-coding method with the extreme learning machine method in the application of sewage treatment, takes the characteristics of extremely high learning speed, high model estimation precision, sparse self-coding, nonlinear data dimension reduction extraction characteristic value and the like of the extreme learning machine into consideration, can realize the rapid and effective estimation of the concentration of key water quality in sewage treatment, and effectively reduces the calculation complexity by combining a method of repeated resampling and averaging on the premise of ensuring the performance. The method is applied to the soft measurement of the ammonia nitrogen ion concentration in the sewage treatment, and can realize the rapid and accurate estimation of the ammonia nitrogen ion concentration, thereby realizing the soft measurement effect aiming at key components in the sewage treatment, reducing the restriction and limitation of the cost of the sensor on the sewage treatment process, and further providing support for the improvement of the sewage treatment process and the improvement of the effluent quality.

Description

Water quality soft measurement method based on sparse self-coding and extreme learning machine
Technical Field
The invention relates to the field of control science and engineering and environmental science and engineering, in particular to a water quality soft measurement method based on sparse self-coding and an extreme learning machine.
Background
The water resource reserves all over the world are abundant, but the fresh water resources account for only 2.53 percent, mainly deep water and glaciers, and the fresh water of lakes and rivers only accounts for 0.3 percent of the fresh water resources, so the fresh water resources available for human beings are very limited. Meanwhile, the development and the utilization of water resources by human beings are unreasonable, so that the water resources are greatly wasted and polluted, and the space of the available water resources is further compressed. Meanwhile, polluted water resources can cause damage to the environment, vegetation decline, animal death and the like, and can also harm human society and endanger human health and life safety. Therefore, water resource remediation is a research subject with great significance, and sewage treatment is a very effective means, and various kinds of sewage generated by human society are purified and discharged into rivers and lakes after the water quality reaches the standard or harmlessly utilized, so that not only can damage to the environment and the human society be avoided, but also the problem of water resource shortage caused by excessive development of the human society can be relieved.
At present, most sewage treatment in the world adopts anaerobic and aerobic biochemical reactions to realize sewage treatment, the main reason for adopting the method is that the sewage contains a large amount of organic matters which come from a garbage landfill, resident domestic wastewater, pharmaceutical factories, food factories and other scenes, the most main content of the organic matters is nitrogen element, ammonia nitrogen comes from coking plants, chemical fertilizer plants, petrochemical plants and the like, the wastewater containing a large amount of ammonia nitrogen ions is discharged into the nature to enrich and blacken and odorize water, and toxic action is generated on human beings and organisms. Therefore, the detection of the concentration of the ammonia nitrogen sample in the effluent quality of the sewage treatment plant is important. However, the existing sensor specially used for detection has high unreliability and high cost, and a plurality of soft measurement methods are provided for realizing accurate and rapid detection, but the effect of the existing soft measurement method can be further restrained due to the complexity of the sewage treatment process and the mutual influence among highly coupled components, and in order to further improve the soft measurement effect, the invention provides a water quality soft measurement method based on sparse self-coding and an extreme learning machine to overcome the existing difficulty.
Disclosure of Invention
In order to realize the rapid estimation of some components which are difficult to measure in the sewage treatment water quality and facilitate workers to adjust a control strategy in time, a plurality of scientific research works try to realize soft measurement methods for the components which are difficult to measure by using a machine learning method, but as the sewage treatment is a very complex system with strong coupling and the variable types are complex and diverse, different types of components are difficult to separate manually. Aiming at the problem, the invention provides a water quality soft measurement method based on sparse self-coding and an extreme learning machine, which can quickly separate a plurality of components and quickly and accurately estimate key components which are difficult to measure in sewage treatment reaction, thereby providing reasonable guidance for technicians to timely adjust control strategies.
The purpose of the invention is realized by the following technical scheme: a water quality soft measurement method based on sparse self-coding and extreme learning machine comprises the following steps:
(1) acquiring sample data: obtaining N from a wastewater treatment process0Group sample data
Figure BDA0002771055280000021
Each set of input vectors XiCharacterizing a plurality of wastewater quality components, corresponding expected output TiAnd characterizing the concentration of ammonia nitrogen ions in the effluent quality.
(2) Compressing the sample data by adopting a sampling mode, which specifically comprises the following steps: in [1,10 ]]Randomly selecting an integer initial value a, and acquiring data which is ten times compressed in a batch by acquiring every 10 points
Figure BDA0002771055280000022
And repeatedly sampling, and resetting the initial value a every time to obtain p batches of sample data.
(3) Sample data normalization: and respectively carrying out descaler dimensionalization on each batch of sample data, and normalizing the data with different dimensions to the range of [ -1,1] to obtain normalized sample data x.
(4) Performing dimensionality reduction on data according to a sparse self-encoder, specifically:
from the input layer to the hidden layer:
h＝f(W1x+b1)
from the hidden layer to the output layer:
Figure BDA0002771055280000023
where h is the output of the hidden layer,
Figure BDA0002771055280000024
for the output of the output layer, i.e., the reconstructed vector, f (-) is the non-linear mapping, and W and b are the neural network weights and bias parameters.
The decoding function is a linear function or a Sigmoid function, so that the reconstruction error is minimum, and the reconstruction error is as follows:
Figure BDA0002771055280000025
adding sparseness limitation in encoder to control number of hidden layer neuron activation, supposing aj(x) Representing the activation function of the jth neuron in the hidden layer, the average activation amount of the jth neuron
Figure BDA0002771055280000026
Can be expressed as:
Figure BDA0002771055280000027
in order to render most of the hidden neurons inactive, let
Figure BDA0002771055280000028
Equal to a constant p, called the sparseness constant, close to 0. Selecting KL divergence as an expression of a penalty term PN:
Figure BDA0002771055280000031
wherein M is the number of neurons in the hidden layer,
Figure BDA0002771055280000032
is the KL divergence. The KL divergence expression is:
Figure BDA0002771055280000033
for an auto-encoder, the cost function is:
Figure BDA0002771055280000034
wherein λ is weight decay constant, nlNumber of layers of neural network, slThe number of the layer I neurons is shown as,
Figure BDA0002771055280000035
is the ji weight value of the l-th layer neural network. The total cost function containing the sparse penalty term is then:
Jsparse(W,b)＝J(W,b)+βPN
where β is the sparse penalty term coefficient.
Updating the weight W and the bias b, the update equation can be obtained as:
Figure BDA0002771055280000036
Figure BDA0002771055280000037
wherein b isi lThe optimal W and b are obtained for the ith bias value of the l-th layer neural network and alpha is the learning rate, and better hidden layer output h belongs to RN×MThe method is used for representing the characteristics of the detection sample data, so that the dimension reduction of the detection sample data to M dimension is realized; let Y be h.
(5) The method comprises the following steps of constructing an extreme learning machine to realize water quality key component soft measurement, wherein a neural network of the extreme learning machine is formed by an input layer, a hidden layer and an output layer together, setting the input layer of the neural network to have M nodes according to the characteristics of sample data, setting the hidden layer to have L nodes, and setting the output layer to have M nodes, and the method comprises the following steps:
step 1: according to the reduced sample data set
Figure BDA0002771055280000038
Determines the type M and the data length N of the input data.
Figure BDA0002771055280000039
Wherein G (-) is the excitation function of the neural network, al,bl(L ═ 1, 2., L) are weights and offset values from the input layer to the hidden layer, L represents the number of hidden layer nodes of the neural network, Y represents a total of N groups of neural network input data, each group has M eigenvalues, i.e. the number of nodes corresponding to the input layer of the neural network, and H is the output of the hidden layer of the neural network;
step 2: taking the effluent quality of the sewage as target historical data T:
Figure BDA0002771055280000041
wherein t isj(j 1, 2.... N) is an output vector of the j-th group of target history data;
step 3: constructing a network from the hidden layer to the output layer has
Figure BDA0002771055280000042
Writing this formula as a matrix form
T＝βH
Wherein wlmIs a weight vector from the hidden layer to the output layer, and the matrix is beta epsilon Rm×L，G(al,blY) is the hidden layer output and also the output layer input, in matrix formThen is H ∈ RL×N；
Step 4: obtaining the weight value from the hidden layer to the output layer by adopting a Moore-Penrose method:
Figure BDA0002771055280000043
wherein ILIs an identity matrix of dimension L, and C is a normal value.
(6) Completing the calculation of sample data of one batch, and then calculating the sample data of the next batch until the calculation of the sample data of p batches is completed; and finally, respectively carrying out soft measurement by using the training results of the p batches of sample data, and averaging the soft measurement results to obtain a final soft measurement result, namely the concentration of the ammonia nitrogen ions in the effluent quality. By the method of dividing the soft measurement model at intervals, the performance of the soft measurement model is guaranteed, single calculated amount can be effectively reduced, the requirement on hardware equipment is reduced, and the calculation complexity can be reduced, so that the calculation complexity is reduced by multiple times.
Further, in the step (1), N is obtained from the sewage treatment process0Group sample data
Figure BDA0002771055280000044
Wherein each set of input vectors is of specific form Xi＝[SI,i,SS,i,XI,i,XS,i,XBH,i,XBA,i,XP,i,SNO,i,SO,i,SND,i,XND,i]TRespectively representing 11 components of soluble inert organic matters, easily biodegradable substrates, insoluble inert organic matters, slowly biodegradable substrates, active heterotrophic organisms, active autotrophic organisms, biomass decay insoluble products, nitrate and nitrite, ammonium ions, soluble degradable organic nitrogen and insoluble degradable organic nitrogen in the sewage.
Further, in the step (3), the data of different dimensions are normalized to [ -1,1] by a method of minimum and maximum normalization, respectively, for each batch of sample data, and the formula is as follows:
Figure BDA0002771055280000051
wherein X is sample data compressed in sewage treatment, and X isminIs the minimum value of X, and XmaxThen it is the maximum value in X, which is the normalized sample data.
The invention has the beneficial effects that: the method combines the sparse self-coding with the extreme learning machine, on one hand, the sparse self-coding is utilized to carry out dimensionality reduction feature extraction on sample data, on the other hand, the extreme learning machine is utilized to quickly and effectively realize quick estimation on the key components of sewage treatment, meanwhile, the calculated amount is considered to be large, and the calculation complexity and the calculation conditions are effectively reduced by adopting repeated resampling and mean value calculation, so that the effect of soft measurement is effectively realized, and the constraint and limitation of the sensor cost on the sewage treatment process are reduced.
Drawings
FIG. 1 is a schematic view of the structure of the water quality soft measurement of the present invention;
FIG. 2 is a flow chart of a water quality soft measurement method based on sparse self-coding and extreme learning machine.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the detailed description and specific examples, while indicating the scope of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The invention provides a water quality soft measurement method based on sparse self-coding and extreme learning machine by combining sparse self-coding with extreme learning machine and utilizing a method of repeated resampling and averaging, which can quickly and accurately estimate key components in sewage treatment. As shown in fig. 1 and 2, the specific implementation steps are as follows:
(1) obtaining sample data
Obtaining N from a wastewater treatment process0Group sample data
Figure BDA0002771055280000052
Wherein each set of input vectors is of specific form Xi＝[SI,i,SS,i,XI,i,XS,i,XBH,i,XBA,i,XP,i,SNO,i,SO,i,SND,i,XND,i]TRespectively representing 11 components in the sewage, such as soluble inert organic matters, easily biodegradable substrates, insoluble inert organic matters, slowly biodegradable substrates, active heterotrophic organisms, active autotrophic organisms, biomass decay insoluble products, nitrate and nitrite, ammonium ions, soluble degradable organic nitrogen, insoluble degradable organic nitrogen and the like, and correspondingly expecting output Ti＝SNH,iAnd characterizing the component of ammonia nitrogen ion concentration in the effluent quality.
(2) Compressing sample data
In order to reduce the computational complexity without affecting the performance of the method, the invention adopts a method of multi-sampling computation. Knowing the original sample data
Figure BDA0002771055280000061
Sampling method is adopted to obtain compressed sample data in [1,10 ]]Randomly selecting an integer initial value a, and acquiring data which is ten times compressed in a batch by acquiring every 10 points
Figure BDA0002771055280000062
Sampling is repeatedly carried out, the initial value a is reset every time, p batches of sample data are obtained, and the following processing and training are respectively carried out on the p batches of sample data.
(3) Sample data normalization
Because the dimensions of different components in sewage treatment are different and the scale difference between numerical values is huge, in order to eliminate the influence caused by the dimensions, the data of different dimensions are normalized to between [ -1,1] by a minimum maximum value normalization method aiming at each batch of sample data respectively, so that the influence of the dimensions on soft measurement is eliminated. The concrete form is as follows:
Figure BDA0002771055280000063
wherein X is sample data compressed in sewage treatment, and X isminIs the minimum value of X, and XmaxThen it is the maximum value in X, where X is the normalized sample data, specifically X ═ SIn,SSn,XIn,XSn,XBHn,XBAn,XPn,SNOn,SOn,SNDn,XNDn]T。
The following calculation steps are performed for each batch of normalized sample data.
(4) Dimensionality reduction of data from sparse self-encoder
The self-encoder is a three-layer symmetric deep learning neural network which extracts the hierarchical characteristics of high-dimensional complex input data from a non-tag data center by using unsupervised learning and optimization system parameters and obtains the distribution characteristic representation of original data. The neural network consists of an input layer, an implicit layer and an output layer, wherein the implicit layer encodes original input data, and the output layer decodes the implicit expression to reconstruct the original data, so that the reconstruction error is minimum to obtain the optimal implicit expression.
From the input layer to the hidden layer there are:
h＝f(W1x+b1)
from the hidden layer to the output layer there are:
Figure BDA0002771055280000064
where h is the output of the hidden layer,
Figure BDA0002771055280000065
for the output of the output layer, i.e., the reconstructed vector, f (-) is a non-linear mapping, and W and b are the neural network weights and bias parameters.
The decoding function is typically a linear function or Sigmoid function, so that the reconstruction error is minimal, and is:
Figure BDA0002771055280000066
in order to enable the self-encoder to learn useful features, the encoder is added with sparse limitation to control the number of hidden layer neuron activations, and the self-encoder with hidden layer added with sparse limitation is called a sparse self-encoder. Suppose aj(x) Representing the activation function of the jth neuron in the hidden layer, the average activation amount of the jth neuron
Figure BDA0002771055280000071
Can be expressed as:
Figure BDA0002771055280000072
in order to render most of the hidden neurons inactive, let
Figure BDA0002771055280000073
Equal to a constant p, called the sparseness constant, close to 0. Selecting KL divergence as an expression of a penalty term PN:
Figure BDA0002771055280000074
wherein M is the number of hidden layer neurons (M < 11 in this embodiment),
Figure BDA0002771055280000075
is the KL divergence. The KL divergence expression is:
Figure BDA0002771055280000076
for an auto-encoder, the general cost function can be written as:
Figure BDA0002771055280000077
wherein λ is weight decay constant, nlNumber of layers of neural network, slThe number of the layer I neurons is shown as,
Figure BDA0002771055280000078
is the ji weight value of the l-th layer neural network. The total cost function containing the sparse penalty term can be written as:
Jsparse(W,b)＝J(W,b)+βPN
where β is the sparse penalty term coefficient.
Updating the weight W and the bias b, the update equation can be obtained as:
Figure BDA0002771055280000079
Figure BDA00027710552800000710
wherein
Figure BDA00027710552800000711
The optimal W and b are obtained for the ith bias value of the l-th layer neural network and alpha is the learning rate, and then better hidden layer output h belongs to RN×MThe method is used for representing the characteristics of the detection sample data, thereby realizing the dimension reduction of the detection sample data to M dimension.
For convenience of subsequent description, Y ═ h is introduced here;
(5) water quality key component soft measuring-extreme learning machine
The neural network of the general extreme learning machine is composed of an input layer, a hidden layer and an output layer, wherein according to the characteristics of sample data, the input layer of the neural network is set to have M nodes (M equals to 3 in the embodiment), the hidden layer has L nodes (L equals to 100 in the embodiment), and the output layer has M nodes (M equals to 1 in the embodiment). Comprises the following steps:
step 1: according to the reduced sample data set
Figure BDA0002771055280000081
Determines the type M and the data length N of the input data.
Figure BDA0002771055280000082
Wherein G (-) is the excitation function of the neural network, al,bl(L ═ 1, 2., L) are weights and offset values from the input layer to the hidden layer, L represents the number of hidden layer nodes of the neural network, Y represents a total of N groups of neural network input data, each group has M eigenvalues, i.e. the number of nodes corresponding to the input layer of the neural network, and H is the output of the hidden layer of the neural network;
step 2: taking the effluent quality of the sewage as target historical data T:
Figure BDA0002771055280000083
wherein t isj(j 1, 2.... N) is an output vector of the j-th group of target history data;
step 3: constructing a network from a hidden layer to an output layer, and selecting a Purelin function according to the output layer, wherein the Purelin function has the following characteristics
Figure BDA0002771055280000084
Writing this formula as a matrix form
T＝βH
Wherein wlmIs a weight vector from the hidden layer to the output layer, and the matrix is beta epsilon Rm×L，G(al,blY) is the hidden layer output and the output layer input, and the matrix form is H e RL×N。
Step 4: under the premise of obtaining step1 and step2, step3 is processed by a Moore-Penrose method to obtain a weight value from a hidden layer to an output layer:
Figure BDA0002771055280000085
wherein ILIs an identity matrix of dimension L, and C is a normal value.
(6) And finishing the calculation of one batch of sample data, and then calculating the next batch of sample data until the last p batches of sample data are calculated. And finally, respectively carrying out soft measurement by using the training results of the p batches of sample data, and averaging the soft measurement results to obtain a final soft measurement result, namely the concentration of the ammonia nitrogen ions in the effluent quality.
The foregoing is only a preferred embodiment of the present invention, and although the present invention has been disclosed in the preferred embodiments, it is not intended to limit the present invention. Those skilled in the art can make numerous possible variations and modifications to the present teachings, or modify equivalent embodiments to equivalent variations, without departing from the scope of the present teachings, using the methods and techniques disclosed above. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are still within the scope of the protection of the technical solution of the present invention, unless the contents of the technical solution of the present invention are departed.

Claims (3)

1. A water quality soft measurement method based on sparse self-coding and extreme learning machine is characterized by comprising the following steps:
(1) acquiring sample data: obtaining N from a wastewater treatment process0Group sample data
Figure FDA0002771055270000011
Each set of input vectors XiCharacterizing a plurality of wastewater quality components, corresponding expected output TiAnd characterizing the concentration of ammonia nitrogen ions in the effluent quality.
(2) Compressing the sample data by adopting a sampling mode, which specifically comprises the following steps: in [1,10 ]]Randomly selecting an integer initial value a, and acquiring a batch of data at intervals of 10 pointsTen times as much data is compressed
Figure FDA0002771055270000012
And repeatedly sampling, and resetting the initial value a every time to obtain p batches of sample data.
(3) Sample data normalization: and respectively carrying out descaler dimensionalization on each batch of sample data, and normalizing the data with different dimensions to the range of [ -1,1] to obtain normalized sample data x.
(4) Performing dimensionality reduction on data according to a sparse self-encoder, specifically:
from the input layer to the hidden layer:
h＝f(W1x+b1)
from the hidden layer to the output layer:
Figure FDA0002771055270000013
where h is the output of the hidden layer,
Figure FDA0002771055270000014
for the output of the output layer, i.e., the reconstructed vector, f (-) is the non-linear mapping, and W and b are the neural network weights and bias parameters.
The decoding function is a linear function or a Sigmoid function, so that the reconstruction error is minimum, and the reconstruction error is as follows:
Figure FDA0002771055270000015
adding sparseness limitation in encoder to control number of hidden layer neuron activation, supposing aj(x) Representing the activation function of the jth neuron in the hidden layer, the average activation amount of the jth neuron
Figure FDA0002771055270000016
Can be expressed as:
Figure FDA0002771055270000017
in order to render most of the hidden neurons inactive, let
Figure FDA0002771055270000018
Equal to a constant p, called the sparseness constant, close to 0. Selecting KL divergence as an expression of a penalty term PN:
Figure FDA0002771055270000019
wherein M is the number of neurons in the hidden layer,
Figure FDA0002771055270000021
is the KL divergence. The KL divergence expression is:
Figure FDA0002771055270000022
for an auto-encoder, the cost function is:
Figure FDA0002771055270000023
wherein λ is weight decay constant, nlNumber of layers of neural network, slThe number of the layer I neurons is shown as,
Figure FDA0002771055270000024
is the ji weight value of the l-th layer neural network. The total cost function containing the sparse penalty term is then:
Jsparse(W,b)＝J(W,b)+βPN
where β is the sparse penalty term coefficient.
Updating the weight W and the bias b, the update equation can be obtained as:
Figure FDA0002771055270000025
Figure FDA0002771055270000026
wherein
Figure FDA0002771055270000027
The optimal W and b are obtained for the ith bias value of the l-th layer neural network and alpha is the learning rate, and better hidden layer output h belongs to RN×MThe method is used for representing the characteristics of the detection sample data, so that the dimension reduction of the detection sample data to M dimension is realized; let Y be h.
(5) The method comprises the following steps of constructing an extreme learning machine to realize water quality key component soft measurement, wherein a neural network of the extreme learning machine is formed by an input layer, a hidden layer and an output layer together, setting the input layer of the neural network to have M nodes according to the characteristics of sample data, setting the hidden layer to have L nodes, and setting the output layer to have M nodes, and the method comprises the following steps:
step 1: according to the reduced sample data set
Figure FDA0002771055270000028
Determines the type M and the data length N of the input data.
Figure FDA0002771055270000029
Wherein G (-) is the excitation function of the neural network, al,bl(L ═ 1, 2., L) are weights and offset values from the input layer to the hidden layer, L represents the number of hidden layer nodes of the neural network, Y represents a total of N groups of neural network input data, each group has M eigenvalues, i.e. the number of nodes corresponding to the input layer of the neural network, and H is the output of the hidden layer of the neural network;
step 2: taking the effluent quality of the sewage as target historical data T:
Figure FDA0002771055270000031
wherein t isj(j 1, 2.... N) is an output vector of the j-th group of target history data;
step 3: constructing a network from the hidden layer to the output layer has
Figure FDA0002771055270000032
Writing this formula as a matrix form
T＝βH
Wherein wlmIs a weight vector from the hidden layer to the output layer, and the matrix is beta epsilon Rm×L，G(al,blY) is the hidden layer output and the output layer input, and the matrix form is H e RL×N；
Step 4: obtaining the weight value from the hidden layer to the output layer by adopting a Moore-Penrose method:
Figure FDA0002771055270000033
wherein ILIs an identity matrix of dimension L, and C is a normal value.
(6) Completing the calculation of sample data of one batch, and then calculating the sample data of the next batch until the calculation of the sample data of p batches is completed; and finally, respectively carrying out soft measurement by using the training results of the p batches of sample data, and averaging the soft measurement results to obtain a final soft measurement result, namely the concentration of the ammonia nitrogen ions in the effluent quality.
2. The sparse self-coding and extreme learning machine-based water quality soft measurement method according to claim 1, wherein in the step (1), N is obtained from a sewage treatment process0Group sample data
Figure FDA0002771055270000034
Wherein each set of input vectors is of specific form Xi＝[SI,i,SS,i,XI,i,XS,i,XBH,i,XBA,i,XP,i,SNO,i,SO,i,SND,i,XND,i]TRespectively representing 11 components of soluble inert organic matters, easily biodegradable substrates, insoluble inert organic matters, slowly biodegradable substrates, active heterotrophic organisms, active autotrophic organisms, biomass decay insoluble products, nitrate and nitrite, ammonium ions, soluble degradable organic nitrogen and insoluble degradable organic nitrogen in the sewage.
3. The sparse self-coding and extreme learning machine-based water quality soft measurement method according to claim 1, wherein in the step (3), the data of different dimensions are normalized to [ -1,1] by a minimum maximum normalization method by respectively performing de-dimensioning on each batch of sample data, and the formula is as follows:
Figure FDA0002771055270000035
wherein X is sample data compressed in sewage treatment, and X isminIs the minimum value of X, and XmaxThen it is the maximum value in X, which is the normalized sample data.
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