CN110837886A - A Soft-Sensing Method for Effluent NH4-N Based on ELM-SL0 Neural Network - Google Patents

Abstract

The invention discloses an effluent NH4-N soft measurement method based on an ELM-SL0 neural network, belonging to the field of water treatment and intelligent information control. The method mainly comprises the following operation processes: the L0 regularization penalty term is first added to the conventional error function to approximate the insignificant weight to 0, and then the improved error function is updated using a batch gradient descent algorithm to achieve training and pruning of the network. The soft measurement method of the effluent NH4-N based on the neural network formed by the steps belongs to the protection scope of the invention. The invention combines the regularization technology and the batch gradient algorithm to optimize the ELM network structure, thereby reducing the network computation complexity, improving the prediction accuracy and increasing the generalization performance.

Description

A Soft-Sensing Method for Effluent NH4-N Based on ELM-SL0 Neural Network

technical field

Aiming at the problem that the ammonia nitrogen concentration is difficult to measure in the sewage treatment process, the invention combines the batch gradient descent algorithm with the L0 regularization and applies it to the neural network to predict the ammonia nitrogen concentration in the sewage treatment process. Neural network is one of the main branches of intelligent information processing technology. The prediction technology of ammonia nitrogen concentration in sewage based on neural network belongs not only to the field of water treatment, but also to the field of intelligent information.

Background technique

With the rapid development of urbanization and industrialization in today's society, my country's water environment has been seriously damaged. Sewage discharge not only seriously affects the daily life of residents, but also destroys the ecological balance of nature. In order to reduce the discharge of sewage and realize the recycling of water, sewage treatment plants have been established all over the country. In the sewage treatment process, the NH4-N concentration is an important parameter to measure the performance of the sewage treatment process (WWTP). systems, and they are expensive to maintain, so forecasting them remains an open question. Therefore, how to predict the concentration of NH4-N in the effluent with low cost and high efficiency is very necessary for the assessment of the effluent quality and the stable operation of the sewage treatment plant.

The soft sensing method utilizes easy-to-measure variables and builds models to predict difficult-to-measure variables in real time, providing an efficient and fast solution for the measurement of key water quality parameters in the sewage treatment process. Because of its good learning ability, information processing ability and self-adaptive characteristics, neural network can approximate nonlinear systems with high precision. The invention designs a soft measurement method of effluent NH4-N based on ELM-SL0 neural network, so as to realize the online prediction of effluent NH4-N concentration.

SUMMARY OF THE INVENTION

A soft sensing method for effluent NH4-N based on ELM-SL0 neural network. The main operation process is as follows: First, add the L0 regularization penalty term to the traditional error function to make the unimportant weights approach 0, and then use the batch gradient descent algorithm to The improved error function is updated to enable training and pruning of the network. This method uses the learning ability of the neural network to optimize the output weights according to the training error, eliminate the unimportant output weights, and then predict the ammonia nitrogen concentration in the sewage treatment process to minimize the error and improve the sparsity of the network structure. . It is characterized in that, comprises the following steps:

Step 1: Initialize the network structure and parameters

Step 1.1: Initialize the network structure

Taking temperature, dissolved oxygen, total suspended solids content, pH value, and effluent redox potential as input variables, and ammonia nitrogen concentration as output variables, the network structure of the echo state is determined as 5-N-1, where N represents the number of nodes in the reservoir. The number N of the reserve pool nodes of a typical echo state network is 50≤N≤1000. In order to better observe the pruning effect of the proposed algorithm, the value of N should not be too small. In this network, N is 500, that is, the network contains 5 input nodes, 500 reserve pool nodes, and 1 output node.

Step 1.2: Initialize network parameters

u_k表示第k组输入样本，t_k表示第k组实际输出值，表示输入样本维度为n，L为样本总数；随机初始化网络输入权值W和阈值向量b在(0,1)之间，设置初始输出权值W＝0。Take the sigmoid function as the network activation function G( ), determine the initial number of iterations i=0, the maximum number of iterations i _max ≥ 5000, and the training samples

u _k represents the kth group of input samples, _tk represents the kth group of actual output values, Indicates that the input sample dimension is n, and L is the total number of samples; the random initialization network input weight W and the threshold vector b are between (0, 1), and the initial output weight W=0.

Step 2: Use the grid search method to determine the learning rate η and the regularization parameter λ

(1) First, set the regularization parameter to 0, that is, λ=0, then set the search range of the learning rate to [0.0005, 0.01] with a step size of 0.0005, run the program, and select the optimal learning rate η with the smallest training error .

(2) In the case of the optimal learning rate η, the search range of the regularization parameter is set to [0.0025, 0.05] with a step size of 0.0025 to ensure that the optimal regularization parameter with the best sparsity effect is selected without affecting the training error. λ.

Step 3: Calculate the network output y _k and the prediction error d _k of the input kth group of samples

For a given activation function G(·), input sample _uk , input weight W and threshold vector b, the output of the hidden layer is obtained as:

Among them, g _j ,1<j<N represents the activation function of the jth neuron in the reserve pool, and W _j u _k ,1<j<N represents the input weight between the jth neuron in the reserve pool and the input layer The inner product of the vector W _j and the input vector _uk , b _j , 1<j<N represents the threshold of the jth neuron in the reserve pool.

Input the kth group of samples, the network output _yk is obtained by the following formula:

y _k =W·G(Wuk ₊ b) (2)

The training error d _k between the expected output t _k of the network and the actual output y _k is defined as:

d _k =t _k -y _k (3)

Step 4: Calculate the gradient of the output weights and update the output weights

The standard mean squared error function is defined as:

in,

Adding the L0 regularization term to the error function, the improved error function is:

为W的L0范数，被定义如下：in,

is the L0 norm of W, defined as follows:

Among them, W _j (1<j<N) is the jth output weight.

However, the L0 norm is a non-convex function, so formula (5) is an NP-hard minimization combinatorial problem. To solve this problem, we use a continuously differentiable function f(·) to approximate the L0 norm, and the function f(γ, W _j ) about W is defined as follows:

的程度，γ较大时，函数f(γ,W_j)对权值向量的修剪程度较低，γ接近0时,函数f(γ,W_j)能够更好修剪权值向量W的非零元素，本专利中γ取0.05。由此可得，f(γ,W_j)的一阶导数为：Among them, γ is a positive number, which controls the approximation of f(γ, W _j )

When γ is large, the function f(γ, W _j ) trims the weight vector to a lower degree. When γ is close to 0, the function f(γ, W _j ) can better trim the non-zero value of the weight vector W element, γ is taken as 0.05 in this patent. From this, the first derivative of f(γ, W _j ) is:

So formula (5) is updated to:

The batch gradient descent algorithm is introduced. In the case of the initial weight W=W ⁰ , the gradient formula of E(W) is:

为第i次

的梯度。in, is the gradient of the i-th E(W),

for the ith time

gradient.

From this, the update formula of the output weight is:

Among them, Wi ⁺¹ is the output weight of the i+1th iteration, and Wi is the output weight of the ⁱ -th iteration. Each time the output weight is updated, i accumulates 1, that is, i=i+1.

Step 5: Determine whether the training is over

If i≥i _max is satisfied, go to step 6, otherwise go back to step 3.

Step 6: Test the Network

Use the output weight W obtained in the above steps to input test samples to test the network.

The inventive step of the present invention is mainly reflected in:

(1) Aiming at the problem that the ammonia nitrogen concentration is difficult to measure in the sewage treatment process, the present invention designs a effluent NH4-N soft measurement method based on the ELM-SL0 neural network according to the feature of the extreme learning machine's strong nonlinear mapping capability. It has the advantages of high prediction accuracy, strong stability and low maintenance cost.

(2) The present invention combines the L0 regularization method and the batch gradient descent method to train the neural network, effectively pruning the neurons with low contribution in the network, reducing the computing time of the network, and improving the sparseness of the network structure. sex.

Description of drawings

Fig. 1. neural network topology structure diagram of the present invention;

Fig. 2. effluent NH4-N concentration prediction method training root mean square error (RMSE) variation diagram of the present invention;

Figure 3. Change graph of the number of output weights m whose absolute value is less than 0.005 during the training process;

Fig. 4. effluent NH4-N concentration prediction result diagram of the present invention;

Figure 5. Prediction error diagram of effluent NH4-N concentration of the present invention.

Detailed ways

A soft-sensor method for effluent NH4-N based on ELM-SL0 neural network. The main operation process is as follows: First, add the L0 regularization penalty term to the traditional error function to make the unimportant weights approach 0, and then use the batch gradient descent algorithm to The improved error function is updated to enable training and pruning of the network. This method uses the learning ability of the neural network to optimize the output weights according to the training error, eliminate the unimportant output weights, and then predict the ammonia nitrogen concentration in the sewage treatment process to minimize the error and improve the sparsity of the network structure. . It is characterized in that, comprises the following steps:

Step 1: Initialize the network structure and parameters

Step 1.1: Initialize the network structure

Taking temperature, dissolved oxygen, total suspended solids content, pH value and effluent redox potential as input variables, and ammonia nitrogen concentration as output variables, the network structure of the echo state is determined as 5-N-1, where N represents the number of neurons in the reserve pool . In this network, N is 500, that is, the network contains 5 input nodes, 500 reserve pool nodes, and 1 output node.

Step 1.2: Initialize network parameters

u_k表示第k组输入样本，t_k表示第k组实际输出值，

表示输入样本维度为n，L为样本总数；随机初始化网络输入权值W和阈值向量b在(0,1)之间，设置初始输出权值W＝0。Take the sigmoid function as the network activation function G( ), the initial number of iterations i = 0, the maximum number of iterations i _max ≥ 5000, the training sample

u _k represents the kth group of input samples, _tk represents the kth group of actual output values,

Indicates that the input sample dimension is n, and L is the total number of samples; the random initialization network input weight W and the threshold vector b are between (0, 1), and the initial output weight W=0.

Step 2: Use the grid search method to determine the learning rate η and the regularization parameter λ

(1) First, set the regularization parameter to 0, that is, λ=0, then set the search range of the learning rate to [0.0005, 0.01] with a step size of 0.0005, run the program, and select the optimal learning rate with the smallest training error n=0.01.

(2) In the case of the optimal learning rate η=0.01, the search range of the regularization parameter is set to [0.0025, 0.05] with a step size of 0.0025 to ensure that the best sparsity effect is selected without affecting the training error. The optimal regularization parameter λ=0.05.

Step 3: Calculate the network output y _k and the prediction error d _k of the input kth group of samples

For a given activation function G(·), input sample _uk , input weight W and threshold vector b, the output of the hidden layer is obtained as:

Among them, g _j ,1<j<N represents the activation function of the jth neuron in the reserve pool, and W _j u _k ,1<j<N represents the input weight between the jth neuron in the reserve pool and the input layer The inner product of the vector W _j and the input vector _uk , b _j , 1<j<N represents the threshold of the jth neuron in the reserve pool.

Input the kth group of samples, the network output _yk is obtained by the following formula:

y _k =W·G(Wuk ₊ b) (2)

The training error d _k between the expected output t _k of the network and the actual output y _k is defined as:

d _k =t _k -y _k (3)

Step 4: Calculate the gradient of the output weights and update the output weights

The standard mean squared error function is defined as:

in,

Adding the L0 regularization term to the error function, the improved error function is:

为W的L0范数，被定义如下：in,

is the L0 norm of W, defined as follows:

Among them, W _j (1<j<N) is the jth output weight.

However, the L0 norm is a non-convex function, so formula (5) is an NP-hard minimization combinatorial problem. To solve this problem, we use a continuously differentiable function f(·) to approximate the L0 norm, and the function f(γ, W _j ) about W is defined as follows:

的程度，γ较大时，函数f(γ,W_j)对权值向量的修剪程度较低，γ接近0时,函数f(γ,W_j)能够更好修剪权值向量W的非零元素，本专利中γ取0.05。Among them, γ is a positive number, which controls the approximation of f(γ, W _j )

When γ is large, the function f(γ, W _j ) trims the weight vector to a lower degree. When γ is close to 0, the function f(γ, W _j ) can better trim the non-zero value of the weight vector W element, γ is taken as 0.05 in this patent.

From this, the first derivative of f(γ,W _j ) is:

So formula (5) is updated to:

The batch gradient descent algorithm is introduced. In the case of the initial weight W=W ⁰ , the gradient formula of E(W) is:

为第i次E(W)的梯度，

为第i次

的梯度。in,

is the gradient of the i-th E(W),

for the ith time

gradient.

From this, the update formula of the output weight is:

Among them, Wi ⁺¹ is the output weight of the i+1th iteration, and Wi is the output weight of the ⁱ -th iteration. Each time the output weight is updated, i accumulates 1, that is, i=i+1.

Step 5: Determine whether the training is over

If i≥i _max is satisfied, go to step 6, otherwise go back to step 3.

Step 6: Test the Network

Use the output weight W obtained in the above steps to input test samples to test the network.

data sample

Tables 1-12 are the experimental data of the present invention. Table 1-5 is the training input sample: inlet water temperature, dissolved oxygen at the end of aerobic, total suspended solids at the end of aerobic, pH of effluent, redox potential of effluent, Table 6 is the concentration of ammonia nitrogen in the effluent of the training sample, Table 7- 11 is the test input sample: inlet water temperature, dissolved oxygen at the aerobic end, total suspended solids at the aerobic end, effluent pH, effluent redox potential, and Table 12 is the concentration of ammonia nitrogen in the effluent of the test sample.

Training samples:

Table 1. Auxiliary Variable Inlet Water Temperature (°C)

Table 2. Auxiliary Variable Dissolved Oxygen (mg/L)

0.0851 0.2667 0.0428 0.0336 0.0313 0.3165 0.0441 5.5228 0.2654 0.0451 0.0328 0.0399 0.0355 0.0341 0.0655 0.0314 5.7940 0.0317 5.7143 0.3624 0.0474 0.0441 1.2213 0.0743 0.0545 0.4207 5.1883 0.4694 0.0453 0.1624 0.0612 0.0345 6.1271 0.0965 0.0363 0.0312 0.0518 0.0319 0.0664 0.0309 0.5400 0.2701 1.1610 0.6857 0.0768 0.0329 0.0313 0.0467 0.3987 0.0339 0.0715 0.0338 0.9670 3.6627 0.0311 0.4564 0.3942 0.4684 0.5487 0.2066 0.0410 2.5088 0.2566 0.0464 6.1833 0.2890 0.5426 0.3782 0.0302 0.0309 0.0555 0.0373 0.2557 0.4711 0.0615 0.0312 0.0390 0.0416 0.0591 0.0451 0.0345 0.0540 0.4478 0.0637 6.1654 0.0308 0.4508 0.5192 0.1481 0.0396 0.0318 0.0489 2.9631 0.0357 0.0530 0.2282 0.5539 0.0384 0.2232 0.4448 0.0691 0.1172 0.0683 3.0178 0.5287 0.2558 0.0561 0.0309 0.0936 0.0311 0.0356 0.0412 0.0510 0.0448 0.0318 0.0387 5.5628 0.0350 0.0907 0.0363 5.3787 0.0472 0.0364 0.1396 0.8063 0.0686 0.0340 0.4833 0.2687 0.2740 0.2546 0.4329 0.0300 0.0312 0.0411 0.4291 0.0382 0.5351 0.0532 0.0302 0.3301 0.0909 0.0297 0.0346 0.0592 0.0461 0.0492 0.2079 0.0706 0.0334 0.0375 1.6391 0.0683 0.0406 0.0398 0.0562 0.4340 0.0291 0.0337 0.4621 0.2489 0.3703 0.3096 0.2646 0.0706 6.0993 0.4649 0.2659 0.0327 0.1247 1.2662 0.0308 2.1216 0.5378 5.3780 0.0338 0.0397 0.0411 0.0336 0.0870 0.0427 0.0956 0.0505 0.4026 0.0350 0.0286 0.0488 0.0559 0.0318 0.3640 0.0352 0.0455 0.0412 0.4273 0.0640 0.0792 0.0308 1.0497 0.0483 0.0309 0.0582 0.0971 0.0571 0.0478 0.0582 0.0494 0.0317 0.3930 0.0378 0.0410 0.0361 0.0529 0.0565 0.0447 0.7617 0.0963 0.0353 0.3812 0.1343 0.0535 0.0441 0.0692 0.0668 5.7520 0.0403 0.0442 0.0408 0.0799 0.3272 0.0307 0.2365 0.0464 5.4811 0.0769 0.4512 0.5309 0.0657 2.7794 0.0784 0.0617 0.3554 0.0422 0.0582 0.2470 0.4073 5.9548 0.0379 0.0796 0.2997 0.5858 0.0316 2.6852 0.4316 0.4455 0.0421 0.0548 0.0356 5.8531 2.0604 0.1009 0.0310 0.4379 0.0370 0.0432 0.5815 0.0480 0.0787 0.0567 0.2380 0.0486 0.0339 0.0415 0.4889 2.5040 0.0673 0.3274 0.5043 0.1995 0.0365 0.0297 0.0711 0.2404 0.0946 1.5057 0.5498 0.0696 0.0522 0.2974 0.0361 0.1865 0.0309 0.0831 0.0346 0.0683 5.9711 3.4109 0.0823 0.0561 0.1978 1.6931

Table 3. Auxiliary Variable Total Suspended Solids (mg/L)

Table 4. Auxiliary Variable pH

Table 5. Auxiliary Variable Redox Potential

Table 6. Measured NH4-N concentration in effluent (mg/L)

Test sample:

Table 7. Auxiliary Variable Inlet Water Temperature (°C)

26.6664 25.5925 26.0751 26.8655 24.9307 24.9436 25.2516 25.8255 24.9177 25.4691 25.6463 23.6239 26.7961 23.3835 25.5664 25.6231 23.6806 24.1833 25.5388 25.7410 25.9991 25.5576 24.9465 24.9725 24.7418 27.2087 25.8663 26.7136 24.9061 25.6696 24.6813 23.2770 23.8631 24.9667 26.8065 24.4801 24.8874 25.4850 22.9625 25.2472 25.9962 27.1094 25.6289 25.4081 24.2291 25.4720 27.2028 25.3994 25.5649 24.6698 24.9018 24.5476 25.3617 23.7378 24.3022 24.9840 22.8098 25.0100 25.2979 25.0303 27.0784 24.2721 24.4198 24.9826 25.6667 23.0559 23.7307 25.4778 25.3893 25.5126 25.6725 25.4067 25.0534 23.1565 25.0881 24.9119 24.9667 24.9480 24.8686 26.9098 25.9305 23.2841 25.3486 25.2993 24.5188 25.4371 24.9480 27.2933 25.9845 25.4618 25.2212 27.0562 23.1027 24.8614 25.0852 24.5591 25.4153 25.6260 26.9349 25.3501 25.3486 24.3796 25.2936 23.6253 24.5404 24.2047 26.7917 24.6051 25.6158 24.6368 22.9115 24.9047 25.2559 26.5046 27.1331 25.9641 24.9999 26.0429 23.6295 24.6698 24.7908 24.7490 26.0283 23.0630 25.4952 25.1589 23.2032 23.5598 25.6522 23.3310 25.5402 23.1551 23.8745 24.6152 26.7858 25.1633 25.9436 23.6295 25.1532 25.8255 24.8052 25.2950 25.1778 23.9902 27.3334 27.1880 23.4745 26.9556 25.3399 23.4048 25.9539 26.8153 25.6740 25.4458 26.0400 25.1315 24.8225 24.9494 23.4318 25.5053 26.6723 26.8212 23.0956 25.4981 25.2299 23.5769 23.6096 23.1381 23.7006 25.5068 23.5114 25.6405 25.1488 23.8717 26.9763 27.2147 26.9526 25.1040 23.6422 25.1285 25.1300 23.8477 23.4190 23.0191 24.9595 24.1218 23.6338 25.2849 23.6295 26.7652

Table 8. Auxiliary Variable Dissolved Oxygen (mg/L)

Table 9. Auxiliary Variable Total Suspended Solids (mg/L)

2.8203 2.9460 2.8678 2.8202 2.5611 2.5829 2.8432 2.8892 2.5314 3.0358 2.9424 2.5450 2.7539 2.3089 2.9585 2.9651 2.6572 2.4949 2.9497 2.8061 2.8056 2.9405 3.1266 2.5765 3.0128 2.8251 2.7974 2.7827 3.0233 2.8753 2.8377 2.2740 2.4693 2.8942 2.8151 2.4982 3.2238 3.0289 2.2692 2.7131 2.7684 3.1727 2.9420 3.0138 2.4700 2.9379 2.8182 2.9699 2.9699 2.9696 2.5363 2.4573 2.9005 2.4428 2.4121 2.4505 2.3100 2.8173 2.8868 3.0912 2.8053 2.5025 3.1527 2.9324 2.9416 2.3157 2.3829 2.8973 3.0728 3.1456 2.8617 3.0857 3.0329 2.2105 2.8024 2.4376 2.6005 2.9275 2.4709 2.7997 2.8238 2.4789 2.9423 2.9435 3.1618 2.9997 2.8217 2.7176 2.7800 3.0250 2.7410 2.8029 2.2935 2.3933 2.4443 3.0369 3.0349 2.9285 2.7858 2.9329 3.0151 2.3839 2.7219 2.5113 3.0535 2.4245 2.7999 2.9979 2.9201 2.4916 2.3119 2.5664 2.7491 2.8509 2.8060 2.7973 2.9019 2.8119 2.5754 3.1621 2.4192 2.7953 2.8213 2.3439 2.9265 2.4068 2.2200 2.3514 2.8738 2.2805 2.8895 2.4196 2.5045 2.4345 2.7979 2.8979 2.8572 2.4255 2.6941 2.8306 2.8052 2.7744 2.7306 2.4820 2.8343 2.8523 2.3883 2.8536 2.9709 2.5321 2.8260 2.7556 2.8632 3.1004 2.8337 3.0059 2.4971 2.7832 2.3155 3.0640 2.8295 2.8165 2.4155 3.0494 2.9023 2.3655 2.4784 2.4161 2.4331 3.0726 2.4347 2.9480 2.7790 2.5286 2.7725 2.8985 2.7998 2.9557 2.5519 2.8087 2.4082 2.2835 2.4440 2.2668 2.5590 2.6305 2.3938 2.7067 2.4866 2.9067

Table 10. Auxiliary Variable pH

Table 11. Auxiliary Variable Redox Potential

-5.3838 38.3272 -45.9542 -122.6730 -196.9560 -196.1870 -126.8390 -40.0577 -194.4560 16.3435 35.3790 -170.4860 -87.8065 -163.3710 33.1357 32.1744 -168.6270 -190.8670 0.0641 -66.2715 -21.5991 29.9952 19.7404 -194.4560 48.0052 -17.4331 -41.2755 -97.8049 46.8515 36.0199 -88.8961 -165.2940 -163.0510 27.6238 -5.7042 -200.9940 18.2663 19.3559 -199.9040 -170.1650 -46.2106 -115.4940 33.8408 7.9475 -161.0000 34.9303 -67.2329 45.9542 -3.0764 41.2114 -196.8920 -205.3520 36.6608 -154.1420 -158.5640 -202.5960 -170.1650 -146.5150 30.4439 21.3427 -16.7281 -161.0640 18.6509 30.7643 35.3149 -194.8410 -155.1680 29.9952 8.1397 17.8177 -15.5103 19.4200 45.3133 -169.7810 -142.6700 -205.0960 -187.0860 26.4701 -196.5710 -5.7683 -45.6337 -172.3440 15.8949 30.4439 19.5482 6.8579 -27.8161 -16.5358 -10.2548 4.8069 -172.7930 -117.9940 -161.3850 -205.9290 -202.7240 30.3798 28.7775 34.0971 -13.5876 21.0223 9.0370 -190.8030 -163.2430 -170.6140 20.7018 -161.3200 -15.5103 36.0199 34.5458 -201.8910 -165.9990 -197.0200 -155.4880 -8.7807 -112.1620 -13.3312 33.3280 -12.4980 -171.9600 18.9713 -196.6990 -63.9001 -12.8185 -158.5000 31.3412 -202.3400 -174.0750 -157.7950 -61.3364 -164.5250 37.6863 -164.0120 -163.4350 -206.2490 -76.3340 -138.9520 -18.4586 -152.8600 -178.4330 -38.0068 -55.9526 -160.8720 -176.7030 -162.3460 -16.7922 -73.8344 -162.6020 -121.6470 46.0183 -157.5390 -39.7373 -89.2806 39.5450 19.4200 -6.0888 44.9287 -196.6990 -102.4200 -163.0510 18.0740 -20.3814 -99.7277 -161.7690 17.5613 -135.4270 -159.9750 -151.5140 -173.4980 -177.4080 18.6509 -161.9610 35.0585 -108.6370 -186.5730 -5.2556 -71.1425 -76.8467 37.4940 -172.8570 -150.6170 -202.7880 -145.4900 -157.8590 -201.2500 -194.5840 -161.6410 -160.5510 -157.2830 -174.7800 -120.7500

Table 12. Measured NH4-N concentration in effluent (mg/L)

Claims (1)

1. a kind of effluent NH based on ELM-SL0 neural network -N soft measurement method, is characterized in that, comprises the following steps: Step 1: Initialize the network structure and parameters Step 1.1: Initialize the network structure Taking temperature, dissolved oxygen, total suspended solids content, pH value and effluent redox potential as input variables, and ammonia nitrogen concentration as output variables, the network structure of the echo state is determined as 5-N-1, where N represents the number of nodes in the reserve pool; The number N of the reserve pool nodes of a typical echo state network is 50≤N≤1000; Step 1.2: Initialize network parameters Take the sigmoid function as the network activation function G( ), determine the initial number of iterations i=0, the maximum number of iterations i _max ≥ 5000, and the training samples

u _k represents the kth group of input samples, _tk represents the kth group of actual output values,

Indicates that the input sample dimension is n, and L is the total number of samples; randomly initialize the network input weight W and the threshold vector b between (0, 1), and set the initial output weight W=0; Step 2: Use the grid search method to determine the learning rate η and the regularization parameter λ (1) First, set the regularization parameter to 0, that is, λ=0, then set the search range of the learning rate to [0.0005, 0.01] with a step size of 0.0005, run the program, and select the optimal learning rate η with the smallest training error ; (2) In the case of the optimal learning rate η, the search range of the regularization parameter is set to [0.0025, 0.05] with a step size of 0.0025 to ensure that the optimal regularization parameter with the best sparsity effect is selected without affecting the training error. λ; Step 3: Calculate the network output y _k and the prediction error d _k of the input kth group of samples For a given activation function G(·), input sample _uk , input weight W and threshold vector b, the output of the hidden layer is obtained as:

Among them, g _j ,1<j<N represents the activation function of the jth neuron in the reserve pool, and W _j u _k ,1<j<N represents the input weight between the jth neuron in the reserve pool and the input layer The inner product of the vector W _j and the input vector _uk , b _j , 1<j<N represents the threshold of the jth neuron in the reserve pool; Input the kth group of samples, the network output _yk is obtained by the following formula: y _k =W·G(Wuk ₊ b) (2) The training error d _k between the expected output t _k of the network and the actual output y _k is defined as: d _k =t _k -y _k (3) Step 4: Calculate the gradient of the output weights and update the output weights The standard mean squared error function is defined as:

in,

Adding the L0 regularization term to the error function, the improved error function is:

in,

is the L0 norm of W, defined as follows:

Among them, W _j , 1<j<N is the jth output weight; However, the L0 norm is a non-convex function, so formula (5) is an NP-hard minimization combinatorial problem; using a continuously differentiable function f( ) to approximate the L0 norm, the function f(γ with respect to W , W _j ) is defined as follows:

Among them, γ is a positive number, and γ is taken as 0.05; thus, the first derivative of f(γ, W _j ) is:

So formula (5) is updated to:

The batch gradient descent algorithm is introduced. In the case of the initial weight W=W ⁰ , the gradient formula of E(W) is:

in,

is the gradient of the i-th E(W),

for the ith time

the gradient of ; From this, the update formula of the output weight is:

Among them, Wi ⁺¹ is the output weight of the i+1th iteration, and Wi is the output weight of the ⁱ -th iteration; every time the output weight is updated, i accumulates 1, that is, i=i+1; Step 5: Determine whether the training is over If i ≥ i _max , go to step 6, otherwise go back to step 3; Step 6: Test the Network Using the output weights W obtained in the above steps, input test samples to test the network.

Images