Abstract:
In this present disclosure, a computing implemented method is designed for predicting the effluent total nitrogen concentration (TN) in an urban wastewater treatment process (WWTP). The technology of this present disclosure is part of advanced manufacturing technology and belongs to both the field of control engineer and environment engineer. To improve the predicting efficiency, a recurrent self-organizing RBF neural network (RSORBFNN) can adjust the structure and parameters simultaneously. This RSORBFNN is developed to implement this method, and then the proposed RSORBFNN-based method can predict the effluent TN with acceptable accuracy. Moreover, online information of effluent TN may be predicted by this computing implemented method to enhance the quality monitoring level to alleviate the current situation of wastewater and to strengthen the management of WWTP.

Description:
CROSS REFERENCE TO RELATED PATENT APPLICATIONS 
       [0001]    This application claims priority to Chinese Patent Application No. 201610606146.X, filed on Jul. 28, 2016, entitled “a method for effluent total nitrogen based on a recurrent self-organizing RBF neural network,” which is hereby incorporated by reference in its entirety. 
       Technical Field 
       [0002]    In this present disclosure, a computing implemented method is designed for predicting the effluent total nitrogen TN concentration (TN) in the urban wastewater treatment process (WWTP) by a recurrent self-organizing RBF neural network (RSORBFNN). To improve the measurement efficiency, the RSORBFNN can adjust the structure and parameters concurrently: a growing and pruning algorithm is proposed to design the structure, and an adaptive second-order algorithm is utilized to train the parameters. The technology of this present disclosure is part of advanced manufacturing technology and belongs to both the field of control engineer and environment engineer. 
       Background 
       [0003]    The urban WWTP not only guarantees the reliability and stability of the wastewater treatment system but also meets the water quality national discharge standard. However, the influence factors are various for effluent TN of wastewater treatment process and the relationship between different influencing factors are complex. Therefore, it is hard to make real-time detecting for effluent TN, which seriously affected the stable operation of the urban WWTP. The computing implemented a method for effluent TN, based on RSORBFNN, is helpful to improve the efficiency, strengthen delicacy management and ensure water quality effluent standards of urban WWTP. It has better economic benefit as well as significant environmental and social benefits. Thus, the research achievements have wide application prospect in this present disclosure. 
         [0004]    The control target of urban WWTP is to make the water quality meet the national discharge standards, mainly related to the parameters of effluent TN, chemical oxygen demand (COD), effluent suspended solids (SS), ammonia nitrogen (NH4-N), biochemical oxygen demand (BOD) and effluent total phosphorus (TP). Effluent TN refers to the sum of all the nitrogen pollution of the water after dealing with the sewage treatment plant process facilities, mainly for the ammonia nitrogen, nitrate nitrogen, inorganic nitrogen, protein, amino acid and organic amine organic nitrogen combined. According to statistics, nitrogen fixation rate of about 150 million tons per year in nature and chemical nitrogen fertilizer production rate of about 5000˜6000 tons a year. If nature denitrification reaction failed to complete the nitrogen cycle, too much nitrogen compounds and the ammonia nitrogen nutrient caused a significant number of algae in the water, the plants breeding, appearance of eutrophication status. To curb the trend of worsening of water environment, many sewage treatment facilities have spent a large sum of money to build and put into operation in the country, the cities, and towns. The general method for determination is the alkaline potassium persulfate UV spectrophotometry and molecular absorption spectrometry. However, the determination of total nitrogen TN is often offline and can&#39;t realize the effluent TN real-time measurement, which led directly to the sewage treatment process is hard to achieve closed loop control. Moreover, it is a big challenge for detection due to a significant amount of pollutants in wastewater and different content. Developing new hardware measuring instrument, although directly solving various wastewater treatment process variables and the detection problem of water quality parameters, due to the very complex organic matter in sewage, research and development of the new sensor will be a significant cost and a time-consuming project. Hence, the new method presented to solve the problem of the real-time measurement of the process parameters of WWTP has become an important topic to research in the field of wastewater control engineering and has important practical significance. 
         [0005]    To obtain more reliable information on effluent TN in urban WWTP, we have investigated a computing implemented method based on the RSORBFNN. The neural network uses competitiveness of the hidden neuron to determine whether to add or delete the hidden neurons and to use an adaptive second order algorithm to ensure the accuracy of RSORBFNN. The objective of this present disclosure is to develop a computing implemented method for estimating the effluent TN online and with high precision. 
       SUMMARY 
       [0006]    A computing implemented method is designed for the effluent TN based on an RSORBFNN in this present disclosure. For this computing implemented method, the inputs are those variables that are easy to measure and the outputs are estimates of the effluent TN. By constructing the RSORBFNN, it realizes the mapping between auxiliary variables and effluent TN. Also, the method can obtain a real-time measurement of effluent TN, solve the problems of long measurement cycle for effluent TN. 
         [0007]    A computing implemented method for the effluent TN based on an RSORBFNN, its characteristic and steps include the following steps: 
         [0008]    (1) Determine the input and output variables of effluent TN: 
         [0009]    For sewage treatment process of activated sludge system, the variables of sewage treatment process are analyzed and select the input variables of effluent TN soft-computing model: ammonia nitrogen —NH 4 —N, nitrate nitrogen —NO 3 —N, effluent suspended solids—SS, biochemical oxygen demand—BOD, total phosphorus—TP, The output value of soft-computing model is detected effluent TN. 
         [0010]    (2) Initialize RSORBFNN 
         [0011]    The initial structure of RSORBFNN consists of three layers: an input layer, hidden layer, and an output layer. There are 5 neurons in the input layer, J neurons in the hidden layer and 1 neuron in the output layer; J&gt;2 is a positive integer. Connection weights between input layer and hidden layer are assigned 1, the feedback weights between hidden layer and output layer randomly assign values, the assignment internal is [1, 1]; the number of the training sample is P, and the input vector of RSORBFNN is x(t)=[x 1 (t), x 2 (t), x 3 (t), x 4 (t), x 5 (t)] at time t; y(t) is the output of RSORBFNN, and y d (t) is the real value of effluent TN at time t, respectively; The output of RSORBFNN can be described: 
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         [0000]    wherein w2 j(t) is the output weight between the jth hidden neuron and the output neuron, w 2 (t)=[w2 1(t), w2 2(t), . . . , w2 J(t)] T  is the output weight vector between hidden neurons and output neuron, j=1, 2, . . . , J, J is the number of hidden neurons, and θ j (t) is the output value of the jth hidden neuron which is usually defined by a normalized Gaussian function: 
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         [0000]    wherein ||h j -c j || represents the Euclidean distance between h j  and c j , c j (t)=[c 1j (t), c 2j (t), . . . , c 5j (t)] T  and σ j  represent the center vector and radius of the jth hidden neuron, respectively; c ij (t) is ith element of jth hidden neuron, and h j  is the input vector of jth hidden neuron 
         [0000]        h   j ( t )=[ h   j1 ( t ),  h   j2 ( t ), . . . ,  h   j1 ( t )],   (3)
 
         [0000]        h   ij ( t )= u   j ( t ),   (4)
 
         [0000]    wherein w1j(t) is the feedback weight connecting the jth hidden neuron with the output neuron, w 1 (t)=[w1 1(t), w1 2(t), . . . , w1 J(t)] T  is the feedback weight vector connecting the jth hidden neuron with the output neuron and y(t-1) is the output value of RSORBFNN at time t-1. 
         [0012]    The training error function of RSORBFNN is defined 
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         [0000]    wherein P is the number of the training samples. 
         [0013]    (3) Train RSORBFNN 
         [0014]    1) Given RSORBFNN, the initial number of hidden layer neurons is J; J&gt;2 is a positive integer. The input of RSORBFNN is x(1), x(2), . . . , x(t), . . . , x(P), the desired output is y d (1), y d (2), . . . , y d (t), . . . , y d (P); the desired error value is set to E d , E d ∈(0, 0.01), the initial center is c j (1)∈(−2, 2), the initial width value σ j (1)∈(0, 1), the initial feedback weight is w1 j(1)∈(0, 1), and the initial weight is w2 j(1)∈(0, 1), j=1, 2, . . . , J; 
         [0015]    2) Set the learning step s=1; 
         [0016]    3) t=s, calculate the output y(t) of RSORBFNN, update the weight, width, and center of RSORBFNN using the rule: 
         [0000]      Θ( t +1)=Θ( t )+(Ψ( t )+η( t )× I ) −1 ×Ω( t ),   (6)
 
         [0000]    where Θ(t)=[w 1 (t), w 2 (t), C(t), σ(t)] is the variable vector at time t, Ψ(t) is quasi 
         [0017]    Hessian matrix at time t, I is the identity matrix, η(t) is the adaptive learning rate defined as: 
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         [0000]    wherein μ(t) is the adapting factor at time t, and the initial value of μ(t) is μ(1)=1, β max (t) and β min (t) are the maximum and minimum eigenvalues of Ψ(t), respectively; 0&lt;β min (t)&lt;β max (t), 0&lt;η(t)&lt;1 and η(1)=1. Θ(t) contains four kinds of variables: the feedback connection weight vector w 1 (t) at time t, the connection weight vector w 2 (t) at time t, the centre matrix C(t)=[c 1 (t), c 2 (t), . . . , c j (t)] T  and width vector σ(t)=[σ 1 (t), σ 2 (t), . . . , σ j (t)] T  at time t. 
         [0000]      Θ(1)=[ w   1 (1),  w   2 (1),  C (1), σ(1)],   (9)
 
         [0000]    the quasi Hessian matrix Ψ(t) and the gradient vector Ω(t) are accumulated as the sum of related submatrices and vectors: 
         [0000]      Ψ( t )= j   T ( t ) j ( t ),   (10)
 
         [0000]      Ω( t )=j T   e ( t ),   (11)
 
         [0000]        e ( t )= y   d ( t )− y ( t ),   (12)
 
         [0018]    e(t) is the approximating error at time t, y d (t) is the desired output and y(t) is the network output at time t, and the Jacobian-vector j(t) is calculated as: 
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         [0019]    4) t&gt;3, calculate competitiveness of the jth hidden neuron: 
         [0000]    wherein cp j (t) is the competitiveness of the jth hidden neuron, ρ denotes the correlation coefficient between the hidden layer output and network output, ρ∈(0, 1), f j (t) is the active state of the jth hidden neuron, σ j (t) is the width of the jth hidden neuron; the active state f j (t) is defined as 
         [0000]      f j ( t )=χ −|   j (t)−c j (t)|,   (15)
 
         [0000]    wherein χ∈(1,2), and f(t)=[f 1 (t), f 2 (t), . . . , f j (t)], the correlation coefficient ρ j (t) at time t is calculated as 
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         [0000]    wherein the correlation coefficient of hidden neurons A j (t)=w2 j(t)θ j  (t), the correlation coefficient of output layer B(t)=y(t), Ā(t) is the average value of correlation coefficient of hidden neurons at time t,    B (t)  is the average value of correlation coefficient of output layer at time t; 
         [0020]    5) Adjust the structure of RSORBFNN: 
         [0021]    If the competitiveness of the jth hidden neuron and training error at time t and t+τ satisfy 
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         [0000]    denotes the value of j when cp j (t) owns the maximum value. E(t) and E(t+τ) are the training errors at times t and t+τ, respectively, τ is a time interval, τ&gt;2, and ε is the preset threshold, ε∈(0,0.01). Add one hidden neuron, and the number of hidden neurons is M 1 =J+1. Otherwise, the structure of RSORBFNN will be not adjusted, M 1 =J. 
         [0022]    When the competitiveness of the jth hidden neuron satisfies 
         [0000]        cp   j ( t )&lt;ξ,   (19)
 
         [0000]    wherein ξ is the preset pruning threshold, ξ∈(0, E d ), E d  is the preset error, E d ∈(0,0.01]. The jth hidden neuron will be pruned, the number of hidden neurons will be updated M 2 =M 1 −1. Otherwise, the structure of RSORBFNN will be not adjusted, M 2 =M 1 . 
         [0023]    6) Increase 1 learning step for s, if s&lt;P, go to step 3); if s=N, proceed to step 7). 
         [0024]    7) Per Eq. (5), calculate the performance of RSORBFNN. If E(t)≧E d , proceed to step 3); if E(t)&lt;E d , stop the training process. 
         [0025]    (4) Effluent TN concentration prediction; 
         [0026]    The testing samples are used as the input of RSORBFNN, the output of RSORBFNN is the soft-computing values of effluent TN. 
         [0000]    The Novelties of this Present Disclosure Contain: 
         [0027]    (1) To detect the effluent TN online and with acceptable accuracy, a computing implemented method is developed in this present disclosure. The results demonstrate that the effluent TN trends in WWTP can be predicted with acceptable accuracy using the NH 4 —N, NO 3 —N, effluent SS, BOD, TP as input variables. This computing implemented method can predict the effluent TN with acceptable accuracy and solve the problem that the effluent TN ‘s hard to be measured online. 
         [0028]    (2) Since wastewater treatment process has the features of a complicated mechanism, and many influential factors, it was difficult to build a precise mathematical model to predict the effluent TN. Hence, the computing implemented method is based on the RSORBFNN in this present disclosure, which is proposed to predict it. The advantages of the proposed RSORBFNN are that it can simplify and accelerate the structure optimization process of the recurrent neural network, and can predict the effluent TN accurately. Moreover, the predicting performance shows that the RSORBFNN-based computing implemented method can adapt well to environment change. Therefore, this computing implemented method performs well in the whole operating space. 
         [0029]    Attention: this present disclosure utilizes five input variables in this RSORBFNN method to predict the effluent TN. In fact, it is in the scope of this present disclosure that any of the variables: the NH 4 —N, NO 3 —N, effluent SS, BOD, TP are used to predict the effluent TN. Moreover, this RSORBFNN method is also able to predict the others variables in urban WWTP. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0030]      FIG. 1  shows the structure of computing implemented method based on the RSORBFNN in this present disclosure. 
           [0031]      FIG. 2  shows the training result of the computing implemented method. 
           [0032]      FIG. 3  shows the training error of the computing implemented method. 
           [0033]      FIG. 4  shows the predicting result of the computing implemented method. 
           [0034]      FIG. 5  shows the predicting error of the computing implemented method. 
       
    
    
     DETAILED DESCRIPTION 
       [0035]    Various A computing implemented method is developed to predict the effluent TN based on an RSORBFNN in this present disclosure. For this computing implemented method, the inputs are those variables that are easy to measure and the outputs are estimates of the effluent TN. In general, the procedure of computing implemented method consists of three parts: data acquisition, data pre-processing and model design. For this present disclosure, an experimental hardware is set up as shown in  FIG. 1 . The historical process data are routinely acquired and stored in the data acquisition system. The input-output water quality data can be easily retrieved, measured during the year 2011. The variables whose data are easy to measure by the instruments consist of NH 4 —N, NO 3 —N, effluent SS, BOD, TP and effluent TN were used as experimental samples. After deleting abnormal data, 100 groups were obtained and normalized, 60 groups were used as training data, whilst the remaining 40 were used as testing data. 
         [0036]    This present disclosure adopts the following technical scheme and implementation steps: 
         [0037]    A computing implemented method for the effluent TN based on an RSORBFNN, its characteristic and steps include the following steps: 
         [0038]    (1) Determine the input and output variables of effluent TN: 
         [0039]    For sewage treatment process of activated sludge system, the variables of sewage treatment process are analyzed and select the input variables of effluent TN soft-computing model: ammonia nitrogen—NH 4 —N, nitrate nitrogen—NO 3 —N, effluent suspended solids—SS, biochemical oxygen demand—BOD, total phosphorus—TP, The output value of soft-computing model is detected effluent TN. 
         [0040]    (2) Initialize RSORBFNN 
         [0041]    The initial structure of RSORBFNN consists of three layers: input layer, hidden layer, and output layer. There are 5 neurons in the input layer, J neurons in the hidden layer and 1 neuron in the output layer; J&gt;2 is a positive integer. Connection weights between input layer and hidden layer are assigned 1, the feedback weights between hidden layer and output layer randomly assign values, the assignment internal is [1, 1]; the number of the training sample is P, and the input vector of RSORBFNN is x(t)=[x 1 (t), x 2 (t), x 3 (t), x 4 (t), x 5 (t)] at time t; y(t) is the output of RSORBFNN, and y d (t) is the real value of effluent TN at time t, respectively; The output of RSORBFNN can be described: 
         [0000]    
       
         
           
             
               
                 
                   
                     
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                           j 
                           = 
                           1 
                         
                         J 
                       
                        
                       
                         
                           
                             w 
                             j 
                             2 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                          
                         
                           
                             θ 
                             j 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein w2 j(t) is the output weight between the jth hidden neuron and the output neuron, w 2 (t)=[w2 1(t), w2 2(t), . . . , w2 J(t)] T  is the output weight vector between hidden neurons and output neuron, j=1, 2, . . . , J, J is the number of hidden neurons, and θ j (t) is the output value of the jth hidden neuron which is usually defined by a normalized Gaussian function: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         θ 
                         j 
                       
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       e 
                       
                         
                           
                             - 
                             
                               
                                  
                                 
                                   
                                     
                                       h 
                                       j 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       c 
                                       j 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                                  
                               
                               2 
                             
                           
                           / 
                           2 
                         
                          
                         
                           
                             σ 
                             j 
                             2 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein ||h j -c j || represents the Euclidean distance between h j  and c j , c j (t)=[c 1j (t), c 2j (t), . . . , c 5j (t)] T  and σ j  represent the center vector and radius of the jth hidden neuron, respectively; c ij (t) is ith element of jth hidden neuron, and h j  is the input vector of jth hidden neuron 
         [0000]        h   j ( t )=[ h   j1 ( t ),  h   j2 ( t ), . . . ,  h   j1 ( t )],   (22)
 
         [0000]        h   ij ( t )= u   i ( t ),   (23)
 
         [0000]    wherein w1 j(t) is the feedback weight connecting the jth hidden neuron with the output neuron, w 1 (t)=[w1 1(t), w1 2(t), . . . , w1 J(t)] T  is the feedback weight vector connecting the jth hidden neuron with the output neuron and y(t-1) is the output value of RSORBFNN at time t-1. 
         [0042]    The training error function of RSORBFNN is defined 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         P 
                       
                        
                       
                         
                           ∑ 
                           
                             t 
                             = 
                             1 
                           
                           P 
                         
                          
                         
                           
                             ( 
                             
                               
                                 
                                   y 
                                   d 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               - 
                               
                                 y 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
         [0043]    wherein P is the number of the training samples. 
         [0044]    (3) Train RSORBFNN 
         [0045]    1) Given RSORBFNN, the initial number of hidden layer neurons isJ;J&gt;2 is a positive integer. The input of RSORBFNN is x(1), x(2), . . . , x(t), . . . , x(P), the desired output is y d (1), y d (2), . . . , y d (t), . . . , y d (P); the desired error value is set to E d , E d ∈(0, 0.01), the initial center is CJ(1)∈(−2, 2), the initial width value σ j (1) ∈(0, 1), the initial feedback weight is w1 j(1)∈(0, 1), and the initial weight is w2 j(1)∈(0, 1), j=1, 2, . . . , J; 
         [0046]    2) Set the learning step s=1; 
         [0047]    3) t=s, calculate the output y(t) of RSORBFNN, update the weight, width, and center of RSORBFNN using the rule: 
         [0000]      Θ( t +1)=Θ( t )+(Ψ( t )+η( t )× I ) −1 ×Ω( t ),   (25)
 
         [0000]    where Θ(t+1)=[w 1 (t), w 2 (t), C(t), σ(t)[ is the variable vector at time t, Ψ(t) is quasi 
         [0048]    Hessian matrix at time t, I is the identity matrix, η(t) is the adaptive learning rate defined as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       η 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         μ 
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                        
                       
                         η 
                          
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       μ 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               
                                 
                                   β 
                                   max 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               + 
                               
                                 η 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                           / 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 
                                   β 
                                   max 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           
                             β 
                             min 
                           
                            
                           
                             ( 
                             
                               t 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                       
                         η 
                          
                         
                           ( 
                           
                             t 
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein μ(t) is the adapting factor at time t, and the initial value of μ(t) is μ(1)=1, β max (t) and β min (t) are the maximum and minimum eigenvalues of Ψ(t), respectively; 0&lt;β min (t)&lt;β max (t), 0&lt;η(t)&lt;1 and η(1)=1. Θ(t) contains four kinds of variables: the feedback connection weight vector w 1 (t) at time t, the connection weight vector w 2 (t) at time t, the centre matrix C(t)=[c 1 (t), c 2 (t), . . . , c j (t)] T  and width vector σ(t)=[σ 1 (t), σ 2 (t), . . . , σ j (t)] T  at time t. 
         [0000]      Θ(1)=[ w   1 (1),  w   2 (1),  C (1), σ(1)],   (28)
 
         [0049]    the quasi Hessian matrix Ψ(t) and the gradient vector Ω(t) are accumulated as the sum of related submatrices and vectors: 
         [0000]      Ψ( t )= j   T ( t ) j ( t ),   (29)
 
         [0000]      Ω( t )= j   T   e ( t ),   (30)
 
         [0000]        e ( t )= y   d ( t )− y ( t ),   (31)
 
         [0050]    e(t) is the approximating error at time t, y d (t) is the desired output and y(t) is the network output at time t, and the Jacobian-vector j(t) is calculated as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       j 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       [ 
                       
                         
                           
                             ∂ 
                             
                               e 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                           
                             ∂ 
                             
                               
                                 w 
                                 1 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         , 
                         
                           
                             ∂ 
                             
                               e 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                           
                             ∂ 
                             
                               
                                 w 
                                 2 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         , 
                         
                           
                             ∂ 
                             
                               e 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                           
                             ∂ 
                             
                               C 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         , 
                         
                           
                             ∂ 
                             
                               e 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                           
                             ∂ 
                             
                               σ 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
         [0051]    4) t&gt;3, calculate competitiveness of the jth hidden neuron: 
         [0000]        cp   j ( t )=ρ f   j ( t )σ j ( t ),  j =1, 2, . . . , J ,   (33)
 
         [0000]    wherein cp j (t) is the competitiveness of the jth hidden neuron, ρ denotes the correlation coefficient between the hidden layer output and network output, ρ∈(0, 1),f i (t) is the active state of the jth hidden neuron, σ j (t) is the width of the jth hidden neuron; the active state f j (t) is defined as
 
wherein χ∈(1,2), and f(t)=[f 1 (t), f 2 (t), . . . , f j (t)], the correlation coefficient  A M at time t is calculated as
 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ρ 
                         j 
                       
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           3 
                         
                          
                         
                           
                             [ 
                             
                               
                                 
                                   A 
                                   j 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     k 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   A 
                                   _ 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             ] 
                           
                            
                           
                             [ 
                             
                               
                                 B 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     k 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   B 
                                   _ 
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             3 
                           
                            
                           
                             
                               
                                 [ 
                                 
                                   
                                     
                                       A 
                                       j 
                                     
                                      
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         k 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       A 
                                       _ 
                                     
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                                 ] 
                               
                               2 
                             
                              
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 3 
                               
                                
                               
                                 
                                   [ 
                                   
                                     
                                       B 
                                        
                                       
                                         ( 
                                         
                                           t 
                                           - 
                                           k 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         B 
                                         _ 
                                       
                                        
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                   
                                   ] 
                                 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein the correlation coefficient of hidden neurons A j (t)=w2 j(t) θ j (t), the correlation coefficient of output layer B(t)=y(t), Ā(t) is the average value of correlation coefficient of hidden neurons at time t,    B (t)  is the average value of correlation coefficient of output layer at time t; 
         [0052]    5) Adjust the structure of RSORBFNN: 
         [0053]    If the competitiveness of the jth hidden neuron and training error at time t and t+τ satisfy 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         E 
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                       - 
                       
                         E 
                          
                         
                           ( 
                           
                             t 
                             + 
                             τ 
                           
                           ) 
                         
                       
                     
                     ≤ 
                     ɛ 
                   
                   , 
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
             
               
                 
                   
                     j 
                     = 
                     
                       arg 
                        
                       
                           
                       
                        
                       
                         
                           max 
                           
                             1 
                             ≤ 
                             j 
                             ≤ 
                             J 
                           
                         
                          
                         
                           ( 
                           
                             
                               cp 
                               j 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     where 
                      
                     
                         
                     
                      
                     arg 
                      
                     
                       
                         max 
                         
                           1 
                           ≤ 
                           j 
                           ≤ 
                           J 
                         
                       
                        
                       
                         ( 
                         
                           
                             cp 
                             j 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
         [0000]    denotes the value of jwhen cp j (t) obtain the maximum value. E(t) and E(t+τ) are the training errors at times t and t+τ, respectively, τ is a time interval, τ=5, and ε is the preset threshold, ε=0.001. Add one hidden neuron, and the number of hidden neurons is M 1 =J+1. Otherwise, the structure of RSORBFNN will be not adjusted, M 1 =J. 
         [0054]    When the competitiveness of the jth hidden neuron satisfies 
         [0000]        cp   j ( t )&lt;ξ,   (38)
 
         [0000]    wherein ξ is the preset pruning threshold, ξ∈(0, E d ), E d  is the preset error, E d =0.002. The jth hidden neuron will be pruned, the number of hidden neurons will be updated M 2 =M 1 −1. Otherwise, the structure of RSORBFNN will be not adjusted, M 2 =M 1 . 
         [0055]    6) Increase 1 learning step for s, if s&lt;P, go to step 3); if s=N, proceed to step 7). 
         [0056]    7) According to Eq. (24), calculate the performance of RSORBFNN. If E(t)≧E d , proceed to step 3); if E(t)&lt;E d , stop the training process. 
         [0057]    The training result of the computing implemented method for effluent TN is shown in  FIG. 2 . X-axis indicates the number of samples. Y axis shows the effluent TN. The unit of Y axis is mg/L. The solid line presents the real values of effluent TN. The dotted line shows the outputs of computing implemented method in the training process. The errors between the true values and the outputs of intelligent detecting method in the training process are shown in  FIG. 3 . X-axis indicates the number of samples. Y axis shows the training error. The unit of Y axis is mg/L. 
         [0058]    (4) Effluent TN concentration prediction; 
         [0059]    The testing samples are used as the input of RSORBFNN, and the output of RSORBFNN is the soft-computing values of effluent TN. The predicting result is shown in  FIG. 4 . X-axis indicates the number of testing samples. Y axis shows the effluent TN. The unit of Y axis is mg/L. The solid line presents the real values of effluent TN. The dotted line shows the outputs of intelligent detecting method in the testing process. The errors between the true values and the outputs of intelligent detecting method in the testing process are shown in  FIG. 5 . X-axis shows the number of samples. Y axis shows the testing error. The unit of Y axis is mg/L. 
         [0060]    Tables 1-14 show the experimental data in this present disclosure. Tables 1-6 show the training samples of biochemical oxygen demand - BOD, ammonia nitrogen—NH 4 —N, nitrate nitrogen—NO 3 —N, effluent suspended solids —SS, total phosphorus—TP real effluent TN. Table 7 shows the outputs of the RSORBFNN in the training process. Tables 8-14 show the testing samples of biochemical oxygen demand—BOD, ammonia nitrogen—NH 4 —N, nitrate nitrogen —NO 3 —N, effluent suspended solids—SS, total phosphorus—TP and real effluent TN. Table 14 shows the outputs of the RSORBFNN in the predicting process 
         [0061]    Training samples are provided as follow. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 The training samples of biochemical oxygen demand-BOD (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 192 
                 222 
                 201 
                 264 
                 195 
                 209 
                 260 
                 197 
                 206 
                 289 
               
               
                 188 
                 350 
                 210 
                 204 
                 200 
                 180 
                 230 
                 338 
                 200 
                 330 
               
               
                 320 
                 232 
                 260 
                 240 
                 218 
                 316 
                 310 
                 172 
                 210 
                 316 
               
               
                 310 
                 244 
                 248 
                 168 
                 204 
                 145 
                 170 
                 142 
                 190 
                 260 
               
               
                 200 
                 240 
                 280 
                 174 
                 250 
                 136 
                 222 
                 204 
                 239 
                 242 
               
               
                 310 
                 232 
                 290 
                 210 
                 144 
                 214 
                 251 
                 158 
                 262 
                 290 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 The training samples of ammonia nitrogen-NH4—N (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 64.3 
                 69.4 
                 72.6 
                 71.7 
                 71.5 
                 63.5 
                 70.7 
                 68.4 
                 64.3 
                 68.3 
               
               
                 71.9 
                 64.3 
                 63.8 
                 56.9 
                 44.6 
                 64.9 
                 68.9 
                 76.9 
                 63.5 
                 70 
               
               
                 60.3 
                 60 
                 72.1 
                 69.7 
                 70.5 
                 66.1 
                 62.2 
                 58.8 
                 60.5 
                 63.5 
               
               
                 65.7 
                 59.4 
                 54.8 
                 60 
                 59.1 
                 63.7 
                 64.5 
                 58.1 
                 61.9 
                 66.7 
               
               
                 57.6 
                 70.7 
                 61.3 
                 57.8 
                 55.3 
                 65.8 
                 65.1 
                 61.3 
                 72 
                 62.8 
               
               
                 63.4 
                 61.4 
                 71.3 
                 61.2 
                 58.7 
                 55.7 
                 67.7 
                 58.5 
                 61.5 
                 73.2 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 The training samples of nitrate nitrogen-NO3—N (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 13.8325 
                 13.7215 
                 13.6408 
                 13.6666 
                 13.7288 
                 13.8617 
                 13.8873 
                 13.9157 
                 13.9758 
                 14.1119 
               
               
                 14.4164 
                 14.4829 
                 15.2031 
                 15.2791 
                 15.6909 
                 16.1498 
                 16.6379 
                 16.9443 
                 16.8975 
                 16.8101 
               
               
                 16.5498 
                 16.2205 
                 15.7517 
                 15.3732 
                 14.5885 
                 13.9968 
                 13.5851 
                 12.9808 
                 12.6256 
                 12.2428 
               
               
                 11.9133 
                 11.6286 
                 11.4642 
                 10.7946 
                 10.3934 
                 10.4852 
                 10.9491 
                 11.5281 
                 12.2201 
                 12.8419 
               
               
                 13.3324 
                 13.0934 
                 12.8794 
                 12.9103 
                 12.5906 
                 12.3108 
                 12.0798 
                 11.9742 
                 11.8102 
                 11.6730 
               
               
                 11.6093 
                 11.4942 
                 11.4940 
                 11.5036 
                 11.4617 
                 11.4878 
                 11.3927 
                 11.3851 
                 11.4866 
                 11.7895 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 The training samples of effluent suspended solids-SS (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 146 
                 192 
                 226 
                 208 
                 154 
                 264 
                 276 
                 208 
                 178 
                 250 
               
               
                 204 
                 288 
                 210 
                 172 
                 200 
                 170 
                 214 
                 324 
                 186 
                 422 
               
               
                 168 
                 238 
                 232 
                 260 
                 184 
                 330 
                 312 
                 230 
                 162 
                 300 
               
               
                 268 
                 231 
                 270 
                 132 
                 252 
                 204 
                 148 
                 116 
                 182 
                 292 
               
               
                 210 
                 210 
                 350 
                 214 
                 212 
                 170 
                 262 
                 178 
                 228 
                 164 
               
               
                 296 
                 308 
                 240 
                 170 
                 140 
                 178 
                 196 
                 312 
                 164 
                 320 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                 The training samples of total phosphorus-TP (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 6.38 
                 6.71 
                 7.15 
                 7.29 
                 6.31 
                 7.03 
                 7.35 
                 7.05 
                 6.66 
                 7.28 
               
               
                 7.06 
                 7.73 
                 6.92 
                 6.7 
                 6.91 
                 6.38 
                 7.18 
                 7.81 
                 7.39 
                 8.21 
               
               
                 6.56 
                 6.83 
                 6.95 
                 7.41 
                 6.82 
                 9.84 
                 7.91 
                 7.23 
                 6.64 
                 7.3 
               
               
                 7.81 
                 7.19 
                 6.63 
                 6 
                 6.65 
                 5.84 
                 5.87 
                 6.15 
                 6.53 
                 7.62 
               
               
                 6.9 
                 6.2 
                 8.08 
                 6.47 
                 7.2 
                 5.86 
                 7.69 
                 6.55 
                 6.94 
                 7.01 
               
               
                 7.78 
                 6.98 
                 7.55 
                 6.56 
                 5.92 
                 6.17 
                 7.05 
                 6.73 
                 7.65 
                 8.09 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 The training samples of real effluent TN (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 75.3 
                 86 
                 91.3 
                 91.8 
                 88.5 
                 83.9 
                 84.8 
                 82.1 
                 80 
                 84.4 
               
               
                 80 
                 89.6 
                 79.9 
                 82.2 
                 77.6 
                 55.5 
                 85.1 
                 85.4 
                 90.4 
                 84.2 
               
               
                 80.9 
                 76.1 
                 73.7 
                 86.6 
                 83.1 
                 85.9 
                 81.7 
                 79.6 
                 72 
                 78 
               
               
                 79.3 
                 81.77 
                 73.7 
                 62.4 
                 73.2 
                 70.7 
                 72.2 
                 71.1 
                 63 
                 75.3 
               
               
                 81.8 
                 72.7 
                 88.9 
                 77.4 
                 74.1 
                 71.2 
                 80.5 
                 76.5 
                 75.8 
                 82.6 
               
               
                 80.1 
                 70.3 
                 86.5 
                 71.5 
                 67.9 
                 65.6 
                 68.6 
                 70.9 
                 77.4 
                 87.2 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                 The effluent TN outputs in the training process (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 75.09123 
                 85.75465 
                 91.29607 
                 91.6917 
                 88.23302 
                 83.95164 
                 85.46349 
                 82.11712 
                 79.64609 
                 84.5503 
               
               
                 79.87456 
                 89.64711 
                 79.92864 
                 81.83561 
                 77.36899 
                 57.73073 
                 84.80773 
                 85.69525 
                 90.44198 
                 82.75301 
               
               
                 81.46583 
                 76.12251 
                 73.87198 
                 86.63506 
                 82.91107 
                 85.88516 
                 81.91191 
                 79.37446 
                 72.01563 
                 78.18965 
               
               
                 79.34218 
                 81.66961 
                 73.74434 
                 62.82255 
                 73.0666 
                 70.48056 
                 72.29508 
                 71.25872 
                 63.62556 
                 74.98458 
               
               
                 81.483 
                 72.48675 
                 88.93721 
                 77.31496 
                 74.22315 
                 70.59969 
                 80.91807 
                 76.37911 
                 75.78082 
                 82.65934 
               
               
                 80.05047 
                 71.01168 
                 85.82914 
                 71.58082 
                 67.73245 
                 65.72093 
                 69.74704 
                 69.91498 
                 76.98607 
                 87.36917 
               
               
                   
               
             
          
         
       
     
       Testing Samples: 
       [0062]      
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 The testing samples of biochemical oxygen demand-BOD (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 217 
                 226 
                 218 
                 390 
                 260 
                 200 
                 248 
                 370 
                 342 
                 347 
               
               
                 290 
                 440 
                 289 
                 460 
                 188 
                 318 
                 334 
                 290 
                 341 
                 335 
               
               
                 287 
                 346 
                 266 
                 430 
                 294 
                 450 
                 262 
                 372 
                 370 
                 198 
               
               
                 347 
                 610 
                 326 
                 283 
                 395 
                 233 
                 331 
                 209 
                 282 
                 174 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 9 
               
               
                   
               
               
                 The testing samples of ammonia nitrogen-NH4—N (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 48.6 
                 56.9 
                 64.2 
                 58.9 
                 50.3 
                 61.3 
                 63.7 
                 68.6 
                 54 
                 40.8 
               
               
                 53.4 
                 60.2 
                 66.4 
                 60.9 
                 63.4 
                 54.4 
                 40.7 
                 69 
                 63.4 
                 55 
               
               
                 66.3 
                 63.2 
                 62.3 
                 52.7 
                 60.5 
                 57 
                 62.1 
                 68.2 
                 64 
                 69 
               
               
                 67.2 
                 61.5 
                 66 
                 64.5 
                 62.1 
                 51.4 
                 51 
                 55.5 
                 55.5 
                 58.5 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 The testing samples of nitrate nitrogen-NO3—N (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 12.3085 
                 12.6792 
                 13.0400 
                 13.2389 
                 13.5262 
                 13.4614 
                 13.2849 
                 12.9682 
                 12.7089 
                 12.2269 
               
               
                 12.0995 
                 12.1315 
                 12.1361 
                 12.2122 
                 12.2197 
                 12.3499 
                 12.4464 
                 12.4927 
                 12.7326 
                 12.8156 
               
               
                 12.9392 
                 13.0438 
                 13.7367 
                 14.1627 
                 14.8751 
                 15.9604 
                 16.7487 
                 17.6572 
                 18.6773 
                 19.1970 
               
               
                 19.9069 
                 20.5030 
                 20.9495 
                 21.3475 
                 21.8734 
                 22.4720 
                 22.7922 
                 23.2325 
                 23.4924 
                 23.2459 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
               
                 The testing samples of effluent suspended solids-SS (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 154 
                 158 
                 214 
                 204 
                 110 
                 232 
                 226 
                 254 
                 122 
                 538 
               
               
                 130 
                 162 
                 142 
                 360 
                 376 
                 231.2 
                 166 
                 118 
                 142 
                 220 
               
               
                 266 
                 172 
                 296 
                 235 
                 180 
                 146 
                 206 
                 208 
                 202 
                 146 
               
               
                 398 
                 270 
                 328 
                 126 
                 244 
                 218 
                 272 
                 168 
                 262 
                 110 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 12 
               
               
                   
               
               
                 The testing samples of total phosphorus-TP (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 5.17 
                 5.39 
                 6.03 
                 5.96 
                 5.24 
                 6.22 
                 5.78 
                 6.17 
                 5.6 
                 5.22 
               
               
                 4.75 
                 5.46 
                 6.1 
                 6.48 
                 6.84 
                 5.5 
                 4.06 
                 5.74 
                 5.73 
                 5.8 
               
               
                 6.71 
                 5.63 
                 6.18 
                 5.11 
                 5.03 
                 4.6 
                 5.24 
                 5.86 
                 5.62 
                 6.13 
               
               
                 7.01 
                 6.11 
                 6.65 
                 5.56 
                 6.52 
                 6.22 
                 6.25 
                 5.2 
                 5.77 
                 6.17 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 13 
               
               
                   
               
               
                 The testing samples of real effluent TN (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 62.8 
                 67.4 
                 75.3 
                 70.1 
                 59.4 
                 78.5 
                 75.4 
                 77.3 
                 70.2 
                 54.5 
               
               
                 60.7 
                 66.7 
                 74.1 
                 74.9 
                 78.6 
                 66 
                 60.9 
                 65.4 
                 52.3 
                 60.5 
               
               
                 72.7 
                 68.2 
                 70 
                 65.1 
                 69.1 
                 61.9 
                 69.3 
                 71.5 
                 70.7 
                 76.7 
               
               
                 80.8 
                 73.9 
                 77.3 
                 73.5 
                 76.3 
                 73.4 
                 74.1 
                 64.5 
                 66.6 
                 67.8 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
               
                   
               
               
                 The effluent TN outputs in the testing process (mg/L) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 60.43193 
                 67.16412 
                 75.34496 
                 70.96676 
                 63.11076 
                 67.66785 
                 81.3452 
                 79.78831 
                 64.06407 
                 58.64447 
               
               
                 63.99991 
                 66.24501 
                 72.44785 
                 72.43734 
                 77.82645 
                 67.75635 
                 57.96904 
                 75.32191 
                 63.95107 
                 56.05289 
               
               
                 62.8231 
                 65.67208 
                 71.03243 
                 61.22433 
                 66.2433 
                 65.8583 
                 68.8428 
                 76.71578 
                 67.04345 
                 74.80853 
               
               
                 78.61247 
                 75.88474 
                 80.21718 
                 68.98426 
                 77.51966 
                 67.57056 
                 73.42719 
                 71.17669 
                 65.88281 
                 66.41494