CN107992645A - Sewage disposal process soft-measuring modeling method based on chaos-fireworks hybrid algorithm - Google Patents

Sewage disposal process soft-measuring modeling method based on chaos-fireworks hybrid algorithm Download PDF

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CN107992645A
CN107992645A CN201711035380.2A CN201711035380A CN107992645A CN 107992645 A CN107992645 A CN 107992645A CN 201711035380 A CN201711035380 A CN 201711035380A CN 107992645 A CN107992645 A CN 107992645A
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陈如清
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Abstract

The invention discloses a kind of sewage disposal process soft-measuring modeling method based on chaos fireworks hybrid algorithm, and to improve the quality of the initial fireworks members of FWA, invention defines a kind of improved two-stage sine chaotic map；To improve the optimization performance of basic FWA, chaotic optimization algorithm and FWA algorithms are merged, it is proposed that a kind of chaos fireworks hybrid optimization algorithm.The effective information exchanging and sharing enhanced in population between member of the present invention, improve the diversity of population, expand the Premature Convergence in the search range of solution space, avoiding algorithm.In addition, for the soft sensor modeling problem of biochemical processing procedure of sewage dissolved oxygen mass concentration, define a new Sample Similarity measurement index and propose a kind of extracting method of representative sample, for extracting more representative modeling data, and improved chaos fireworks hybrid optimization algorithm is applied to the training of neutral net in soft sensor modeling, achieve good application effect.

Description

Sewage treatment process soft measurement modeling method based on chaos-firework hybrid algorithm
Technical Field
The invention relates to the field of soft measurement modeling, in particular to a soft measurement modeling method for a sewage treatment process based on a chaos-firework hybrid algorithm.
Background
Along with the continuous increase of industrial and domestic sewage discharge, water resource pollution is increasingly serious, so that the originally short water resource is more concerned. The treatment and the recycling of the town sewage are one of effective ways for improving the ecological environment and solving the problem of water shortage in cities. At present, the sewage treatment mostly adopts a biochemical method, and is the most main way for industrial and urban sewage treatment. In a sewage biochemical treatment system, the Dissolved Oxygen (DO) concentration in water is an important index in the biochemical reaction process of sewage treatment, the operation condition of the whole sewage treatment system can be timely and visually reflected, and the monitoring and control of the dissolved oxygen concentration are important for improving the treatment effect and the treatment efficiency of the sewage treatment process. The method is influenced by factors such as various sewage components, uncertainty of sewage sludge flow and the like in the sewage treatment process, the real-time accurate measurement of the mass concentration of the dissolved oxygen is difficult to realize by the conventional method, the requirement of the sewage treatment process is difficult to meet, and the research on the online soft measurement technology of the parameters such as the mass concentration of the dissolved oxygen has important significance.
Artificial neural networks are a common soft-measurement modeling approach. In order to further improve the performance of the neural network soft measurement model, a PSO (particle swarm optimization) and other group intelligent optimization algorithms are often used for network weight optimization of the neural network. Since 2000, many new group intelligent optimization algorithms have been proposed in succession. In 2010, students such as Tan and Zhu propose a firework algorithm (FWA) according to the phenomenon that sparks are generated due to firework explosion, and the students in different fields pay attention to the FWa due to strong robustness and global optimization capability. The method is successfully used for solving the problems of training of neural network weights, parameter optimization of continuous and discrete systems, solution of combined optimization problems and the like. In order to further improve the optimization performance of the algorithm, a plurality of scholars put forward a plurality of improved algorithms from different angles and perform mechanism analysis and comparative study, and all the improved algorithms achieve good results. The firework algorithm belongs to a guided randomness heuristic algorithm and has strong optimization problem solving capability. However, when a complex optimization problem is processed, the solution results may be different or a global optimal solution may not be found each time; the method has the defects of easy falling into local optimization, low convergence speed in the later evolution stage, poor robustness and the like.
The basic firework algorithm is realized by regarding fireworks as a feasible solution in an optimal problem solution space, wherein a process of generating a certain number of sparks by firework explosion is a process of searching an optimal solution from a neighborhood; the algorithm is described in detail as follows:
1) Randomly generating N fireworks, namely randomly initializing N positions x in solving space i N initial solutions of the problem are characterized.
2) Calculating the fitness value of each firework, evaluating the quality of the fireworks and generating different quantities of sparks under different explosion radiuses; firework x i Radius of detonation R i And number of explosion sparks S i The formula (c) is represented by formula (3) and formula (4), respectively, wherein ymin = min (f (x) i ) (i =1,2, \ 8230;, N) is the minimum value (optimal value) of fitness in the current firework population; ymax = max (f (x) i ) (i =1,2, \ 8230;, N) is the maximum value (worst value) of fitness in the current firework population. The constants R and M are used to adjust the explosion radius and the number of explosion sparks, respectively, and ε is a small quantity used to avoid zero operation. In addition, in order to limit the number of spark particles generated at the firework position with better adaptability value and poorer adaptability value, the number of the generated sparks is limited as follows:
where a, b are two constants and round is a rounding function.
3) Generating an explosion spark, randomly selecting z dimensions to form a set DS, z = round (D × rand (0, 1)), wherein D represents fireworks x i Dimension number; round is a rounding function and rand is a function that yields uniformly distributed random numbers within the interval. Performing explosion operation on each dimension k of the DS according to the formula (8), and performing out-of-range processing on ex ik And storing in the explosive spark population.
ex ik ＝x ik +h，h＝R i Xrand(-1，1) (8)
Wherein h represents a position offset; x is the number of ik The k dimension, ex, of the ith individual firework ik Represents x ik Explosion spark after explosion operation.
4) Generating G Gaussian variant sparks, randomly selecting the sparks x i And randomly extracting z dimensions to form a set DS, wherein z = round (D multiplied by rand (0, 1)), and D represents a firework member x i Dimension (d) of (a). Performing Gaussian variation operation on each dimension k of DS according to formula (9), performing border crossing processing, and then performing mx ik And preserving the strain in the Gaussian variant spark population.
mx ik ＝x ik ×e (9)
In the formula: e to N (1, 1), mx ik Is x ik A gaussian variant spark is generated after the gaussian variant.
5) Selecting N members from the three kinds of population members of fireworks, explosion sparks and Gaussian variation sparks to form a firework population for the next iterative operation. Setting a candidate set as S (including three types of population members), and setting the firework population scale as N; the individual with the optimal fitness value in S is firstly determined as the next generation firework member, the rest N-1 firework members are sequentially selected from S in a roulette mode, and the candidate x i The probability of being selected is:
in the formula, R (x) i ) Is x i And the sum of the distances from the individual entities in S. The higher the density of individuals in S, the lower the probability of being selected.
6) It is determined whether a termination condition is satisfied. If yes, stopping searching, otherwise, returning to the step 2).
Disclosure of Invention
Based on the existing problems, the invention discloses a soft measurement modeling method for a sewage treatment process based on a chaos-firework hybrid algorithm, which adopts the following technical scheme:
a soft measurement modeling method for a sewage treatment process based on a chaos-firework hybrid algorithm defines an improved two-stage sine chaotic mapping, and improves an extraction method of an FWA initial member by utilizing the ergodicity of chaotic motion; in order to further improve the optimization performance of the existing FWA, the FWA algorithm and the COA algorithm are organically fused, and an improved chaos-firework hybrid optimization algorithm (CFWA) is defined; aiming at the problem of soft measurement modeling of dissolved oxygen mass concentration in the sewage biochemical treatment process, a new sample similarity measurement index and a representative sample extraction method are defined, and are used for extracting more representative modeling data and applying an improved chaos-firework mixed optimization algorithm to training of a neural network in soft measurement modeling.
The method for extracting the FWA initial members utilizes the ergodicity of chaotic motion to generate a larger-scale initial group in a solution space, and extracts the FWA initial fireworks which are uniformly distributed according to the Euclidean distance among the members so that the fireworks with limited scale are uniformly distributed in the solution space; the extraction method of the FWA initial firework member is described as follows:
(1) Chaotic iteration is carried out on a plurality of different initial values by adopting a multi-track sine chaotic mapping SM to generate a multidimensional chaotic vector X, X = (X =) 1 ,…,x n ) N represents the solution space dimension;
(2) Calculating the spatial distance (i.e., euclidean distance) d between n-dimensional vectors ij When d is ij &Removing one vector of the two vectors i and j when the epsilon is smaller than the preset value;
(3) Linearly transforming the screened vector to a solving space to serve as an initial position of a FWA group member;
wherein the sinusoidal chaotic map SM can be expressed by formula (1),
z n+2 ＝rsin(5.65/z n+1 )+(1-r)sin(5.65/z n )，-1≤z n ≤1,z n ≠0 (1)
fractal coefficients r ~ (0, 1) in the formula, and when r =0 or r =1, the mapping is converted into a sinusoidal chaotic full mapping; initial value z of iteration 0 Cannot be 0, and z 0 Cannot be taken to be any of an infinite number of balance points; when r =0.005, the randomness is almost close to the full mapping, and the chaotic characteristics are good, so r =0.005 is an optimum value.
The Lyapunov index is an important index for measuring the chaos property, and the maximum Lyapunov index lambda of the sinusoidal chaos mapping SM max Can be represented by the formula (2),
when r is (0, 1) < lambda > max The chaos characteristic is more obvious than the common limited folding time mapping.
The chaos-firework hybrid optimization algorithm (CFWA) improves the optimization performance of basic FWA by fusing the COA algorithm and the FWA algorithm; the whole optimization process is divided into two stages, wherein two groups are simultaneously carried out by adopting a COA strategy and a FWA strategy respectively, wherein the two groups are respectively an FWA group (F group) and a COA group (C group);
the optimization process is carried out in two stages:
in the first stage, an F group and a C group are searched simultaneously according to a FWA mechanism and a COA mechanism respectively; firework x according to the basic Firework Algorithm principle i Radius of detonation R i And number of explosion sparks S i The calculation formulas of (a) and (b) are respectively formula (3) and formula (4);
in the searching process, the F group member of the CFWA calculates the firework explosion radius R i And number of explosion sparks S i When y in the formulae (3) and (4) min And y max Respectively obtaining the fitness optimal value and the fitness worst value of the whole optimizing group (including the group F and the group C) at the time t; c group members of the CFWA avoid the group members from being trapped in a local optimal area or premature convergence by using the global ergodicity of the COA algorithm, and realize the information sharing of the F group and the C group in the whole optimizing process;
and in the second stage, when the F group firework members fall into the local optimal area, searching and iterating the C group members in a nearby area with the local extreme point as the center, and replacing the same number of poor members in the F group with partial members with better C group adaptive values to help the F group members to be far away from the local optimal area.
Let Fy min (t)、Fy max (t) respectively representing the optimal value and the worst value of the F group fitness at the moment t, cy min (t)、Cy max (t) represents the optimal value and the worst value of the fitness of the group C at the moment t, y min And y max Respectively representing the optimal value and the worst value of the fitness of the whole group at the time t, and the execution flow of the chaos-firework hybrid optimization algorithm is described as follows:
step1: initializing the positions of two cluster members according to claim 1, performing cluster size N, maximum number of searches T max The optimization precision, the initial setting of relevant parameters of the FWA algorithm and the COA algorithm, calculating the initial adaptation values of all group members and recording the optimal value, the worst value and the corresponding spatial position of the fitness of the whole group;
step2: a first stage search comprising: 1) Searching the F group members in a solution space according to a basic firework algorithm, generating new positions of the members and calculating new adaptive values each time of iteration, and updating Fy min (t)、Fy max (t) and its spatial position; 2) Generating a new chaotic vector by the group C according to the formula (1) and carrying out linear transformation, generating a new member position by each iteration, calculating a new adaptive value, and recording Cy min (t)、Cy max (t) and its spatial position; 3) Comparing Fy min (t)、Fy max (t) and Cy min (t)、Cy max (t) adapting the value size, updating y min 、y max And corresponding spatial positions; 4) Repeating the steps 1) to 3), turning to Step4 when the optimization accuracy meets the requirement, and if the F group members fall into the local optimal area (such as y) min Keeping the state or not obviously changing within 10-15 iterations), entering Step3;
step3: a second stage search comprising:
1) Regenerating N chaotic vectors Y of the C group according to the formula (1) i (i =1,2, \ 8230;, N) according to formula (5) in y min Corresponding spatial position x * (t) chaotic search in neighborhood with center and radius R, where X i Representing the position of a solving space member i; f group member location and adaptation valueThe updating method is the same as that of Step 2;
X i ＝x * (t)+RY i ，i＝1,2,…,N (5)
2) Calculating the adaptive value of each member of the two sub-groups, sequencing according to the adaptive value, and replacing the member with the poor adaptive value of the F group with the member with the good adaptive value of the C group;
3) Comparison Fy min (t)、Fy max (t) and Cy min (t)、Cy max (t) adaptation value size, save y min 、y max And the corresponding spatial position;
4) Gradually reducing the radius R and repeating the steps 1) to 3), and turning to Step4 if the precision requirement is met or the maximum iteration times are reached;
step4: and stopping searching, and outputting the whole group of historical optimal solutions and corresponding optimal adaptive values.
A defined new sample similarity measurement index integrates cosine distance measurement and Euclidean distance measurement, namely:
δ＝secθ·dist (6)
wherein sec θ =1/Abs (cos θ), cos θ and dist respectively represent a cosine distance and a euclidean distance between two samples, δ represents a similarity value between the two samples, and a larger value represents a larger difference or a stronger independence between the two samples, or vice versa;
the method for extracting the representative sample is specifically described as follows: the set of n-dimensional data in the original sample set can be represented as x 1 ,…x i …,x l ∈R n I =1, \8230;, l. Calculating the similarity value delta between every two n-dimensional samples in the group of l to obtain an l x l dimensional upper triangular matrix A = (delta) ij ) l×l (i, j =1, \8230;, l) when i.gtoreq.j, δ ij ＝0；δ ij The smaller the sample is, the greater the similarity degree of the two samples is, and the sample is considered to be a pair of similar samples when the sample is smaller than a set threshold; i.e. when | δ ij |<θ 1 (wherein theta) 1 &0), one sample of the i, j two similar samples is removed; repeating the screening process to ensure that the residual sample data has the maximum difference or the minimum similarity; the remaining sample after screening is from the original data setAnd the extracted representative sample is used as modeling data of the neural network soft measurement model.
Soft measurement modeling of dissolved oxygen mass concentration in the sewage treatment process, selecting 6 auxiliary variables of biochemical oxygen demand, solid suspended matters, total nitrogen mass concentration, total phosphorus mass concentration, chemical oxygen demand and inflow water flow as input variables of a model, and selecting dissolved oxygen mass concentration as an output variable of the model; i.e. vector X = [ X ] 1 ,x 2 ,…,x 6 ]Corresponding to 6 auxiliary variables of different types, and taking the auxiliary variables as the input of the soft measurement model; y is a leading variable corresponding to the mass concentration of dissolved oxygen and is used as the output of the soft measurement model; preprocessing (data transformation and error processing) data acquired from a field to obtain an original sample set with a certain scale, randomly selecting 4/5 samples from the original sample set as modeling data of a soft measurement model, and taking 1/5 samples as generalization data of the soft measurement model; carrying out similarity analysis on the modeling data by adopting the method for extracting the representative sample so as to remove redundant samples in the sample set; the specific operation method comprises the following steps: calculating Euclidean distance, cosine distance and corresponding delta value between every two samples after sample normalization processing to obtain a l x l dimension upper triangular square matrix A = (delta) ij ) l × l (l is the size of the data set sample, i, j =1, \8230;, l), when i ≧ j, δ ij =0; setting a threshold value theta according to the actual situation of the preprocessed data 1 If delta ij |<θ 1 One of the samples is rejected; and processing according to the method to obtain a soft measurement modeling sample.
In order to improve the quality of FWA initial firework members, the invention defines an improved two-stage sinusoidal chaotic mapping and utilizes the ergodicity of chaotic motion to generate a larger-scale initial group in a solution space, and the FWA initial fireworks which are uniformly distributed are extracted from the members according to the Euclidean distance among the members, so that the fireworks with limited scale are uniformly distributed in the solution space; in order to improve the basic FWA optimization performance, a chaos-firework hybrid optimization algorithm is provided by fusing a COA algorithm and a FWA algorithm; the optimization process is divided into two stages, and two groups are simultaneously carried out by adopting a COA strategy and a FWA strategy respectively. The improved algorithm effectively enhances the information exchange and sharing among members in the population, improves the diversity of the population, enlarges the search range in the solution space and avoids the premature convergence of the algorithm. Aiming at the problem of soft measurement modeling of dissolved oxygen mass concentration in the sewage biochemical treatment process, a new sample similarity measurement index is defined, a representative sample extraction method is provided for extracting more representative modeling data, and an improved chaos-firework hybrid optimization algorithm is used for training a neural network in soft measurement modeling, so that a good application effect is achieved.
Drawings
FIG. 1 is a diagram of a structure of a soft measurement method of dissolved oxygen mass concentration;
FIG. 2 is a chaotic vector resulting from Logistic mapping with 2000 iterations of a single initial value;
FIG. 3 is a chaotic vector resulting from an SM map iterating 2000 times over a single initial value;
FIG. 4 is a chaotic vector produced by SM mapping 40 iterations for 50 different initial values;
FIG. 5 is a training result of a dissolved oxygen mass concentration soft measurement model;
FIG. 6 is a generalized result of a soft measurement model of dissolved oxygen mass concentration.
Detailed Description
The technical solution of the present invention is described in detail below. The embodiments of the present invention are provided only for illustrating a specific structure, and the scale of the structure is not limited by the embodiments.
A soft measurement modeling method for a sewage treatment process based on a chaos-firework hybrid algorithm defines an improved two-stage sine chaotic mapping, and improves an extraction method of an FWA initial member by utilizing the ergodicity of chaotic motion; in order to further improve the optimization performance of the existing FWA, the FWA algorithm and the COA algorithm are organically fused, and an improved chaos-firework hybrid optimization algorithm (CFWA) is defined; aiming at the problem of soft measurement modeling of dissolved oxygen mass concentration in the sewage biochemical treatment process, a new sample similarity measurement index and a representative sample extraction method are defined, and are used for extracting more representative modeling data and applying an improved chaos-firework mixed optimization algorithm to training of a neural network in soft measurement modeling.
In order to improve the quality of FWA initial firework members, a larger-scale initial group is generated in a solution space by utilizing the ergodicity of chaotic motion, and the FWA initial fireworks which are uniformly distributed are extracted from the solution space according to the Euclidean distance among the members, so that the fireworks with limited scale are uniformly distributed in the solution space; the selection process of the FWA initial firework member is as follows:
(1) Chaotic iteration is carried out on a plurality of different initial values by adopting a multi-track sine chaotic mapping SM to generate a multidimensional chaotic vector X with a certain scale, wherein X = [ X ] 1 ,x 2 ,…,x 6 ]N represents the solution space dimension;
(2) Calculating the spatial distance (i.e., euclidean distance) d between n-dimensional vectors ij When d is ij &Removing one vector of the two vectors i and j when the epsilon is smaller than the preset value;
(3) Linearly transforming the screened vector to a solving space as an initial position of the FWA group member;
wherein the sinusoidal chaotic map SM can be expressed by formula (1),
z n+2 ＝rsin(5.65/z n+1 )+(1-r)sin(5.65/z n )，-1≤z n ≤1,z n ≠0 (1)
fractal coefficients r (0, 1) in the formula, and when r =0 or r =1, the mapping is converted into a sinusoidal chaotic full mapping; initial value z of iteration 0 Cannot be 0, and z 0 Cannot be taken to be any of an infinite number of balance points; the optimal value of r is 0.005, the randomness of the r is basically close to full mapping, and the chaotic characteristic is good;
the Lyapunov index is an important index for measuring the chaos property, and the maximum Lyapunov index lambda of the sinusoidal chaos mapping SM max Can be represented by the formula (2),
when r is (0, 1) < lambda > max The chaos characteristic is more obvious than the common limited folding times mapping.
The ergodic simulation analysis shows that the ergodic performance of a multi-chaotic track (namely, a plurality of initial values are selected to carry out chaotic iteration respectively) is obviously superior to that of a single chaotic track (namely, a single initial value is selected to carry out chaotic iteration). As shown in fig. 2, 3 and 4, wherein fig. 2 is a chaotic vector generated by Logistic mapping for a single initial value iteration 2000 times; FIG. 3 is a chaotic vector resulting from an SM map iterating 2000 times over a single initial value; FIG. 4 is a chaotic vector produced by SM mapping 40 iterations for 50 different initial values; the comparison results show that the traversability of fig. 4 is better than that of fig. 3 and 2.
In order to improve the optimization performance of the basic FWA, a chaotic firework hybrid optimization algorithm (CFWA) is provided by fusing a COA algorithm and a FWA algorithm; the whole optimization process is divided into two stages, wherein two groups are simultaneously carried out by adopting a COA strategy and a FWA strategy respectively, wherein the two groups are respectively an FWA group (F group) and a COA group (C group);
the optimization process is carried out in two stages:
the first stage, the F group and the C group are searched simultaneously according to a FWA mechanism and a COA mechanism respectively; firework x according to the basic Firework Algorithm principle i Radius of detonation R i And number of explosion sparks S i Are respectively shown as
(3) And formula (4);
in the searching process, the F group member of the CFWA calculates the firework explosion radius R i And number of explosion sparks S i When y in the formulae (3) and (4) min And y max Respectively obtaining the fitness optimal value and the fitness worst value of the whole optimizing group (including the group F and the group C) at the moment t; group C member utilization C of CFWAThe global ergodicity of the OA algorithm avoids the group members from being trapped in a local optimal area or premature convergence, and realizes the information sharing of the F group and the C group in the whole optimizing process;
and in the second stage, when the F group firework members are trapped in the local optimal area, searching and iterating the C group firework members in a nearby area with the local extreme point as the center, and replacing the same number of poor members in the F group with partial members with better C group adaptive values to help the F group members to be far away from the local optimal area.
Let Fy min (t)、Fy max (t) represents the optimal value and the worst value of the fitness of the F group at the time t, cy min (t)、Cy max (t) represents the optimal value and the worst value of the fitness of the group C at the moment t, y min And y max Respectively representing the fitness optimal value and the fitness worst value of the whole group at the moment t, and the execution flow of the chaos-firework hybrid optimization algorithm is described as follows:
step1: initializing the positions of two members of a subgroup according to claim 1, performing the subgroup size N, the maximum number of searches T max The optimization precision, the initial setting of relevant parameters of the FWA algorithm and the COA algorithm, calculating the initial adaptation values of all group members and recording the optimal value, the worst value and the corresponding spatial position of the fitness of the whole group;
step2: a first stage search comprising: 1) Searching the F group members in a solution space according to a basic firework algorithm, generating new positions of the members and calculating new adaptive values each time of iteration, and updating Fy min (t)、Fy max (t) and its spatial position; 2) Generating a new chaotic vector by the group C according to the formula (1) and carrying out linear transformation, generating a new member position by each iteration and calculating a new adaptive value, and recording Cy min (t)、Cy max (t) and its spatial position; 3) Comparing Fy min (t)、Fy max (t) and Cy min (t)、Cy max (t) adapting the value size, updating y min 、y max And corresponding spatial positions; 4) Repeating the steps 1) to 3), turning to Step4 when the optimization accuracy meets the requirement, and if the F group members fall into the local optimal area (such as y) min Keeping the state or not obviously changing within 10-15 iterations), entering Step3;
step3: a second stage search comprising:
1) Regenerating N chaotic vectors Y of the C group according to the formula (1) i (i =1,2, \8230;, N) in accordance with formula (5) in the presence of y min Corresponding spatial position x * (t) chaotic search in neighborhood with center and radius R, where X i Representing the position of a solution space member i; the updating method of the positions and the adaptive values of the F group members is the same as that of Step 2;
X i ＝x * (t)+RY i ，i＝1,2,…,N (5)
2) Calculating the adaptive value of each member of the two sub-groups, sequencing according to the adaptive value, and replacing the member with the poor adaptive value of the F group with the member with the good adaptive value of the C group;
3) Comparing Fy min (t)、Fy max (t) and Cy min (t)、Cy max (t) adaptation value size, save y min 、y max And the corresponding spatial position;
4) Gradually reducing the radius R and repeating the steps 1) to 3), and turning to Step4 if the precision requirement is met or the maximum iteration number is reached;
step4: and stopping searching, and outputting the whole group of historical optimal solutions and corresponding optimal adaptive values.
In order to verify the effectiveness of the chaos-firework hybrid optimization algorithm (CFWA), a simulation experiment is carried out; three optimization algorithms of basic PSO, GA and FWA are introduced in the experimental process and compared with an improved chaotic firework hybrid optimization algorithm (CFWA). The optimization test objects are four classical functions (Ackley, rastrigrin, griewank and Rosenbrock) with multiple peaks, multiple local extrema and independent or mutual influence among independent variables. Wherein f is 1 (x)～f 3 (x) The global minimum of the function is 0 and the corresponding optimal solution is x * ＝(0,0,…,0)；f 4 (x) The global minimum of the function is also 0, corresponding to the optimal solution being x * =1, 8230, 1. Under the condition of low dimension (such as 2-3 dimensions) of the four classical functions, due to the fact that local extreme points are few, the conventional PSO, GA and FWA algorithms can find an ideal solution quickly; however, as the number of local extrema increases dramatically with increasing dimensions (e.g., more than 10 dimensions), the optimization of the three basic optimization algorithms is difficult. Wherein the high-dimensional RosenbronThe k function is recognized as a pathological quadratic function which is difficult to minimize, most of optimization algorithms are easy to fall into a local optimal area during optimization, and the search of a global minimum point is extremely difficult. The four functional expressions are specifically described as follows:
the optimizing precision setting conditions of the four functions in simulation analysis are respectively 10 -6 ,10 -2 ,10 -2 ,10 -2 (ii) a The PSO, GA, FWA and CFWA population sizes were all 40, with the maximum number of iterations set to 2000. The rest parameter setting conditions are as follows:
FWA and CFWA: the detonation radius regulation constant R =240; the explosion spark number adjusting constant M =200; the upper limit am =20 of the number of explosion sparks; the lower limit of the number of explosion sparks bm =1; number of gaussian variant sparks G =50. The chaos algorithm adopts the improved sine chaos mapping SM provided by the invention, and the details are shown in the formula (1). PSO: c. C 1 ＝c 2 ＝2.0；ω max ＝0.60,ω min =0.06.GA: the crossover probability is 0.6; the mutation probability was 0.01.
The four methods of basic PSO, basic GA, basic FWA and CFWA were used to randomly perform 300 independent experiments for each function, and the test results are shown in table 1.
TABLE 1 four optimization algorithms optimization performance comparison (300 experiments)
The test results of the four classical functions show that: the indexes such as robustness (mainly embodied in finding out the optimal rate), convergence precision and speed of the FWA algorithm are better than those of the conventional PSO and GA algorithms, and the overall optimization performance of the CFWA algorithm provided by the invention is strongest; compared with the GA algorithm, the PSO algorithm is relatively simple and has higher convergence speed, but the probability of trapping into local optimum is higher; for the Ackley function, the optimal solution can be quickly found by the four methods, and the optimization performance is good. For the Rastrigrin function and the Griewank function, under the condition of low precision requirement (10) -2 ) The four methods also have higher optimization rate and convergence precision; the four methods are used for the optimization test comparison of the 10-dimensional Rosenbrock complex function, the CFWA algorithm performs best under the same preset condition, and the overall optimization performance is obviously superior to the three basic algorithms of PSO, GA and FWA. In the best case, only 978 iterations are performed to achieve the convergence accuracy of 0.00082, statistics show that if the number of optimization iterations exceeds 1500, the CFWA guides the group members to escape from the local optimum 17 times on average, and the probability of the basic FWA algorithm falling into the local optimum is greatly reduced.
A soft measurement modeling method for a sewage treatment process based on a chaos-firework hybrid algorithm defines a new sample similarity measurement index and integrates cosine distance measurement and Euclidean distance measurement, namely:
δ＝secθ·dist (6)
sec θ =1/Abs (cos θ), cos θ and dist respectively represent a cosine distance and an euclidean distance between two samples, δ represents a similarity value between the two samples, and a larger value represents a larger difference or a stronger independence between the two samples, or vice versa;
the method for extracting the representative sample is specifically described as follows: the set of n-dimensional data in the original sample set can be represented as x 1 ,…x i …,x l ∈R n I =1, \ 8230;, l. Calculating the similarity value delta between every two n-dimensional samples of the l groups to obtain an l multiplied by l dimensional upper triangular matrix A = (delta) ij ) l×l (i, j =1, \8230;, l), when i is not less than j, delta ij ＝0。δ ij The smaller the sample is, the greater the similarity degree of the two samples is, and the sample is considered to be a pair of similar samples when the sample is smaller than a set threshold; i.e. when | δ ij |<θ 1 (wherein theta.theta. 1 &0), one sample of the i, j two similar samples is removed; repeating the screening process to ensure that the residual sample data has the maximum difference or the minimum similarity; and the residual sample after screening is a representative sample extracted from the original data set and used as modeling data of the neural network soft measurement model.
Soft measurement modeling of dissolved oxygen mass concentration in the sewage treatment process, selecting 6 auxiliary variables of biochemical oxygen demand, solid suspended matters, total nitrogen mass concentration, total phosphorus mass concentration, chemical oxygen demand and inflow water flow as input variables of a model, and selecting dissolved oxygen mass concentration as an output variable of the model; i.e. vector X = [ X ] 1 ,x 2 ,…,x 6 ]Corresponding to 6 auxiliary variables of different types, and taking the auxiliary variables as the input of the soft measurement model; y is a dominant variable corresponding to the mass concentration of dissolved oxygen and used as the output of the soft measurement model, as shown in FIG. 1; acquiring 500 groups of samples from data acquired from an industrial field DCS through preprocessing (data transformation and error processing), randomly selecting 400 groups (4/5 of total data) as modeling data of a soft measurement model, and taking the remaining 100 groups (1/5 of total data) as generalization data of the soft measurement model; in order to simplify the soft measurement model, a representative sample extraction method is adopted to carry out similarity analysis on modeling data, and redundant samples in a data set are removed; the specific operation method comprises the following steps: calculating Euclidean distance, cosine distance and corresponding delta value between every two samples after sample normalization processing to obtain a l x l dimension upper triangular square matrix A = (delta) ij ) l×l (l =400,i, j =1, \8230;, l), when i ≧ j, δ ij =0. Setting a threshold value theta according to the actual situation of the preprocessed data 1 I.e. when | δ ij |<θ 1 E.g. theta 1 =0.49 and rejects one of themAnd (4) sampling. The processed soft measurement modeling samples are simplified from 400 sets to 237 sets.
A soft measurement modeling method for a sewage treatment process based on a chaos-firework hybrid algorithm is used for constructing a soft measurement model for the sewage treatment process based on an artificial neural network (the structure is 6-13-1; the total number of network weight thresholds is 105), an offline training algorithm is a CFWA hybrid optimization algorithm, and three optimization algorithms of basic PSO, GA and FWA are introduced to form a comparison with an improved algorithm. In the soft measurement modeling process, the group member scales of the four optimization algorithms are all 50, the maximum iteration number is set to 6000, and the group member dimension is 105. The rest experimental parameter setting conditions are as follows: FWA and CFWA, explosion radius tuning constant R =240; the explosion spark number adjusting constant M =250; the upper limit am =25 of the number of explosion sparks; the lower limit of the number of explosion sparks bm =1; number of gaussian variant sparks G =60. The chaos algorithm adopts the improved sine chaos mapping SM provided by the invention. PSO, c 1 ＝c 2 ＝2.0；ω max ＝0.60,ω min =0.06.GA: the crossover probability is 0.6; the mutation probability was 0.01.
And after training, storing the optimal weight threshold value for the soft measurement model to measure the dissolved oxygen mass concentration on line. Table 2 shows the comparison of the simulation results of four soft measurement models based on four algorithms, where MSE represents the root mean square error and ABSE represents the average generalization error (the average of the absolute values of the errors). The training and generalization effect of the CFWA algorithm-based soft measurement model is shown in fig. 5 and 6.
TABLE 2 comparison of simulation results of four soft measurement models
The comparison result shows that compared with three basic soft measurement models of PSO, GA and FWA, the soft measurement model based on the CFWA algorithm has lower training error and generalization error, the generalization capability of the soft measurement model is obviously superior to that of the other three soft measurement models, the precision is also greatly improved, as shown in fig. 5 and 6, the fitting degree of the measured value (shown by a dotted line) and the actual value (shown by a solid line) of the model is good, the training process meets the requirements, and the generalization performance is better.

Claims (6)

1. The soft measurement modeling method for the sewage treatment process based on the chaos-firework hybrid algorithm is characterized in that an improved two-stage sine chaos mapping is defined, and the extraction method of FWA initial members is improved by utilizing the ergodicity of chaotic motion; in order to further improve the optimization performance of the existing FWA, the FWA algorithm and the chaos optimization algorithm (COA algorithm) are organically fused, and an improved chaos-firework hybrid optimization algorithm (CFWA) is defined; aiming at the problem of soft measurement modeling of dissolved oxygen mass concentration in the sewage biochemical treatment process, a new sample similarity measurement index and a representative sample extraction method are defined, and are used for extracting more representative modeling data and applying an improved chaos-firework mixed optimization algorithm to training of a neural network in soft measurement modeling.
2. The chaos-firework hybrid algorithm-based sewage treatment process soft measurement modeling method as claimed in claim 1, wherein the FWA initial member extraction method generates a larger scale initial population in a solution space by using the chaos motion ergodicity, and extracts the FWA initial fireworks with uniform distribution from the initial population according to the euclidean distance between the members, so that the limited scale fireworks are uniformly distributed in the solution space; the extraction method of the FWA initial firework member is described as follows:
(1) Chaotic iteration is carried out on a plurality of different initial values by adopting a multi-track sine chaotic mapping SM to generate a multidimensional chaotic vector X, X = (X =) with a certain scale 1 ,…,x n ) N represents the solution space dimension;
(2) Calculating the spatial distance (i.e., euclidean distance) d between n-dimensional vectors ij When d is present ij &When epsilon is smaller than t, removing one vector in the two vectors i and j;
(3) Linearly transforming the screened vector to a solving space as an initial position of the FWA group member;
wherein the sinusoidal chaotic map SM can be expressed by formula (1),
z n+2 ＝rsin(5.65/z n+1 )+(1-r)sin(5.65/z n )，-1≤z n ≤1,z n ≠0 (1)
fractal coefficients r ~ (0, 1) in the formula, and when r =0 or r =1, the mapping is converted into a sinusoidal chaotic full mapping; initial value z of iteration 0 Cannot be 0, and z 0 Cannot be taken to be any of an infinite number of balance points;
the Lyapunov index is an important index for measuring the chaos property, and the maximum Lyapunov index lambda of the sinusoidal chaos mapping SM max Can be represented by the formula (2),
when r is (0, 1) lambda max The chaos characteristic is more obvious than the common limited folding times mapping.
3. The chaos-firework hybrid algorithm based sewage treatment process soft measurement modeling method as claimed in claim 1, wherein the chaos-firework hybrid optimization algorithm (CFWA) improves basic FWA optimization performance by fusing COA algorithm and FWA algorithm; the whole optimization process is divided into two stages, wherein two groups are simultaneously carried out by adopting a COA strategy and a FWA strategy respectively, wherein the two groups are respectively an FWA group (F group) and a COA group (C group);
the optimization process is carried out in two stages:
in the first stage, an F group and a C group are searched simultaneously according to a FWA mechanism and a COA mechanism respectively; firework x according to the basic Firework Algorithm principle i Radius of detonation R i And number of explosion sparks S i The calculation formulas of (a) and (b) are respectively formula (3) and formula (4);
f group of CFWA in search processThe member calculates the explosion radius R of the fireworks i And number of explosion sparks S i When y in the formulae (3) and (4) min And y max Respectively obtaining the fitness optimal value and the fitness worst value of the whole optimizing group (including the group F and the group C) at the moment t; c group members of the CFWA avoid the group members from falling into a local optimal area or premature convergence by using the global ergodicity of the COA algorithm, and realize the information sharing of the F group and the C group in the whole optimizing process;
and in the second stage, when the F group firework members fall into the local optimal area, searching and iterating the C group members in a nearby area with the local extreme point as the center, and replacing the same number of poor members in the F group with partial members with better C group adaptive values to help the F group members to be far away from the local optimal area.
Let Fy min (t)、Fy max (t) represents the optimal value and the worst value of the fitness of the F group at the time t, cy min (t)、Cy max (t) represents the optimal value and the worst value of the fitness of the group C at the moment t, y min And y max Respectively representing the optimal value and the worst value of the fitness of the whole group at the time t, and the execution flow of the chaos-firework hybrid optimization algorithm is described as follows:
step1: initializing the positions of two members of a subgroup according to claim 1, performing the subgroup size N, the maximum number of searches T max The optimization precision, the initial setting of relevant parameters of the FWA algorithm and the COA algorithm, calculating the initial adaptation values of all group members and recording the optimal value, the worst value and the corresponding spatial position of the fitness of the whole group;
step2: a first stage search comprising: 1) The F group members search in a solution space according to a basic firework algorithm, generate new positions of the members in each iteration, calculate new adaptive values and update Fy min (t)、Fy max (t) and its spatial position; 2) Generating a new chaotic vector by the group C according to the formula (1) and carrying out linear transformation, generating a new member position by each iteration, calculating a new adaptive value, and recording Cy min (t)、Cy max (t) and its spatial position; 3) Comparison Fy min (t)、Fy max (t) and Cy min (t)、Cy max (t) adapting the value size, updating y min 、y max And the corresponding spatial position; 4) Repeating the steps 1) to 3), and optimizingIf the degree is reached, go to Step4, if the F group member falls into the local optimum area (e.g. y) min Keeping the state or not obviously changing within 10-15 iterations), entering Step3;
step3: a second stage search comprising:
1) Regenerating N chaotic vectors Y of the C group according to the formula (1) i (i =1,2, \ 8230;, N) according to formula (5) in y min Corresponding spatial position x * (t) chaotic search in neighborhoods with center and radius R, where X i Representing the position of a solving space member i; the updating method of the positions and the adaptive values of the F group members is the same as that of Step 2;
X i ＝x * (t)+R Y i ，i＝1,2,…,N (5)
2) Calculating the adaptive value of each member of the two sub-groups, sorting according to the adaptive value, and replacing the member with the poor adaptive value of the F group with the member with the good adaptive value of the C group;
3) Comparison Fy min (t)、Fy max (t) and Cy min (t)、Cy max (t) adaptation value size, save y min 、y max And the corresponding spatial position;
4) Gradually reducing the radius R and repeating the steps 1) to 3), and turning to Step4 if the precision requirement is met or the maximum iteration number is reached;
step4: and stopping searching, and outputting the whole group of historical optimal solutions and corresponding optimal adaptive values.
4. The chaos-firework hybrid algorithm-based sewage treatment process soft measurement modeling method as claimed in claim 2, wherein the optimal value of r in the formula (1) is 0.005.
5. The chaos-firework hybrid algorithm-based sewage treatment process soft measurement modeling method as claimed in claim 1, wherein the new sample similarity measure index integrates cosine distance measure and Euclidean distance measure, namely:
δ＝secθ·dist (6)
wherein sec θ =1/Abs (cos θ), cos θ and dist respectively represent a cosine distance and a euclidean distance between two samples, δ represents a similarity value between the two samples, and a larger value represents a larger difference or a stronger independence between the two samples, or vice versa;
the method for extracting the representative sample is specifically described as follows: the set of n-dimensional data in the original sample set can be represented as x 1 ,…x i …,x l ∈R n I =1, \8230;, l. Calculating the similarity value delta between every two n-dimensional samples of the l groups to obtain an l multiplied by l dimensional upper triangular matrix A = (delta) ij ) l×l (i, j =1, \8230;, l), when i is not less than j, delta ij ＝0；δ ij The smaller the sample is, the greater the similarity degree of the two samples is, and the sample is considered to be a pair of similar samples when the sample is smaller than a set threshold; i.e. when | δ ij |<θ 1 (wherein theta) 1 &0), one sample of the i, j two similar samples is removed; repeating the screening process to ensure that the residual sample data has the maximum difference or the minimum similarity; and the residual sample after screening is a representative sample extracted from the original data set and used as modeling data of the neural network soft measurement model.
6. The chaos-firework hybrid algorithm-based soft measurement modeling method for the sewage treatment process according to claim 1, wherein soft measurement modeling of mass concentration of dissolved oxygen in the sewage treatment process is performed by selecting 6 auxiliary variables of biochemical oxygen demand, suspended solids, total nitrogen mass concentration, total phosphorus mass concentration, chemical oxygen demand and inflow water flow as input variables of a model, and the mass concentration of dissolved oxygen is an output variable of the model; i.e. vector X = [ X ] 1 ,x 2 ,…,x 6 ]Corresponding to 6 auxiliary variables of different types, and taking the auxiliary variables as the input of the soft measurement model; y is a leading variable corresponding to the mass concentration of dissolved oxygen and used as the output of the soft measurement model; preprocessing (data transformation and error processing) data acquired from a field to obtain an original sample set with a certain scale, randomly selecting 4/5 samples from the original sample set as modeling data of a soft measurement model, and taking 1/5 samples as generalization data of the soft measurement model; similarity of modeling data is carried out by adopting the method for extracting the representative sampleAnalyzing and removing redundant samples in the data set; the specific operation method comprises the following steps: calculating Euclidean distance, cosine distance and corresponding delta value between every two samples after sample normalization processing to obtain a l x l dimension upper triangular square matrix A = (delta) ij ) l×l (l is the size of the data set sample, i, j =1, \8230;, l), when i ≧ j, δ ij =0; setting a threshold value theta according to the actual situation of the preprocessed data 1 If | δ ij |<θ 1 One of the samples is rejected; and processing according to the method to obtain a soft measurement modeling sample.
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