A modeling and optimization method for biogas high-pressure water washing

Abstract

The present invention discloses a modeling and optimization method for high-pressure water washing of biogas, comprising the following steps: step 1: collecting initial sample data of the high-pressure water washing process of biogas; step 2: establishing a multi-objective initial model of product gas quality and equipment energy consumption of sample data of the high-pressure water washing process of biogas based on an adaptive online learning machine, collecting new samples of the high-pressure water washing process of biogas, and using an adaptive iterative optimization model that weighs the characteristics of the old model and the new sample to form a multi-objective optimization model of product gas quality and equipment energy consumption; step 3: solving the multi-objective optimization model of product gas quality and equipment energy consumption of the high-pressure water washing process of biogas based on a novel multi-objective differential evolution algorithm; step 4: the decision maker selects the best operating variable with high product gas quality and low equipment energy consumption according to the Pareto optimal solution set. The present invention provides an efficient modeling method for the high-pressure water washing process of biogas, reduces the computational cost of retraining the model, and improves the accuracy of the model.

Description

Technical Field

[0001] The invention relates to the technical field of biogas high-pressure water washing, and in particular to a modeling and optimization method for biogas high-pressure water washing. Background Art

[0002] The biogas high-pressure water washing process is widely used in the purification process of biogas projects at home and abroad due to its advantages such as simple control, low cost, high absorption efficiency and large processing capacity. At present, scholars have established detailed mechanism models for the physical dissolution process, gas-liquid mass transfer process and material transfer process between equipment involved in the biogas high-pressure water washing process. However, the parameters involved in the mechanism model are difficult to obtain and the solution of the numerical model is cumbersome. In addition, there are many theoretical assumptions in the mechanism model, which makes the model difficult to apply in practice. For process systems with strong coupling and high nonlinearity between the operating variables of biogas high-pressure water washing, most scholars usually use process simulation software for optimization design. However, as a gray box model, the process software also involves the setting of theoretical parameters, the verification of material conservation and energy conservation, and the operation is complicated. For the optimization of biogas high-pressure water washing, scholars use process simulation software combined with optimization algorithms to solve the optimal operating conditions. The optimization process will call the simulation software multiple times, resulting in an increase in calculation costs, and during the optimization process, the process simulation may not converge, resulting in inaccurate optimization results. At the same time, the quality of the optimization algorithm will affect the selection of the optimal operating conditions. Due to these existing problems, it is very important to study appropriate modeling methods and optimization algorithms for the design of biogas high-pressure water washing process.

[0003] For engineering problems with complex internal mechanisms and relying on process software optimization solutions, a common solution is to establish a corresponding proxy model. The proxy model is established in a data-driven manner, mainly including response surface method, kriging method, support vector machine, and artificial neural network. The present invention adopts an online extreme learning machine neural network method. The online extreme learning machine includes an initial sample training stage and a new sample learning stage. For the biogas high-pressure water washing process, sampling is a batch sampling process. The initial model is established based on the sampled data points. When new sampling data enters, there is no need to retrain the model, but directly use the iteration of the online extreme learning machine to update the initial model, providing an online modeling strategy. However, some old data will only bring errors to the model, reducing the global prediction effect of ELM. Secondly, the quality of the new sample will affect the accuracy of the prediction. For example, the data characteristics of the new sample are quite different from those of the old sample, which will cause the prediction curve to change transiently. If the network is trained according to the data trend of the new sample, the training deviation is large, and the generalization performance of the online extreme learning machine is reduced. Most scholars only considered the role of old data and added a forgetting factor, but ignored the impact of changes in new sample characteristics, which affects the accuracy of the biogas high-pressure water washing model. Summary of the invention

[0004] In order to solve the deficiencies of the prior art, the present invention provides a modeling and optimization method for biogas high-pressure water washing, provides an efficient modeling method for the biogas high-pressure water washing process, establishes a multi-objective initial model of product gas quality and equipment energy consumption for the biogas high-pressure water washing process based on an adaptive online learning machine, and forms a multi-objective optimization model of product gas quality and equipment energy consumption by using an adaptive iterative optimization model that weighs old models and new sample features; and solves the multi-objective optimization model of product gas quality and equipment energy consumption for the biogas high-pressure water washing process based on a new multi-objective differential evolution algorithm; the decision maker selects the best operating variables with high product gas quality and low equipment energy consumption according to the Pareto optimal solution set, thereby reducing the computational cost of retraining the model and improving the accuracy of the model.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A modeling and optimization method for biogas high-pressure water washing, the method comprising the following steps:

[0007] Step 1: Collect initial sample data of biogas high-pressure water washing process;

[0008] Step 2: Based on the adaptive online learning machine, a multi-objective initial model of product gas quality and equipment energy consumption for sample data of biogas high-pressure water washing process is established, new samples of biogas high-pressure water washing process are collected, and an adaptive iterative optimization model that weighs the characteristics of the old model and the new samples is used to form a multi-objective optimization model of product gas quality and equipment energy consumption;

[0009] Step 3: Solve the multi-objective optimization model of product gas quality and equipment energy consumption of biogas high-pressure water washing process based on the new multi-objective differential evolution algorithm;

[0010] Step 4: The decision maker selects the best operating variables with high product gas quality and low equipment energy consumption based on the Pareto optimal solution set.

[0011] Furthermore, step 2 includes the following steps:

[0012] Step 2.1: Based on the initial sample data of the biogas high-pressure water washing process, the main variables affecting the product gas quality and equipment energy consumption of the biogas high-pressure water washing process are taken as input, and the indicators for evaluating the product gas quality and equipment energy consumption of the biogas high-pressure water washing process are taken as output, respectively, to establish the initial model of the product gas quality and equipment energy consumption of the biogas high-pressure water washing process;

[0013] Step 2.2: Establish an initial model for the product gas quality and equipment energy consumption of the biogas high-pressure water washing process PCH4 With f Es ;

[0014] Step 2.3: Collect Nk New sample data, using adaptive iterative update model that weighs the old model and new sample features;

[0015] Step 2.4: Through continuous iteration and update of step 2.3, N0+N is formed k A multi-objective optimization model for product gas quality and equipment energy consumption was developed.

[0016] Furthermore, the model and input in step 2.1 are based on the collected initial sample data of N0 biogas high-pressure water washing, and the input of the extreme learning machine is determined to be X N0*D , D represents the dimension of the input variable, which is the number of main variables that affect the product gas quality and equipment energy consumption of the biogas high-pressure water washing process; the output of the extreme learning machine is determined to be T N0*M , M represents the dimension of the output variable, which is the product gas quality index and equipment energy consumption index of the biogas high-pressure water washing process. The product gas quality index refers to the concentration of methane in the product gas PCH4, and the equipment energy consumption index refers to the sum of the compressor energy consumption, pump energy consumption, condenser energy consumption, blower energy consumption and other auxiliary equipment energy consumption E s .

[0017] Further, step 2.2 includes the following steps:

[0018] Initial model of product gas quality and equipment energy consumption of biogas high-pressure water washing process PCH4 With f Es ; Initialize the extreme learning machine parameters, including the number of hidden layer nodes L, the hidden layer weight W and the bias b; According to the hidden layer output matrix H0 and the input matrix X ij (i=1,2,…,N0,j=1,2,…,D), the model of product gas quality and equipment energy consumption of biogas high-pressure water washing process is obtained:

[0019]

[0020] Among them, W n =[w n1 ,w n2 ,…,w nD ] T is the connection weight between the nth hidden layer node and the input layer; X i =[x i1 ,x i2 ,…,x iD ] T is the i-th D-dimensional variable; β n =[w n1 ,w n2 ,…,w nM ] T is the connection weight between the nth hidden layer node and the output layer; b nis the bias of the nth hidden layer node; G(W n ,b n ,X i )=g(W n T *X i +b n ), g is the activation function. H0 is the hidden layer output matrix of N0 sample data of biogas high-pressure water washing, which is expressed as:

[0021]

[0022] According to the output of product gas quality and equipment energy consumption obtained by the extreme learning machine and the actual output of the two, the weight β0 of N0 sample data is calculated using the least squares method:

[0023]

[0024] Among them, β0 corresponds to the output weight matrix under N0 sample data of biogas high-pressure water washing; T0 corresponds to the output matrix under N0 sample data of biogas high-pressure water washing; K0 corresponds to the square of the determinant of the hidden layer output matrix H0 under N0 sample data of biogas high-pressure water washing.

[0025] Preferably, step 2.3 comprises the following steps:

[0026] After the biogas high-pressure water washing equipment had been running for a period of time, N k New sample data, according to the following trade-off between the old model and the new sample features, the adaptive iterative update model is updated, that is, the output weights β and K are updated:

[0027]

[0028] Among them, β (k-1) According to N k -1 sample-based model output weight; T k For the current N k The output matrix of data; H k For the current N k The hidden layer output matrix of data; is the adaptive factor. (k-1) and K k-1 represents the model characteristics established based on the previous sample data, and T k , H k For the current N k The features of the newly sampled data.

[0029] Furthermore, the adaptive factor The calculation formula is:

[0030]

[0031] Among them, error new represents the mean square error of the new model established by adding sample data; error old represents the mean square error of the old model established based on the initial sample data.

[0032] Preferably, step 3 includes the following steps:

[0033] Step 3.1: Set the parameters involved in the new multi-objective differential evolution algorithm and initialize the population. Set the population size N, the maximum number of iterations G, and the value range of the mutation factor F as [F min , F max , and the value range of the crossover factor CR as [CR min , CR max ; Take the main variables that affect the product gas quality and equipment energy consumption as decision variables, and randomly generate N individuals within the operation interval of the decision variables to form the initial population P;

[0034] Step 3.2: Use the multi-objective optimization model of product gas quality and equipment energy consumption established in step 2.4 as the fitness function, calculate the fitness function values on the two objectives respectively, and perform non-dominated sorting and crowding distance calculation for each individual;

[0035] Step 3.3: Perform a mutation operation on each individual in the population P based on the mutation strategy of the number of non-dominated solutions and the adaptive mutation factor;

[0036] Step 3.4: According to the mutation strategy of the number of non-dominated solutions, use its corresponding crossover strategy based on the number of non-dominated solutions to perform a crossover operation on the mutated individuals;

[0037] Step 3.5: After the mutation and crossover operations, generate new individuals to form population Q; Merge population P and Q to form population R, and form the next-generation evolutionary new population P' according to the non-dominated relationship and crowding distance strategy

[0038] Step 3.6: Judge the algorithm termination condition. If t < G, return to steps 3.3 - 3.5 to continue the optimization, otherwise terminate the calculation and obtain the Pareto optimal solution set corresponding to the product gas quality and equipment energy consumption.

[0039] Furthermore, the formula for step 3.3 is:

[0040]

[0041] Among them, V i (t + 1) is the mutated individual corresponding to the i-th individual X i (t) in the t-th generation population, X r1 (t), Xr2 (t),X r3 (t) Different individuals randomly selected from the tth generation population, X best (t) represents the individual with the largest crowding distance among all non-dominated individuals in the t-th generation population; F is the variation factor; SP represents the number of non-dominated solutions, and N is the population size.

[0042] Furthermore, the number of non-dominated solutions is compared with the population size. If SP is less than N, it means that the non-dominated solutions are not enough. The random individuals in the population are used to perform mutation operations with the differential vector. The mutation factor F1 should be adaptively changed according to the population evolution generation and the quality of the individual solutions in the population. The quality of the individual solutions is measured by the fitness function value. If SP is equal to N, it means that the population is full of non-dominated solutions. The individuals with the largest crowding distance of the non-dominated individuals in the population are used to perform mutation operations with the differential vector. The mutation factor F2 should be adaptively changed according to the population evolution generation and the distance between individuals. The distance between individuals is measured by the crowding distance of the non-dominated solution. The adaptive expressions of mutation factors F1 and F2 are as follows:

[0043]

[0044] Among them, f k max ,f k min are the maximum and minimum values ​​of the kth target, i.e., the maximum and minimum values ​​of product gas quality and equipment energy consumption; f k i represents the fitness function value of the current individual at the kth target; d max , d min They represent the maximum and minimum individual crowding distances of non-boundary extreme points in the non-dominated solution; m is the number of targets; d is the crowding distance; f k (i-1) and f k (i+1) are the objective function values ​​of the two individuals adjacent to individual i on the kth target; d i is the crowding distance value of the current individual in the non-dominated solution; t is the current evolutionary generation, G is the maximum number of iterations; F represents the mutation factor; F max ,F min Represent the upper and lower bounds of the variation factor respectively.

[0045] Furthermore, the mutation strategy formula in step 3.4 is:

[0046]

[0047] According to the adaptive strategy of the above mutation factors F1 and F2, the adaptive expressions of the corresponding adaptive crossover factors CR1 and CR2 are as follows:

[0048]

[0049] Among them, i = 1, 2, ... N, j = 1, 2, ... D, D represents the dimension of the individual; ij (t) represents the population individual X i The j-th dimension component of (t); v ij (t+1) is the variant individual V i The j-th dimension component in (t+1); CR represents the crossover factor; k represents a random integer in [1,D]; u ij (t+1) is the experimental individual; CR max ,CR min They represent the upper and lower bounds of the crossover factor respectively.

[0050] The most outstanding features and significant beneficial effects of the present invention are:

[0051] In order to solve the deficiencies of the prior art, the present invention provides a modeling and optimization method for biogas high-pressure water washing, provides an efficient modeling method for the biogas high-pressure water washing process, establishes a multi-objective initial model of product gas quality and equipment energy consumption for the biogas high-pressure water washing process based on an adaptive online learning machine, and forms a multi-objective optimization model of product gas quality and equipment energy consumption by using an adaptive iterative optimization model that weighs old models and new sample features; and solves the multi-objective optimization model of product gas quality and equipment energy consumption for the biogas high-pressure water washing process based on a new multi-objective differential evolution algorithm; the decision maker selects the best operating variables with high product gas quality and low equipment energy consumption according to the Pareto optimal solution set, thereby reducing the computational cost of retraining the model and improving the accuracy of the model.

[0052] 1. The present invention uses an adaptive online extreme learning machine to establish a product gas quality and equipment energy consumption model for the biogas high-pressure water washing process. Since the data sampling of the biogas high-pressure water washing process is a batch sampling process, the features of new samples and old samples may be very different. Therefore, the present invention simultaneously considers the weight relationship between the new sample features and the old model features. When new samples are added, the present invention adopts and Balancing the relationship between the old model and the new data features is to consider the impact of both on the model at the same time and design Adaptive adjustments were made based on the predictions of the new and old models, which improved the accuracy of the model and reduced the computational cost of retraining the model, providing an efficient modeling strategy for the biogas high-pressure water washing process.

[0053] 2. The present invention proposes a new multi-objective differential evolution algorithm, uses the number of non-dominated solutions to measure the different evolutionary stages of the multi-objective differential evolution algorithm, adopts different mutation strategies and crossover strategies to correspond to it, and proposes adaptive mutation factors and crossover factors, which improves the convergence performance and distribution performance of the algorithm, and improves the ability of the multi-objective differential evolution algorithm to solve multi-objective problems. Using the new multi-objective differential evolution algorithm, the product gas quality and equipment energy consumption of the biogas high-pressure water washing process are solved by multi-objective, which is conducive to obtaining a better Pareto optimal solution set of product gas quality and equipment energy consumption. For decision makers in this field, they can choose the best operating variables that meet their needs.

[0054] 3. The modeling and optimization method of the biogas high-pressure water washing process based on the adaptive online extreme learning machine and the new multi-objective differential evolution algorithm proposed in the present invention provides a set of accurate modeling and efficient optimization solutions for decision makers in the field of biogas high-pressure water washing. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a framework diagram of the steps of high-pressure water washing of biogas according to the present invention;

[0056] Figure 2 It is a flow chart of a modeling and optimization method of biogas high-pressure water washing of the present invention;

[0057] Figure 3 The comparison chart of the predicted value and actual value of product gas quality and equipment energy consumption based on the adaptive online extreme learning machine;

[0058] Figure 4 The Pareto frontier diagram obtained by solving the product gas quality and equipment energy consumption using the new differential evolution algorithm. DETAILED DESCRIPTION

[0059] In order to describe the present invention in detail, the present invention will be further described below in conjunction with the accompanying drawings and specific implementation schemes.

[0060] In order to ensure that the biogas high-pressure water washing process can meet the quality standards of the product gas and reduce the operating energy consumption of the equipment, the optimization and control of process parameters is particularly important. The product gas quality index refers to the concentration of methane in the product gas, and the equipment energy consumption mainly includes the energy consumption of the compressor, pump, condenser, blower and other auxiliary equipment. There is a conflict between these two goals. To ensure that the higher the quality of the product gas, the lower the energy consumption, this is obviously a multi-objective problem. Therefore, it is particularly critical to choose a suitable multi-objective optimization algorithm for solution.

[0061] The present invention selects a multi-objective differential evolution algorithm. The mutation strategy in the differential evolution algorithm plays an important role in improving the quality of the individual offspring population and the diversity of the optimal set. Many scholars have improved the mutation strategy and mutation factor, but have not considered it from the perspective of non-dominated solutions. Therefore, the improvement of the multi-objective differential evolution algorithm is of great significance for obtaining the optimal operating conditions with higher product gas quality and lower energy consumption.

[0062] Aiming at the modeling and optimization problem of biogas high-pressure water washing, the present invention proposes a modeling and optimization method based on an adaptive online extreme learning machine and a new multi-objective differential evolution algorithm. Experimental studies have shown that the proposed method can provide an accurate model for decision makers in the field of biogas high-pressure water washing and provide an effective variable control strategy. At the same time, the present invention can also be applied to the modeling and optimization of biogas high-pressure water washing process in actual complex environments, and has important engineering application value.

[0063] The biogas high-pressure water washing process of the present invention takes large and medium-sized biogas projects in my country as an example, and the biogas flow rate treated is 20.8m 3 / h, the biogas composition is 60% CH4, 38% CO2 and 2% other gases (such as H2S, N2, etc.), the temperature is 20℃ and the pressure is 0.1MPa.

[0064] The present invention proposes a modeling and optimization method based on an adaptive online extreme learning machine and a new multi-objective differential evolution algorithm. Figure 1 and Figure 2 , the specific steps are as follows:

[0065] (1) An adaptive online extreme learning machine is used to establish the product gas quality and equipment energy consumption model of the biogas high-pressure water washing process, specifically:

[0066] (1.1) Five main variables that affect the product gas quality and equipment energy consumption of the biogas high-pressure water washing process are selected: the absorption tower pressure P a , Flash tank pressure P f , Stripping tower pressure P s , absorption tower inlet temperature T and absorbent flow rate V, these five variables are used as the input of the adaptive online extreme learning machine; the output of the adaptive online extreme learning machine is the product gas quality index, which refers to the methane concentration PCH4 in the product gas and the equipment energy consumption E s , where the concentration of methane in the product gas refers to the molar fraction of methane in the product gas, and the equipment energy consumption refers to the energy consumed by each device within one hour, in kw·h. 1500 sets of sample data of biogas high-pressure water washing process were collected, 1200 sets were used as training sets, and 300 sets of data were used as test sets. In the training set, 800 sets were selected as initial sampling data, and 400 sets were selected as newly added sampling data, which were added in a block manner to simulate the change of data sliding.

[0067] (1.2) Initialize the parameters of the extreme learning machine, randomly initialize the hidden layer weight W and bias b, and set the number of hidden layer nodes L to 30. Since the number of hidden layer nodes greatly affects the accuracy of the model, after many experiments, L = 60 is selected. According to the hidden layer output matrix H0 and the input matrix X ij (i=1,2,…,800,j=1,2,…,5), and the model of product gas quality and equipment energy consumption of biogas high-pressure water washing process for 800 sets of initial sampling data was obtained:

[0068]

[0069] Among them, W n =[w n1 ,w n2 ,…,w nD ] T is the connection weight between the nth hidden layer node and the input layer; X i =[x i1 ,x i2 ,…,x iD ] T is the i-th D-dimensional variable; β n =[w n1 ,w n2 ,…,w nM ] T is the connection weight between the nth hidden layer node and the output layer; b n is the bias of the nth hidden layer node; G(W n ,b n ,X i )=g(W n T *X i +b n ), the activation function g selects the sigmoid function. H0 is the hidden layer output matrix of 800 sample data of biogas high-pressure water washing, which is expressed as:

[0070]

[0071] According to the output of product gas quality and equipment energy consumption obtained by the extreme learning machine and the actual output of both, the weight β0 of 800 initial sample data is calculated:

[0072] Among them, β0 corresponds to the output weight matrix under 800 sample data of biogas high-pressure water washing; T0 corresponds to the output matrix under 800 sample data of biogas high-pressure water washing; K0 corresponds to the square of the determinant of the hidden layer output matrix H0 under 800 sample data of biogas high-pressure water washing.

[0073] (1.3) Use 400 sets of data in the training set as the newly added sampling data, where the distribution characteristics of these 400 sets of data are inconsistent with the distribution characteristics of the first 800 sets of data; add the 400 sets of data in batches, divided into 10 batches, that is, each batch has 40 data. In order to reduce the computational cost of retraining the model, update the model according to the following iteration, that is, update the output weights β and K:

[0074]

[0075] Among them, k represents the number of batches set, which is 10 here; β (k-1) represents the output weight of the model established based on 800+40*(k-1) sample data; T k is the output matrix of the current 40*k data; H k The hidden layer output matrix of the current 40*k data; is the adaptive factor.

[0076] Since the distribution characteristics of the 400 groups of data added later are inconsistent with the first 800 groups of data, with the continuous addition of new samples, the model features established previously may be outdated. If a larger weight is given to the old model, the established product gas quality and equipment energy consumption model will be inaccurate; if a larger weight is given to the new sample features, the model will be continuously updated with the features of the new data, which will reduce the generalization performance of the model. Therefore, the adaptive factor and Balancing the relationship between the two and considering the degree of influence of both, its adaptive expression is as follows:

[0077]

[0078] Among them, error new Indicates the mean square error of the new model established by adding sample data; error old It represents the mean square error of the old model established based on the previous sample data. Since the previously established model has been stable, the prediction effect of the new model is compared with the old model. If the mean square error of the model is larger when new data is added, the new data sample feature is given a larger weight, that is, 1-φ k Increase, otherwise, the opposite.

[0079] (1.4) The product gas quality and equipment energy consumption model based on 1200 sets of sample data is obtained by continuously iterating and updating the output weight value, and the obtained model is brought into the test set for testing. In order to verify the effectiveness of the adaptive online extreme learning machine method (AOS-ELM) proposed in the present invention, it is compared with radial basis neural network (RBF), least squares support vector machine (LS-SVM), LS-SVM based on particle swarm improvement (PSO-LS-SVM), and original online extreme learning machine (OS-ELM). The first three algorithms do not have an incremental learning mechanism, and 1200 sets of sample data are used as training sets for training. The training data of the OS-ELM algorithm is set the same as that of AOS-ELM. The training function of the RBF network selects the radial basis function, the spread factor spread is set to 90, and the number of hidden layer neurons is 60. The kernel function of the LS-SVM selects the radial basis function, the regularization factor λ is set to 0.3, and the parameter γ is set to 0.01. The number of iterations of the iterative PSO in the PSO-LS-SVM is set to 200. The setting parameters of OS-ELM are consistent with those of AOS-ELM. In order to demonstrate the prediction effect of each algorithm, three parameters are selected as performance evaluation indicators, namely, mean absolute error (MAE), mean square error (MSE) and root mean square error (RMSE). The performance of these five methods on the test set is shown in Table 1, which shows that the adaptive online extreme learning machine method proposed in the present invention has better prediction accuracy and a good balance between the characteristics of new sample data and the old model. In order to vividly demonstrate the adaptive online extreme learning machine method proposed in the present invention, 50 groups of data were randomly selected, and the actual outputs of product gas quality and equipment energy consumption were compared with the predicted outputs based on the adaptive online extreme learning machine, as shown in Figure 1. Figure 3 As shown in the figure, the actual output and predicted output of product gas quality and equipment energy consumption are basically consistent. Therefore, the model established by this method can be used as the objective function of product gas quality and equipment energy consumption.

[0080] Table 1. Comparison of results of different methods

[0081]

[0082] The multi-objective function of biogas high-pressure water washing product gas quality and equipment energy consumption constructed by adaptive online extreme learning machine is expressed as follows:

[0083]

[0084] st L≤P a ,P f ,P s ,V,T≤U (23)

[0085] Among them, L and U represent P a , Pf , P s , V, T lower and upper bounds; f PCH4 and f Es They represent the objective functions of biogas high-pressure water washing product gas quality and equipment energy consumption respectively.

[0086] (2) A new multi-objective differential evolution algorithm method is used to solve the multi-objective function of biogas high-pressure water washing product gas quality and equipment energy consumption. The specific operation steps are as follows:

[0087] (2.1) Set the parameters involved in the new multi-objective differential evolution algorithm and initialize the population. Set the population size N = 100, the maximum number of iterations G = 100, the value range of the mutation factor F to [0.2, 0.9], and the value range of the crossover factor CR to [0.1, 0.9]; set P a , P f , P s , V, and T are used as decision variables. The operating intervals of the five decision variables are shown in Table 2. 100 individuals are randomly generated within the operating intervals of the decision variables to form the initial population P;

[0088] Table 2. Operating intervals of decision variables

[0089]

[0090] (2.2) The two models of product gas quality and equipment energy consumption established above are PCH4 、f Es As the fitness function, the fitness function values ​​on the two targets are calculated respectively; the non-dominated sorting and crowding distance are calculated for each individual;

[0091] (2.3) A mutation strategy based on the number of non-dominated solutions and an adaptive mutation factor are used to perform mutation operations on each individual in the population P. The formula is as follows:

[0092]

[0093] Among them, V i (t+1) is the i-th individual X in the t-th generation population i (t) The corresponding variant individual, X r1 (t),X r2 (t),X r3 (t) Different individuals randomly selected from the tth generation population, X best (t) represents the individual with the largest crowding distance among all non-dominated individuals in the t-th generation population; F is the mutation factor; SP represents the number of non-dominated solutions.

[0094] The number of non-dominated solutions is compared with the population size. If SP is less than 100, random individuals in the population are used to perform mutation operations with the differential vector to improve individual diversity and expand the search range. The mutation factor F1 should be adaptively changed according to the population evolution generation and the quality of individual solutions in the population. The quality of individual solutions is measured by the fitness function value. For individuals with poor fitness, the degree of mutation should be increased. If SP is equal to 100, the individuals with the largest crowding distance of non-dominated individuals in the population are used to perform mutation operations with the differential vector, so that the population has good distribution performance. The mutation factor F2 should be adaptively changed according to the population evolution generation and the distance between individuals. The distance between individuals is measured by the crowding distance of non-dominated solutions. For individuals with more crowded decision space, the degree of mutation should be increased. The adaptive expressions of factors F1 and F2 are as follows:

[0095]

[0096] Among them, f k max ,f k min are the maximum and minimum values ​​of the kth target, i.e., the maximum and minimum values ​​of product gas quality and equipment energy consumption; f k i represents the fitness function value of the current individual at the kth target; d max , d min They represent the maximum and minimum individual crowding distances of non-boundary extreme points in the non-dominated solution; d is the crowding distance; f k (i-1) and f k (i+1) are the objective function values ​​of the two individuals adjacent to individual i on the kth target; d i is the crowding distance value of the current individual in the non-dominated solution; t is the current evolutionary generation.

[0097] (2.4) According to the mutation strategy based on the number of non-dominated solutions described in (2.3), the crossover operation is performed on the mutant individuals using the corresponding crossover strategy based on the number of non-dominated solutions. The formula is as follows:

[0098]

[0099] According to the adaptive strategies of the above mutation factors F1 and F2, the adaptive expressions of the corresponding adaptive crossover factors CR1 and CR2 are as follows:

[0100]

[0101] Where, i = 1, 2, ... 100, j = 1, 2, ... 5; x ij (t) represents the population individual X i The j-th dimension component of (t); vij (t+1) is the variant individual V i The j-th dimension component in (t+1); CR represents the crossover factor; k represents a random integer in [1,D]; u ij (t+1) is the experimental individual;

[0102] (2.5) After mutation and crossover operations, new individuals are generated to form population Q; populations P and Q are merged to form population R, and according to the non-dominated relationship and crowding distance strategy, a new population P' of the next generation of evolution is formed;

[0103] (2.6) Algorithm termination condition judgment: if t < 100, return to steps (2.3)-(2.5) to continue to optimize; otherwise, terminate the calculation and output the Pareto optimal frontier corresponding to product gas quality and equipment energy consumption;

[0104] (2.7) According to the expectations of decision makers, the corresponding Pareto optimal solution set is selected on the Pareto optimal frontier of product gas quality and equipment energy consumption. Decision makers in the field of high-pressure water washing are usually more concerned about product gas quality. Therefore, the optimal operating variables with high product gas quality and low equipment energy consumption can be selected according to the Pareto optimal solution set.

[0105] Figure 4 The Pareto optimal frontier is shown by using a new multi-objective differential evolution algorithm to solve the two objectives of the biogas high-pressure water washing process, product gas quality and equipment energy consumption. Figure 3 A1 and A2 in the figure represent boundary areas. Points in the A1 area represent high product gas quality but high equipment energy consumption. Points in the A2 area represent low product gas quality but low equipment energy consumption. The A3 area represents the ideal area, which can find ideal operating variables with high product gas quality and low equipment energy consumption. Decision makers can choose the corresponding optimal operating variables according to actual needs. The biogas high-pressure water washing process usually does not take into account the energy consumption of the equipment and makes the product gas quality reach 97%, as shown by point P in the figure. Therefore, decision makers can find the optimal operating variables in the space above point P in the A1 area.

[0106] Finally, it should be noted that the present invention does not explain in detail the common knowledge recognized by technicians in this field. The above is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A modeling and optimization method for biogas high-pressure water washing, characterized in that: The method includes the following steps: Step 1: Collect the initial sample data of the biogas high-pressure water washing process; Step 2: Based on the adaptive online learning machine, establish a multi-objective initial model of product gas quality and equipment energy consumption for the sample data of the biogas high-pressure water washing process. Collect new samples of the biogas high-pressure water washing process, and use an adaptive iterative optimization model that weighs the characteristics of the old model and the new samples to form a multi-objective optimization model of product gas quality and equipment energy consumption; Step 3: Solve the multi-objective optimization model of product gas quality and equipment energy consumption of the biogas high-pressure water washing process based on the new multi-objective differential evolution algorithm; Step 4: The decision maker selects the best operating variables with high product gas quality and low equipment energy consumption according to the Pareto optimal solution set; Step 2 includes the following steps: Step 2.1: Based on the initial sample data of the biogas high-pressure water washing process, use the main variables that affect the product gas quality and equipment energy consumption of the biogas high-pressure water washing process as inputs, and use the indicators for evaluating the product gas quality and the indicators for equipment energy consumption of the biogas high-pressure water washing process as outputs respectively to establish an initial model of the product gas quality and equipment energy consumption of the biogas high-pressure water washing process; Step 2.2: Establish an initial model for product gas quality and equipment energy consumption of the biogas high-pressure water washing process and Step 2.3: Collect N k New sample data, using adaptive iterative update model that weighs the old model and new sample features; Step 2.4: Through continuous iteration and update of step 2.3, N0+N is formed k The multi-objective optimization model of product gas quality and equipment energy consumption is constructed, and N0 represents the number of initial sample data of biogas high-pressure water washing; Step 3 includes the following steps: Step 3.1: Set the parameters involved in the new multi-objective differential evolution algorithm and initialize the population, set the population size N, the maximum number of iterations G, and the value range of the mutation factor F [F min ,F max ], the value range of the cross factor CR is [CR min ,CR max ]; The main variables that affect the product gas quality and equipment energy consumption are taken as decision variables, and N individuals are randomly generated within the operation range of the decision variables to form an initial population P; Step 3.2: Take the multi-objective optimization model of product gas quality and equipment energy consumption established in Step 2.4 as the fitness function, calculate the fitness function values on the two objectives respectively, and perform non-dominated sorting and crowding distance calculation for each individual; Step 3.3: Perform a mutation operation on each individual in the population P based on the mutation strategy of the number of non-dominated solutions and the adaptive mutation factor; Step 3.4: According to the mutation strategy of the number of non-dominated solutions, use its corresponding crossover strategy based on the number of non-dominated solutions to perform a crossover operation on the mutated individuals; Step 3.5: After the mutation and crossover operations, generate new individuals to form a population Q; merge the populations P and Q to form a population R, and form a new generation of evolutionary population P' according to the non-dominated relationship and crowding distance strategy; Step 3.6: Judge the algorithm termination condition. If t < G, return to Steps 3.3 - 3.5 to continue the optimization, otherwise terminate the calculation and obtain the Pareto optimal solution set corresponding to the product gas quality and equipment energy consumption; The formula for Step 3.3 is: Among them, V i (t+1) is the i-th individual X in the t-th generation population i (t) The corresponding variant individual, X r1 (t),X r2 (t),X r3 (t) is a different individual randomly selected from the t-th generation population, X best (t) represents the individual with the largest crowding distance among all non-dominated individuals in the t-th generation population; F is the variation factor; SP represents the number of non-dominated solutions, and N is the population size; Compare the number of non-dominated solutions with the population size. If SP is less than N, it indicates that the number of non-dominated solutions is not enough. Use a random individual in the population to perform a mutation operation with the differential vector. Its mutation factor F1 should adaptively change according to the population evolution generation and the quality of the individual solutions in the population. The quality of the individual solutions is measured by the fitness function value. If SP is equal to N, it indicates that all individuals in the population are non-dominated solutions. Use the individual with the largest crowding distance among the non-dominated individuals in the population to perform a mutation operation with the differential vector. Its mutation factor F2 should adaptively change according to the population evolution generation and the distance between individuals. The distance between individuals is measured by the crowding distance of the non-dominated solutions. The adaptive expressions of the mutation factors F1 and F2 are as follows: in, are the maximum and minimum values ​​of the kth target, i.e., the maximum and minimum values ​​of product gas quality and equipment energy consumption; f k i represents the fitness function value of the current individual at the kth target; d max , d min They represent the maximum and minimum individual crowding distances of non-boundary extreme points in the non-dominated solution; m is the number of targets; d is the crowding distance; f k (i-1) and f k (i+1) are the objective function values ​​of the two individuals adjacent to individual i on the kth target; d i is the crowding distance value of the current individual in the non-dominated solution; t is the current evolutionary generation, G is the maximum number of iterations; F represents the mutation factor; F max ,F min Represent the upper and lower bounds of the variation factor respectively; The mutation strategy formula for Step 3.4 is: Based on the above adaptive strategies of the mutation factors F1 and F2, the corresponding adaptive crossover factors CR1 and CR2 have the following adaptive expressions: Where i = 1, 2, ... N, j = 1, 2, ... D, D represents the dimension of the individual; x ij (t) represents the population individual X i The j-th dimension component of (t); v ij (t+1) is the variant individual V i The j-th dimension component in (t+1); CR represents the crossover factor; k represents a random integer in [1,D]; u ij (t+1) is the experimental individual; CR max ,CR min They represent the upper and lower bounds of the crossover factor respectively.

2. The modeling and optimization method of biogas high-pressure water washing according to claim 1 is characterized in that: The input and output of the model in step 2.1 are based on the collected initial sample data of N0 biogas high-pressure water washing, and the input of the extreme learning machine is determined as D represents the dimension of the input variable, which is the number of main variables that affect the product gas quality and equipment energy consumption of the biogas high-pressure water washing process; the output of the extreme learning machine is determined as M represents the dimension of the output variable, which is the product gas quality index and equipment energy consumption index of the biogas high-pressure water washing process. The product gas quality index refers to the concentration of methane in the product gas PCH4, and the equipment energy consumption index refers to the sum of the compressor energy consumption, pump energy consumption, condenser energy consumption, blower energy consumption and other auxiliary equipment energy consumption E s .

3. The modeling and optimization method of biogas high-pressure water washing according to claim 2 is characterized in that: Step 2.2 includes the following steps: Initial model of product gas quality and equipment energy consumption of biogas high-pressure water washing process and Initialize the extreme learning machine parameters, including the number of hidden layer nodes L, the hidden layer weight W and the bias b; according to the hidden layer output matrix H0 and the input matrix X ij (i=1,2,…,N0,j=1,2,…,D), the model of product gas quality and equipment energy consumption of biogas high-pressure water washing process is obtained: Among them, W n =[w n1 ,w n2 ,…,w nD ] T is the connection weight between the nth hidden layer node and the input layer; X i =[x i1 ,x i2 ,…,x iD ] T is the i-th D-dimensional variable; β n =[w n1 ,w n2 ,…,w nM ] T is the connection weight between the nth hidden layer node and the output layer; b n is the bias of the nth hidden layer node; G(W n ,b n ,X i )=g(W n T *X i +b n ), g is the activation function, H0 is the hidden layer output matrix of N0 sample data of biogas high-pressure water washing, which is expressed as: According to the output of product gas quality and equipment energy consumption obtained by the extreme learning machine and the actual output of the two, the weight β0 of N0 sample data is calculated using the least squares method: Among them, β0 corresponds to the output weight matrix under N0 sample data of biogas high-pressure water washing; T0 corresponds to the output matrix under N0 sample data of biogas high-pressure water washing; K0 corresponds to the square of the determinant of the hidden layer output matrix H0 under N0 sample data of biogas high-pressure water washing.

4. A modeling and optimization method for biogas high-pressure water washing according to claim 3, characterized in that: Step 2.3 includes the following steps: After the biogas high-pressure water washing equipment had been running for a period of time, N k New sample data, according to the following trade-off between the old model and the new sample features, the adaptive iterative update model is updated, that is, the output weights β and K are updated: Among them, β (k-1) According to N k -1 sample-based model output weight; T k For the current N k The output matrix of data; H k For the current N k The hidden layer output matrix of data; is the adaptive factor, β (k-1) and K k-1 represents the model characteristics established based on the previous sample data, and T k , H k For the current N k The features of the newly sampled data.

5. A modeling and optimization method for biogas high-pressure water washing according to claim 4, characterized in that: Adaptive Factor The calculation formula is: Among them, error new Indicates the mean square error of the new model established by adding sample data; error old Represents the mean square error of the old model built based on the initial sample data.

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