CN114741772B - Method for solving design problem of partition wall rectifying tower based on heuristic algorithm - Google Patents
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- LFQSCWFLJHTTHZ-UHFFFAOYSA-N Ethanol Chemical compound CCO LFQSCWFLJHTTHZ-UHFFFAOYSA-N 0.000 description 8
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Abstract
The invention relates to a method for solving the design problem of a partition wall rectifying tower based on a heuristic algorithm, belongs to the field of chemical engineering design, and is used for solving the problem of determining key parameters in the design of the partition wall rectifying tower. Specifically, an improved cell particle swarm optimization method (KCPSO) based on an online Kriging model is adopted. By introducing an online Kriging model to assist in searching of cell particle swarms and matching with a partition wall rectifying tower model in simulation software, the optimal solution can be found in a short time. The invention can greatly improve the convergence quality and convergence speed of particle swarm, effectively solve the design problem of the dividing wall rectifying tower, and the result can be used as the basis of the design of the dividing wall rectifying tower.
Description
Technical Field
A method for solving the design problem of a partition wall rectifying tower based on a heuristic algorithm belongs to the field of chemical industry.
Technical Field
The partition wall rectifying tower is one kind of important operation unit and equipment for separation and purification in petroleum production and chemical engineering. Compared with the traditional rectifying tower, the prior separating wall rectifying tower and the thermal coupling rectifying tower are used as a novel rectifying device, so that the thermodynamic efficiency of the rectifying tower is greatly improved, and the investment cost of equipment is further reduced.
The design problem of the dividing wall rectifying tower is an important problem in the chemical industry field. The design of the device is more complex than that of a traditional rectifying tower because the interior of the rectifying tower with the separation wall is complex, decision variables are numerous, and the variables are mutually coupled.
Heuristic algorithms are one algorithm that solves complex problems with acceptable computational costs. In complex problems, the method of traversing the solution often requires computation time and space beyond the acceptable range, thus resulting in problems that cannot solve the optimal solution under the existing state of the art. The heuristic algorithm can solve the optimal solution with high probability through a reasonable guiding mechanism and a limited number of attempts at acceptable calculation cost.
The current heuristic algorithms such as standard particle swarm algorithm, genetic algorithm, simulated annealing algorithm and the like generally refer to production life experience or natural law. The algorithms have remarkable effect in solving specific problems, but problems such as sinking into local optimal solutions are easy to occur in solving the design problems of the rectifying tower.
Disclosure of Invention
The invention provides an improved cell particle swarm optimization method (KCPSO) based on an online Kriging model, which is used for solving the problem of determining key parameters in the design of a dividing wall rectifying tower. In the running process of the method, the Kriging model is trained by sampling the initial state of the cell particles, and then specific points are continuously added in the cell search iteration process, so that the defect that a large amount of simulation data is required by an offline agent model and the defect of fluctuation of the predicted value of the online agent model are effectively avoided, the speed and direction of the particles are improved through the prediction of the model, and the optimal solution can be found in a shorter iteration process. The method has the characteristics of good stability and high convergence efficiency, and simultaneously shows good effect when applied to the optimization problem of the three-component dividing wall rectifying tower, and the convergence quality and the convergence speed are greatly improved.
The main flow of the method is to continuously adjust related parameters by KCPSO through connecting simulation software and KCPSO programs so as to find ideal optimal parameters. The invention is characterized in that the method further comprises the following steps in sequence:
step one: determining information of a partition wall rectifying tower to be solved, wherein the information comprises component numbers, raw material information and product requirement information; determining decision variables to be solved; determining an objective function T (x), wherein the function value is used for describing the advantages and disadvantages of the design, and is generally annual total cost or energy consumption; the design problem of the dividing wall rectifying tower is converted into a minimization problem;
step two: establishing a simulation model of the partition wall rectifying tower to be solved in Aspen Plus flow simulation software, and connecting Aspen Plus and KCPSO self-programming algorithm programs, wherein the KCPSO program comprises the steps three to ten;
Step three: randomly initializing the positions and the speeds of m particles, wherein m is a complete square number, m is more than or equal to 9, the positions of m are vectors x= (x 1,x2,…,xD)T, input Aspen Plus for checking validity, if the vectors are legal, carrying out objective function to calculate the fitness J, J=T (x) of each particle, and if the vectors are illegal, re-initializing the positions of the illegal particles;
step four: according to the rules of the cellular neighbors of Moore type (see fig. 2), 8 neighbor particles per particle are calculated: the particles being placed in one by number In the grid of (2), a periodic boundary is adopted, and 8 particles of each particle, namely an upper particle, a lower particle, a left particle, a right particle, an upper particle, a lower particle and a lower particle, are neighbors;
Step five: training an online Kriging proxy model by using the positions and fitness J of all particles, predicting to obtain a position x Kriging, carrying in Aspen Plus to check validity, and carrying in an objective function to obtain the fitness J Kriging＝T(xKriging of the point if the position x Kriging is legal; if not, retraining an online Kriging agent model, predicting to obtain a new position x Kriging until legal, and then calculating the adaptability J Kriging＝T(xKriging of the point;
Step six: the position where the fitness J of the neighbor of the ith particle and the neighbor is the largest is marked as x cbest,i, and the corresponding fitness J cbest,i＝T(xcbest,i);
step seven: comparing J cbest,i and J Kriging for each particle, the position of smaller fitness is the attractor AF i for the ith particle;
Step eight: counting and updating the position P i of the i-th particle from the first iteration to the minimum value of the fitness of the first iteration and the corresponding minimum fitness thereof;
step nine: judging whether the upper limit of the iteration times is reached, if the upper limit of the iteration times is reached, stopping the operation, and continuing the next step; if the upper limit of the iteration times is not reached, updating the position of the next iteration according to a position updating formula, inputting the position of the next iteration into Aspen Plus for checking validity, if the position is not legal, repeatedly calling the position updating formula until the data are legal, and returning to the step five to continue searching after the data are all legal data;
Step ten: and the position x * of the minimum adaptability of all particles from the first iteration to the iteration is the design result.
In the first step, the optimization problem of the design problem conversion of the dividing wall rectifying tower is as follows:
minf＝T(x)
s.t.MESH equations (1)
ci≥pi
The vector x= (x 1,x2,…,xD)T is a vector formed by D decision variables, the decision variables are selected from tray number, reboiling ratio, reflux ratio, gas phase partition ratio, liquid phase partition ratio and side line extraction quantity, T (x) is an objective function, the function value of which is used for describing the advantages and disadvantages of design, generally the annual total cost or energy consumption, the smaller the objective function is, the better the design is, MESH equations are a material balance, phase balance, normalization and energy conservation equation set of a separation wall rectifying tower, c i represents the purity of the ith product, and p i represents the minimum requirement of the purity of the ith product.
In the fourth step, a Moore type cell neighbor rule is adopted, and the neighbor rule of the ith cell is as follows:
Nmoore＝{vo＝(vox,voy)||vox-vix|+|voy-viy∣∣≤1,(vox,voy)∈Z2} (2)
Wherein v ox,voy represents the coordinate value of the row and column of the neighbor cells, v ix,viy represents the coordinate value of the row and column of the ith cell, i.e. m particles are placed in one according to the number sequence In the grid of (a), a periodic boundary is adopted, and 8 particles of which each particle has an upper, lower, left, right, upper left, upper right, lower left and lower right are neighbors, and Z 2 represents a set formed by row and column coordinate values of all particles.
In the seventh step, the selection rule of the attractor AF i of the ith particle is:
in step eight, the update formula of the position X i and the velocity V i of the particle is as follows:
Vi(t+1)＝ωtVi(t)+c1r1(Pi(t)-Xi(t))+c2r2(AFi(t)-Xi(t)) (4)
Xi(t+1)＝Xi(t)+Vi(t) (5)
Wherein t is the iteration number, P i (t) is the historical optimal position of the particle i for stopping the current t iteration, X i (t) is the position of the particle i at the t iteration, AF i (t) is the attractor of the particle i at the t iteration, omega t is the inertial weight, and the size of the attractor determines the size of the particle for changing the current speed; non-negative numbers c 1 and c 2 are learning factors, and the value is 2; r 1 and r 2 are random values in the range of [0,1], ω t is inertial weight, and its calculation formula is as follows:
Wherein t max is the maximum iteration number; omega max takes 0.9 and omega end takes 0.4.
The method is characterized in that the method comprises the steps of firstly carrying the tray number represented by a particle position vector x, reboiling ratio, reflux ratio, gas phase division ratio, liquid phase division ratio and side line extraction amount into Aspen Plus software to test whether the purity of a product meets the requirement, and if so, legal, otherwise, illegal.
Advantageous results
According to the test result of the mathematical calculation example, the KCPSO method in the invention is higher than the traditional method in the aspects of convergence speed and convergence quality. Fig. 3,4, and 5 show KCPSO comparisons with conventional cellular particle swarm algorithm (CPSO) and standard particle swarm algorithm (PSO) at 3, 7, and 11 dimensions, respectively. In the graph, the horizontal axis of the curve represents the iteration times, and the vertical axis represents the iteration results; the faster the drop, the faster the convergence speed is indicated; the vertical axis value of the lowest point to which the final drop is made represents the final iteration result, and the smaller the value is, the better the convergence quality is. From the comparison, KCPSO exhibits better effect at higher dimensions.
In the application test in the chemical industry field, the invention has good performance in the analysis of sensitivity analysis, performance analysis, result analysis and the like. The invention can also solve the design problem of various types of dividing wall rectifying towers.
Therefore, the invention can effectively solve the problem of the optimal design of the dividing wall rectifying tower, and the result can be used as the basis of the design of the dividing wall rectifying tower.
Drawings
FIG. 1 is a flow chart of the core part of the invention;
FIG. 2 is a schematic diagram of a Moore two-dimensional cellular automaton spatial structure;
FIG. 3 is an iteration curve of KCPSO, CPSO, PSO in the 5-dimensional case;
FIG. 4 is an iteration curve of KSCPSO, CPSO, PSO in the 7-dimensional case;
FIG. 5 is an iteration curve of KSCPSO, CPSO, PSO in the 11-dimensional case;
FIG. 6 is a schematic structural view of a three-component dividing wall rectifying column (DWDC);
FIG. 7 is a schematic diagram of a fully thermally coupled column equivalent to DWDC;
FIG. 8 is a simulation model of DWDC;
Fig. 9 shows the optimal DWDC design scheme obtained by the algorithm.
Detailed Description
In the embodiment, simulation software is adopted to model the isolation wall rectifying tower, and then KCPSO programs are connected to automatically solve the problem of determining key parameters in the design of the isolation wall rectifying tower. The key of the design of the dividing wall rectifying tower is that the determination of 11 decision variables such as the number of different tower plates, reboiling ratio, reflux ratio, gas phase dividing ratio, liquid phase dividing ratio, side line extraction amount and the like is that in practice, some of the decision variables are generally selected as variables to be solved, and the others are determined through engineering experience or professional software.
For the purpose of illustrating the invention in more detail, this section illustrates a specific embodiment of the invention by way of example of a three-component dividing wall rectifying column. The exemplary embodiments of the present invention and the descriptions thereof are used herein to explain the present invention, but are not intended to limit the invention.
The three-component dividing wall rectifying column (DWDC) is shown in fig. 6, the equivalent structure of the fully thermally coupled column is shown in fig. 7, wherein DWDC can be divided into six parts (I-VI), three-component mixed feed F to be separated is input into the column and is subjected to preliminary separation (a/C) through the parts I and II, two mixtures (AB and BC) are generated due to the difference of relative volatilities and enter the upper part III and IV (AB) and the lower part V and VI (BC) of the main column respectively for further separation, and then high-purity products a and C are produced through the top and bottom of the column, and the target product B with high purity can be obtained by reasonably arranging side discharge positions. The purpose of this example was to rapidly obtain the optimum tray numbers of 6 column sections, reboiling ratio, reflux ratio, gas phase dividing ratio, liquid phase dividing ratio and side offtake.
Step one: determining information of a partition wall rectifying tower to be solved, wherein the information comprises component numbers, raw material information and product requirement information; in the embodiment, the composition is 3, the raw material is an equimolar fraction saturated liquid mixture of ethanol, propanol and butanol, the feeding pressure is 0.1Mpa, the feeding temperature is 365.93K, and the molar fractions of the corresponding ethanol, propanol and butanol in the product flow at the top, the side line and the bottom of the tower are all more than or equal to 99 percent.
Determining decision variables to be solved, wherein the decision variables are respectively the column plate numbers of 6 column sections (N i, i=1, 2,3,4,5, 6), the gas phase flow rate returned to the prefractionation column (F V) and the liquid phase flow rate returned to the prefractionation column (F L); reboiling ratio, reflux ratio and side offtake ensure product purity requirements in the product stream.
The objective function T (x) is determined, and the function value is used to describe the merits of the design, in this example, the Total Annual Cost (TAC) of the dividing wall rectifying tower, so the calculation formula of the objective function can be expressed as:
T(x)＝Cop+0.3Cca
wherein the operating costs (C op) include cooling water costs and steam costs, i.e., cold and hot utility costs; the equipment cost (C ca) comprises equipment investment cost, tower plate cost, heat exchanger cost and the like; 0.3 is the annual depreciation rate of the device; the operating and equipment costs are determined by the values of 8 decision variables.
The design problem of the dividing wall rectifying tower is converted into the minimization problem. The optimization problem expression method is shown in the formula (7).
minf＝T(N1,N2,N3,N4,N5,N6,Vp,Lp)
s.t.MESH equations
c1≥p1 (7)
c2≥p2
c3≥p3
Wherein N i (i=1, 2,3, …) is the number of six stages of trays of the dividing wall rectifying column, respectively; v P is the gas phase flow back to the prefractionator (instead of the gas phase split ratio in this example); l P is the liquid phase flow rate back to the prefractionator (instead of the liquid phase split ratio in this example); MESH equations represent basic balance equations, namely a partition wall rectifying tower material balance, phase balance, normalization and energy conservation equation set; c 1、c2、c3 represents the purity of the corresponding ethanol, propanol, butanol in the product streams at the top, side and bottom, respectively, and p 1、p2、p3 represents the minimum requirement for the purity of ethanol, propanol, butanol, respectively. All constraints are calculated in Aspen Plus.
Step two: establishing a simulation model of the partition wall rectifying tower to be solved in Aspen Plus (see FIG. 8), and connecting Aspen Plus and KCPSO programs;
Step three: randomly initializing the positions and the speeds of 49 particles, wherein the positions are vectors x= (x 1,x2,…,x8)T, input Aspen Plus for checking validity) formed by 8 decision variables;
Step four: according to the Moore-type cellular neighbor rule shown in fig. 2, 8 neighbor particles per particle are calculated: the particles being placed in one by number (I.e., 7*7) using periodic boundaries, each particle has 8 particles up, down, left, right, up-left, up-right, down-left, down-right as neighbors; taking the particle with the number of 2 as an example, the neighbor particles are 8 particles with the numbers of 43, 44, 45,1,3,8,9 and 10 respectively.
Step five: training an online Kriging proxy model by using the positions and fitness J of all particles, predicting to obtain a position x Kriging, carrying in Aspen Plus to check validity, and carrying in an objective function to obtain the fitness J Kriging＝T(xKriging of the point if the position x Kriging is legal; if not, retraining an online Kriging agent model, predicting to obtain a new position x Kriging until legal, and then calculating the adaptability J Kriging＝T(xKriging of the point;
Step six: the position where the fitness J of the neighbor of the ith particle and itself is greatest is noted as x cbest,i, corresponding fitness J cbest,i＝T(xcbest,i).
Step seven: comparing J cbest,i and J Kriging for each particle, the position of smaller fitness is the attractor AF i for the ith particle.
Step eight: counting and updating the position P i of the i-th particle from the first iteration to the minimum value of the fitness of the first iteration and the corresponding minimum fitness thereof;
Step nine: judging whether the upper limit of the iteration times is reached, if the upper limit of the iteration times is reached, stopping the operation, and continuing the next step; if the upper limit of the iteration times is not reached, updating the position of the next iteration according to the position updating formula, inputting the position of the next iteration into AspenPlus to check validity, and if the position of the next iteration is not legal, repeatedly calling the position updating formula until the data are legal. And after the data are legal data, returning to the step five to continue searching.
Step ten: and the position x * of the minimum adaptability of all particles from the first iteration to the iteration is the design result. Fig. 9 shows the final design from this example.
According to the test result of the mathematical calculation example, the KCPSO method in the invention is higher than the traditional method in the aspects of convergence speed and convergence quality. Fig. 3,4, and 5 show KCPSO comparisons with conventional cellular particle swarm algorithm (CPSO) and standard particle swarm algorithm (PSO) at3, 7, and 11 dimensions, respectively. In the graph, the horizontal axis of the curve represents the iteration times, and the vertical axis represents the iteration results; the faster the drop, the faster the convergence speed is indicated; the vertical axis value of the lowest point to which the final drop is made represents the final iteration result, and the smaller the value is, the better the convergence quality is. From the comparison, KCPSO exhibits better effect at higher dimensions.
In addition, the invention has good performance in the analysis of sensitivity analysis, performance analysis, result analysis and the like. The invention can also solve the design problem of various types of dividing wall rectifying towers.
Therefore, the invention can effectively solve the design problem of the dividing wall rectifying tower, and the result can be used as the basis of the design of the dividing wall rectifying tower.
Claims (6)
1. A heuristic algorithm-based method for solving the design problem of a dividing wall rectifying tower is characterized by comprising the following steps:
Step one: determining information of a partition wall rectifying tower to be solved, wherein the information comprises component numbers, raw material information and product requirement information; determining decision variables to be solved; determining an objective function T (x), wherein the function value is used for describing the advantages and disadvantages of the design; the design problem of the dividing wall rectifying tower is converted into an optimization problem;
step two: establishing a simulation model of the partition wall rectifying tower to be solved in Aspen Plus flow simulation software, and connecting Aspen Plus and KCPSO self-programming algorithm programs, wherein the KCPSO program comprises the steps three to ten;
Step three: randomly initializing the positions and the speeds of m particles, wherein m is a complete square number, m is more than or equal to 9, the positions of m are vectors x= (x 1,x2,…,xD)T, input Aspen Plus for checking validity, if the vectors are legal, carrying out objective function to calculate the fitness J, J=T (x) of each particle, and if the vectors are illegal, re-initializing the positions of the illegal particles;
Step four: according to Moore type cell neighbor rules, 8 neighbor particles of each particle are calculated: the particles being placed in one by number In the grid of (2), a periodic boundary is adopted, and 8 particles of each particle, namely an upper particle, a lower particle, a left particle, a right particle, an upper particle, a lower particle and a lower particle, are neighbors;
Step five: training an online Kriging proxy model by using the positions and fitness J of all particles, predicting to obtain a position x Kriging, carrying in Aspen Plus to check validity, and carrying in an objective function to obtain the fitness J Kriging＝T(xKriging of the point if the position x Kriging is legal; if not, retraining an online Kriging agent model, predicting to obtain a new position x Kriging until legal, and then calculating the adaptability J Kriging＝T(xKriging of the point;
Step six: the position where the fitness J of the neighbor of the ith particle and the neighbor is the largest is marked as x cbest,i, and the corresponding fitness J cbest,i＝T(xcbest,i);
step seven: comparing J cbest,i and J Kringing for each particle, the position of smaller fitness is the attractor AF i for the ith particle;
Step eight: counting and updating the position P i of the i-th particle from the first iteration to the minimum value of the fitness of the first iteration and the corresponding minimum fitness thereof;
step nine: judging whether the upper limit of the iteration times is reached, if the upper limit of the iteration times is reached, stopping the operation, and continuing the next step; if the upper limit of the iteration times is not reached, updating the position of the next iteration according to a position updating formula, inputting the position of the next iteration into Aspen Plus for checking validity, if the position is not legal, repeatedly calling the position updating formula until the data are legal, and returning to the step five to continue searching after the data are all legal data;
Step ten: and the position x * of the minimum adaptability of all particles from the first iteration to the iteration is the design result.
2. The method for solving the design problem of the dividing wall rectifying tower based on the heuristic algorithm as claimed in claim 1, wherein the method comprises the following steps: in the first step, the optimization problem for the design problem conversion of the dividing wall rectifying tower is as follows:
minf＝T(x)
s.t.MESH equations (1)
ci≥pi
The vector x= (x 1,x2,…,xD)T is a vector formed by D decision variables, the decision variables are selected from the column plate number, reboiling ratio, reflux ratio, gas phase partition ratio, liquid phase partition ratio and side line extraction quantity, T (x) is an objective function, the function value of which is used for describing the advantages and disadvantages of design, including total annual cost or energy consumption, the smaller the objective function is, the better the design is, MESH equations are a material balance, phase balance, normalization and energy conservation equation set of a separation wall rectifying tower, c i represents the purity of the ith product, and p i represents the minimum requirement of the purity of the ith product.
3. The method for solving the design problem of the dividing wall rectifying tower based on the heuristic algorithm as claimed in claim 1, wherein the method comprises the following steps: in the fourth step, adopting a Moore cell neighbor rule, wherein the neighbor rule of the ith cell is as follows:
Nmoore＝{vo＝(vox,voy)||vox-vix|+|voy-viy∣≤1,(vox,voy)∈Z2} (2)
Wherein v ox,voy represents the coordinate value of the row and column of the neighbor cells, v ix,viy represents the coordinate value of the row and column of the ith cell, i.e. m particles are placed in one according to the number sequence In the grid of (a), a periodic boundary is adopted, each particle has 8 particles of up, down, left, right, upper left, upper right, lower left and lower right as neighbors, the ith cell refers to the ith particle, and Z 2 represents a set formed by row and column coordinate values of all particles.
4. The method for solving the design problem of the dividing wall rectifying tower based on the heuristic algorithm as claimed in claim 1, wherein the method comprises the following steps: in step seven, the selection rule of the attractor AF i of the ith particle is:
5. The method for solving the design problem of the dividing wall rectifying tower based on the heuristic algorithm as claimed in claim 1, wherein the method comprises the following steps: in step eight, the position X i and velocity V i update formula for the particles is as follows:
Vi(t+1)＝ωtVi(t)+c1r1(Pi(t)-Xi(t))+c2r2(AFi(t)-Xi(t)) (4)
Xi(t+1)＝Xi(t)+Vi(t) (5)
Wherein t is the iteration number, P i (t) is the historical optimal position of the particle i for stopping the current t iteration, the position with smaller fitness is more optimal, X i (t) is the position of the particle i at the t iteration, AF i (t) is the attractor of the particle i at the t iteration, omega t is the inertial weight, and the size of the attractor determines the size of the particle for changing the current speed; non-negative numbers c 1 and c 2 are learning factors, and the value is 2; r 1 and r 2 are random values in the range of [0,1], ω t is inertial weight, and its calculation formula is as follows:
Wherein t max is the maximum iteration number; omega max takes 0.9 and omega end takes 0.4.
6. The method for solving the design problem of the dividing wall rectifying tower based on the heuristic algorithm as claimed in claim 1, wherein the method comprises the following steps: in the third, fifth and seventh steps, checking the legality means that the tray number represented by the particle position vector x, the reboiling ratio, the reflux ratio, the gas phase division ratio, the liquid phase division ratio and the side line extraction amount are brought into Aspen Plus, whether the purity of the product meets the requirement or not is tested, if the purity meets the requirement, the method is legal, and otherwise, the method is illegal.
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