CN114741772A - Method for solving design problem of partition wall rectifying tower based on heuristic algorithm - Google Patents
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Abstract
The invention relates to a method for solving the design problem of a dividing wall rectifying tower based on a heuristic algorithm, belongs to the field of chemical design, and is used for solving the problem of determining key parameters during the design of the dividing wall rectifying tower. Specifically, a cell particle swarm optimization method (KCPSO) improved based on an online Kriging model is adopted. By introducing an online Kriging model to assist the search of cellular particle swarm 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 the convergence speed of the particle swarm, effectively solve the design problem of the dividing wall rectifying tower, and the result can be used as the basis for the design of the dividing wall rectifying tower.
Description
Technical Field
A method for solving the design problem of a dividing wall rectifying tower based on a heuristic algorithm belongs to the field of chemical engineering.
Technical Field
The dividing wall rectifying tower is an important operation unit and equipment widely used for separation and purification in the petroleum production and chemical process. Compared with the traditional rectifying tower, the existing dividing wall rectifying tower and the thermal coupling rectifying tower are used as a new 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 field. The design of the device is more complex than that of the traditional rectifying tower due to the complex inside of the dividing wall rectifying tower, a plurality of decision variables and mutual coupling among the variables.
A heuristic algorithm is one that solves complex problems at an acceptable computational cost. In a complex problem, the method of traversing solution often requires computation time and space beyond an acceptable range, so that the problem cannot solve the optimal solution under the existing technical level. Heuristic algorithms, however, can solve the optimal solution with a high probability through a reasonable guiding mechanism, with an acceptable computational cost, through a limited number of attempts.
At present, heuristic algorithms such as a standard particle swarm algorithm, a genetic algorithm, a simulated annealing algorithm and the like generally use the experience of production and living or natural rules for reference. The algorithms have remarkable effect when solving specific problems, but the algorithms are easy to fall into local optimal solutions when solving the design problems of the rectifying tower.
Disclosure of Invention
The invention provides a cell particle swarm optimization (KCPSO) method improved based on an online Kriging model, which is used for solving the problem of determining key parameters during the design of a dividing wall rectifying tower. In the running process of the method, the initial state of the cell particles is sampled to train the Kriging model, and then specific points are continuously added in the cell search iteration process, so that the design not only effectively avoids the defect that an off-line agent model needs a large amount of simulation data and the defect of fluctuation of the on-line agent model predicted value, but also improves the speed and direction of the particles 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 has good effect when being applied to the optimization problem of a three-component partition wall rectifying tower, thereby greatly improving the convergence quality and the convergence speed, and the technical process of the invention is shown in figure 1.
The main flow of the method is to continuously adjust related parameters by connecting simulation software and a KCPSO program and utilizing the KCPSO to find out ideal optimal parameters. The invention is characterized in that the method also comprises the following steps in sequence:
the method comprises the following steps: determining information of a to-be-solved dividing wall rectifying tower, including component number, raw material information and product requirement information; determining decision variables needing to be solved; determining an objective function T (x), wherein the function value of the objective function T (x) is used for describing the advantages and disadvantages of the design, and the function value 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 dividing wall rectifying tower to be solved in Aspen Plus process simulation software, and connecting the Aspen Plus and a KCPSO self-programming algorithm program, wherein the KCPSO program comprises three to ten steps;
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, and the position of the vector is formed by D decision variables, namely x (x)1,x2,…,xD)TInputting Aspen Plus to check the legality; if the fitness is legal, the fitness J is substituted into the objective function to calculate the fitness J of each particle, wherein J is T (x), and if the fitness J is illegal, the position of the illegal particle is initialized again;
step four: according to the Moore type cellular neighbor (see FIG. 2) rule, 8 neighbor particles per particle are calculated: placing particles in one according to the number
In the grid, a periodic boundary is adopted, and each particle has 8 particles of upper, lower, left, right, upper left, upper right, lower left and lower right as neighbors;
step five: using the positions and the fitness J of all the particles to train an online Kriging agent model, and predicting to obtain a position xKrigingIntroducing Aspen Plus to check the legality, and if the legality is legal, introducing an objective function to obtain the fitness J of the pointKriging＝T(xKriging) (ii) a If the position is illegal, retraining the online Kriging agent model, and predicting to obtain a new position xKrigingUntil legal, then calculate the fitness J of the pointKriging＝T(xKriging)；
Step six: let x be the position where the fitness J of the i-th particle's neighbor and itself is greatestcbest,iCorresponding fitness Jcbest,i＝T(xcbest,i)；
Step seven: comparing J of each particlecbest,iAnd JKrigingThe location of smaller fitness is the attractor AF of the ith particlei；
Step eight: counting and updating the position P of the ith particle from the first iteration to the fitness minimum value of the iterationiAnd its corresponding minimum fitness;
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 Aspen Plus to check the legality, if the position updating formula is illegal, repeatedly calling the position updating formula until the data is legal, and returning to the fifth step to continue searching after the data is legal;
step ten: all particles from the first iteration to the position x of the fitness minimum for this iteration*Namely 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
wherein, the vector x is (x)1,x2,…,xD)TThe decision variables are vectors formed by D decision variables, and the decision variables are selected from the number of tower plates, reboiling ratio, reflux ratio, gas phase partition ratio, liquid phase partition ratio and side-draw amount; t (x) is an objective function, the function value of the objective function is used for describing the advantages and disadvantages of the design, generally the annual total cost or the energy consumption, and the smaller the objective function is, the better the design is; MESH equions are a material balance, phase balance, normalization and energy conservation equation set of the dividing wall rectifying tower; c. CiDenotes the purity of the ith product, piRepresents the minimum requirement for the purity of the ith product.
In the fourth step, Moore type cellular neighbor rule is adopted, and the neighbor rule of the ith cellular is as follows:
Nmoore＝{vo＝(vox,voy)||vox-vix|+|voy-viy∣∣≤1,(vox,voy)∈Z2} (2)
wherein v isox,voyA row and column coordinate value, v, representing a neighbor cellix,viyCoordinate values of rows and columns representing the ith cell, i.e. m particles are placed in one by one in the order of the numbers
In the grid, a periodic boundary is adopted, each particle has 8 particles of upper, lower, left, right, upper left, upper right, lower left and lower right as neighbors, and Z is2Representing a set of particle matrix coordinate values of the whole particle array.
Wherein in step seven, the attractor AF of the ith particleiThe selection rule of (1) is:
wherein in step eight, the position X of the particleiAnd velocity ViThe update formula 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)
where t is the number of iterations, Pi(t) historical optimal position of particle i by current t-th iteration, Xi(t) position of particle i at the t-th iteration, AFi(t) is the attractor of particle i at the t-th iteration, ωtIs an inertial weight, the magnitude of which determines the magnitude of the particle change to the current velocity; non-negative number c1And c2The value is 2 for the learning factor; r is1And r2Is at [0,1 ]]Random value in the range, ωtFor inertial weight, its calculation formula is as follows:
in the formula, tmaxIs the maximum iteration number; omegamaxTake 0.9, omegaend0.4 is taken.
Wherein, the legality is checked by introducing the number of the tower plates represented by the particle position vector x, the reboiling ratio, the reflux ratio, the gas phase partition ratio, the liquid phase partition ratio and the side line extraction amount into Aspen Plus software to test whether the purity of the product meets the requirement, if so, legality is judged, otherwise, legality is judged.
Beneficial results
According to the test result of the mathematical example, the KCPSO method in the invention is higher than the traditional method in convergence speed and convergence quality. Fig. 3,4 and 5 show the comparison of KCPSO with conventional cellular particle swarm algorithm (CPSO) and standard particle swarm algorithm (PSO) in 3, 7 and 11 dimensions, respectively. In the graph, the horizontal axis represents the iteration times, and the vertical axis represents the iteration result; the faster the drop, the faster the convergence speed; the vertical axis value of the final lowest point represents the final iteration result, and the smaller the value is, the better the convergence quality is. As can be seen from the comparison, KCPSO exhibits better effects at higher dimensions.
In the application test in the chemical field, the invention has good performance in sensitivity analysis, performance analysis, result analysis and other analysis. 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 for 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 the spatial structure of a Moore two-dimensional cellular automaton;
FIG. 3 is an iteration curve of KCPSO, CPSO, PSO in a 5-dimensional case;
FIG. 4 is an iteration curve for the 7-dimensional case of KSCPSO, CPSO, PSO;
FIG. 5 is an iteration curve for the 11-dimensional case of KSCPSO, CPSO, PSO;
FIG. 6 is a schematic diagram of a three component Dividing Wall Distillation Column (DWDC);
figure 7 is a schematic of the structure of a fully thermally coupled column equivalent to DWDC;
FIG. 8 is a simulation model of DWDC;
fig. 9 shows that the algorithm yields an optimal DWDC design.
Detailed Description
In the embodiment, simulation software is adopted to model the dividing wall rectifying tower, and then a KCPSO program is connected to automatically solve the problem of determining key parameters during the design of the dividing wall rectifying tower. The design key of the dividing wall rectifying tower is the determination of 11 decision variables such as the number of different tower plates, the reboiling ratio, the reflux ratio, the gas phase dividing ratio, the liquid phase dividing ratio, the side line extraction amount and the like, wherein some of the decision variables are generally selected as variables needing to be solved in practice, and others are determined by engineering experience or professional software.
In order to make the description of the present invention more detailed, this section shows an embodiment of the present invention by taking three sets of divided dividing wall rectification columns as an example. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
The structure of a three-component dividing wall rectifying tower (DWDC) is shown in figure 6, the structure of an equivalent complete thermal coupling tower is shown in figure 7, wherein the DWDC can be divided into six parts (I-VI), three-component mixed feed F needing to be separated is input into the tower and then is subjected to preliminary separation (A/C) through the parts I and II, two mixtures (AB and BC) are generated due to different relative volatilities and respectively enter an upper III area and an upper IV Area (AB) of a main tower and are further separated from a lower V area and a lower VI area (BC), then high-purity products A and C are produced through the top and the bottom of the tower, and a high-purity target product B can be obtained by reasonably arranging side-line discharging positions. The purpose of this example is to obtain the optimum number of 6 stages of trays, reboiling ratio, reflux ratio, gas phase split ratio, liquid phase split ratio and side draw.
The method comprises the following steps: determining information of a to-be-solved dividing wall rectifying tower, including component number, raw material information and product requirement information; in the example, the component number is 3, the raw material is a saturated liquid mixture with equal mole fractions of ethanol, propanol and butanol, the feeding pressure is 0.1Mpa, the feeding temperature is 365.93K, and the mole fractions of the ethanol, the propanol and the butanol in the product streams at the top, the side line and the bottom are all more than or equal to 99 percent.
Determining decision variables to be solved, wherein the decision variables are the tower plate numbers (N) of 6 tower sections respectivelyiI ═ 1,2,3,4,5,6), gas phase flow rate back to the prefractionator (F)V) Liquid phase flow (F) to the prefractionatorL) (ii) a The reboiling ratio, reflux ratio and side draw ensure product purity requirements in the product stream.
Determining an objective function T (x), wherein the function value of the objective function T (x) is used for describing the quality of the design, and the objective function is the Total Annual Cost (TAC) of the dividing wall rectifying tower in the example, so that the calculation formula of the objective function can be expressed as:
T(x)＝Cop+0.3Cca
wherein the operation cost (C)op) Including cooling water costs and steam costs, i.e. cold and hot utility costsUsing; equipment charge (C)ca) Including equipment investment cost, tower plate cost, heat exchanger cost and the like; 0.3 is the annual depreciation rate of the equipment; the operating and equipment fees are determined by the values of 8 decision variables.
The design problem of the dividing wall rectifying tower is converted into a minimization problem. The optimization problem representation 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
In the formula, Ni(i ═ 1,2,3, … 6) are the number of six stages in the dividing wall column; vPThe gas phase flow rate back to the prefractionator (in this example, instead of the gas phase split ratio); l is a radical of an alcoholPThe liquid phase flow rate back to the prefractionator (in this example, instead of the liquid phase split ratio); MESH equions represent basic equilibrium equations, namely a material equilibrium, phase equilibrium, normalization and energy conservation equation set of the dividing wall rectifying tower; c. C1、c2、c3Respectively representing the purity of corresponding ethanol, propanol and butanol in product streams at the top, the side and the bottom of the tower, p1、p2、p3Respectively representing the minimum requirements of the purity of ethanol, propanol and butanol. All constraints are calculated in Aspen Plus.
Step two: establishing a simulation model of the dividing wall rectifying tower to be solved in Aspen Plus (see figure 8), and connecting Aspen Plus and a KCPSO program;
step three: randomly initializing the position and speed of 49 particles, wherein the position is a vector x formed by 8 decision variables (x ═ x1,x2,…,x8)TInputting Aspen Plus to check the legality; if the fitness is legal, the fitness J is substituted into the objective function to calculate the fitness J of each particle, wherein J is T (x), and if the fitness J is illegal, the position of the illegal particle is initialized again;
step four: root of herbaceous plantAccording to the Moore type cellular neighbor rule shown in FIG. 2, 8 neighbor particles per particle were calculated: placing particles in one by number
(namely 7 x 7) in the grid, a periodic boundary is adopted, and each particle has 8 particles of upper, lower, left, right, upper left, upper right, lower left and lower right as neighbors; taking the particle number 2 as an example, the neighboring particles are 8 particles numbered 43, 44, 45, 1, 3, 8, 9, 10, respectively.
Step five: using the positions and the fitness J of all the particles to train an online Kriging agent model, and predicting to obtain a position xKrigingIntroducing Aspen Plus to check the legality, and if the legality is legal, introducing an objective function to obtain the fitness J of the pointKriging＝T(xKriging) (ii) a If the position is illegal, retraining the online Kriging agent model, and predicting to obtain a new position xKrigingUntil legal, then calculate the fitness J of the pointKriging＝T(xKriging)；
Step six: let x be the position where the fitness J of the i-th particle's neighbor and itself is greatestcbest,iCorresponding fitness Jcbest,i＝T(xcbest,i)。
Step seven: comparing J of each particlecbest,iAnd JKrigingThe position of smaller fitness is the attractor AF of the ith particlei。
Step eight: counting and updating the position P of the ith particle from the first iteration to the fitness minimum value of the iterationiAnd its corresponding minimum fitness;
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; and 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 the legality, and if the position of the next iteration is not legal, repeatedly calling the position updating formula until the data is legal. And returning to the fifth step to continue searching after the data are legal data.
Step ten: all particles from the first iteration to the position x of the fitness minimum for this iteration*The result is the design result. Fig. 9 shows the final design resulting from this example.
According to the test result of the mathematical example, the KCPSO method in the invention is higher than the traditional method in convergence speed and convergence quality. FIGS. 3,4, and 5 show the comparison of KCPSO with conventional Cellular Particle Swarm Optimization (CPSO) and standard Particle Swarm Optimization (PSO) in 3, 7, and 11 dimensions, respectively. In the graph, the horizontal axis represents the iteration times, and the vertical axis represents the iteration result; the faster the drop, the faster the convergence speed; the vertical axis value of the final lowest point represents the final iteration result, and the smaller the value is, the better the convergence quality is. As can be seen from the comparison, KCPSO exhibits better effects at higher dimensions.
In addition, the invention has good performance in sensitivity analysis, performance analysis, result analysis and other analysis. 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 for the design of the dividing wall rectifying tower.
Claims (6)
1. A method for solving the design problem of a dividing wall rectifying tower based on a heuristic algorithm is characterized by comprising the following steps:
the method comprises the following steps: determining information of a to-be-solved dividing wall rectifying tower, including component number, raw material information and product requirement information; determining decision variables needing to be solved; determining a target function T (x), wherein the function value of the target function T (x) is used for describing the quality of the design; converting the design problem of the dividing wall rectifying tower into an optimization problem;
step two: establishing a simulation model of the dividing wall rectifying tower to be solved in Aspen Plus process simulation software, and connecting the Aspen Plus and a KCPSO self-programming algorithm program, wherein the KCPSO program comprises three to ten steps;
step three: randomly initializing the positions and velocities of m particles, m being the perfect square number, mThe position of the vector x is equal to (x) formed by D decision variables, wherein the vector x is equal to or more than 91,x2,…,xD)TInputting Aspen Plus to check the validity; if the fitness is legal, the fitness J is substituted into the objective function to calculate the fitness J of each particle, wherein J is T (x), and if the fitness J is illegal, the position of the illegal particle is initialized again;
step four: according to the cellular neighbor rule of Moore type, 8 neighbor particles of each particle are calculated: placing particles in one by number
In the grid, a periodic boundary is adopted, and each particle has 8 particles of upper, lower, left, right, upper left, upper right, lower left and lower right as neighbors;
step five: using the positions and the fitness J of all the particles to train an online Kriging agent model, and predicting to obtain a position xKrigingIntroducing Aspen Plus to check the legality, and if the legality is legal, introducing an objective function to obtain the fitness J of the pointKriging＝T(xKriging) (ii) a If the position is illegal, retraining the online Kriging agent model, and predicting to obtain a new position xKrigingUntil legal, then calculate the fitness J of the pointKriging＝T(xKriging)；
Step six: let the position of the i-th particle's neighbor and its own fitness J maximum be xcbest,iCorresponding fitness Jcbest,i＝T(xcbest,i)；
Step seven: comparing J of each particlecbest,iAnd JKringingThe position of smaller fitness is the attractor AF of the ith particlei；
Step eight: counting and updating the position P of the ith particle from the first iteration to the fitness minimum value of the iterationiAnd its corresponding minimum fitness;
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 Aspen Plus to check the validity, if the position of the next iteration is not legal, repeatedly calling the position updating formula until the data are legal, and returning to the fifth step to continue searching after the data are legal;
step ten: all particles from the first iteration to the position x of the fitness minimum for this iteration*Namely 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: in the first step, the optimization problem of the design problem transformation of the dividing wall rectifying tower is as follows:
minf＝T(x)
s.t.MESH equations (1)
ci≥pi
wherein, the vector x is (x)1,x2,…,xD)TThe decision variables are vectors formed by D decision variables, and the decision variables are selected from the number of tower plates, reboiling ratio, reflux ratio, gas phase partition ratio, liquid phase partition ratio and side-draw amount; t (x) is an objective function, and a function value of the objective function is used for describing the advantages and disadvantages of the design, including annual total cost or energy consumption, and the smaller the objective function is, the better the design is; MESH equions are a material balance, phase balance, normalization and energy conservation equation set of the dividing wall rectifying tower; c. CiDenotes the purity of the ith product, piIndicating the minimum requirement for 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: in the fourth step, Moore type cellular neighbor rule is adopted, and the neighbor rule of the ith cellular is as follows:
Nmoore＝{vo＝(vox,voy)||vox-vix|+|voy-viy∣≤1,(vox,voy)∈Z2} (2)
wherein v isox,voyRepresenting neighbour cellsCoordinate values of rows and columns, vix,viyCoordinate values of rows and columns representing the ith cell, i.e. m particles are placed in one by one in the order of the numbers
In the grid, a periodic boundary is adopted, each particle has 8 particles of upper, lower, left, right, upper left, upper right, lower left and lower right as neighbors, the ith cell refers to the ith particle, Z2Representing a set of particle matrix coordinate values of the whole particle array.
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: in step seven, the attractor AF of the ith particleiThe selection rule of (1) 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: in step eight, the position X of the particleiAnd velocity ViThe update formula 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)
where t is the number of iterations, Pi(t) is the historical optimal position of the particle i in the current t th iteration, the position with smaller fitness is more optimal, and X isi(t) position of particle i at the t-th iteration, AFi(t) is the attractor of particle i at the t-th iteration, ωtIs an inertial weight, the magnitude of which determines the magnitude of the particle change to the current velocity; non-negative number c1And c2The value is 2 for the learning factor; r is a radical of hydrogen1And r2Is at [0,1 ]]Random value in the range, ωtFor inertial weight, its calculation formula is as follows:
wherein, tmaxIs the maximum number of iterations; omegamaxTake 0.9, omegaend0.4 is taken.
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: in the third, fifth and seventh steps, the legality is checked, namely the number of tower plates represented by the particle position vector x, the reboiling ratio, the reflux ratio, the gas phase separation ratio, the liquid phase separation ratio and the side line extraction amount are brought into Aspen Plus, whether the purity of the product meets the requirement is tested, if so, the product is legal, and otherwise, the product is illegal.
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