CN113158325B - Train energy consumption-time Pareto curve generation method based on simulation - Google Patents
Train energy consumption-time Pareto curve generation method based on simulation Download PDFInfo
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Abstract
The invention provides a train energy consumption-time Pareto curve generation method based on simulation. Comprising the following steps: combining the gradients of the slope sections meeting the simplification conditions in the line of the train operation, converting the curve into equivalent gradients, obtaining a line addition gradient, and dividing a calculation section based on the addition gradient and the line speed limit; giving a control strategy according to the magnitude relation of the target speeds of the adjacent calculation sections, and realizing a simulation process by adopting variable step sizes; combining a DE algorithm and a new crowding distance operator to obtain an improved INSSGA-II algorithm; and randomly generating an initial solution of a set of target speeds of the calculation sections, taking the target speeds as genes on chromosomes in the improved INSSGA-II algorithm, taking energy consumption-time as an optimization target, and calculating an energy consumption-time Pareto curve of the train on the line. The invention simplifies the line condition and divides the calculation section, combines the DE algorithm and the new crowding distance operator, and obtains the energy consumption-time Pareto curve of the train line by using INSSGA-II division calculation section and variable step simulation.
Description
Technical Field
The invention relates to the technical field of train energy-saving control, in particular to a train energy consumption-time Pareto curve generation method based on simulation.
Background
The railway system consumes huge energy, improves the energy-saving efficiency of the railway on the premise of meeting the transportation requirement, is beneficial to reducing the railway cost and accords with the concept of green traffic. Train operation control is a multi-objective optimization problem, such as time and energy consumption gaming, the longer the given operation time is, the smaller the energy consumption of the train is, but the transportation efficiency of the railway is greatly reduced; in contrast, a significant reduction in run time does not take full advantage of the redundant time in the schedule, and the overall energy consumption of the road network will increase substantially. Therefore, the train energy-saving operation is an effective means for railway energy saving, on one hand, the traction operation energy consumption of the train in the section can be reduced, and on the other hand, the obtained speed-distance curve provides a reference for the establishment of an energy-saving schedule.
Currently, in the prior art, a great deal of research is conducted by the SCG group of the university of south Australia on train energy saving operation, and an optimal control strategy is mainly deduced based on the principle of Pontryagin maximum value and Hamiltonian function, such as maximum acceleration/deceleration, starting coasting as early as possible, and the like, but a great deal of assumptions are needed by a theoretical deducing method for a line and a train. In addition, most researches adopt a subjective target weight giving mode, and only a small number of students apply a multi-target optimization method to subway trains, but the result is not completely applicable to railway systems with more complex line conditions and longer running distance.
At present, regarding energy-saving operation of a train in the prior art, the method mainly comprises the following three steps: an analytical algorithm for solving differential equations based on a dynamics principle, a numerical algorithm for converting a problem into a mathematical optimization problem solution, and an optimization algorithm for solving the problem by a simulation/heuristic algorithm. The analytic method and the numerical method greatly simplify the problem, and if more complex actual conditions are considered, nonlinear equations and constraints are introduced, which brings difficulty to problem solving. While simulation/heuristic algorithms easily include complex practical problems (e.g., train attributes, line conditions, etc.) in the model, with rapid development of computing power, advantages are evident in solving the complex problems.
Disclosure of Invention
The embodiment of the invention provides a train energy consumption-time Pareto curve generation method based on simulation, which is used for realizing energy-saving operation of a train under different time conditions.
In order to achieve the above purpose, the present invention adopts the following technical scheme. A train energy consumption-time Pareto curve generation method based on simulation comprises the following steps:
calculating the average speed of a line based on the existing timetable, determining the range of a section to be simplified, merging the gradients of slope sections meeting the simplifying conditions in the range of the section to be simplified, converting the curve into equivalent gradients, obtaining the line adding gradient, and re-dividing the calculation section in the range of the section to be simplified based on the adding gradient and the line speed limit;
giving a control strategy according to the magnitude relation of the target speeds of adjacent calculation sections, analyzing the quantity relation among stress, speed, distance, time and energy consumption in the running process of the train, and realizing the simulation process by adopting a variable step length of 100-10-1 m;
combining a DE algorithm and a new crowding distance operator, obtaining an improved INSSGA-II algorithm by taking the target speed of a calculated section as an independent variable, randomly generating an initial solution of the target speed of each calculated section, taking the target speed as a gene on a chromosome in the improved INSSGA-II algorithm, taking energy consumption-time as an optimization target, and calculating an energy consumption-time Pareto curve of a train on a line through variable step-length simulation by utilizing the improved INSSGA-II algorithm.
Preferably, said calculating the average speed of the line based on the existing schedule, determining the range of the calculation section to be simplified, includes:
the average line speed is calculated based on the existing schedule, namely:
wherein,the average running speed of the train on the line is represented by L, the total length of the line is represented by T, and the running time of the train in the existing schedule is represented by T;
determining the range of the calculation section to be simplified, namely:
where K is the set of segments to be computed, v(s) p ) Is the train at position s p Speed at that time. The calculation sections are divided according to the line conditions, and the line conditions such as gradient and speed limit in the same calculation section are the same. Using maximum acceleration strategy from the start point of the line when the speed isS is then p The calculation section p where is located starts to be simplified; the maximum deceleration braking strategy is adopted from the line end point in the reverse direction, when the speed is +>S is then q The calculation of the section q need not be simplified.
Preferably, the step of merging the gradients of the slope segments meeting the simplifying condition in the range of the section to be simplified and calculating is performed to convert the curve into an equivalent gradient to obtain a line additive gradient, and includes:
combining the gradients of the slope sections meeting the simplifying conditions in the range of the section needing to be simplified, converting the curve into an equivalent gradient, and calculating the line addition gradient, namely:
i h ＝(H 2 -H 1 )/l h ·1000＝(H 2 -H 1 )/∑l i ·1000
i r ＝B·∑α/l h
i all ＝i h +i r
wherein i is h Is the combined gradient, i r Is the equivalent gradient of a curve, i all Is the added gradient of the simplified slope section, H 1 And H 2 The elevation of the beginning and the ending of the simplified slope section, l h Is to simplify the length of the slope section, l i Is the length of the slope section i to be simplified, alpha is the central angle of the curve, A and B are empirical constants, if and only if l i ≤A/|i h -i|, i is the line gradient, merging the line gradients when the reduction condition is met.
Preferably, the re-dividing the calculation section within the range of the calculation section to be simplified based on the addition gradient and the line speed limit includes:
starting from calculation section p, i is calculated all The same circuit with the same speed limit value is divided into a calculation section i all The value or speed limit value changes, the next calculation section is entered, and so on until calculation section q is stopped.
Preferably, the steering strategy is given according to the magnitude relation of the adjacent calculated section target speeds, including:
(1) If the target speed of section k is calculatedTarget speed +.sub.equal to or less than calculated section k+1>I.e.And no intersection point is formed with the braking curve, the train accelerates with maximum acceleration from the starting point of the calculated section k to +.>Then the speed is maintained into calculation section k+1;
(2) If it isAnd no intersection point is formed with the braking curve, the train is searched from the calculation section k end point to the reverse idle running untilIntersecting the forward curve;
(3) If intersecting the braking curve, is manipulated according to the braking curve.
Preferably, the quantitative relation among stress, speed, distance, time and energy consumption in the train running process is analyzed, and a variable step length of 100-10-1m is adopted to realize the simulation process, which comprises the following steps:
analyzing the quantitative relation among stress, speed, distance, time and energy consumption in the running process of the train, namely:
F r (v)＝μ+κ·v+γ·v 2
F g (s)＝M·g·sin(i all (s))≈M·g·i all (s)
where s is distance, t is time, M is mass of the train, ρ is moment of inertia, F f Is the train traction force, F b Is the train braking force, F r And F g The basic resistance and equivalent ramp resistance of the train are respectively received, mu, kappa and gamma are respectively reference resistance, rolling resistance and air resistance parameters in the davis formula, g is the gravity acceleration, and the relation among the train speed, the distance, the time and the energy consumption is as follows:
wherein v is k,o ,v k,e Is to calculate the start and end speeds of segment k,is the highest allowable running speed of the calculated section k, S k Is to calculate the length of the segment k, < >>Respectively calculating traction, uniform speed, idle running and braking distances of a section k, t k Is the run time of the computation section k, E (s k ) Calculating the energy consumption of the section k;
the simulation process is realized by adopting a variable step length of 100-10-1m, namely:
step 1: initializing. Let step ds=100, cumulative distance l=0, index i=0, (s, t, E) = (0, 0); inputting the speed v, and calculating a distance array tag (if the line distance is 12345m, tag= [123,4,5 ]);
step 2: simulating the distance in the tag by using a step length of 100-10-1 m;
Step 2.1：While s<l+tag[i]·ds
step 2.1.1: calculating acceleration, speed v, distance s and time of the train under the current speed condition;
Step 2.1.2：IfAND(ds>1) Calculating energy consumption E, and converting into Step 2.1.1; otherwise, turning to Step 2.1.3;
Step 2.1.3：IfAND(ds>1) Let tag [ i+1 ]]=10, s=s-ds, transfer step2.2; otherwise, turning to Step 2.1.4;
Step 2.1.4：IfAND (ds= 1), step2.2;
step 2.2: let ds=ds/10, l=s, i=i+1;
step 2.3: if i is less than or equal to 2, turning to Step 2.1; otherwise, turning to Step 3;
Step 3.If l<S k turning to Step 4, otherwise turning to Step 5;
step 4, running at a speed v for a remaining distance;
step 5. Output (v, s, t, E).
Preferably, the INSSGA-II algorithm which combines the DE algorithm and the new crowding distance operator to calculate the target speed of the section as the independent variable is improved, and comprises the following steps:
the basic principles of the NSGA-II algorithm include: randomly generating a parent P of size N 0 ( Chromosome representing the h individual in the 0 th iteration), and obtaining offspring Q by selection, crossover and mutation operations of the genetic algorithm 0 The method comprises the steps of carrying out a first treatment on the surface of the Then, P is merged 0 And Q 0 Obtaining R containing 2N individuals 0 Non-dominant ranking and calculating crowding distance of individuals in dominant layer, selecting optimal N individuals according to dominant level and crowding distance to generate new father P 1 The method comprises the steps of carrying out a first treatment on the surface of the Finally, generating a new offspring population through basic operations of the genetic algorithm; and so on until the condition for ending the program is satisfied;
the DE algorithm is used to replace the analog binary crossover algorithm in the basic NSGA-II algorithm, namely:
wherein, beta is a control factor, beta is [0,1]. To improve algorithm efficiency, two new individuals are generated at a time. The mutation operator and the selection operator still adopt a polynomial mutation and elite retention strategy used in an NSGA-II algorithm, if the target speed after crossing/mutation does not meet the speed limit, a value is assigned to limit a speed value, and then the energy consumption and time corresponding to N individuals can be obtained through simulation calculation;
designing a new crowding distance operator, namely:
wherein D is h Is a new crowding distance operator for individual h, f e (h) And f t (h) The energy consumption and the time value of the individual h,and->Is the maximum and minimum value of energy consumption in N individuals, f t max And f t min Is the maximum and minimum of time among N individuals, the conventional crowding distance only considers the distance between the two targets of the individual h-1 and the individual h+1, and the new crowding distance D h Consider the distance between three individuals and two targets.
Preferably, said randomly generating an initial solution of a target speed of each calculation section, using the target speed as a gene on a chromosome in said modified INSGA-II algorithm, using energy consumption-time as an optimization target, and calculating an energy consumption-time Pareto curve of a train on a line by variable step-size simulation using said modified INSGA-II algorithm, including:
randomly generating a target speed of each calculation section, and generating an initial solution of the target speed of a group of calculation sections after three times of smoothing by using five points, namely:
wherein V is obj Is a randomly generated set of calculated segment target speeds,is a randomly generated target speed for the calculated segment k, the function rand () generates a random number between 0 and 1,/for>Is the target velocity for the calculated segment k after smoothing;
and taking the target speed as a gene on a chromosome in the improved INSSGA-II algorithm, and taking energy consumption-time as an optimization target, and calculating an energy consumption-time Pareto curve on a train line through the improved INSSGA-II algorithm, namely:
generating N groups of target speed sets V obj Initial solution P as an improvement of INSSGA-II algorithm 0 Calculating the values of each individual on two targets of energy consumption and time through variable step-size simulation, performing selection, DE and mutation operation, and obtaining offspring Q after simulation calculation 0 The method comprises the steps of carrying out a first treatment on the surface of the Combining to obtain R 0 Non-dominant ranking and calculating new crowding distances of individuals in dominant layers, selecting optimal N individuals to generate new father P according to dominant level and new crowding distances 1 The method comprises the steps of carrying out a first treatment on the surface of the Performing selection, DE and mutation operation, and obtaining a new offspring population after simulation calculation; and so on until the condition of ending the program is met, and obtaining the energy consumption-time Pareto curve of the train on the line.
According to the technical scheme provided by the embodiment of the invention, the characteristics of frequent gradient/curve change and long running distance in an actual line of a railway system are considered, the line condition is simplified, the calculation section is divided again, meanwhile, an improved INSSGA-II is provided by combining a DE algorithm and a new crowding distance operator according to the problem, on the basis, the energy consumption-time is taken as an optimization target, and the energy consumption-time Pareto curve on the line of a train is obtained by calculating the section and simulating the variable step length by utilizing the INSSGA-II.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a process flow diagram of a train energy consumption-time Pareto curve generation method based on simulation provided by an embodiment of the invention;
FIG. 2 is a simplified circuit condition and a schematic diagram of dividing calculation sections according to an embodiment of the present invention;
FIG. 3 is a flowchart of an improved INSSGA-II algorithm provided in an embodiment of the present invention;
fig. 4a and fig. 4b are simplified front-back line condition comparison diagrams of the beijing nan-gallery segment provided by the embodiment of the present invention;
FIG. 5 is a graph of speed versus distance for a Beijing nan-gallery segment of 995s run time provided by an embodiment of the present invention;
fig. 6 is a graph of beijing nan-gallery segment energy consumption versus time Pareto provided by an embodiment of the present invention;
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present invention and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless expressly stated otherwise, as understood by those skilled in the art. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the purpose of facilitating an understanding of the embodiments of the invention, reference will now be made to the drawings of several specific embodiments illustrated in the drawings and in no way should be taken to limit the embodiments of the invention.
The embodiment of the invention uses energy consumption-time as an optimization target on the basis of simplifying line conditions, dividing calculation sections, combining an DE (Differential Evolution Algorithm) algorithm and an improved INSSGA (Improved Nondominated Sorting Genetic Algorithm, improved non-dominant ranking genetic algorithm) -II of a new crowding distance operator, and utilizes the improved INSSGA-II algorithm to divide the calculation sections and variable step simulation to obtain an energy consumption-time Pareto curve of a train line. The method has strong operability, can support energy-saving operation of the railway train under different time conditions and further optimize the energy-saving schedule of the road network, and has great practical value and popularization significance.
Example 1
The embodiment of the invention provides a train energy consumption-time Pareto curve generation method based on simulation, which has a processing flow shown in a figure 1 and comprises the following processing steps:
step (1): calculating the average speed of a line based on the existing timetable, determining the range of a section to be calculated in a simplified manner, combining the gradients of slope sections meeting the simplifying condition in the range of the section to be calculated in a simplified manner according to the 'train traction calculation procedure', taking the characteristics of frequent change of gradients and curves in actual line conditions into consideration, converting the curves into equivalent gradients to obtain an additional gradient of the line, and re-dividing the calculation section in the range of the line based on the additional gradient and the line speed limit, wherein fig. 2 is a schematic diagram of simplifying the line conditions and dividing the calculation section provided by the embodiment of the invention;
1.1. the average line speed is calculated based on the existing schedule, namely:
wherein,the average running speed of the train on the line is represented by L, the total length of the line is represented by T, and the running time of the train in the existing schedule is represented by T;
1.2. determining the range of the calculation section to be simplified, namely:
where K is the set of segments to be computed, v(s) p ) Is the train at position s p Speed at that time. The calculation sections are divided according to the line conditions, and the line conditions such as gradient and speed limit in the same calculation section are the same. Using maximum acceleration strategy from the start point of the line when the speed isS is then p The calculation section p where is located starts to be simplified; the maximum deceleration braking strategy is adopted from the line end point in the reverse direction, when the speed is +>S is then q The section q is calculated without simplification;
1.3. combining the gradients of the slope sections meeting the simplifying conditions in the range of the section to be simplified according to the 'train traction calculation procedure', converting the curve into an equivalent gradient, and calculating an added gradient, namely:
i h ＝(H 2 -H 1 )/l h ·1000＝(H 2 -H 1 )/∑l i ·1000
i r ＝B·∑α/l h
i all ＝i h +i r
wherein i is h Is the combined gradient, i r Is the equivalent gradient of a curve, i all Is the added gradient of the simplified slope section, H 1 And H 2 The elevation of the beginning and the ending of the simplified slope section, l h Is to simplify the length of the slope section, l i Is the length of the slope section i to be simplified, alpha is the central angle of the curve, and A and B are empirical constants. If and only if l i ≤A/|i h -merging line gradients when i| satisfies a reduction condition, i being the line gradient;
1.4. the calculated sections within the line range are repartitioned based on the line addition grade and the line speed limit, namely:
starting from calculation section p, i is calculated all The same circuit with the same speed limit value is divided into a calculation section i all The value or speed limit value changes, the next calculation section is entered, and so on until calculation section q is stopped.
Step (2) giving a control strategy according to the magnitude relation of the target speeds of adjacent calculation sections, analyzing the quantity relation among stress, speed, distance, time and energy consumption in the running process of the train, and realizing a simulation process by adopting a variable step length of 100-10-1 m;
2.1. the magnitude relation of the adjacent calculated segment target speeds gives the steering strategy, namely:
(1) If the target speed of section k is calculatedTarget speed +.sub.equal to or less than calculated section k+1>I.e.And no intersection point is formed with the braking curve, the train accelerates with maximum acceleration from the starting point of the calculated section k to +.>Then the speed is maintained into calculation section k+1;
(2) If it isAnd no intersection point exists with the braking curve, the train performs reverse idle search from the end point of the calculated section k until the train intersects with the forward curve;
(3) If crossing the braking curve, steering according to the braking curve;
2.2. analyzing the quantitative relation among stress, speed, distance, time and energy consumption in the running process of the train, namely:
F r (v)＝μ+κ·v+γ·v 2
F g (s)＝M·g·sin(i all (s))≈M·g·i all (s)
where s is distance, t is time, M is mass of the train, ρ is moment of inertia, F f Is the train traction force, F b Is the train braking force, F r And F g The basic resistance and equivalent ramp resistance of the train are respectively, and mu, kappa and gamma are respectively Daviss' publicWhere g is the gravitational acceleration, reference resistance, rolling resistance and air resistance parameters. The relationship among train speed, distance, time and energy consumption is as follows:
wherein v is ko ,v ke Is to calculate the start and end speeds of segment k,is the highest allowable running speed of the calculated section k, S k Is to calculate the length of the segment k, < >>Respectively calculating traction, uniform speed, idle running and braking distances of a section k, t k Is the run time of the computation section k, E (s k ) Calculating the energy consumption of the section k;
2.3. the simulation process is realized by adopting a variable step length of 100-10-1m, namely:
step 1: initializing. Let step ds=100, cumulative distance l=0, index i=0, (s, t, E) = (0, 0); the velocity v is input, and a distance array tag (if the line distance is 12345m, tag= [123,4,5 ]).
Step 2: the distance in tag is simulated with a step size of 100-10-1 m.
Step 2.1：While s<l+tag[i]·ds
Step 2.1.1: calculating acceleration, speed v, distance s and time of the train under the current speed condition;
Step 2.1.2：IfAND(ds>1) Calculating energy consumption E, and converting into Step 2.1.1; otherwise, turning to Step 2.1.3;
Step 2.1.3：IfAND(ds>1) Let tag [ i+1 ]]=10, s=s-ds, step2.2; otherwise, turning to Step 2.1.4;
Step 2.1.4：IfAND (ds= 1), step2.2;
step 2.2: let ds=ds/10, l=s, i=i+1;
step 2.3: if i is less than or equal to 2, turning to Step 2.1; otherwise, turning to Step 3;
Step 3.If l<S k turning to Step 4, otherwise turning to Step 5.
Step 4. Run at speed v for the remaining distance.
Step 5. Output (v, s, t, E).
Step (3) combining a DE algorithm and a new crowding distance operator, obtaining an improved INSSGA-II algorithm by taking the target speed of a calculated section as an independent variable, randomly generating an initial solution of the target speed of each calculated section, taking the target speed as a gene on a chromosome in the improved INSSGA-II algorithm, taking energy consumption-time as an optimization target, and calculating an energy consumption-time Pareto curve of a train on a line by utilizing the improved INSSGA-II algorithm through variable step-length simulation, wherein a flow chart of the improved INSSGA-II algorithm in the embodiment of the invention is shown in a figure 3;
3.1. the DE algorithm is used to replace the analog binary crossover algorithm in the basic NSGA-II algorithm, namely:
wherein, beta is a control factor, beta is [0,1]. To improve algorithm efficiency, two new individuals are generated at a time. The mutation operator and the selection operator still adopt a polynomial mutation and elite retention strategy used in an NSGA-II algorithm, if the target speed after crossing/mutation does not meet the speed limit, a value is assigned to limit a speed value, and then the energy consumption and time corresponding to N individuals can be obtained through simulation calculation;
3.2. designing a new crowding distance operator, namely:
wherein D is h Is a new crowding distance operator for individual h, f e (h) And f t (h) The energy consumption and the time value of the individual h,and->Is the maximum and minimum value of energy consumption in N individuals, f t max And f t min Is the maximum and minimum of time among N individuals. The conventional crowding distance only considers the distance between the two targets of the individual h-1 and the individual h+1, and the new crowding distance D h The distances between the three individuals and the two targets are considered, so that the uniformity of knowing the distribution in the target space is effectively improved.
3.3. Randomly generating a target speed of each calculation section, and generating an initial solution of the target speed of a group of calculation sections after three times of smoothing by using five points, namely:
wherein V is obj Is a randomly generated set of calculated segment target speeds,is a randomly generated target speed for the calculated segment k, the function rand () generates a random number between 0 and 1,/for>Is the target velocity for the calculated segment k after smoothing;
3.4. and taking the target speed as a gene on a chromosome in the improved INSSGA-II algorithm, and taking energy consumption-time as an optimization target, and calculating an energy consumption-time Pareto curve on a train line through the improved INSSGA-II algorithm, namely:
generating N groups of target speed sets V obj Initial solution P as an improvement of INSSGA-II algorithm 0 Calculating the values of each individual on two targets of energy consumption and time through variable step-size simulation, performing selection, DE and mutation operation, and obtaining offspring Q after simulation calculation 0 The method comprises the steps of carrying out a first treatment on the surface of the Combining to obtain R 0 Non-dominant ranking and calculating new crowding distances of individuals in dominant layers, selecting optimal N individuals to generate new father P according to dominant level and new crowding distances 1 The method comprises the steps of carrying out a first treatment on the surface of the Performing selection, DE and mutation operation, and obtaining a new offspring population after simulation calculation; and so on until the condition of ending the program is met, and obtaining the energy consumption-time Pareto curve of the train on the line.
Example two
In recent years, as the running speed of trains and the departure frequency of trains are increased, energy saving research of high-speed railway systems is attracting more and more attention. The jinghu high-speed railway is a passenger special line with heavy Chinese transportation business and huge growth potential, and has great significance for Chinese economy and social development. Thus, the process of the present invention will be described by taking Beijing south-gallery section of Beijing Shanghai iron as an example.
According to the process flow chart of the energy consumption-time Pareto curve generating method shown in fig. 1, firstly, a route from Beijing to gallery is simplified to 59km, the running time of a train in the existing timetable is 1260, the average speed of the route is 168.57km/h calculated due to the fact that the speed limit of the route is more, gradients meeting the conditions are combined according to the 'train traction calculation procedure', the curve is converted into equivalent gradients, and the added gradient is calculated. After simplification, the number of calculated sections is reduced from 88 (see fig. 4 (a)) to 33 (see fig. 4 (b)), which is only 37.5% of the number of calculated sections. Wherein the longest calculated section after simplification is 5.10km, the shortest is 0.85km, and the average is 1.79km.
Giving an operation strategy according to the magnitude relation of the target speeds of adjacent calculation sections, adopting a variable step length of 100-10-1m to realize a simulation process, and adopting a speed-distance curve of the Beijing south-gallery section and the operation time of 995s as shown in FIG. 5, wherein the corresponding energy consumption is 8.55X10 9 J。
Based on the INSSGA-II, taking energy consumption-time as an optimization target, sequentially adopting variable step-length simulation of 100-10-1m in 33 calculation sections, calculating and drawing train energy consumption values under different time conditions, and obtaining an energy consumption-time Pareto curve of the train on the line through continuous iterative optimization, wherein each point on the curve is a non-dominant solution (see figure 6). In the Pareto plot of fig. 6, the basic trend has been relatively evident from passage 30, and the newly generated solution remains within the trend through passage 50, so we consider that it has fully converged at this time.
In summary, the embodiments of the present invention take the beijing nan-gallery section in the jinghu high-speed railway as an example, simplify the curve/gradient frequently changing in the actual line on the basis of determining the line average speed to determine the simplified range, re-divide the calculation section, and then calculate the section and step-by-step long simulation based on the improved INSGA-II with the energy consumption-time as the optimization target, so as to finally obtain the energy consumption-time Pareto curve of the train on the whole line. The method has strong operability, can support energy-saving operation of the railway train under different time conditions and further optimize the energy-saving schedule of the road network, and can be further applied to the whole high-speed railway system.
The method provided by the embodiment of the invention has stronger operability, the optimal operation strategy set of the train under different time conditions in different intervals can be obtained, the energy-saving operation of the train under different time conditions is realized, the reference is provided for the energy-saving operation of the train under the late condition, the energy-saving optimization of the subsequent train schedule is supported, and the method has great practical value and popularization significance.
Those of ordinary skill in the art will appreciate that: the drawing is a schematic diagram of one embodiment and the modules or flows in the drawing are not necessarily required to practice the invention.
From the above description of embodiments, it will be apparent to those skilled in the art that the present invention may be implemented in software plus a necessary general hardware platform. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the embodiments or some parts of the embodiments of the present invention.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, with reference to the description of method embodiments in part. The apparatus and system embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (1)
1. The train energy consumption-time Pareto curve generation method based on simulation is characterized by comprising the following steps of:
calculating the average speed of a line based on the existing timetable, determining the range of a section to be simplified, merging the gradients of slope sections meeting the simplifying conditions in the range of the section to be simplified, converting the curve into equivalent gradients, obtaining the line adding gradient, and re-dividing the calculation section in the range of the section to be simplified based on the adding gradient and the line speed limit;
giving a control strategy according to the magnitude relation of the target speeds of adjacent calculation sections, analyzing the quantity relation among stress, speed, distance, time and energy consumption in the running process of the train, and realizing the simulation process by adopting a variable step length of 100-10-1 m;
combining a DE algorithm and a new crowding distance operator, obtaining an improved INSSGA-II algorithm by taking the target speed of a calculated section as an independent variable, randomly generating an initial solution of the target speed of each calculated section, taking the target speed as a gene on a chromosome in the improved INSSGA-II algorithm, taking energy consumption-time as an optimization target, and calculating an energy consumption-time Pareto curve of a train on a line through variable step-length simulation by utilizing the improved INSSGA-II algorithm;
the calculating the average speed of the line based on the existing timetable, and determining the range of the section to be calculated in a simplified way comprises the following steps:
the average line speed is calculated based on the existing schedule, namely:
wherein,the average running speed of the train on the line is that S is the total length of the line, and T is the running time of the train in the existing schedule;
determining the range of the calculation section to be simplified, namely:
where K is the set of segments to be computed, v(s) p ) Is the train at position s p The speed is calculated according to the line conditions, the gradient, speed limit and other line conditions in the same calculation section are the same, the maximum acceleration strategy is adopted from the starting point of the line, and when the speed is the sameS is then p The calculation section p where is located starts to be simplified; the maximum deceleration braking strategy is adopted from the line end point in the reverse direction, when the speed is +>S is then q The section q is calculated without simplification;
combining the gradients of the slope sections meeting the simplifying conditions in the range of the section needing to be simplified to be calculated, converting the curve into an equivalent gradient, and obtaining a line addition gradient, wherein the method comprises the following steps:
combining the gradients of the slope sections meeting the simplifying conditions in the range of the section needing to be simplified, converting the curve into an equivalent gradient, and calculating the line addition gradient, namely:
i h ＝(H 2 -H 1 )/l h ·1000＝(H 2 -H 1 )/∑l i ·1000
i r ＝B·∑α/l h
i all ＝i h +i r
wherein i is h Is the combined gradient, i r Is the equivalent gradient of a curve, i all Is the added gradient of the simplified slope section, H 1 And H 2 The elevation of the beginning and the ending of the simplified slope section, l h Is to simplify the length of the slope section, l i Is the length of the slope section i to be simplified, alpha is the central angle of the curve, A and B are empirical constants, if and only if l i ≤A/|i h -i|, i is the line gradient, merging the line gradients when the simplification condition is satisfied;
the calculating section in the range of the calculating section to be simplified is reclassified based on the added gradient and the line speed limit, and the calculating section comprises:
starting from calculation section p, i is calculated all The same circuit with the same speed limit value is divided into a calculation section i all If the value or the speed limit value is changed, the next calculation section is entered, and the like until the calculation section q is stopped;
giving a manipulation strategy according to the magnitude relation of the target speeds of adjacent calculation sections, wherein the manipulation strategy comprises the following steps:
(1) If the target speed of section k is calculatedTarget speed +.sub.equal to or less than calculated section k+1>I.e.And no intersection point is formed with the braking curve, the train accelerates with maximum acceleration from the starting point of the calculated section k to +.>Then the speed is maintained into calculation section k+1;
(2) If it isAnd no intersection point exists with the braking curve, the train performs reverse idle search from the end point of the calculated section k until the train intersects with the forward curve;
(3) If crossing the braking curve, steering according to the braking curve;
analyzing the number relation among stress, speed, distance, time and energy consumption in the running process of the train, and realizing the simulation process by adopting a variable step length of 100-10-1m, wherein the method comprises the following steps:
analyzing the quantitative relation among stress, speed, distance, time and energy consumption in the running process of the train, namely:
F r (v)＝μ+κ·v+γ·v 2
F g (s)＝M·g·sin(i all (s))≈M·g·i all (s)
where s is distance, t is time, M is mass of the train, ρ is moment of inertia, F f Is the train traction force, F b Is the train braking force, F r And F g The basic resistance and equivalent ramp resistance of the train are respectively received, mu, kappa and gamma are respectively reference resistance, rolling resistance and air resistance parameters in the davis formula, g is the gravity acceleration, and the relation among the train speed, the distance, the time and the energy consumption is as follows:
wherein v is k,o ,v k,e Is to calculate the start and end speeds of segment k,is the highest allowable running speed of the calculated section k, S k Is to calculate the length of the segment k, < >>Respectively calculating traction, uniform speed, idle running and braking distances of a section k, t k Is the run time of the computation section k, E (s k ) Calculating the energy consumption of the section k;
the simulation process is realized by adopting a variable step length of 100-10-1m, namely:
step 1: initializing, to make the step ds=100, the accumulated distance l=0, the index i=0, (s, t, E) = (0, 0); inputting the speed v, calculating a distance array tag, and if the line distance is 12345m, determining tag= [123,4,5];
step 2: simulating the distance in the tag by using a step length of 100-10-1 m;
Step 2.1：While s<l+tag[i]·ds
step 2.1.1: calculating acceleration, speed v, distance s and time of the train under the current speed condition;
Step 2.1.2：AND(ds>1) Calculating energy consumption E, and converting into Step 2.1.1; otherwise, turning to Step 2.1.3;
Step 2.1.3：AND(ds>1) Let tag [ i+1 ]]=10, s=s-ds, step2.2; otherwise, go to Step2.1.4；
Step 2.1.4：AND (ds= 1), step2.2;
step 2.2: let ds=ds/10, l=s, i=i+1;
step 2.3: if i is less than or equal to 2, turning to Step 2.1; otherwise, turning to Step 3;
Step 3.Ifl<S k turning to Step 4, otherwise turning to Step 5;
step 4, running at a speed v for a remaining distance;
step 5. Output (v, s, t, E);
the INSSGA-II algorithm which combines the DE algorithm and the new crowding distance operator and takes the target speed of a calculated section as an independent variable is improved, and comprises the following steps:
the basic principles of the NSGA-II algorithm include: randomly generating a parent P of size N 0 ， Chromosome representing the h individual in the 0 th iteration, and obtaining offspring Q through selection, crossover and mutation operation of genetic algorithm 0 The method comprises the steps of carrying out a first treatment on the surface of the Then, P is merged 0 And Q 0 Obtaining R containing 2N individuals 0 Non-dominant ranking and calculating crowding distance of individuals in dominant layer, selecting optimal N individuals according to dominant level and crowding distance to generate new father P 1 The method comprises the steps of carrying out a first treatment on the surface of the Finally, generating a new offspring population through basic operations of the genetic algorithm; and so on until the condition for ending the program is satisfied;
the DE algorithm is used to replace the analog binary crossover algorithm in the basic NSGA-II algorithm, namely:
wherein, beta is a control factor, beta is E [0,1], in order to improve algorithm efficiency, two new individuals are generated each time, a mutation operator and a selection operator still adopt a polynomial mutation and elite retention strategy used in an NSGA-II algorithm, if the target speed after crossing/mutation does not meet the speed limit, a value is assigned to limit a speed value, and then the energy consumption and time corresponding to N individuals can be obtained through simulation calculation;
designing a new crowding distance operator, namely:
wherein D is h Is a new crowding distance operator for individual h, f e (h) And f t (h) The energy consumption and the time value of the individual h,and->Is the maximum and minimum value of energy consumption in N individuals, < >>And->Is the maximum and minimum of time among N individuals, the conventional crowding distance only considers the distance between the two targets of the individual h-1 and the individual h+1, and the new crowding distance D h Consider the distance of three individuals between two targets;
the method comprises the steps of randomly generating an initial solution of a target speed of each calculation section, taking the target speed as a gene on a chromosome in the improved INSSGA-II algorithm, taking energy consumption-time as an optimization target, and calculating an energy consumption-time Pareto curve of a train on a line through variable step-size simulation by utilizing the improved INSSGA-II algorithm, wherein the method comprises the following steps:
randomly generating a target speed of each calculation section, and generating an initial solution of the target speed of a group of calculation sections after three times of smoothing by using five points, namely:
wherein V is obj Is a randomly generated set of calculated segment target speeds,is a randomly generated target speed for the calculated segment k, the function rand () generates a random number between 0 and 1,/for>Is the target velocity for the calculated segment k after smoothing;
the target speed is used as a gene on a chromosome in the improved INSSGA-II algorithm, energy consumption-time is used as an optimization target, and the improved INSSGA-II algorithm is used for calculating an energy consumption-time Pareto curve of a train on a line through variable step-size simulation, namely:
generating N groups of target speed sets V obj Initial solution P as an improvement of INSSGA-II algorithm 0 Calculating the values of each individual on two targets of energy consumption and time through variable step-size simulation, performing selection, DE and mutation operation, and obtaining offspring Q after simulation calculation 0 The method comprises the steps of carrying out a first treatment on the surface of the Combining to obtain R 0 Non-dominant ranking and calculating new crowding distances of individuals in dominant layers, selecting optimal N individuals to generate new father P according to dominant level and new crowding distances 1 The method comprises the steps of carrying out a first treatment on the surface of the Performing selection, DE and mutation operation, and obtaining a new offspring population after simulation calculation; and so on until the condition of ending the program is met, and obtaining the energy consumption-time Pareto curve of the train on the line.
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