Node flow optimization distribution method for improving accuracy of transient hydraulic simulation of water supply in-series pipeline

Abstract

The present invention discloses a node flow optimization distribution method for improving the accuracy of transient hydraulic simulation of a water supply in-series pipeline. The present invention optimizes the flow distribution coefficients of intermediate nodes to minimize the impact thereof on the calculation and analysis of transient flow. Further, the simplified error generated by the node flow distribution can be quantified and evaluated by the control threshold of the simplified errors to achieve effective control of the simplified process. In addition, the simplified operation of the method of the present invention is carried out sequentially from the intermediate node with the smallest simplified error, which effectively overcomes the potential defect of the conventional node flow distribution that leads to a significant reduction in the accuracy of the model, and can ensure the reliability and accuracy of the simplified operation of the same-diameter in-series pipeline.

Claims

1. A method for preventing a transient flow in a water supply pipeline network, comprising following steps: (1) identify same-diameter in-series pipeline systems (IDP) in a pipeline network model to form a collection IDP={IDP.sub.1, IDP.sub.2, . . . , IDP.sub.N} of the same-diameter in-series pipeline systems, the pipeline network model being a geographic information system (GIS) based hydraulic model of the water supply pipeline network, the GIS system having pipeline network topological information and component property information of the water supply pipeline network, and each node of the pipeline network model representing a user of the water supply pipeline network, wherein N is a number of the same-diameter in-series pipeline systems in the pipeline network model; the same-diameter in-series pipeline systems are basic objects of simplification of the same-diameter in-series pipelines, for example, one of the same-diameter in-series pipeline systems IDP.sub.i comprises four pipelines P.sub.1, P.sub.2, P.sub.3 and P.sub.4 that are connected in series, three nodes N.sub.1, N.sub.2 and N.sub.3 that are connected at middles thereof, and nodes N.sub.4 and N.sub.5 that are connected at both ends thereof and pipelines P.sub.5, P.sub.6, P.sub.7 and P.sub.8 that are connected externally; wherein a node flow rates of nodes N.sub.1, N.sub.2, N.sub.3, N.sub.4 and N.sub.5 are q.sub.1, q.sub.2, q.sub.3, q.sub.4 and q.sub.5 in sequence; a mathematical expression of the same-pipeline in-series pipeline systems IDP.sub.i (i=1, . . . N) is as follows:
IDP.sub.i={(P.sub.1,P.sub.2,P.sub.3,P.sub.4),(N.sub.1,N.sub.2,N.sub.3),(N.sub.4,N.sub.5),(P.sub.5,P.sub.6),(P.sub.7,P.sub.8)}  (1); (2) for the same diameter in-series pipeline systems IDP, (i=1, 2, 3 . . . N) in a set of the IDP, establish an optimization objective function to calculate a simplified error Err generated by the flow distribution of each intermediate node to form the set Err.sub.i={Err.sub.1, Err.sub.2, . . . , Err.sub.i} (I is the number of intermediate nodes); taking intermediate nodes N.sub.1, N.sub.2 and N.sub.3 as examples, the established optimization objective functions are as follows respectively: $\begin{array}{cc}\mathrm{Min}\text{:}{\mathrm{Err}}_1=w_1^1\left\{\begin{array}{c}{\left[\left({\tilde{\Psi }}_0^{N_4}-{\tilde{\Psi }}_d^{N_4}\right)\left(T_0^{P_5.fwdarw.N_4}+T_0^{P_6.fwdarw.N_4}\right)\right]}^2+\\ \{[\left(1-{\tilde{\Psi }}_0^{N_2}\right)\left(1-{\tilde{\Psi }}_0^{N_1}\right)\left(1-{\tilde{\Psi }}_0^{N_4}\right)-\\ {\left(1-{\tilde{\Psi }}_d^{N_2}\right)\left(1-{\tilde{\Psi }}_d^{N_4}\right)]T_0^{P_1.fwdarw.N_4}\}}^2\end{array}\right\}+w_1^2\left\{\begin{array}{c}{\left({\tilde{\Psi }}_0^{N_2}-{\tilde{\Psi }}_d^{N_2}\right)}^2+\\ \{[\left(1-{\tilde{\Psi }}_0^{N_4}\right)\left(1-{\tilde{\Psi }}_0^{N_1}\right)\left(1-{\tilde{\Psi }}_0^{N_2}\right)-\\ {\left(1-{\tilde{\Psi }}_d^{N_4}\right)\left(1-{\tilde{\Psi }}_d^{N_2}\right)]\left(T_0^{P_5.fwdarw.N_4}+T_0^{P_6.fwdarw.N_4}\right)\}}^2\end{array}\right\};& \left(2\right)\\ \mathrm{Min}\text{:}{\mathrm{Err}}_2=w_2^1\left\{{\left({\tilde{\Psi }}_0^{N_1}-{\tilde{\Psi }}_d^{N_1}\right)}^2+{\left[\left(1-{\tilde{\Psi }}_0^{N_3}\right)\left(1-{\tilde{\Psi }}_0^{N_2}\right)\left(1-{\tilde{\Psi }}_0^{N_1}\right)-\left(1-{\tilde{\Psi }}_d^{N_3}\right)\left(1-{\tilde{\Psi }}_d^{N_1}\right)\right]}^2\right\}+w_2^2\left\{{\left({\tilde{\Psi }}_0^{N_3}-{\tilde{\Psi }}_d^{N_3}\right)}^2+{\left[\left(1-{\tilde{\Psi }}_0^{N_1}\right)\left(1-{\tilde{\Psi }}_0^{N_2}\right)\left(1-{\tilde{\Psi }}_0^{N_3}\right)-\left(1-{\tilde{\Psi }}_d^{N_1}\right)\left(1-{\tilde{\Psi }}_d^{N_3}\right)\right]}^2\right\};& \left(3\right)\\ \mathrm{Min}\text{:}{\mathrm{Err}}_3=w_3^1\left\{\begin{array}{c}{\left({\tilde{\Psi }}_0^{N_2}-{\tilde{\Psi }}_d^{N_2}\right)}^2+\\ \{[\left(1-{\tilde{\Psi }}_0^{N_5}\right)\left(1-{\tilde{\Psi }}_0^{N_3}\right)\left(1-{\tilde{\Psi }}_0^{N_2}\right)-\\ {\left(1-{\tilde{\Psi }}_d^{N_5}\right)\left(1-{\tilde{\Psi }}_d^{N_2}\right)]\left(T_0^{P_7.fwdarw.N_5}+T_0^{P_8.fwdarw.N_5}\right)\}}^2\end{array}\right\}+w_3^2\left\{\begin{array}{c}{\left[\left({\tilde{\Psi }}_0^{N_5}-{\tilde{\Psi }}_d^{N_5}\right)\left(T_0^{P_7.fwdarw.N_5}+T_0^{P_8.fwdarw.N_5}\right)\right]}^2+\\ \{[\left(1-{\tilde{\Psi }}_0^{N_2}\right)\left(1-{\tilde{\Psi }}_0^{N_3}\right)\left(1-{\tilde{\Psi }}_0^{N_5}\right)-\\ {\left(1-{\tilde{\Psi }}_d^{N_2}\right)\left(1-{\tilde{\Psi }}_d^{N_5}\right)]T_0^{P_4.fwdarw.N_5}\}}^2\end{array}\right\};& \left(4\right)\end{array}$ in formulas above, subscripts 0 and d represent the original same-diameter in-series pipeline system and the same-diameter in-series pipeline system after a water volume of the intermediate nodes is distributed; w.sup.1 and w.sup.2 are the weight coefficients, which indicate the relative importance of the two simplified in-series pipelines; {tilde over (Ψ)}.sup.N.sup.i is the influence factor of the transient water volume at the node N.sub.i, which indicates the degree of influence of the water volume at a node N.sub.i on a transient flow process, and the value thereof is between 0-100%; T.sup.P.sup.j.sup..fwdarw.N.sup.i is the propagation coefficient of the connecting pipeline P.sub.j at the node Ni, and the mathematical expression thereof is T.sup.P.sup.j.sup..fwdarw.N.sup.i=(2A.sub.j/a.sub.j)/Σ.sub.m=1.sup.M(A.sub.m/a.sub.m), A=πD.sup.2/4, A is the sectional area of the pipeline, D is the diameter of the pipeline, a is the wave velocity of the pipeline, M is the total number of connection pipelines at the node N.sub.i, and m is the m-th connection pipeline at a node of N.sub.i; the value of the propagation coefficient T.sup.P.sup.j.sup..fwdarw.N.sup.i is between 0˜2, which means the change degree of the pressure fluctuation amplitude of the transient pressure wave that propagates along the pipeline P.sub.j to the node N.sub.i, specifically, in the formula, T.sup.P.sup.5.sup..fwdarw.N.sup.4 represents the multiples of the transient pressure wave propagating along the pipeline P.sub.5 to the node N.sub.4 relative to an initial amplitude before reaching a node N.sub.4; T.sub.0.sup.P.sup.6.sup..fwdarw.N.sup.4 represents the multiples of the transient pressure wave propagating along the pipeline P.sub.6 to the node N.sub.4 relative to the initial amplitude before reaching the node N.sub.4; the initial steady-state hydraulic state at the node and the properties of the connection pipeline are used to determine the influence factor {tilde over (Ψ)}.sup.N.sup.i of the transient water volume of the node N.sub.i, that is,
{tilde over (Ψ)}.sup.N.sup.i=−1.1×10.sup.−14S.sub.N.sub.i.sup.4+8.9×10.sup.−11S.sub.N.sub.i.sup.3−3.1×10.sup.−7S.sub.N.sub.i.sup.2+6.2×10.sup.−4S.sub.N.sub.i.sup.4+3.8×10.sup.−3  (5); in the formula, S.sub.N.sub.i represents the static property at the node N.sub.i, which is determined by the initial steady-state hydraulic state at the node and the properties of the connection pipeline, namely, S.sub.N.sub.i=q.sub.0(N.sub.i)/[gH.sub.0.sup.0.5(N.sub.i)Σ.sub.m=1.sup.M(A.sub.m/a.sub.m)], where q.sub.0(N.sub.i) and H.sub.0(N.sub.i) represent the initial steady-state water volume and pressure at the node N.sub.i, respectively, and g is the acceleration of gravity; the ratio of the length of the in-series pipelines is used to express the weight coefficient of two in-series pipelines, namely:
w.sub.1.sup.1=L(P.sub.1)/[L(P.sub.1)+L(P.sub.2)]  (6);
w.sub.1.sup.2=L(P.sub.2)/[L(P.sub.1)+L(P.sub.2)]  (7);
w.sub.2.sup.1=L(P.sub.2)/[L(P.sub.2)+L(P.sub.3)]  (8);
w.sub.2.sup.2=L(P.sub.3)/[L(P.sub.2)+L(P.sub.3)]  (9);
w.sub.3.sup.1=L(P.sub.3)/[L(P.sub.3)+L(P.sub.4)]  (10);
w.sub.3.sup.2=L(P.sub.4)/[L(P.sub.3)+L(P.sub.4)]  (11); in the formula, L represents the length of the pipeline; solving the optimization objective function can obtain the simplified error Err and the corresponding optimization decision variable value r; specifically, solving the formulas (2), (3) and (4) can obtain the simplified errors Err.sub.1, Err.sub.2 and Err.sub.3 of the intermediate nodes N.sub.1, N.sub.2 and N.sub.3, and the corresponding optimization decision variable values r.sub.1, r.sub.2 and r.sub.3, respectively; (3) according to Err.sub.min=min(Err.sub.i), determine the intermediate nodes that are preferably simplified, in order to ensure the accuracy of the simplified model, according to the control threshold Err.sub.tol of the simplified error to judge whether the combining operation of the same-diameter in-series pipelines are suitably conducted:
If Err.sub.min≤Err.sub.tol, it can be simplified.  (12);
If Err.sub.min>Err.sub.tol, it is not appropriate to be simplified.  (13); If Err.sub.min≤Err.sub.tol, it then continues to execute downward; otherwise, jump to Step (6); (4) perform a simplified operation on intermediate nodes that can be simplified, to determine the flow of simplified nodes at two ends and the parameters of an equivalent pipeline; (5) remove the simplified intermediate nodes in the same-diameter in-series pipeline systems IDP.sub.i; at this time, if the number of intermediate nodes in the IDP.sub.i is 0, it means that the in-series pipelines in the current same diameter in-series pipeline systems have all been simplified, then jump to Step (6); otherwise, jump to Step (2) and continue to simplify the current same-diameter in-series pipeline systems; (6) complete the simplification of the current same-diameter in-series pipeline systems, start the simplification of the next group of the same-diameter in-series pipeline systems, and return to Step (2) until all the same-diameter in-series pipeline systems have been simplified, which means a simplified process is ended; and (7) generating indication of prevention of the transient flow to an intelligent management system of the water supply pipeline network such that the intelligent management system controls water supply of the water supply pipeline network based on the indication.

2. The method according to claim 1, wherein in step (2), the value of the optimization decision variable r is between 0 and 1.

3. The method according to claim 1, wherein in Step (3), the control threshold Err.sub.tol ranges from 0.01 to 0.03.

4. The method according to claim 1, wherein in Step (4), the flow of the simplified nodes at both ends can be determined according to the value of the optimization decision variable r corresponding to Err.sub.min, for example, the intermediate node N.sub.2 is simplified, and the water volumes of the nodes N.sub.1 and N.sub.3 at two ends are q.sub.1+r.sub.2q.sub.2 and q.sub.3+(1−r.sub.2)q.sub.2, respectively; the parameters of the equivalent pipelines are determined as follows: (1) The pipeline diameter and wave velocity are equal to the diameter and wave velocity of the in-series pipelines, respectively; (2) the length of the pipelines is equal to the sum of the length of the two in-series pipelines; (3) the resistance coefficient of the pipelines is determined according to the principle of hydraulic equivalence, that is, the head loss of the equivalent pipelines after water flow is simplified is the same as the head loss of the in-series pipelines before the water flow is simplified.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1(a)-(b) is a diagram of the flow distribution of same-diameter in-series pipeline systems and nodes.

(2) FIG. 2 is a diagram of the topological structure of a water supply pipeline network of an embodiment.

(3) FIG. 3(a)-(b) is a diagram of a topological structure of a pipeline network during and after the simplified implementation of a same-diameter in-series pipeline of an embodiment.

(4) FIG. 4(a)-(d) is a comparison diagram of transient pressure fluctuation at a node obtained by the method of the present invention and the conventional method.

DETAILED DESCRIPTION

(5) The technical solution of the present invention will be further described in details below in conjunction with the drawings. It should be noted that the specific embodiments are only detailed descriptions of the present invention and should not be considered as limiting the present invention.

(6) A node flow optimization distribution method for improving the accuracy of transient hydraulic simulation of a water supply in-series pipeline comprises the following steps:

(7) (1) Identify the same-diameter in-series pipeline systems (IDP) in a pipeline network model to form a collection IDP={IDP.sub.1, IDP.sub.2, . . . , IDP.sub.N} of the same-diameter in-series pipeline systems, wherein N is the number of the same-diameter in-series pipeline systems in the pipeline network model. The same-diameter in-series pipeline systems are the basic objects of simplification of the same-diameter in-series pipelines proposed by the present invention, and consist of a plurality of pipelines (P.sub.1, P.sub.2, P.sub.3, and P.sub.4) that are connected in series, a plurality of nodes (N.sub.1, N.sub.2, and N.sub.3) that are connected at the middles thereof, and nodes (N.sub.4 and N.sub.5) that are connected at both ends thereof and pipelines (P.sub.5, P.sub.6, P.sub.7 and P.sub.8) that are connected externally, as shown in FIG. 1(a). The node flow rates of nodes N.sub.1, N.sub.2, N.sub.3, N.sub.4 and N.sub.5 are q.sub.1, q.sub.2, q.sub.3, q.sub.4 and q.sub.5 in sequence. The mathematical expression of the same-pipeline in-series pipeline systems IDPi (i=1, . . . N) as shown in FIG. 1(a) is as follows:
IDP.sub.i={(P.sub.1,P.sub.2,P.sub.3,P.sub.4),(N.sub.1,N.sub.2,N.sub.3),(N.sub.4,N.sub.5),(P.sub.5,P.sub.6),(P.sub.7,P.sub.8)}  (1);

(8) Note that Formula (1) expresses the case where the same-diameter in-series pipeline system has three intermediate nodes and two externally connected pipelines at the connection nodes at both ends. This is a common case of the same-diameter in-series pipeline in the pipeline network model. The situation of having more than three intermediate nodes and a plurality of externally connected pipes (3 or more) at the connection nodes at both ends can be expanded accordingly, and the method of the present invention is still applicable;

(9) (2) For the same-diameter in-series pipeline systems IDP.sub.i in a set IDP, the combination and simplification of the pipeline is to distribute the flow of the intermediate nodes to the nodes at two ends. For example, for the intermediate node N.sub.2 in FIG. 1 (b), the flow distribution of the nodes is to distribute the flow of the nodes to the nodes Ni and N.sub.3 at both ends to keep the water volume conserved. That is, the water volume of the simplified nodes N.sub.1 and N.sub.3 are q.sub.1+r.sub.2q.sub.2 and q.sub.3+(1−r.sub.2)q.sub.2, respectively, wherein r.sub.2 represents the distribution coefficient of the water volume of the intermediate node N.sub.2. Because the same-diameter in-series pipeline system generally has a plurality of intermediate nodes, it is necessary to determine the simplified error Err generated by the flow distribution of each intermediate node to form a set Err.sub.i={Err.sub.i, Err.sub.2, . . . , Err.sub.1} (I is the number of the intermediate nodes). The present invention comprehensively considers the minimization in the difference in the propagation process of the transient pressure wave in the system before and after simplification, establishes an optimization objective function to calculate the simplified error generated by the flow distribution of the nodes. Taking the intermediate nodes N.sub.1, N.sub.2, and N.sub.3 shown in FIG. 1 (a) as an example, the established optimization objective functions are as follows:

(10) $\begin{array}{cc}\mathrm{Min}\text{:}{\mathrm{Err}}_1=w_1^1\left\{\begin{array}{c}{\left[\left({\tilde{\Psi }}_0^{N_4}-{\tilde{\Psi }}_d^{N_4}\right)\left(T_0^{P_5.fwdarw.N_4}+T_0^{P_6.fwdarw.N_4}\right)\right]}^2+\\ \{[\left(1-{\tilde{\Psi }}_0^{N_2}\right)\left(1-{\tilde{\Psi }}_0^{N_1}\right)\left(1-{\tilde{\Psi }}_0^{N_4}\right)-\\ {\left(1-{\tilde{\Psi }}_d^{N_2}\right)\left(1-{\tilde{\Psi }}_d^{N_4}\right)]T_0^{P_1.fwdarw.N_4}\}}^2\end{array}\right\}+w_1^2\left\{\begin{array}{c}{\left({\tilde{\Psi }}_0^{N_2}-{\tilde{\Psi }}_d^{N_2}\right)}^2+\\ \{[\left(1-{\tilde{\Psi }}_0^{N_4}\right)\left(1-{\tilde{\Psi }}_0^{N_1}\right)\left(1-{\tilde{\Psi }}_0^{N_2}\right)-\\ {\left(1-{\tilde{\Psi }}_d^{N_4}\right)\left(1-{\tilde{\Psi }}_d^{N_2}\right)]\left(T_0^{P_5.fwdarw.N_4}+T_0^{P_6.fwdarw.N_4}\right)\}}^2\end{array}\right\};& \left(2\right)\\ \mathrm{Min}\text{:}{\mathrm{Err}}_2=w_2^1\left\{{\left({\tilde{\Psi }}_0^{N_1}-{\tilde{\Psi }}_d^{N_1}\right)}^2+{\left[\left(1-{\tilde{\Psi }}_0^{N_3}\right)\left(1-{\tilde{\Psi }}_0^{N_2}\right)\left(1-{\tilde{\Psi }}_0^{N_1}\right)-\left(1-{\tilde{\Psi }}_d^{N_3}\right)\left(1-{\tilde{\Psi }}_d^{N_1}\right)\right]}^2\right\}+w_2^2\left\{{\left({\tilde{\Psi }}_0^{N_3}-{\tilde{\Psi }}_d^{N_3}\right)}^2+{\left[\left(1-{\tilde{\Psi }}_0^{N_1}\right)\left(1-{\tilde{\Psi }}_0^{N_2}\right)\left(1-{\tilde{\Psi }}_0^{N_3}\right)-\left(1-{\tilde{\Psi }}_d^{N_1}\right)\left(1-{\tilde{\Psi }}_d^{N_3}\right)\right]}^2\right\};& \left(3\right)\\ \mathrm{Min}\text{:}{\mathrm{Err}}_3=w_3^1\left\{\begin{array}{c}{\left({\tilde{\Psi }}_0^{N_2}-{\tilde{\Psi }}_d^{N_2}\right)}^2+\\ \{[\left(1-{\tilde{\Psi }}_0^{N_5}\right)\left(1-{\tilde{\Psi }}_0^{N_3}\right)\left(1-{\tilde{\Psi }}_0^{N_2}\right)-\\ {\left(1-{\tilde{\Psi }}_d^{N_5}\right)\left(1-{\tilde{\Psi }}_d^{N_2}\right)]\left(T_0^{P_7.fwdarw.N_5}+T_0^{P_8.fwdarw.N_5}\right)\}}^2\end{array}\right\}+w_3^2\left\{\begin{array}{c}{\left[\left({\tilde{\Psi }}_0^{N_5}-{\tilde{\Psi }}_d^{N_5}\right)\left(T_0^{P_7.fwdarw.N_5}+T_0^{P_8.fwdarw.N_5}\right)\right]}^2+\\ \{[\left(1-{\tilde{\Psi }}_0^{N_2}\right)\left(1-{\tilde{\Psi }}_0^{N_3}\right)\left(1-{\tilde{\Psi }}_0^{N_5}\right)-\\ {\left(1-{\tilde{\Psi }}_d^{N_2}\right)\left(1-{\tilde{\Psi }}_d^{N_5}\right)]T_0^{P_4.fwdarw.N_5}\}}^2\end{array}\right\};& \left(4\right)\end{array}$

(11) In the formula, subscripts 0 and d represent the original systems and the system after the water volume of the intermediate nodes is distributed. w.sup.1 and w.sup.2 are the weight coefficients, which indicate the relative importance of the two simplified in-series pipelines. {tilde over (Ψ)}.sup.N.sup.i is the influence factor of the transient water volume at the node Ni, which indicates the degree of influence of the water volume at a node N.sub.i on a transient flow process, and the value thereof is between 0-100%. T.sup.P.sup.j.sup..fwdarw.N.sup.i is the propagation coefficient of the connecting pipeline P.sub.j at the node Ni. And the mathematical expression thereof is T.sup.P.sup.j.sup..fwdarw.N.sup.i=(2A.sub.j/a.sub.j)/Σ.sub.m=1.sup.M(A.sub.m/a.sub.m), A=πD.sup.2/4. A is the sectional area of the pipeline. D is the diameter of the pipeline. a is the wave velocity of the pipeline. M is the total number of connection pipelines at the node N.sub.i, and m is the m-th connection pipeline at the node N.sub.i. The value of the propagation coefficient T.sup.P.sup.j.sup..fwdarw.N.sup.i is between 0˜2, which means the change degree of the pressure fluctuation amplitude of the transient pressure wave that propagates along the pipeline P.sub.j to the node N.sub.i. for example, in the formula, T.sup.P.sup.5.sup..fwdarw.N.sup.4 represents the multiples of the transient pressure wave propagating along the pipeline P.sub.5 to the node N.sub.4 relative to an initial amplitude before reaching a node N.sub.4, because the pressure wave amplitude of the transient pressure wave that propagates along the pipeline P5 to the node N.sub.4 will change. T.sub.0.sup.P.sup.6.sup..fwdarw.N.sup.4 represents the multiples of the transient pressure wave propagating along the pipeline P.sub.6 to the node N.sub.4 relative to the initial amplitude before reaching the node N.sub.4.

(12) For the present invention, the initial steady-state hydraulic state at the node and the properties of the connection pipeline are used to determine the influence factor {tilde over (Ψ)}.sup.N.sup.i of the transient water volume of the node N.sub.i, that is,

(13) In the formula, S.sub.N.sub.i represents the static property at the node N.sub.i, which is determined by the initial steady-state hydraulic state at the node and the properties of the connection pipeline, namely, S.sub.N.sub.i=q.sub.0(N.sub.i)/[gH.sub.0.sup.0.5(N.sub.i)Σ.sub.m=1.sup.M(A.sub.m/a.sub.m)], where q.sub.0(N.sub.i) and H.sub.0(N.sub.i) represent the initial steady-state water volume and pressure at the node N.sub.i, respectively, and g is the acceleration of gravity;

(14) The present invention uses the ratio of the length of the in-series pipeline to represent the weight coefficient of the two in-series pipelines, namely:
w.sub.1.sup.1=L(P.sub.1)/[L(P.sub.1)+L(P.sub.2)]  (6);
w.sub.1.sup.2=L(P.sub.2)/[L(P.sub.1)+L(P.sub.2)]  (7);
w.sub.2.sup.1=L(P.sub.2)/[L(P.sub.2)+L(P.sub.3)]  (8);
w.sub.2.sup.2=L(P.sub.3)/[L(P.sub.2)+L(P.sub.3)]  (9);
w.sub.3.sup.1=L(P.sub.3)/[L(P.sub.3)+L(P.sub.4)]  (10);
w.sub.3.sup.2=L(P.sub.4)/[L(P.sub.3)+L(P.sub.4)]  (11);

(15) In the formula, L represents the length of the pipeline.

(16) In the optimization objective function Min: Err, the propagation coefficient is related to the pipeline properties and the initial steady-state hydraulic state of the system before simplification, and is a known parameter. {tilde over (Ψ)}.sub.d.sup.N.sup.i is related to the static properties at the node N.sub.i in the simplified system (that is, after the node flow is distributed) (that is, Formula 5). S.sub.N.sub.i is related to the node water volume at the node N.sub.i (here, it refers to the node water volume at the node N.sub.i after the water volume of the intermediate node is distributed). Therefore, the optimization decision variable of the optimization objective function is the water distribution coefficient r of the intermediate node, which can be solved to get the simplified error Err and the corresponding optimization decision variable value r. Specifically, Formulas (2), (3) and (4) can be solved to get the simplified errors Err.sub.1, Err.sub.2 and Err.sub.3 of the intermediate nodes N.sub.1, N.sub.2 and N.sub.3, and the corresponding optimization decision variable values r.sub.1, r.sub.2 and r.sub.3. In order to ensure that the optimization objective function Min: Err is optimized and solved reasonably, the present invention limits the value of the optimization decision variable r to be between 0 and 1.

(17) Formulas (2), (3), and (4) give simplified error solving methods for intermediate nodes at different positions (respectively at the left, middle, and right boundaries) of the same-diameter in-series pipeline system, which can be generalized and applied to the same-diameter in in-series pipeline system with any intermediate node and different externally connected pipelines.

(18) (3) determine the intermediate nodes that can be preferably simplified according to Err.sub.min=min(Err.sub.i). In order to ensure the accuracy of the simplified model, the present invention proposes a simplified error control threshold Err.sub.tol to judge whether the combination and operation of the same-diameter in-series pipeline (that is, the water volume of the intermediate node is distributed) is suitably conducted:
If Err.sub.min≤Err.sub.tol, it can be simplified  (12);
If Err.sub.min>Err.sub.tol, it is not appropriate to simplify  (13);

(19) For the setting of this threshold, the larger Errtol is, the more in-series pipelines are used to distribute the water volume of the intermediate node, and the more transient characteristics of the original system the simplified model will lose. The present invention proposes that the reasonable range of the control threshold Err.sub.tol is between 0.01 and 0.03, so as to be suitable for the application requirements of the hydraulic model of the pipeline network at different levels.

(20) If Err.sub.min≤Err.sub.tol, then continue to execute downward; otherwise, jump to Step (6).

(21) (4) perform a simplified operation on the simplified intermediate nodes to determine the flow of the simplified nodes at two ends and parameters of an equivalent pipeline. The flow of the simplified nodes at both ends can be determined according to the optimization decision variable value r corresponding to Err.sub.min. For example, the intermediate node N.sub.2 is simplified, and the water volume of the nodes N.sub.1 and N.sub.3 at two ends are q.sub.1+r.sub.2q.sub.2 and, q.sub.3+(1−r.sub.2)q.sub.2, respectively. The parameters of the equivalent pipeline are determined as follows: (1) the pipeline diameter and the wave velocity of the equivalent pipeline are equal to the pipeline diameter and the wave velocity of the in-series pipe, respectively. The wave velocity of the two in-series pipelines is the same; (2) The length of the pipeline is equal to the sum of the length of the two in-series pipelines; (3) the coefficient of resistance of the pipeline is determined according to the principle of hydraulic equivalence, that is, the head loss of the equivalent pipeline after the flow is simplified is the same as the head loss of the in-series pipeline before the flow is simplified.

(22) (5) remove the simplified intermediate nodes in the same-diameter in-series pipeline system IDPi. At this time, if the number of the intermediate nodes in IDPi is 0, it means that the in-series pipelines in the current same-diameter in-series pipeline system have been simplified, then jump to Step (6); otherwise, jump to Step (2) and continue to simplify the current same-diameter in-series pipeline system.

(23) (6) complete the simplification of the current same-diameter in-series pipeline systems, start the simplification of the next group of the same-diameter in-series pipeline systems, and return to Step (2) until all the same-diameter in-series pipeline systems have been simplified, which means a simplified process is ended.

EXAMPLE

(24) FIG. 2 is a diagram of the topological structure of a water supply pipeline network of this embodiment. The water supply pipeline network has 4 water source pools, 317 pipes, and 268 nodes. In-series pipelines in a pipeline network model are all the same-diameter in-series pipeline type, and the intermediate nodes all have node flow. The method of the present invention is used to simplify the same-diameter in-series pipeline in the pipeline network model (the simplified error control threshold Err.sub.tol is set according to the application requirements of the model).

(25) A node flow optimization distribution method for improving the accuracy of transient hydraulic simulation of a water supply in-series pipeline comprises the following steps:

(26) (1) Identify same-diameter in-series pipeline systems (IDP) in a pipeline network model. In this example, a total of 70 groups are identified to form a set IDP={IDP.sub.1, IDP.sub.2, . . . , IDP.sub.70} of the same-diameter in-series pipeline system. FIG. 3 (a) shows the first group of the same-diameter in-series pipeline systems is mathematically expressed as:
IDP.sub.1={([1],[2],[3]),(1,2),(3,4),([4],[5],[6]),([7],[8])}  (14);

(27) (2) For the same-diameter in-series pipeline system IDP.sub.1 in the set IDP, calculate the simplified error generated by the node flow distribution of the intermediate nodes 1 and 2 according to Formulas (2), (3) and (4).

(28) In this example, the intermediate nodes 1 and 2 are the intermediate nodes on the left and right boundaries, respectively, and the simplified errors that are calculated using Formulas (2) and (4) are Err.sub.1 and Err.sub.2 (Err.sub.1<Err.sub.2), respectively, thereby forming a system IDP1's simplified error set Err.sub.1={Err.sub.1, Err.sub.2}.

(29) (3) According to Err.sub.min=min(Err.sub.i), the intermediate node that can be preferably simplified is node 1, that is, Err.sub.min=Err.sub.1. According to Formulas (12) and (13), it is determined whether the simplified operation is appropriate; if Err.sub.min≤Err.sub.tol, continue to perform downward; otherwise, jump to Step (10).

(30) (4) Perform a simplified operation on the simplified intermediate node 1. The simplified in-series pipelines [1] and [2] are combined into one equivalent pipeline [12]. The node flow and the parameters of the equivalent pipeline of the simplified nodes 3 and 2 at both ends are determined. The flow of the simplified nodes at both ends can be determined according to the optimization decision variable value r.sub.1 corresponding to Err.sub.min (that is, Err.sub.1), that is, the water volume of the simplified nodes 3 and 2 at two ends are q.sub.3+r.sub.1q.sub.1 and q.sub.2+(1−r.sub.1)q.sub.1, respectively. The parameters of the equivalent pipeline [12] are determined as follows: (1) The pipeline diameter and the wave velocity of the equivalent pipeline are equal to the pipeline diameter and the wave velocity of the in-series pipeline, respectively; (2) the length of the pipeline is equal to the sum of the length of the two in-series pipelines; (3) the resistance coefficient of the pipeline is determined according to the principle of hydraulic equivalence, that is, the head loss of the equivalent pipeline after the water flow is simplified is the same as the head loss of the in-series pipeline before the water flow is simplified.

(31) (5) Remove the simplified intermediate node 1 in the same-diameter in-series pipeline system IDP.sub.1 to obtain IDP.sub.1={[12],[3]), (2), (3,4), ([4],[5],[6]), ([7],[8])}. At this time, the intermediate node of the system IDP.sub.1 is node 2, and the number of intermediate nodes is greater than 0, then the current same-diameter in in-series pipeline system continues to be simplified.

(32) (6) For the same-diameter in-series pipeline system IDP.sub.1 in the set IDP, the simplified error of the intermediate node 2 is calculated according to Formulas (2), (3) and (4), and the simplified error set Err.sub.1={Err.sub.2} is obtained.

(33) (7) According to Err.sub.min=min(Err.sub.i), the intermediate node that can be preferably simplified is node 2, namely, Err.sub.min=Err.sub.2. According to Formulas (12) and (13), it is judged whether the simplified operation is appropriately conducted. If Err.sub.min≤Err.sub.tol, then continue to execute downward; otherwise, jump directly to Step (10).

(34) (8) Perform the simplified operation on the intermediate node 2 that can be simplified. The simplified in-series pipelines [12] and [3] are combined into one equivalent pipeline [123]. The node flow and the parameters of the equivalent pipeline of the simplified nodes 3 and 4 at both ends are determined.

(35) (9) Remove the simplified intermediate node 2 in the same-diameter in-series pipeline system IDP.sub.1 to obtain IDP.sub.1={([123]), ( ), (3, 4), ([4],[5],[6]), ([7],[8])}. At this time, the number of intermediate nodes in the system IDP.sub.1 is 0, indicating that the in-series pipelines in the current same-diameter in-series pipeline system have been simplified, and the execution continues downward.

(36) (10) complete the simplification of the current system IDP.sub.1, start the simplification of the next group of the same-diameter in-series pipeline system IDP.sub.2, and return to Step (2) until all the same-diameter in-series pipeline systems are traversed, indicating the end of the simplification process.

(37) The above steps are taken to achieve the simplification of the same-diameter in-series pipelines in the pipeline network of the example. FIG. 3 (b) shows the simplified result of the simplified error control threshold Err.sub.tol=0.03; it can be seen from the figure that by setting simplified error control threshold and in the pipeline network model, some simplified nodes that will cause a significant increase in transient hydraulic simulation errors are retained, ensuring the accuracy and reliability of the pipeline network model.

(38) The same transient flow event (i.e., a valve closing event) is triggered in the original model and the simplified model. A transient flow process is simulated and calculated. The simplified pipeline network model used for calculation and analysis results of transient flow is shown in FIG. 4(a)-(d), where FIG. 4 (b) is a partially enlarged diagram of a graph in the dotted box of FIG. 4 (a). FIG. 4 (d) is a partially enlarged diagram of a graph in the dotted box of FIG. 4 (c). FIG. 4(a)-(d) shows the comparison of the calculation results of transient flow of the obtained simplified model and those of the original model obtained by the simplified model obtained by using the method of the present invention and the conventional simplified method (in this example, the conventional simplified method uses the intermediate node flow to share).

(39) It can be clearly seen from FIG. 4(a)-(d) that the simplified method of the present invention is in good agreement with the original model in terms of a peak value and a phase of instantaneous pressure fluctuations. Compared with the conventional simplified method, the method of the present invention has obvious advantages in calculation accuracy. Especially when severe water column separation occurs, as shown in FIGS. 4 (c) and (d). The simplified method of the present invention can still ensure that the calculation results of the transient flow are basically consistent with the original model, while the conventional simplified method will cause the calculation results of the transient flow to be significantly different from the original model in terms of the moment when the water column separation occurs, the volume formed of an air cavity, and the moment and intensity of the water column closing. Therefore, in practical engineering applications, the implementation method of the present invention should be used to simplify the same-diameter in-series pipeline to ensure the accuracy of the calculation of the transient flow, and then provide a scientific basis for the prevention and control of the transient damage of the pipeline network.

(40) Obviously, the described example is only a part of the examples of the present invention, but not all the examples. Based on the examples of the present invention, all other examples obtained by those of the person skilled in the art without creative efforts shall fall within the protection scope of the present invention.