CN105389469A - Automatic calibration method of storm water management model parameters - Google Patents

Abstract

The present invention discloses an automatic calibration method of storm water management model (SWMM) parameters. The method comprises: based on an SWMM model, building a regional runoff-conflux model, performing linearization on a nonlinear relationship between a model parameter set and a flow; using a computing strategy with the Levenberg-Marquardt algorithm as the core to search for an optimal parameter combination, so as to automatically calibrating SWMM model parameters. The advantage of the method is as follows: according to the method provided by the present invention, when automatically calibrating SWMM model parameters, a target function is solved through iterative optimization, so as to automatically and efficiently calibrate specified regional runoff-conflux model parameters, thereby greatly improving the efficiency of optimizing and solving parameters, avoiding effects from subjective factors, avoiding consumption of a lot of manpower, lowering requirements on knowledge and experience of operators, and enabling obtained parameters to be more scientific. According to the method provided by the present invention, SWMM model parameters can be automatically calibrated, and moreover, the optimal parameter combination can be obtained efficiently and accurately. The method provided by the present invention is an automatic calibration method of SWMM parameters that is effective and robust.

Description

The automatic rating method of a kind of storm flood administrative model parameter

Technical field

Invention relates to Urban Hydrologic theory field, urban flood defence application can be applied to, more specifically, relate to the automatic rating method of a kind of storm flood administrative model (SWMM) parameter, adopt and a kind ofly optimize the automatic calibration problem that calculative strategy solves SWMM model parameter.

Background technology

Since mid-twentieth century, hydrological model is developed fast, and the earth science data such as weather, the hydrology combines with computing technique by it, analyzes the Spatial Variability of earth science data and the continuity of period, to grasp the rule of Regional Rainfall-runoff process.Practice through nearly decades shows, many hydrological models have good effect in simulated rainfall-runoff process, and it is significant to flood control and disaster reduction, water resources management, unwatering system planning, design etc.

Can hydrological model produce the accuracy that rule of confluxing depends primarily on model parameter by reflecting regional truly.Therefore, simulated domain produces to conflux inevitably needs to carry out calibration to Hydro-Model Parameter Calibration Technology.Calibration Hydro-Model Parameter Calibration Technology was mainly undertaken debugging and determining by manual in the past, but the consuming time and effort of this process, determined parameter value affects very greatly by subjective factor, requires high to the relevant knowledge deposit, experience etc. of operating personnel.Along with further developing of computer technology and mathematical optimization techniques, a large amount of hydrological model introduces the automatic Offered model parameters of algorithms of automatic optimization, and the effect of institute's calibration is ideal.Wherein, storm flood administrative model (stormwatermanagementmodel, SWMM) since exploitation in 1971, continuous renewal through decades develops, be regarded as the outstanding representative of Urban Hydrologic model, in hydrology calculating, contaminant transportation simulation etc., show power, used widely in the world, but its latest edition SWMM5.1 still fails to realize automatic calibration parameter function.

SWMM relates to impermeable area ratio, earth's surface penetrating power, overland flow width, low-lying area, impermeable earth's surface store the dozens of parameters such as the storage degree of depth, and every sub-watershed, parameter corresponding to pipeline are all different, this model farthest makes constructed model similar to actual conditions, but also has higher requirement to calibration parameter.If sub-watershed is more, the parameter of calibration needed for it will reach hundreds if not thousands of, only carries out the calibration of parameter by artificial trial and error, will the time and efforts of at substantial, and calibration effect cannot be guaranteed.Except the artificial trial and error of employing, most researcher adopts experience value to carry out the calibration of parameter, and calibration effect is also undesirable, and cannot reflect the parameter sensitivity degree of zones of different.The parameter that SWMM model relates to is complicated nonlinear system, conventional method cannot be utilized to carry out studying, calibration, and how accurately and efficiently Offered model parameters is the significant challenge that SWMM model faces.

Summary of the invention

Due to SWMM model, to relate to parameter numerous and make that parameter rating of the model work is numerous and diverse, accuracy is not high without carrying automatic calibration module, the present invention introduces optimized algorithm and improves on the basis of SWMM model, to reach the object of automatic calibration SWMM model parameter, making up current SWMM model cannot the weakness of calibration tool parameter automatically, the requirement to multiparameter calibration can be met preferably, be one efficiently, automatically, SWMM parameter rating of the model instrument accurately.

Substance of the present invention is the parameter calibration problem for SWMM model, proposes the automatic rating method of a kind of SWMM model parameter.Can the arbitrarily specified parameter of calibration based on the method, make it reach optimum state.The present invention is based on SWMM model platform and build region product Confluence Model, by specifying parameter and the variation range thereof of required calibration, flow and nonlinearity in parameters relation are converted to linear relationship, build corresponding objective function, define weighing computation method and the solve for parameter matrix update rule of each measured discharge again, minimum value when solving objective function converges by a kind of calculative strategy that is core with Levenberg-Marquardt algorithm, finally obtains the constructed optimal value of product Confluence Model parameter and the susceptibility of relevant parameter thereof.

To achieve these goals, invention have employed following technical scheme:

The automatic rating method of a kind of storm flood administrative model parameter, the method comprises the following steps:

(1) region master data is obtained, with SWMM model for Confluence Model is produced in platform construction region;

(2) specify the parameter group of producing required calibration in Confluence Model and number, set the variation range of each parameter, build the nonlinear relationship between flow actual observed value and Models Sets parameter;

(3) linearization process is carried out to the relation of flow actual observed value and Models Sets parameter;

(4) build the objective function of parameter optimization, and define each actual flow observed reading weight calculation rule and solve for parameter matrix update rule;

(5) corresponding actual observed value weight matrix and Increment Matrix when calculating different iterations;

(6) solve minimum value during objective function converges, if objective function is not restrained, then forward step (5) to; If function convergence also obtains minimum value, then Output rusults, Output rusults comprises optimized parameter group, optimum analogue flow rate, each parametric sensitivity of constructed product Confluence Model parameter;

(7) measured discharge and optimum analogue flow rate degree of fitting are evaluated.

Preferably, in step (2), the nonlinear relationship between described structure flow actual observed value and Models Sets parameter is defined as: c ₀=M (b ₀), wherein c ₀by being formed matrix, b by m actual observed value ₀for the matrix be made up of n parameter, the incidence relation between actual observed value and model parameter represents with nonlinear function M.

Preferably, in step (3), the described relation to flow actual observed value and Models Sets parameter is carried out linearization process and is defined as:

c＝c ₀+J(b-b ₀)

In formula, c is model result matrix, and b is solve for parameter matrix, and J is the capable Jacobi local derviation matrix about M of n row m.

Preferably, in step (4), the objective function φ of described structure parameter optimization is expressed as:

φ＝[c-c ₀-J(b-b ₀)] ^tQ[c-c ₀-J(b-b ₀]

In formula, t is matrix transpose symbol, and Q is the measured value weight matrix with the capable m row of m, adopts Levenberg-Marquardt algorithm it to be solved to the minimum value of this objective function;

Described definition each actual flow observed reading weight calculation rule, the diagonal matrix Q that the weight by actual observed value is tieed up with m represents, the weight w of i-th actual observed value _ifor diagonal element Q _ii, Q ^-1=C (c)/σ ², wherein C (c) represents that the m of actual observed value vector c ties up covariance matrix, and supposes in c separate between each element, and the variance of each element is defined as

Described solve for parameter matrix update rule, namely the renewal of solve for parameter matrix b is by Increment Matrix u _kcarrying out, for solving that magnitude between c and b exists that difference is comparatively large and element magnitude that is that cause J to comprise occurs huge difference and produces larger round-off error, by solve for parameter matrix update Rule Expression being:

b _k ⁺＝b _k ^-+u _k

S _k ^-1u _k＝[(J _kS _k) ^tQJ _kS _k+αS _k ^tS _k] ^-1(J _kS _k) ^tQr

In formula, k is iterations, b _k ⁺for the parameter matrix after renewal, b _k ^-for the parameter matrix before renewal, u _kfor Increment Matrix, r is c _k ^-residual error, α is Marquardt parameter, and S is the diagonal matrix of n × n, then i-th diagonal element in S is expressed as:

$S_{ii}={{\left(J_k^t{\mathrm{QJ}}_k\right)}_{ii}}^{-1/2}$

If by α S _k ^ts _kin greatest member be defined as the λ value of Marquart, then (J _ks _k) ^tqJ _ks _k+ α S _k ^ts _kelement value maximum in matrix is expressed as 1+ λ.

Preferably, in step (6), described each parameter sensitivity calculates and is defined as:

$s_j=\frac{{\left(J^{t}QJ\right)}_u^{1/2}}{m}$

In formula, s _jrepresent the susceptibility of i-th parameter, i.e. the complexity of this parameter optimization, s _jlarger parameter is relative to whole optimizing process, and it is more easily optimized; s _jless, then represent the more difficult optimization of response parameter.

Preferably, in step (7), measured discharge and the evaluation of optimum analogue flow rate degree of fitting are evaluated with relative coefficient R, deterministic coefficient NSE and Kling-Gupta COEFFICIENT K GE, and its computing formula is as follows:

$R=\frac{\underset{i=1}{\overset{m}{\Σ}}(w_i{c}_{oi}-P)(w_i{c}_i-p)}{\sqrt{\underset{i=1}{\overset{m}{\Σ}}{(w_i{c}_{oi}-P)}^2{(w_i{c}_i-p)}^2}}$

$NSE=1-\frac{\underset{i=1}{\overset{m}{\Σ}}{(c_i-c_{oi})}^2}{\underset{i=1}{\overset{m}{\Σ}}{(c_{oi}-\stackrel{\‾}{c_o})}^2}$

$KGE=1-\sqrt{{(R-1)}^2+{(\mathrm{\ξ}-1)}^2+{(\mathrm{\γ}-1)}^2}$

In formula, R is relative coefficient, c _oii-th measured discharge value, c _ifor with the analogue flow rate corresponding to i-th measured discharge value, P is mean value, p is mean value, for mean value, ξ is analogue flow rate standard deviation and measured discharge standard deviation ratio, and γ is the average of analogue flow rate and the ratio of measured discharge average.

Compared with prior art, beneficial effect of the present invention is:

Technique scheme builds region based on SWMM model platform and produces Confluence Model, flow and nonlinearity in parameters relation are converted to linear relationship, build corresponding objective function, define weighing computation method and the solve for parameter matrix update rule of each measured discharge again, minimum value when solving objective function converges by a kind of calculative strategy that is core with Levenberg-Marquardt algorithm, correspondence obtains the constructed optimal value of product Confluence Model parameter and the susceptibility of relevant parameter thereof.Its maximum advantage is when carrying out calibration to SWMM model parameter, the present invention solves objective function by iteration optimizing and realizes automatic, efficiently specified by calibration region product Confluence Model parameter, the efficiency of Optimization Solution parameter is improved greatly and avoids the impact of artificial subjective factor and a large amount of manpower expends, reduce the requirement such as relevant knowledge deposit, experience to operating personnel, make obtained parameter have more science.

Accompanying drawing explanation

Fig. 1 is the method flow diagram utilizing the invention process to solve the automatic calibration of SWMM model parameter.

Fig. 2 is survey region present status of land utilization and unwatering system generally change figure.

Fig. 3 adopts the inventive method to simulate large rainfall sight lower area to produce the design sketch that confluxes.

Fig. 4 adopts rainfall sight lower area in the inventive method simulation to produce the design sketch that confluxes.

Fig. 5 adopts the inventive method to simulate little rainfall sight lower area to produce the design sketch that confluxes.

Embodiment

Below in conjunction with the method that accompanying drawing is specifically addressed the automatic calibration of a kind of SWMM model parameter to the present invention, it is worthy of note, described example is intended to help and understands the present invention, and does not play any restriction effect to it.

The automatic rating method of a kind of SWMM model parameter, comprises the following steps:

(1) master datas such as Land_use change situation, unwatering system, landform are obtained, with SWMM model for Confluence Model is produced in platform construction region;

(2) specify the parameter group of producing required calibration in Confluence Model and number, set the variation range of each parameter, build the nonlinear relationship between flow actual observed value and Models Sets parameter;

(3) linearization process is carried out to the relation of flow actual observed value and Models Sets parameter;

(4) build the objective function of parameter optimization, and define each actual flow observed reading weight calculation rule and solve for parameter matrix update rule;

(5) corresponding actual observed value weight matrix and Increment Matrix when calculating different iterations;

(6) solve minimum value during objective function converges, if objective function is not restrained, then forward step (5) to; If function convergence also obtains minimum value, then Output rusults, Output rusults is the optimized parameter group, optimum analogue flow rate, each parametric sensitivity etc. of constructed product Confluence Model parameter;

(7) measured discharge and optimum analogue flow rate degree of fitting are evaluated.

According to embodiments of the invention, in step (2), the variation range of each parameter sets according to former achievements and SWMM service manual recommended range.

According to embodiments of the invention, in step (2), the nonlinear relationship between described structure flow actual observed value and Models Sets parameter is defined as: c ₀=M (b ₀), wherein c ₀by being formed matrix, b by m actual observed value ₀for the matrix be made up of n parameter, the incidence relation between actual observed value and model parameter represents with nonlinear function M.

According to embodiments of the invention, in step (3), the described relation to flow actual observed value and Models Sets parameter is carried out linearization process and is defined as:

c＝c ₀+J(b-b ₀)

Wherein, c is model result matrix, and b is solve for parameter matrix, and J is the capable Jacobi local derviation matrix about M of n row m, and is expressed as:

$J\[i,j\]=\frac{\∂M\left(\stackrel{\→}{x}\right)\[i\]}{\∂x\left(j\right)}$

In formula, i, j represent the i-th row, the j columns of Jacobi local derviation matrix J.

According to embodiments of the invention, in step (4), the objective function of described structure parameter optimization is expressed as:

φ＝[c-c ₀-J(b-b ₀)] ^tQ[c-c ₀-J(b-b ₀]

In formula, t is matrix transpose symbol, and Q is the measured value weight matrix with the capable m row of m, adopts Levenberg-Marquardt algorithm it to be solved to the minimum value of this objective function;

According to embodiments of the invention, in step (4), described definition each actual flow observed reading weight calculation rule, the diagonal matrix Q that the weight by actual observed value is tieed up with m represents, the weight w of i-th actual observed value _ifor diagonal element Q _ii, wherein Q ^-1=C (c)/σ ², wherein C (c) represents that the m of actual observed value vector c ties up covariance matrix, and supposes in c separate between each element, and the variance of each element is defined as ${\mathrm{\σ}}^2=\frac{\mathrm{\φ}}{m-n};$

According to embodiments of the invention, in step (4), described solve for parameter matrix update rule, namely the renewal of solve for parameter matrix b is by Increment Matrix u _kcarrying out, for solving that magnitude between c and b exists that difference is comparatively large and element magnitude that is that cause J to comprise occurs huge difference and produces larger round-off error, by solve for parameter matrix update Rule Expression being:

b _k ⁺＝b _k ^-+u _k

${S_k}^{-1}{u}_k={\[{\left(J_k{S}_k\right)}^t{\mathrm{QJ}}_k{S}_k+{{\mathrm{\αS}}_k}^t{S}_k\]}^{-1}{\left(J_k{S}_k\right)}^{t}Qr$

In formula, k is iterations, subscript b _k ⁺for the parameter matrix after renewal, subscript b _k ^-for the parameter matrix before renewal, u _kfor Increment Matrix, r is c _k ^-residual error, α is Marquardt parameter, and S is the diagonal matrix of n × n, then i-th diagonal element in S can be expressed as:

$S_{ii}={{\left(J_k^t{\mathrm{QJ}}_k\right)}_{ii}}^{-1/2}$

If by α S _k ^ts _kin greatest member be defined as Marquart λ value, then (J _ks _k) ^tqJ _ks _k+ α S _k ^ts _kelement value maximum in matrix is expressed as 1+ λ.

According to embodiments of the invention, in step (6), described each parameter sensitivity calculates and is defined as:

$s_j=\frac{{\left(J^{t}QJ\right)}_u^{1/2}}{m}$

In formula, s _jrepresent the susceptibility of i-th parameter, represent the complexity of this parameter optimization, s _jlarger parameter is relative to whole optimizing process, and it is more easily optimized; s _jless, then represent that response parameter is more difficult and correctly optimize.

According to embodiments of the invention, in step (6), the minimum value when obtaining objective function converges, Output rusults is the optimized parameter group, optimum analogue flow rate, each parametric sensitivity etc. of constructed product Confluence Model parameter.

According to embodiments of the invention, in step (7), measured discharge and optimum analogue flow rate degree of fitting are evaluated and are evaluated with relative coefficient (R), deterministic coefficient (NSE) and Kling-Gupta coefficient (KGE), and its computing formula is as follows:

$R=\frac{\underset{i=1}{\overset{m}{\Σ}}(w_i{c}_{oi}-P)(w_i{c}_i-p)}{\sqrt{\underset{i=1}{\overset{m}{\Σ}}{(w_i{c}_{oi}-P)}^2{(w_i{c}_i-p)}^2}}$

$NSE=1-\frac{\underset{i=1}{\overset{m}{\Σ}}{(c_i-c_{oi})}^2}{\underset{i=1}{\overset{m}{\Σ}}{(c_{oi}-\stackrel{\‾}{c_o})}^2}$

$KGE=1-\sqrt{{(R-1)}^2+{(\mathrm{\ξ}-1)}^2+{(\mathrm{\γ}-1)}^2}$

In formula, R is relative coefficient, c _oii-th measured discharge value, c _ifor with the analogue flow rate corresponding to i-th measured discharge value, P is mean value, p is mean value, for mean value, ξ is analogue flow rate standard deviation and measured discharge standard deviation ratio, and γ is the average of analogue flow rate and the ratio of measured discharge average.

Technique scheme builds region based on SWMM model platform and produces Confluence Model, flow and nonlinearity in parameters relation are converted to linear relationship, build corresponding objective function, define weighing computation method and the solve for parameter matrix update rule of each measured discharge again, minimum value when solving objective function converges by a kind of calculative strategy that is core with Levenberg-Marquardt algorithm, correspondence obtains the constructed optimal value of product Confluence Model parameter and the susceptibility of relevant parameter thereof.Its maximum advantage is when carrying out calibration to SWMM model parameter, the present invention solves objective function by iteration optimizing and realizes automatic, efficiently specified by calibration region product Confluence Model parameter, the efficiency of Optimization Solution parameter is improved greatly and avoids the impact of artificial subjective factor and a large amount of manpower expends, reduce the requirement such as relevant knowledge deposit, experience to operating personnel, make obtained parameter have more science.

Research object in the present invention is typical residential quarter (113.201 ° ~ 113.214 ° E being positioned at a certain height urbanization of Fang Cun district, Guangzhou, Guangdong, 23.078 ° ~ 23.086 ° N), area is 15.5ha, be mainly construction land in plot, small part is the use of road and greening; Sewerage pipeline network adopts the dirty separate system of rain, and design standards is 2 years chances, and drain pipe diameter is 600 ~ 1650mm, and design grade is 0.001 ~ 0.01, and the sub-watershed in region divides and pipe network generally changes result as shown in Figure 1.Monitored on the spot by the rainfall to this region, pipeline runoff, every 10min record once this Regional Rainfall and footpath flow data.

Survey region in the present invention selects the reason of a certain typical cell, Fang Cun district, Guangzhou, Guangdong to be mainly: this region is positioned at height urbanization, the Fang Cun district that economically developed, population is comparatively intensive, and drainage pipeline networks lays the time comparatively early, belongs to typical urban area.In addition, due to extreme catchment take place frequently, underlying surface hardening proportion increases, cause this Regional Hydrologic condition to become more complicated, region product confluxes rule generation marked change.For probe into Regional Rainfall and product conflux between rule, in the case with SWMM model for platform construction region produce Confluence Model, adopt a kind of calculative strategy being core with Levenberg-Marquardt algorithm, product Confluence Model parameter constructed by automatic calibration, the analogue flow rate that final acquisition and measured discharge are pressed close to the most and corresponding the most optimized parameter combine.

Fig. 1 is method flow diagram of the present invention, can find out that the present invention mainly comprises the following steps by it:

1st step: obtain the master datas such as Land_use change situation, unwatering system, landform, with SWMM model for Confluence Model is produced in platform construction region;

On the basis obtaining the terrain data in this survey region, waste pipe-network design, generally change principle in strict accordance with SWMM model, sub-watershed division is carried out to this region and unwatering system is generally changed, and collect the data such as Land_use change and build region and produce Confluence Model.

2nd step: specify the parameter group and number of producing required calibration in Confluence Model, set the variation range of each parameter, build the nonlinear relationship between flow actual observed value and Models Sets parameter.

In case study on implementation, first determine parameter group and the number thereof of required calibration, and with matrix b ₀form represent, the variation range of each parameter sets according to former achievements and SWMM service manual recommended range; In addition, by obtained a m actual observed value with matrix c ₀form represent, incidence relation is therebetween represented with nonlinear function M, is namely defined as:

c ₀＝M(b ₀)

3rd step: linearization process is carried out to the relation of flow actual observed value and Models Sets parameter.

Both flow actual observed value and Models Sets parameter are nonlinear relationship, cannot directly carry out calculating to excavate its corresponding rule, in the implementation case, the relationship of the two are carried out linearization process, the two linear relationship are expressed as:

c＝c ₀+J(b-b ₀)

Wherein, c is model result matrix, and b is solve for parameter matrix, and J is the capable Jacobi local derviation matrix about M of n row m, and is expressed as:

$J\[i,j\]=\frac{\∂M\left(\stackrel{\→}{x}\right)\[i\]}{\∂x\left(j\right)}$

In formula, i, j represent the i-th row, the j columns of Jacobi local derviation matrix J.

4th step: the objective function building parameter optimization, and define each actual flow observed reading weight calculation rule and solve for parameter matrix update rule.

For finding best parameter group and optimum analogue flow rate, the objective function of parameter optimization is defined as

φ＝[c-c ₀-J(b-b ₀)] ^tQ[c-c ₀-J(b-b ₀]

Wherein t is matrix transpose symbol, and Q is the measured value weight matrix with the capable m row of m, adopts Levenberg-Marquardt algorithm it to be solved to the minimum value of this objective function;

The diagonal matrix Q that the weight of actual observed value is tieed up with m represents, the weight w of its i-th actual observed value _ifor diagonal element Q _ii, wherein Q ^-1=C (c)/σ ², wherein C (c) represents that the m of actual observed value vector c ties up covariance matrix, and supposes in c separate between each element, and the variance of each element is defined as

The renewal of solve for parameter matrix b is by Increment Matrix u _kcarrying out, for solving that magnitude between c and b exists that difference is comparatively large and element magnitude that is that cause J to comprise occurs huge difference and produces larger round-off error, by solve for parameter matrix update Rule Expression being:

b _k ⁺＝b _k ^-+u _k

S _k ^-1u _k＝[(J _kS _k) ^tQJ _kS _k+αS _k ^tS _k] ^-1(J _kS _k) ^tQr

In formula, k is iterations, subscript b _k ⁺for the parameter matrix after renewal, subscript b _k ^-for the parameter matrix before renewal, u _kfor Increment Matrix, r is c _k ^-residual error, α is Marquardt parameter, and S is the diagonal matrix of n × n, then i-th diagonal element in S can be expressed as:

$S_{ii}={{\left(J_k^t{\mathrm{QJ}}_k\right)}_{ii}}^{-1/2}$

If by α S _k ^ts _kin greatest member be defined as Marquart λ value, then (J _ks _k) ^tqJ _ks _k+ α S _k ^ts _kelement value maximum in matrix is expressed as 1+ λ.

5th step: corresponding actual observed value weight matrix and Increment Matrix when calculating different iterations according to the computing method of actual observed value weight in the 4th step and solve for parameter matrix update rule;

6th step: adopt minimum value during Levenberg-Marquardt Algorithm for Solving objective function converges, if objective function is not restrained, then forward the 5th step to; If function convergence also obtains minimum value, then Output rusults, Output rusults is the optimized parameter group, optimum analogue flow rate, each parametric sensitivity etc. of constructed product Confluence Model parameter.

7th step: measured discharge and optimum analogue flow rate degree of fitting are evaluated.

For inspection institute's Offered model parameters and obtain the rationality of optimum analogue flow rate, adopt relative coefficient (R), deterministic coefficient (NSE) and Kling-Gupta coefficient (KGE) to evaluate measured discharge and optimum analogue flow rate degree of fitting, its computing formula is as follows:

$R=\frac{\underset{i=1}{\overset{m}{\Σ}}(w_i{c}_{oi}-P)(w_i{c}_i-p)}{\sqrt{\underset{i=1}{\overset{m}{\Σ}}{(w_i{c}_{oi}-P)}^2{(w_i{c}_i-p)}^2}}$

$NSE=1-\frac{\underset{i=1}{\overset{m}{\Σ}}{(c_i-c_{oi})}^2}{\underset{i=1}{\overset{m}{\Σ}}{(c_{oi}-\stackrel{\‾}{c_o})}^2}$

$KGE=1-\sqrt{{(R-1)}^2+{(\mathrm{\ξ}-1)}^2+{(\mathrm{\γ}-1)}^2}$

In formula, R is relative coefficient, c _oii-th measured discharge value, c _ifor with the analogue flow rate corresponding to i-th measured discharge value, P is mean value, p is mean value, for mean value, ξ is analogue flow rate standard deviation and measured discharge standard deviation ratio, and γ is the average of analogue flow rate and the ratio of measured discharge average.

Sum up: Urban Hydrologic condition constantly increases along with climate change and city underlying surface hardening proportion and changes, cause adopting hydrological model to simulate it and produce rule difficulty increase of confluxing.The present invention proposes the automatic rating method of a kind of SWMM model parameter, first with SWMM model for platform construction region produce Confluence Model, again flow and nonlinearity in parameters relation are converted to linear relationship, and define weighing computation method and the solve for parameter matrix update rule of each measured discharge, and then minimum value when solving objective function converges by a kind of calculative strategy that is core with Levenberg-Marquardt algorithm, it is final that obtain optimum parameter combinations and optimum analogue flow rate thus produce Confluence Model parameter based on region constructed by SWMM under solving changing environment cannot the problem of calibration automatically.

The above is the use as realizing the present invention and embodiment, therefore, this description can not be interpreted as limiting the scope of the invention.It should be appreciated by those skilled in the art, do not departing from any distortion under concept thereof of the present invention, improvement and replacement, the institute's scope protecting and limit that all belongs to the claims in the present invention.

Claims (6)

1. the automatic rating method of storm flood administrative model parameter, is characterized in that: the method comprises the following steps:

(1) region master data is obtained, with SWMM model for Confluence Model is produced in platform construction region;

(2) specify the parameter group of producing required calibration in Confluence Model and number, set the variation range of each parameter, build the nonlinear relationship between flow actual observed value and Models Sets parameter;

(3) linearization process is carried out to the relation of flow actual observed value and Models Sets parameter;

(4) build the objective function of parameter optimization, and define each actual flow observed reading weight calculation rule and solve for parameter matrix update rule;

(5) corresponding actual observed value weight matrix and Increment Matrix when calculating different iterations;

(6) solve minimum value during objective function converges, if objective function is not restrained, then forward step (5) to; If function convergence also obtains minimum value, then Output rusults, Output rusults comprises optimized parameter group, optimum analogue flow rate, each parametric sensitivity of constructed product Confluence Model parameter;

(7) measured discharge and optimum analogue flow rate degree of fitting are evaluated.

2. the automatic rating method of storm flood administrative model parameter according to claim 1, it is characterized in that: in step (2), the nonlinear relationship between described structure flow actual observed value and Models Sets parameter is defined as: c ₀=M (b ₀), wherein c ₀by being formed matrix, b by m actual observed value ₀for the matrix be made up of n parameter, the incidence relation between actual observed value and model parameter represents with nonlinear function M.

3. the automatic rating method of storm flood administrative model parameter according to claim 2, is characterized in that: in step (3), and the described relation to flow actual observed value and Models Sets parameter is carried out linearization process and is defined as:

c＝c ₀+J(b-b ₀)

In formula, c is model result matrix, and b is solve for parameter matrix, and J is the capable Jacobi local derviation matrix about M of n row m.

4. the automatic rating method of storm flood administrative model parameter according to claim 3, it is characterized in that: in step (4), the objective function φ of described structure parameter optimization is expressed as:

φ＝[c-c ₀-J(b-b ₀)] ^tQ[c-c ₀-J(b-b ₀]

In formula, t is matrix transpose symbol, and Q is the measured value weight matrix with the capable m row of m, adopts Levenberg-Marquardt algorithm it to be solved to the minimum value of this objective function;

Described definition each actual flow observed reading weight calculation rule, the diagonal matrix Q that the weight by actual observed value is tieed up with m represents, the weight w of i-th actual observed value _ifor diagonal element Q _ii, Q ^-1=C (c)/σ ², wherein C (c) represents that the m of actual observed value vector c ties up covariance matrix, and supposes in c separate between each element, and the variance of each element is defined as

Described solve for parameter matrix update rule, namely the renewal of solve for parameter matrix b is by Increment Matrix u _kcarrying out, for solving that magnitude between c and b exists that difference is comparatively large and element magnitude that is that cause J to comprise occurs huge difference and produces larger round-off error, by solve for parameter matrix update Rule Expression being:

b _k ⁺＝b _k ^-+u _k

S _k ^-1u _k＝[(J _kS _k) ^tQJ _kS _k+αS _k ^tS _k] ^-1(J _kS _k) ^tQr

In formula, k is iterations, b _k ⁺for the parameter matrix after renewal, b _k ^-for the parameter matrix before renewal, u _kfor Increment Matrix, r is c _k ^-residual error, α is Marquardt parameter, and S is the diagonal matrix of n × n, then i-th diagonal element in S is expressed as:

$S_{ii}={{\left(J_k^t{\mathrm{QJ}}_k\right)}_{ii}}^{-1/2}$

If will in greatest member be defined as the λ value of Marquart, then element value maximum in matrix is expressed as 1+ λ.

5. the automatic rating method of storm flood administrative model parameter according to claim 4, is characterized in that: in step (6), and described each parameter sensitivity calculates and is defined as:

$s_j=\frac{{\left(J^{t}QJ\right)}_u^{1/2}}{m}$

In formula, s _jrepresent the susceptibility of i-th parameter, i.e. the complexity of this parameter optimization, s _jlarger parameter is relative to whole optimizing process, and it is more easily optimized; s _jless, then represent the more difficult optimization of response parameter.

6. the automatic rating method of storm flood administrative model parameter according to claim 5, it is characterized in that: in step (7), measured discharge and the evaluation of optimum analogue flow rate degree of fitting are evaluated with relative coefficient R, deterministic coefficient NSE and Kling-Gupta COEFFICIENT K GE, and its computing formula is as follows:

$R=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}(w_i{c}_{oi}-P)(w_i{c}_i-p)}{\sqrt{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(w_i{c}_{oi}-P)}^2{(w_i{c}_i-p)}^2}}$

$NSE=1-\frac{\underset{i=1}{\overset{m}{\Σ}}{(c_i-c_{oi})}^2}{\underset{i=1}{\overset{m}{\Σ}}{(c_{oi}-\stackrel{\‾}{c_o})}^2}$

$KGE=1-\sqrt{{(R-1)}^2+{(\mathrm{\ξ}-1)}^2+{(\mathrm{\γ}-1)}^2}$

In formula, R is relative coefficient, c _oii-th measured discharge value, c _ifor with the analogue flow rate corresponding to i-th measured discharge value, P is mean value, p is mean value, for mean value, ξ is analogue flow rate standard deviation and measured discharge standard deviation ratio, and γ is the average of analogue flow rate and the ratio of measured discharge average.