CN105956360A - Fuzzy mathematics evaluation method for seawater intrusion - Google Patents

Abstract

The invention discloses a fuzzy mathematics evaluation method for seawater intrusion. The method comprises the steps that evaluation factors of a to-be-evaluated area are selected, and representative values of the evaluation factors are acquired; the single factor is evaluated; then comprehensive fuzzy mathematics evaluation is carried out to all the evaluation factors; and finally, a scientific, rational and practical seawater (saltwater) intrusion fuzzy mathematics evaluation module applicable to a research area is established. In this way, the error between a degree difference among same-grade sampled samples of the seawater intrusion evaluation and a degree difference among different grades of samples can be minimized; transition of water quality evolution in a seawater (saltwater) intrusion area is objectively reflected; the method can be effectively applied in actual engineering; a technical foundation is laid for prevention and control of the seawater intrusion; and research achievements can be used for evaluation of the seawater (saltwater) intrusion in a near-sea distribution area which has similar hydro-geologic conditions.

Description

A kind of seawater invasion Fuzzy Evaluation method

Technical field

Plunge into the commercial sea with the present invention relates to (salty) water intrusion assessment field, particularly relate to a kind of seawater invasion Fuzzy Evaluation side Method.

Background technology

Sea (salty) water invasion refers to that riviera is because of excess groundwater abstraction, Salt lake facies and the natural balance of fresh groundwater body Condition is destroyed, thus causes salt water to be harmful to hydrology geologic process to the one that underground reservoir elapses.Sea (salty) water invasion is A kind of gradual property geological disaster, is the result at the big factor overlaying influence of specific region Nature and Man class socio-economic activity two, It forms the excessive exploitation mainly due to oceanfront subsoil water, causes fresh groundwater hydraulic pressure less than having tight waterpower to join with it The saline groundwater pressure of system, promotes fresh-saline water interface iterative method upcountry.

Sea (salty) water invasion is the common problem of coastal area, and the current whole world has had tens countries and regions to find Sea (salty) water invasion problem, such as China, Holland, Germany, Italy, Belgium, France, Greece, Spain, Portugal, English State, Australia, the U.S., Mexico, Israel etc..Sea (salty) water is invaded and is brought serious harm to local development, gives and works as Ground economy causes huge loss, and universality causes the common concern of international community, the countries concerned actively develop research with Administer.

The research of international Shanghai (salty) water invasion experienced by statics, infiltration pressing and seepage flow-disperse kinetics etc. and grinds Studying carefully the stage, the field of academic research also from the most simple simulation to fresh-saline water interface model, develops into include seawater invasion Basic theories, numerical model, hydrogeochemistry and environmental isotopes, research and investigation method, preventing and treating and preventing measures, The many aspects such as ecology influence, global climate and Sea level changes impact.Wherein in sea (salty) water invasion research, use any index Most important with method judgement, evaluation seawater invasion and Invasive degree.Traditional single index often weighs the method with classification Producing deviation, precision is inadequate.But the most preferably solve this problem and the most not yet have unified understanding.

Summary of the invention

For drawbacks described above or deficiency, it is an object of the invention to provide a kind of seawater invasion Fuzzy Evaluation method, And effectively applied in Practical Project, technical foundation has been established in the enforcement for sea invasion preventing and controlling.

For reaching object above, the technical scheme is that

Comprise the following steps:

1), according to Seawater Intrusion Area quality of groundwater feature and the situation in evaluation district and area to be assessed monitoring condition, adopt Take discriminant by distance and choose the evaluation points in area to be assessed and the representative value of evaluation points；Described evaluation points include chlorine from Sub-concentration, salinity (TDS), sodium adsorption ratio (SAR), and salinization coefficient (A)；

2), according to area to be assessed controlling well sample analysis result, the evaluation collection of all evaluation points is set up；

3), set up each evaluation points membership function U to Seawater Intrusion grade, and according to evaluating collection, obtain and respectively comment The Subject Matrix R of the valency factor；

4), according to evaluation collection and the arithmetic average of three grades of quality representative values of evaluation points, to each evaluation points Weight calculates, and draws weight fuzzy matrix Q；

5), after the Subject Matrix R of comprehensive each evaluation points and weight fuzzy matrix Q, the compound operation of fuzzy matrix is carried out, Drawing synthetical matrix B, according to fuzzy mathematics maximum membership grade principle, the grade taking wherein the maximum is evaluation result.

Described step 3) in membership function U be three grades of membership functions, respectively U_1i、U_2i、U_3i, computing formula is:

$U_{1i}=\left\{\begin{array}{cc}0& (x_i\&GreaterEqual;a_2)\\ \frac{a_2-x_i}{a_2-a_1}& (a_1<x_i<a_2)\\ 1& (x_i\&le;a_1)\end{array}\right.---\left(1\right)$

$U_{2i}=\left\{\begin{array}{cc}0& (xi\&le;a_1,xi\&GreaterEqual;a_3)\\ \frac{x_i-a_1}{a_2-a_1}& (a_1<xi<a_2)\\ \frac{a_3-x_i}{a_3-a_2}& (a_2\&le;xi<a_3)\end{array}\right.---\left(2\right)$

$U_{3i}=\left\{\begin{array}{cc}0& (xi\&GreaterEqual;a_2)\\ \frac{x_i-a_2}{a_3-a_2}& (a_2<xi<a_3)\\ 1& (xi\&GreaterEqual;a_3)\end{array}\right.---\left(3\right)$

Wherein, i=1, the degree of membership of 2,3,4 evaluation points, Xi is the measured value of i evaluation points；a₁、a₂、a₃Evaluate for i Factor pair answers three grades of representative values of evaluation index, and gained R is the matrix of 4 × 3.

Described step 4) each evaluation points weight calculated particularly as follows:

$Wi=\frac{X_i}{\stackrel{\&OverBar;}{C_i}}---\left(4\right)$

$\stackrel{\&OverBar;}{W_i}=\frac{W_i}{\underset{i=1}{\overset{n}{\&Sigma;}}{W}_i}---\left(5\right)$

Wherein, i is evaluation points i=1,2,3,4；Wi is the weight coefficient of i evaluation points；Xi is the reality of i evaluation points Measured value；Arithmetic average for three grades of quality representative values of i evaluation points；For the weight system after i evaluation points normalization Number；By；The weight coefficient of 4 evaluation pointsThe weight fuzzy matrix Q of 1 × 4 can be formed.

Described step 5) in carry out the compound operation of fuzzy matrix, draw synthetical matrix B particularly as follows:

B=Q R=(bj) n=(b1, b2 ..., bn) (n=3) (6)

It is the matrix of 1 × 3 by formula (6) acquired results matrix B, and then draws fuzzy evaluation collection, this is evaluated and concentrates Greatest measure is judged as the rank of the seawater invasion of this evaluation point.

Compared with the prior art, the invention have the benefit that

The invention provides a kind of seawater invasion Fuzzy Evaluation method, by choosing the evaluation points in area to be evaluated And the representative value of acquisition evaluation points, first single-factor is evaluated, then all evaluation points is carried out comprehensive fuzzy number Learning and evaluate, final foundation is applicable to study area science, sea reasonable, practical (salty) water invasion Fuzzy Evaluation Model, makes sea The degree difference error minimize between degree difference and sample the most at the same level between sampling sample at the same level is evaluated in water invasion, makes sea The transitionality that in (salty) water invasion district, water quality develops has obtained objective embodiment, and is effectively applied in Practical Project, for sea Water invasion preventing and controlling established technical foundation, achievement in research can be used in the areal area, coastal waters that hydrogeologic condition is similar The evaluation of sea (salty) water invasion.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of the present invention；

Fig. 2 is (salty) water invasion cutting edge of a knife or a sword value line scattergram in sea in embodiments of the invention.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is described in detail.

Sea (salty) water invasion is a process having quantitative change to qualitative change, and the border that single-factor is evaluated is not ten clearly demarcated Aobvious.For macro-examination on a large scale, this is the most unimportant, but for little scope regional area, annual several meters of leading edge of invasion To the variation of over one hundred meter, this " error " then may make the judgement that people must make mistake.

As it is shown in figure 1, the invention provides a kind of sea (salty) water invasion Fuzzy Evaluation method, comprise the following steps:

1) situation, according to sea (salty) water invasion district's quality of groundwater feature and evaluating district and monitoring bar in area to be assessed Part, takes discriminant by distance to choose the evaluation points in area to be assessed and the representative value of evaluation points；Described evaluation points bag Include chlorine ion concentration, salinity (TDS), sodium adsorption ratio (SAR), and salinization coefficient (A)；

It is difficult to when conventionally employed single-factor is evaluated be attributed to certain classification.As independent with chloride ion and salinity Being evaluated, be evaluated as two different ranks sometimes, traditional single index is weighed and the method for classification seems clear standard Really, but have ignored cambic objective fact in invasion district, often lead to deviation, such as: the degree between " at the same level " sample Difference is vanished, and the degree difference between sample the most at the same level then may be exaggerated.Fuzzy comprehensive evoluation is to process this kind of extension limit The best method of boundary's " smudgy " problem.

In order to sea (salty) water Invasive degree is made the division in grade, comprehensive multi-index is used to pass judgment on method.The evaluation selected Index includes: chloride ion, salinity (TDS), sodium adsorption ratio (SAR), salinization coefficient (A).Wherein sodium adsorption ratio (SAR) is the U.S. Salt water is tested mechanism and is used for representing a parameter of agricultural irrigation suitability, is proved during seawater invasion by experimentation Being implicitly present in cation alternating action, sodium adsorption ratio (SAR) index can reflect during seawater invasion between water rock (native) Cation exchange interaction, salinization coefficient (A) is then defined as characteristic ion ratio in subsoil water.

2), according to area to be assessed controlling well sample analysis result, the evaluation collection of all evaluation points is set up；

Set up with reference to existing sea (salty) water invasion grade classification and evaluate collection, take discriminant by distance to choose its representative value, Specific targets opinion rating scope and representative value are as shown in Table 1 below.

The grade classification of table 1 sea (salty) water invasion specific targets and representative value (mg/L)

Note: (1) SAR is(2) A is(3) concentration of unit in c is bracket (mmol/L)

3), set up each evaluation points membership function U to sea (salty) water Invasive degree grade, and according to evaluating collection, obtain The Subject Matrix R of each evaluation points；

Set up the membership function of each water quality assessment factor pair sea (salty) water Invasive degree grade, obtain the person in servitude of each evaluation points Belong to matrix R.U is the membership function of matrix R, and the degree of membership of i (i=1,2,3,4) evaluation points is calculated by formula (1)～(3):

$U_{1i}=\left\{\begin{array}{cc}0& (x_i\&GreaterEqual;a_2)\\ \frac{a_2-x_i}{a_2-a_1}& (a_1<x_i<a_2)\\ 1& (x_i\&le;a_1)\end{array}\right.---\left(1\right)$

$U_{2i}=\left\{\begin{array}{cc}0& (x_i\&le;a_1,x_i\&GreaterEqual;a_3)\\ \frac{x_i-a_1}{a_2-a_1}& (a_1<x_i<a_2)\\ \frac{a_3-x_i}{a_3-a_2}& (a_2\&le;x_i<a_3)\end{array}\right.---\left(2\right)$

$U_{3i}=\left\{\begin{array}{cc}0& (x_i\&GreaterEqual;a_2)\\ \frac{x_i-a_2}{a_3-a_2}& (a_2<x_i<a_3)\\ 1& (x_i\&GreaterEqual;a_3)\end{array}\right.---\left(3\right)$

In formula, U_1i、U_2i、U₃I is the i evaluation points degree of membership to three grades of quality standards；Xi is the actual measurement of i evaluation points Value；a₁、a₂、a₃Three grades of representative values (table 1) for i evaluation points correspondence evaluation index；Calculate the matrix that gained R is 4 × 3.

4), according to evaluation collection and the arithmetic average of three grades of quality representative values of evaluation points, to each evaluation points Weight calculates, and draws weight fuzzy matrix Q；

W index weights is to represent the tolerance that each index is risen in decision water quality.Owing to each evaluation points is at index value On there is difference, and it also has difference to water quality effect, it is therefore desirable to the power of index each to each evaluation point Heavily calculating, the weight calculation of i (i=1,2,3,4) evaluation points is shown in formula (4), (5):

$W_i=\frac{X_i}{\stackrel{\&OverBar;}{C_i}}---\left(4\right)$

$\stackrel{\&OverBar;}{W_i}=\frac{W_i}{\underset{j=1}{\overset{n}{\&Sigma;}}{W}_i}---\left(5\right)$

In formula, Wi is the weight coefficient of i evaluation points；Xi is the measured value of i evaluation points；For i evaluation points three The arithmetic average of level quality representative value；For the weight coefficient after i evaluation points normalization.Referred to by 4 of each evaluation point Target weight coefficientThe weight fuzzy matrix Q of 1 × 4 can be formed.

5), after the Subject Matrix R of comprehensive each evaluation points and weight fuzzy matrix Q, the compound operation of fuzzy matrix is carried out, Drawing synthetical matrix B, according to fuzzy mathematics maximum membership grade principle, the grade taking wherein the maximum is evaluation result.

After drawing matrix R and matrix Q, the compound operation that it is carried out fuzzy matrix, obtain belonging to evaluation point at different levels Synthetical matrix B.According to fuzzy mathematics maximum membership grade principle, take the evaluation result that grade is evaluation point of wherein the maximum.Square Formula (6) is shown in the calculating of battle array B:

B=Q R=(bj) n=(b1, b2 ..., bn) (n=3) (6)

It is the matrix of 1 × 3 by formula (6) acquired results matrix B, and then draws fuzzy evaluation collection, this is evaluated and concentrates Greatest measure is judged as the rank of sea (salty) the water invasion of this evaluation point.

Below, illustrate according to specific embodiment:

In the range of choosing fosse groundwater reservoir reservoir area, travel resort two, mountain and sea at sunshine sky, it is positioned at the tourism of mountain and sea sky, Rizhao City Caobai River downstream, holiday resort estuary greater coasting area.Travel resort two, mountain and sea at sunshine sky fosse groundwater reservoir offshore seashore line length Degree is more than 5km, due to reasons such as irrational recovery of subterranean water resource and typhoons and promote sea (salty) water to invade.Two The reservoir area seawater invasion of fosse subsoil water is with Quaternary deposit type (rushing proluvial layer of sand invasion type) and Hydrodynamic field change type is (artificially Lower water draws water diffused) it is main, the demonstrative project that this project is built as preventing and treating seawater invasion, by on-the-spot on-site inspection and knot Close sample analysis, draw the spatial distribution position on two (salty) water invasion sharp sides, sea, fosse groundwater reservoir reservoir area, according to hydrology ground Matter investigation and water sample analysis result reflect that earth's surface sea (salty) water and ground (salty) water of plunging into the commercial sea invades spatial and Intrusion Signatures.

As in figure 2 it is shown, (salty) water invasion of visual sea mainly under the influence of tide driving force sea water along Liang Cheng River, river course, Lu Gou river trace back, and form earth's surface sea water at ridge village to village one, East River south band of settling down and recharge invasion.

Under typhoon influence, sea water covers downstream rubber dam and enters in two fosse main stem water catchment areas, due to shallow underground Water and two fosse surface river water hydrodynamic conditions contact closely, form the sea water along two fosse the most wedge shaped shape distributions and enter Invade.According to on-the-spot drinking water sources investigation and sample analysis result, define and determine that sea (salty) water enters with chloride ion 250mg/L Invade cutting edge of a knife or a sword value boundary line, it can be seen that invasion cutting edge of a knife or a sword value line along river course, Lu Gou river-distribution of village of settling down-village one, East River south line, entering encroachment line is wedge Sigmoid curves extends.

The first, hydrogeological mapping

Large scale hydrogeological mapping and investigation are launched in study area, finds out study area geological structure unit, regional water Literary composition geology, Characteristics of Environmental Geology, investigation draws surface water, subsoil water seawater invasion region property invasion boundary in study area.

The second, subsoil water sample analysis

On the basis of combining hydrogeological mapping and investigation, in conjunction with surface water, the invasion of subsoil water seawater invasion region property Boundary, carries out qualitative subregion to subsoil water, takes representative water sample in subregion, carries out indoor ion chemistry analysis.

3rd, sea (salty) water invasion Fuzzy Evaluation

1, choose Cl-, salinity, sodium adsorption ratio (SAR), salinization coefficient (A) four indices as evaluation points set up comment Valency collection.Discriminant by distance is taked to choose its representative value, concrete evaluation water sample point ion component, metrics evaluation rate range and representative Value refers to table 2.

According to table 1, this group water sample evaluation points doing evaluation collection and calculates, its calculating process is prone to represent it in a tabular form Calculating process and purpose, see below table 3.

Table 2 water analysis achievement abridged table

The foundation of collection evaluated by table 3

2, set up the membership function of each water quality assessment factor pair sea (one-tenth) water Invasive degree grade, obtain each evaluation points Subject Matrix R.U is the membership function of matrix R, and the degree of membership of i (i=1,2,3,4) evaluation points is calculated by formula (1)～(3):

In formula, U_1i、U_2i、U_3iFor the i evaluation points degree of membership to three grades of quality standards；Xi is the actual measurement of i evaluation points Value；a₁、a₂、a₃Three grades of representative values (table 3-2) for i evaluation points correspondence evaluation index；Calculate the square that gained R is 4 × 3 Battle array.Mathematical expression form is with shown in table 4.

Table 4 Subject Matrix R

3, there is difference in each evaluation points on index value, and it also has difference to water quality effect, It is thus desirable to the weight of index each to each evaluation point calculates, the weight calculation of evaluation points is shown in formula (4), (5).By each The weight coefficient of 4 indexs of evaluation pointThe weight fuzzy matrix Q of 1 × 4 can be formed.Mathematical expression form is with shown in table 5.

Table 5 weight fuzzy matrix Q

4, after drawing matrix R and matrix Q, the compound operation that it is carried out fuzzy matrix, obtain matrix B.

It is the matrix of 1 × 3 by formula (6) result of calculation gained matrix B, this matrix is set up and evaluates collection, wherein maximum Rank corresponding to numerical value is judged as the rank of sea (salty) the water invasion of this evaluation point.Mathematical expression form is with shown in table 6.

Table 6 matrix B

From (salty) water invasion Fuzzy Evaluation result in subsoil water sea at table 3-5, D24 water sample point it is: seawater invasion Grade is II level (slightly invasion).

Claims (4)

1. a seawater invasion Fuzzy Evaluation method, it is characterised in that comprise the following steps:

1), according to Seawater Intrusion Area quality of groundwater feature and evaluate district situation and to be assessed area monitoring condition, take away from Evaluation points and the representative value of evaluation points in area to be assessed is chosen from diagnostic method；Described evaluation points includes that chloride ion is dense Degree, salinity (TDS), sodium adsorption ratio (SAR), and salinization coefficient (A)；

2), according to area to be assessed controlling well sample analysis result, the evaluation collection of all evaluation points is set up；

3), set up each evaluation points membership function U to Seawater Intrusion grade, and according to evaluating collection, obtain each evaluation because of The Subject Matrix R of son；

4), according to evaluation collection and the arithmetic average of three grades of quality representative values of evaluation points, to each evaluation points weight Calculate, draw weight fuzzy matrix Q；

5), after the Subject Matrix R of comprehensive each evaluation points and weight fuzzy matrix Q, carry out the compound operation of fuzzy matrix, draw Synthetical matrix B, according to fuzzy mathematics maximum membership grade principle, the grade taking wherein the maximum is evaluation result.

Seawater invasion Fuzzy Evaluation method the most according to claim 1, it is characterised in that described step 3) in be subordinate to Function U is three grades of membership functions, respectively U_1i、U_2i、U_3i, computing formula is:

$U_{1i}=\left\{\begin{array}{cc}0& (x_i\&GreaterEqual;a_2)\\ \frac{a_2-x_i}{a_2-a_1}& (a_1<x_i<a_2)\\ 1& (x_i\&le;a_1)\end{array}\right.---\left(1\right)$

$U_{2i}=\left\{\begin{array}{cc}0& (xi\&le;a_1,xi\&GreaterEqual;a_3)\\ \frac{x_i-a_1}{a_2-a_1}& (a_1<xi<a_2)\\ \frac{a_3-x_i}{a_3-a_2}& (a_2\&le;xi<a_3)\end{array}\right.---\left(2\right)$

$U_{3i}=\left\{\begin{array}{cc}0& (xi\&le;a_2)\\ \frac{x_i-a_2}{a_3-a_2}& (a_2<xi<a_3)\\ 1& (xi\&GreaterEqual;a_3)\end{array}\right.---\left(3\right)$

Wherein, i=1, the degree of membership of 2,3,4 evaluation points, Xi is the measured value of i evaluation points；a₁、a₂、a₃For i evaluation points Three grades of representative values of corresponding evaluation index, gained R is the matrix of 4 × 3.

Seawater invasion Fuzzy Evaluation method the most according to claim 1, it is characterised in that described step 4) to each Evaluation points weight carry out calculating particularly as follows:

$Wi=\frac{X_i}{\stackrel{\&OverBar;}{C_i}}---\left(4\right)$

$\stackrel{\&OverBar;}{W_i}=\frac{W_i}{\underset{i=1}{\overset{n}{\&Sigma;}}{W}_i}---\left(5\right)$

Wherein, i is evaluation points i=1,2,3,4；Wi is the weight coefficient of i evaluation points；Xi is the measured value of i evaluation points；Arithmetic average for three grades of quality representative values of i evaluation points；For the weight coefficient after i evaluation points normalization；By； The weight coefficient of 4 evaluation pointsThe weight fuzzy matrix Q of 1 × 4 can be formed.

Seawater invasion Fuzzy Evaluation method the most according to claim 1, it is characterised in that described step 5) in carry out The compound operation of fuzzy matrix, draw synthetical matrix B particularly as follows:

B=Q R=(bj) n=(b1, b2 ..., bn) (n=3) (6)

It is the matrix of 1 × 3 by formula (6) acquired results matrix B, and then draws fuzzy evaluation collection, this is evaluated and concentrates maximum Numerical value is judged as the rank of the seawater invasion of this evaluation point.