CN115409318B - A nature-based water purification solution optimization method integrating fuzzy AHP and MDS - Google Patents

Abstract

The invention discloses a nature-based water purification scheme optimization method that integrates fuzzy AHP and MDS, and relates to the technical fields of water, wastewater, and sewage treatment. It includes the following steps: according to the characteristics of the nature-based water purification scheme, constructing a system including environment, The criterion layer including economy, ecology and management, technology and multiple evaluation indicators of the determined indicator layer are used to obtain the actual data of the evaluation indicators; according to the analytic hierarchy process, a structure including the target, the criterion layer, the indicator layer and water The hierarchical framework of the purification scheme uses fuzzy matter-element theory to normalize the qualitative and quantitative indicators in the criterion layer; a judgment matrix is constructed according to the analytic hierarchy process, and the judgment matrix is used to hierarchize the criterion layer and the indicator layer. Sort, and then conduct consistency testing to output the synthetic weight of each indicator; use multi-dimensional scaling method to sort nature-based water purification solutions and select the optimal solution.

Description

A nature-based water purification solution optimization method integrating fuzzy AHP and MDS

Technical field

The invention relates to the technical fields of water, wastewater and sewage treatment, and specifically relates to a natural-based water purification scheme optimization method that integrates fuzzy AHP (Analytic Hierarchy Process) and MDS (Multidimensional Scaling).

Background technique

Currently, the main methods used for optimizing water purification solutions include the following: linear programming, dynamic programming, non-linear programming, gray relational analysis and analytic hierarchy process. However, these methods have shortcomings in program optimization.

Problems with existing optimization methods: Linear programming methods, dynamic programming methods and non-linear programming methods only consider cost minimization and ignore other aspects, and the solution with the lowest cost may not be the optimal water purification solution because of environmental and ecological issues. Factors are also very important. The optimal water purification plan should be a plan that achieves comprehensive optimization of many factors such as cost, pollutant emissions, and ecological environment; gray correlation analysis ignores the weight of judgment criteria and indicators, and these two factors are the key to the plan. An important basis for optimization; the conventional analytic hierarchy process cannot integrate qualitative indicators when optimizing solutions, and cannot classify solutions with similar advantages and disadvantages, and is not flexible enough.

Problems when the evaluation indicators of existing water purification schemes are used for nature-based water purification schemes: The evaluation indicators of existing water purification schemes cannot be used for nature-based water purification schemes. Nature-based water purification schemes are regulated by the International Union for Conservation of Nature. One of the nature-based solutions proposed by the International Union of Conservation Nature (International Union of Conservation Nature) aims to use the water purification functions of some natural ecosystems to address global water pollution challenges. The evaluation indicators of conventional water purification schemes (such as activated sludge process and A2/O process) usually only include cost (such as investment and operating costs) and pollutant purification efficiency, while nature-based water purification schemes in addition to considering the conventional water purification scheme The evaluation indicators must also consider many aspects such as hydrogeology, floor area, and availability of occupied space.

Contents of the invention

In view of the shortcomings in the existing technology, the present invention provides a nature-based water purification scheme optimization method that integrates fuzzy AHP and MDS. It constructs a judgment matrix based on AHP and combined with FME by constructing a hierarchical framework of nature-based water purification schemes. , sort the plans through MDS, select the best nature-based water purification plan, and further optimize the plan based on relevance.

In order to achieve the above object, the present invention can adopt the following technical solutions:

A natural-based water purification solution optimization method integrating fuzzy AHP and MDS, including:

According to the characteristics of nature-based water purification solutions, construct a criterion layer including environment, economy, ecology and management, and technology, and collect real evaluation index data of nature-based water purification solutions;

Based on the AHP analytic hierarchy process, a hierarchical framework including the target, criterion layer, indicator layer and water purification plan is constructed, and the FME fuzzy matter element theory is used to normalize the qualitative and quantitative indicators in the criterion layer;

Construct a judgment matrix, pass the hierarchical sorting of the indicator layer, and the overall sorting of the levels, conduct consistency testing, and output the composite weight of each indicator;

Through MDS multi-dimensional scaling, the correlation degree is used to rank nature-based water purification solutions, identify similar solutions in the merit evaluation, and select the optimal solution.

As a further technical solution of the present invention, a hierarchical framework including a target, a criterion layer, an indicator layer and a water purification plan is constructed according to the AHP analytic hierarchy process, and the FME fuzzy matter element theory is used to normalize the qualitative and quantitative indicators in the criterion layer. Specific steps include:

First, under the environmental, economic, ecological and management, and technical criterion layers, the characteristic indicators of each criterion are selected to construct a hierarchical framework including goals, criterion layer, indicator layer, and water purification plan; at the same time, FME is used to construct fuzzy matter elements as follows:

R=(N,C,V);

In the formula, R is the fuzzy matter element, N is the name of the object, C is the characteristic of the object, V is the characteristic value of the object, and V includes fuzzy and qualitative description.

For m fuzzy matter elements in n dimensions, the composite fuzzy matter elements are constructed as follows:

In the formula, R _mn is the composite fuzzy matter element, _Ni represents the i-th object (i=1, 2,..., m), and C _k represents the k-th feature (k=1, 2,..., n), V _ik represents the k-th eigenvalue of the i-th object.

Then the indicators are normalized. For the cost indicators, the normalization formula is:

For environmental indicators, the normalized formula is:

In the formula, U _ik is the normalized indicator value, V _ik is the actual value of the indicator, minV _ik is the minimum value of the indicator, and maxV _ik is the maximum value of the indicator.

For qualitative indicators, assign a value to the indicator in the range of [0, 1] based on the qualitative description.

The normalized composite fuzzy matter element is:

As a further technical solution of the present invention, the specific steps of constructing a judgment matrix according to the AHP analytic hierarchy process, through the hierarchical sorting of the indicator layer, and the total hierarchical sorting, and performing a consistency check and outputting the synthetic weight of each indicator include:

First, a judgment matrix is constructed based on the AHP analytic hierarchy process. Any indicator is compared with other indicators under the same criterion (a _ij ), and the criteria are equally important, less important, moderately important, moderately important+, highly important, highly important+, and very important. , very important +, extremely important, assign an importance value within the natural number range of [1, 9], compare the indicators, assign the value a _ji = 1/a _ij during reverse comparison, and construct an n×n-dimensional matrix for:

Matrix A is multiplied by the weight of the vector W = (W1, W2,..., Wn) to obtain AW = nW, that is:

Calculate its maximum eigenvalue λ _max according to the judgment matrix, and then calculate the consistency index CI and the average random consistency index RI. The consistency index calculation formula is:

The formula for calculating the one-time ratio CR of the total ranking of levels is:

When CR≤0.1, the judgment matrix is acceptable. When CR exceeds the limit, the judgment matrix must be corrected.

After completing the consistency check, the weight vector of each criterion relative to the target is obtained:

In the formula, is the weight of the kth criterion Ck relative to the target.

Likewise, the weight vector of each indicator relative to the criterion is:

In the formula, l _s , l _s+1 ,..., l _t (s≤t≤n) represent the index under the kth criterion C _k , s and t are the first sum under the kth criterion C _k The serial number of the last indicator.

Then, the composite weight W of each indicator relative to the target is obtained:

As a further technical solution of the present invention, the specific steps of using MDS multi-dimensional scaling to rank nature-based water purification solutions using correlation, identifying similar solutions in merit evaluation, and selecting the optimal solution include:

First, the correlation degree K _j of the indicators in each scheme is calculated using the synthetic weight of each indicator and the normalized indicator value. The calculation formula is:

K _j =W _i ×U _ji ;

In the formula, _Wi represents the composite weight of the i-th indicator.

Then use the correlation to calculate the Euclidean distance as:

Construct a matrix using Euclidean distance values, perform MDS analysis, and take the first two principal components as eigenvectors:

x(1)=(E ₁₁ , E ₁₂ ,..., E _1k ,..., E _1N )′;

x(2)=(E ₂₁ , E ₂₂ ,..., E _2N ,..., E _2N )′;

In the formula, x(1) and x(2) represent the two eigenvectors of the Euclidean distance value matrix, E _1k represents the 1st eigenvector value of the k-th scheme in the Euclidean distance value matrix, and E _2k represents the Euclidean distance value matrix. The second eigenvector value of the kth solution in .

The dissimilarity between correlation degrees i and j is represented by δ _ij , and the ascending order is as follows:

Using δ _ij as the independent variable and d _ij as the dependent variable, use the Shepard diagram to test the coordination degree of MDS. If the points in the diagram are distributed on or near the 1:1 line, it means that the coordination degree of MDS is better. Otherwise, the coordination degree of MDS is not good. OK, need to check the correlation. Calculate the fitting value of d _ij based on the relationship between d _ij and δ _ij Combine d _ij and/> Calculate pressure value/> The formula is as follows:

In the formula, Indicates the minimum value of pressure value,/> When it indicates that the principal components of MDS are optimal.

Calculate the square root E _k for the eigenvector value of each scenario:

Sorting E _k from large to small is the order of merit of nature-based water purification solutions. The solution with the largest E _k value is the optimal solution. At the same time, MDS analysis can identify which solutions are similar in the evaluation of merits.

Compared with the prior art, the beneficial effects of the present invention are:

1. The present invention builds a hierarchical framework of nature-based water purification solutions by collecting real evaluation index data of nature-based water purification solutions, and builds a judgment matrix based on AHP and combined with FME, through the hierarchical sorting of the indicator layer and the total hierarchical sorting. , and conduct a consistency test to modify the judgment matrix, sort the solutions through MDS, identify similar solutions in the evaluation of pros and cons, select the optimal nature-based water purification solution, and provide flexible choices for decision-makers when there are similar optimal solutions. The final solution provides convenience.

2. In this method, by comparing the correlation of indicators in different plans, the weak links of different plans can be identified and suggestions can be provided for the optimization of different nature-based water purification plans.

3. The present invention mainly designs a complete set of natural-based water purification solution optimization methods with wide applicability and objective and accurate evaluation results. Technically, it can cover the evaluation of various judgment criteria and indicators of nature-based water purification solutions, select the optimal nature-based water purification solution, identify solutions with similar advantages and disadvantages, and provide convenience for decision-makers to flexibly select the final solution. In addition, recommendations are provided for further optimization of different nature-based water purification solutions.

Description of the drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application. Those of ordinary skill in the art can also obtain other drawings based on these drawings without exerting creative efforts.

Figure 1 is a schematic diagram of the steps of a preferred method for a nature-based water purification solution according to an embodiment of the present invention;

Figure 2 is a hierarchical framework diagram of a nature-based water purification solution optimization method according to an embodiment of the present invention;

Figure 3 is a framework diagram of a method for integrating fuzzy AHP and MDS according to an embodiment of the present invention;

Figure 4 is a schematic diagram of a judgment matrix constructed based on the integrated fuzzy AHP and MDS methods according to an embodiment of the present invention;

Figure 5 is a consistency check flow chart according to the embodiment of the present invention;

Figure 6 is a Shepard diagram of the verification MDS according to the embodiment of the present invention;

Figure 7 is a diagram showing the preferred results of the MDS method according to the embodiment of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present application, not all of them. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of this application.

Example:

It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It is to be understood that the data so used are interchangeable under appropriate circumstances so that the embodiments of the invention described herein are capable of being practiced in sequences other than those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof in the embodiments of the present invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or equipment that includes a series of steps or units is not necessarily limited to Those steps or elements that are expressly listed may instead include other steps or elements that are not expressly listed or that are inherent to the process, method, product or apparatus.

It should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "back", "left", "Right", "Vertical", "Horizontal", "Top", "Bottom", "Inside", "Outside", "Clockwise", "Counterclockwise", "Axis", "Radial", " The orientation or positional relationship indicated such as "circumferential direction" is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation. Constructed and operated in specific orientations and therefore not to be construed as limitations of the invention.

In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise expressly and specifically limited. In addition, unless otherwise clearly stated and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection. A connection can also be an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or an internal connection between two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood on a case-by-case basis.

In the present invention, unless otherwise expressly stated and limited, a first feature being "on" or "below" a second feature may mean that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. touch. Furthermore, the terms "above", "above" and "above" the first feature is above the second feature may mean that the first feature is directly above or diagonally above the second feature, or simply means that the first feature is higher in level than the second feature. "Below", "below" and "beneath" the first feature to the second feature may mean that the first feature is directly below or diagonally below the second feature, or simply means that the first feature has a smaller horizontal height than the second feature.

Referring to Figures 1 and 2, in the implementation case of the present invention, a natural-based water purification solution optimization method integrating fuzzy AHP and MDS includes:

S1: Based on the characteristics of nature-based water purification solutions, construct a criterion layer including environment, economy, ecology and management, and technology, and collect real evaluation index data of nature-based water purification solutions. Specific steps include:

According to the characteristics of nature-based water purification systems, economics, environment, ecology and management, and technology are selected as criteria.

Economic criteria for water purification solutions typically include investment, operating and treatment costs. Nature-based water purification systems use soil or plants to maintain microbial activity and remove pollutants in sewage. There are no treatment costs such as chemicals or activated sludge cultivation. Therefore, the cost of land is included in addition to investment and operation. Another economic factor.

In addition to considering the water quality indicators BOD ₅ , COD, suspended solids (SS), total nitrogen, total phosphorus and fecal coliform of the general water purification system, the environmental guidelines also consider hydrogeological factors, such as stabilization ponds and constructed wetlands, which are required to be located in Outside flood plains and where slopes are low, all nature-based water purification systems must consider the effects of floods and landslides.

Ecological and management guidelines consider maintenance and floor space availability. In addition to purifying sewage, nature-based water purification systems can provide green open space for local communities and provide habitat for wildlife. Therefore, floor space can be utilized. It is an important ecological indicator.

Technical criteria are used to evaluate the operation and additional requirements of the scheme. The operation of some nature-based water purification systems is affected by seasonal factors, such as slow percolation and overland flow land treatment systems. Therefore, seasonal effects are used as a technical indicator.

In addition, different nature-based water purification solutions have some additional requirements. Stabilization ponds and constructed wetlands require that the soil at the site be impermeable or that the site is treated to minimize infiltration. Overland flow treatment systems rely on perennial herbaceous plants, while others Nature-based water purification options include a wider variety of plants to choose from.

As shown in Table 1, Table 1 lists the indicators under each evaluation criterion.

Table 1 Indicators and their functions under each evaluation criterion of nature-based water purification solutions

In this implementation case, the index values of each nature-based water purification scheme used are real data. The actual data of the operation of each scheme are obtained from the literature. Therefore, the accuracy and authenticity of the results can be ensured.

S2: Based on the AHP analytic hierarchy process, construct a hierarchical framework including the target, criterion layer, indicator layer and water purification plan, and use FME fuzzy matter element theory to normalize the qualitative and quantitative indicators in the criterion layer. The specific steps include:

Construct a hierarchical framework including goals, criteria layer, indicator layer and water purification plan, with the goal of maximizing benefits. It is not only the realization of optimal economic benefits, but also the optimization of multiple aspects such as cost, environmental acceptability and eco-friendliness. The criterion layer and target layer have been detailed in S1. The water purification scheme includes a rapid percolation treatment system, a slow percolation treatment system, and a slow percolation treatment system. Filter land treatment system, surface overflow land treatment system, constructed wetland and stabilizing pond treatment system. Since the indicators constructed in this implementation case include qualitative and quantitative indicators, the quantitative indicators include percentages and synthetic indicators. Different types of indicators have a greater impact on the weight of constructing the analytic hierarchy process. In order to avoid adverse effects, the indicator values are summarized. Unified processing.

For cost indicators, the normalized formula is:

For environmental indicators, the normalized formula is:

In the formula, U _ik is the normalized indicator value, V _ik is the actual value of the indicator, minV _ik is the minimum value of the indicator, and maxV _ik is the maximum value of the indicator.

For qualitative indicators, assign a value to the indicator in the range of [0, 1] based on the qualitative description.

As shown in Figure 3, the diagram shows the framework diagram of the method for integrating fuzzy AHP and MDS, which is divided into the following steps for detailed explanation: establishing the analytic hierarchy process, pairwise comparison of indicators, weighting of criteria and indicators, consistency test, and calculation of correlation. , calculate the Euclidean distance matrix, establish the relationship between Euclidean distance and dissimilarity, calculate pressure values, MDS analysis and select the optimal nature-based water purification solution.

S3: Construct a judgment matrix based on the AHP analytic hierarchy process, pass the hierarchical sorting of the indicator layer, and the total level sorting, conduct consistency testing, and output the composite weight of each indicator;

As shown in Figure 4, the diagram is a schematic diagram of the steps to construct a judgment matrix. The steps include comparing any indicator with other indicators under the same criterion, and classifying them into equally important, less important, moderately important, moderately important+, highly important, highly important Important+, very important, very important+, extremely important. The importance value a _ij is assigned in the natural number range of [1, 9]. For indicators that have been compared, the assigned value a _ji =1/a _ij during reverse comparison. After all assignments, the final judgment matrix is constructed.

In this implementation case, environmental guidelines are taken as an example. The guidelines include BOD ₅ removal rate, COD removal rate, suspended matter removal rate, total nitrogen removal rate, total phosphorus removal rate, fecal coliform removal rate and hydrogeological risk indicators. . Compare the BOD ₅ removal rate with itself and COD removal rate, suspended solids removal rate, total nitrogen removal rate, total phosphorus removal rate, fecal coliform removal rate and hydrogeological risk and assign values:

In the formula, w ₁ , w ₂ , w ₃ , w ₄ , w ₅ and w ₆ are assigned natural numbers in [1, 9] according to their importance, Indicates the importance of BOD ₅ removal rate to itself and other indicators (i=1, 2,..., 6). On the contrary, when comparing any other indicator with BOD ₅ removal rate, its importance/> That is, a _i1 =1/a _1i . By analogy, we finally get a matrix in which the elements are assigned to the pairwise comparison of each indicator under the environmental criterion. We also construct a matrix in which the elements are assigned to the pairwise comparison of indicators under other criteria. The matrices constructed by each criterion are combined to form a matrix A:

In this implementation case, the hierarchical ordering of the indicator layer is as follows: for a certain criterion, the importance of each indicator under the criterion is expressed by weight. represents the eigenvector of the pairwise comparison matrix of indicators under the above criterion. Similarly, the importance of each criterion is represented by the weight W _C , which is the eigenvector of the pairwise comparison matrix of each criterion. The combined weight of each indicator relative to the target is:

In the formula, l _s , l _s+1 ,..., l _t (s≤t≤n) represent the index under the kth criterion C _k , s and t are the first sum under the kth criterion C _k The serial number of the last indicator.

A is multiplied by the weight W of each criterion = (W ₁ , W ₂ ,..., W _N )′, and the judgment matrix AW is obtained as:

The specific steps to implement the consistency test in this implementation case are shown in Figure 5. The specific steps include: calculating the maximum eigenvalue λ _max of the judgment matrix, calculating the consistency index CI, and calculating the average by combining CI and the selected average random consistency index RI One-time ratio CR.

If CR≤0.1, the consistency test is passed. If CR>0.1, the consistency test is not passed, and the criteria and indicators need to be re-weighted.

The consistency index calculation formula is:

According to the size of the matrix dimension c, find the average random consistency index RI according to Table 2.

Table 2 Average random consistency index RI

The formula for calculating the one-time ratio CR of the total ranking of levels is:

S4: Through MDS multi-dimensional scaling, use correlation to rank nature-based water purification solutions, identify similar solutions in merit evaluation, and select the optimal solution.

According to the composite weight of each indicator relative to the target and the normalized indicator value, the correlation degree K _j of each indicator is calculated:

K _j =W _i ×U _ji ;

In the formula, _Wi represents the composite weight of the i-th indicator, and U _ji is the normalized indicator value.

Calculating the Euclidean distance d _ij using correlation is:

Construct a matrix using Euclidean distance values, perform MDS analysis, and take the first two principal components as eigenvectors:

x(1)=(E ₁₁ , E ₁₂ ,..., E _1k ,..., E _1N )′;

x(2)=(E ₂₁ , E ₂₂ ,..., E _2N ,..., E _2N )′;

In the formula, x(1) and x(2) represent the two eigenvectors of the Euclidean distance value matrix, E _1k represents the 1st eigenvector value of the k-th scheme in the Euclidean distance value matrix, and E _2k represents the Euclidean distance value matrix. The second eigenvector value of the kth solution in .

The dissimilarity between correlation degrees i and j is represented by δ _ij , and the ascending order is as follows:

Using δ _ij as the independent variable and d _ij as the dependent variable, use the Shepard diagram to test the coordination degree of MDS (as shown in Figure 6). If the points in the diagram are distributed on the 1:1 line or close to each other, it means that the coordination degree of MDS is better. Otherwise, the coordination degree of MDS is better. The fit of MDS is not good and the correlation needs to be checked. Calculate the fitting value of d _ij based on the relationship between d _ij and δ _ij Combine d _ij and/> Calculate pressure value/> The formula is as follows:

In the formula, Indicates the minimum value of pressure value,/> When it indicates that the principal components of MDS are optimal.

Calculate the square root E _k for the eigenvector value of each scenario:

Sorting E _k from large to small is the order of merit of nature-based water purification solutions. The solution with the largest E _k value is the optimal solution. At the same time, MDS analysis can identify which solutions are similar in the evaluation of advantages and disadvantages (Figure 7 ).

The MDS method optimization result diagram shows that P4 and P5 are similar, P1, P2 and P3 are similar, and P4 and P5 are better than P1, P2 and P3.

Investment, operating costs, land area costs, BOD ₅ removal rate, COD removal rate, suspended solids removal rate, total nitrogen removal rate, total phosphorus removal rate, fecal coliform removal rate, hydrogeological risk maintenance, and land space availability Utilization, seasonal effects and additional requirements, the indicator correlations of each scheme are: P1-rapid percolation treatment system (0.3, 0.9, 0.81, 0.96, 1.00, 1.00, 1.00, 0.38, 0.33, 0.3, 0.9, 0.5 , 0.9, 0.9), P2-slow percolation land treatment system (0.26, 0.7, 0.13, 1.00, 0.99, 0.72, 0.78, 1.00, 0.93, 0.5, 0.7, 0.9, 0.5, 0.7), P3-surface overflow land Treatment system (0.16, 0.7, 0.19, 0.96, 0.89, 0.89, 0.96, 0.73, 1.00, 0.5, 0.9, 0.7, 0.5, 0.5), P4-constructed wetland (0.88, 0.9, 0.88, 0.81, 0.9, 0.84, 1.00 , 0.53, 0.72, 0.9, 0.7, 0.5, 0.9, 0.5) and P5-stabilized pond treatment system (1.00, 0.9, 1.00, 0.94, 0.85, 0.74, 0.99, 0.65, 0.52, 0.7, 0.9, 0.5, 0.7, 0.7 ). Comparing the correlation of indicators of each plan, P1 has low correlation in terms of investment, total phosphorus removal rate, fecal coliform removal rate and hydrogeological risk maintenance and needs to be optimized; P2 has low correlation in investment and land occupation cost. , needs to be optimized; P3 has low correlation in investment and land occupation costs and needs to be optimized.

It should be noted that the focus of the present invention is not to obtain data, but to combine the AHP and MDS methods, calculate the correlation based on the index synthesis weight calculated by AHP and the normalized index value, and then use MDS to rank the solutions based on the correlation.

For the present invention, the key is not a series of processing of data, but the use of the method of the present invention to enable the original data to be used for program optimization.

The beneficial effects of the present invention include:

1. When optimizing nature-based water purification solutions, this method not only considers cost, but also considers environmental and ecological factors.

2. This method can not only optimize plans, but also identify plans with similar advantages and disadvantages. When several winning plans appear, it provides convenience for decision-makers to flexibly select the optimal plan.

3. By comparing the correlation of indicators in the plans, the weak links of different plans can be identified and suggestions can be provided for the optimization of different nature-based water purification plans.

In the description of this specification, reference to the terms "one embodiment," "some embodiments," "an example," "specific examples," or "some examples" or the like means that specific features are described in connection with the embodiment or example. , structures, materials or features are included in at least one embodiment or example of the invention. In this specification, the schematic expressions of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, those skilled in the art may combine and combine different embodiments or examples and features of different embodiments or examples described in this specification unless they are inconsistent with each other.

The above embodiments are only for illustrating the technical concepts and characteristics of the present invention. Their purpose is to enable those of ordinary skill in the art to understand the content of the present invention and implement it accordingly. They cannot limit the scope of protection of the present invention. All equivalent changes or modifications made based on the essence of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A natural-based water purification scheme optimization method integrating a fuzzy analytic hierarchy process with a multidimensional scaling process, comprising the steps of:

constructing a criterion layer comprising environment, economy, ecology and management and technology and determining a plurality of evaluation indexes of an index layer according to the characteristics of a water purification scheme based on nature, and acquiring actual data of the evaluation indexes;

constructing a hierarchical framework comprising a target, the criterion layer, the index layer and a water purification scheme according to a hierarchical analysis method, and normalizing qualitative and quantitative indexes in the criterion layer by adopting a fuzzy matter element theory;

normalizing the index, and normalizing the cost index according to the following formula:

for the environmental index, the normalization formula is:

in U _ik Is normalized index value V _ik Is the actual value of the index, minV _ik Is the minimum value of the index, maxV _ik Is the maximum value of the index;

assigning a value to the qualitative index within the range of [0,1] according to the qualitative description;

the normalized complex ambiguity bin is:

C ₁ … C _n

constructing a judgment matrix according to a analytic hierarchy process, carrying out hierarchical sequencing on the criterion layer and the index layer by utilizing the judgment matrix, and then carrying out consistency test so as to output the synthetic weight of each index;

the specific steps of weighting the criterion layer and the index layer are as follows:

constructing a judgment matrix according to an analytic hierarchy process, comparing any index under the same criterion with other indexes, and determining the judgment matrix according to the equal importance, the less importance, the moderate importance+, the high importance, the high importance+, the very importance, the very importance+, the very importance and the very importance in [1,9 ]]To assign importance value a within natural number range of (2) _ij Comparing indexes, and assigning value a in reverse comparison _ji ＝1/a _ij The n×n-dimensional matrix is constructed as:

matrix a multiplied by the weight of the vector w= (W ₁ ，W ₂ ，...，W _n ) Aw=nw is obtained, i.e.:

calculating the maximum eigenvalue lambda according to the judgment matrix _max Then, calculating a consistency index CI and an average random consistency index RI;

the consistency index calculation formula is as follows:

the one-time ratio CR calculation formula of the hierarchical total sequence is as follows:

when CR is less than or equal to 0.1, the judgment matrix is acceptable, and when CR exceeds the limit value, the judgment matrix is corrected;

after the consistency test is completed, the weight vector of each criterion relative to the target is obtained as follows:

in the method, in the process of the invention,is the kth criterion C _k Weights relative to the target;

also, the weight vector for each index relative to the criteria is:

wherein, I _s ，l _s+1 ，...，l _t (s.ltoreq.t.ltoreq.n) represents the kth criterion C _k The following index, s and t are the kth criterion C _k Sequence numbers of the first and last indexes;

then, the synthetic weight W of each index with respect to the target is obtained as:

sequencing water purification schemes based on nature through a multidimensional scaling method, and selecting an optimal scheme;

first, calculate the correlation K of the index in each scheme by the combination weight and normalized index value of each index _j The calculation formula is as follows:

K _j ＝W _i ×U _ji ；

in which W is _i A composite weight representing the i-th index;

the Euclidean distance is then calculated with correlation as:

constructing a matrix by using Euclidean distance values, performing MDS analysis, and taking the first two principal components as feature vectors:

x(1)＝(E ₁₁ ,，E ₁₂ ，...，E _1k ，...，E _1N )′；

x(2)＝(E ₂₁ ,，E ₂₂ ，...，E _2N ，...，E _2N )′；

wherein x (1) and x (2) represent two eigenvectors, E, of a Euclidean distance value matrix _1k The 1 st eigenvector value representing the kth scheme in the Euclidean distance value matrix, E _2k A2 nd feature vector value representing a kth scheme in the Euclidean distance value matrix;

the dissimilarity between correlations i and j is represented by delta _ij The incremental ordering is represented as follows:

delta _ij Is an independent variableAnd d _ij As a dependent variable, checking the coordination degree of MDS by using a sheplate graph, if points in the graph are distributed on or close to a 1:1 line, indicating that the coordination degree of MDS is better, otherwise, the coordination degree of MDS is not good, and checking the correlation degree; based on d _ij And delta _ij Relation of d _ij Fitting values of (a)Binding d _ij And->Calculating the pressure value +.>The formula is as follows:

in the method, in the process of the invention,representing the minimum value of the pressure value, +.>When it is indicated that the principal component of MDS is optimal;

computing square root E for eigenvector values for each scheme _k ：

Pair E _k Sorting from big to small, namely, the water purifying scheme based on nature is good and bad order, E _k Scheme with maximum valueFor optimal solutions, MDS analysis can identify which solutions are similar in quality assessment.

2. The method of claim 1, wherein the natural-based water purification scheme is: a water purification regimen utilizing soil or plants to maintain the activity of microorganisms and which are sufficient to remove contaminants from sewage.

3. The method according to claim 1, wherein the specific steps of constructing a hierarchical framework according to a hierarchical analysis method and normalizing qualitative and quantitative indicators in the criterion layer by fuzzy primitive theory are as follows:

under the environmental, economic, ecological and management and technical criterion layers, selecting characteristic indexes of each criterion, and constructing a hierarchical framework comprising a target, a criterion layer, an index layer and a water purifying scheme;

meanwhile, the fuzzy matter element is constructed by adopting FME as follows:

R＝(N,C,V)；

wherein R is a fuzzy matter element, N is a matter name, C is a characteristic of the matter, V is a characteristic value of the matter, and V comprises a fuzzy and qualitative description;

for n-dimensional m fuzzy primitives, a composite fuzzy primitive is constructed as follows:

C ₁ … C _n

wherein R is _mn Is a complex fuzzy element, N _i Represents the ith item (i=1, 2,., m), C _k The characteristics of the kth object (k=1, 2, n.), V _ik The kth eigenvalue of the ith object is represented.