Disclosure of Invention
The invention provides a comprehensive evaluation method for a peak regulation scheme of a natural gas pipeline network-gas storage system. The method comprehensively considers the conditions of peak gas consumption of users, peak regulation capacity of pipelines, peak regulation capacity of gas storage reservoirs and the like, takes the average gas transmission capacity of the pipelines, safe operation of the gas storage reservoirs and other indexes into consideration on the premise of meeting the gas consumption requirements of the users as much as possible, formulates a peak regulation plan meeting the safe operation constraint conditions of pipe networks and the gas storage reservoirs, and effectively improves the optimality and scientificity of formulating and arranging peak regulation schemes.
The technical scheme adopted by the invention is as follows: a comprehensive evaluation method for peak regulation schemes of gas transmission pipe networks and gas storage reservoirs is characterized by comprising the following steps:
step1, urban gas load prediction: establishing an urban gas load prediction model by adopting an artificial neural network model, and predicting the peak-regulated urban gas load by using a differential evolution extreme learning machine algorithm so as to determine the peak regulation amount;
step2, optimizing the peak regulation of the gas storage: according to the peak-regulating operation experience of the conventional gas storage, summarizing the mathematical rules of the gas storage pressure and the gas production rate of the operation parameters of the gas storage, fitting a relational expression of the operation parameters of the gas storage and the peak regulating amount, and combining the peak regulating amount obtained in the step1 to obtain the gas production rate of the gas storage under a certain peak regulating amount;
step3, simulating the peak regulation amount of the pipe network: obtaining the gas production rate of the gas storage according to the calculation result in the step2, fixing the gas production rate of the gas storage, calculating gas use gaps at different gas production times to serve as peak regulation amounts of the pipe network peak regulation, and simulating the peak regulation operation condition of the pipe network under different peak regulation amounts to obtain a preselected peak regulation scheme;
step4, comprehensively evaluating the peak regulation scheme: and (4) comprehensively evaluating the different peak regulation schemes obtained according to the step (3) so as to obtain the optimal peak regulation scheme.
Preferably, the step1 comprises: establishing a training mechanism of an artificial neural network and establishing an annual peak regulation prediction model of the gas storage by adopting a regression method;
the step of establishing the training mechanism of the artificial neural network comprises the following steps:
step1, population initialization: randomly generating a population, wherein each individual in the population is composed of an input layer hidden layer node and a hidden layer deviation,
θ=[ω11,ω12,…,ω21,ω22,…ω2k,…ωn1,ωn2,…ωnk,…,b1,b2,…bk]ω ij, bj is [ -1,1]]The random number of (1);
step2, selecting an objective function: calculating an output weight matrix of the ELM network by using an ELM algorithm for each individual in the population; selecting part of verification samples from the test samples, and setting the root mean square error of the test error of the ELM as a target function of a differential evolution algorithm;
step3, variation: initializing a given population ith individual { theta ] for a populationi,GI | ═ 1,2 … NP }, a new individual based on the differential evolution algorithm is generated as follows: v. ofi,G=xr1,G+F×(xr2,G-xr3,G) Wherein the randomly selected subscript r1≠r2≠r3∈ {1,2, … NP }, mutation factor F ∈ [0,2 ]]In order to control the differential variable (x)r2,G-xr3,G) Amplification of (1);
step4, crossover: let mu leti,G+1=(μ1i,G+1,μ2i,G+1,…μDi,G+1) Wherein
In the formula (1), b (j) belongs to [0,1], and the cross probability CR belongs to [0,1 ];
step5, selecting:
comparing the vectors mui,G+1And the target vector in the current population, the vector with a larger target function value in the optimization process is dominant in the next generation population;
the step of establishing the annual peak regulation prediction model of the gas storage by adopting a regression method comprises the following steps:
the annual peak regulation amount is an amount for compensating seasonal supply and demand difference of natural gas users, and the calculation formula is as follows:
Qt=∑Qti(3)
in formula (3): qtThe unit m3 is the total monthly peak shaving gas storage capacity; qtiThe amount of gas storage required for monthly peak shaving of various users;
the peak regulation amount required by each user depends on the uneven coefficient of the monthly gas consumption of the user, and the calculation formula is
In formula (4): qipThe average gas consumption per month of a certain user, unit m 3; a isijThe average monthly gas consumption coefficient is the uneven coefficient of the monthly gas consumption of a certain user, namely the ratio of each monthly gas consumption to the average monthly gas consumption of the whole year; n is the number of peak months of gas consumption.
Preferably, in the step2, a least square method is adopted to fit a relational expression of the operation parameters of the gas storage, such as gas storage pressure, gas production rate and peak regulation amount, so as to obtain the gas production rate under a certain peak regulation amount.
Preferably, SPS or TGNET simulation software is adopted in the step3 to simulate the peak regulation working condition of the pipe network, so as to obtain a preselected peak regulation scheme; when SPS or TGNET simulation software is adopted to simulate the peak-load regulation working condition of the pipe network, corresponding pipeline and equipment models are established according to the pipeline to be simulated, and the operation parameters of the pipeline are input to complete the simulation of the peak-load regulation capacity of the pipe network.
Preferably, SPS simulation software is adopted to simulate the peak regulation working condition of the pipe network, and when the established large-scale complex pipe network model relates to a plurality of access points, a gas balance area model is adopted.
Preferably, TGNET simulation software is adopted to simulate the peak-shaving working condition of the pipe network, model elements are adopted to represent elements in the actual pipe network, and the connection relation and the operation parameters of all the elements in the pipe network system are consistent with the parameters of the elements in the actual pipe network system.
Preferably, the step4 comprises:
selecting a peak regulation evaluation index: selecting 8 process indexes, namely pipeline tail section pressure fluctuation rate, gas supply point pressure stabilization time, pipeline tail section gas storage amount, gas storage highest pressure, gas storage lowest pressure, supply and demand unbalance number of users, actual gas supply amount and supercharging consumed power; selecting 2 economic indexes: total operating cost and pipe input; selecting 10 indexes as peak regulation evaluation indexes;
and calculating index weight: firstly, subjective weight is calculated by using an analytic hierarchy process, secondly objective weight is calculated by using an entropy weight method, and finally, combination weight is obtained by using subjective and objective weight to calculate index weight;
screening an optimal peak regulation scheme: and performing objective evaluation on the peak regulation preselection scheme by adopting three objective comprehensive evaluation methods, namely a gray correlation method, a rank and ratio method and an ideal solution method, and screening out the optimal peak regulation scheme with the maximum compatibility by adopting a maximum compatibility method on the basis of the three evaluation results.
The invention has the following advantages:
1. the method has the advantages that algorithm improvement is carried out in the urban gas load prediction part, so that the calculation result of the urban peak load regulation amount is more accurate, and a powerful data basis is provided for peak regulation of gas storage reservoirs and pipelines;
2. in the peak regulation part of the gas storage, the prior peak regulation experience is fully considered, a mathematical experience summary formula of a corresponding peak regulation mode (gas quantity) and main operation parameters of the gas storage is established, certain guiding significance is provided for gas production peak regulation of the on-site gas storage, the corresponding peak regulation is favorably formulated, forced production and forced injection are avoided, and the formulation of an optimized management process for operation of the gas storage is provided to ensure safe and stable operation of the gas storage;
3. in the selection of the peak regulation indexes, the peak regulation process and the stable and reliable multi-angle gas supply are fully considered, and the index weight is calculated by adopting an objective weighting method, so that the subjectivity of the indexes is kept, objective bases are not lacked, the obtained index weight has high scientific reliability, the selected objective evaluation method is suitable for the peak regulation system, the method is rigorous and innovative, the evaluation result is real and reliable due to the advantages, and practical scientific bases can be provided for the selection of the on-site peak regulation scheme.
Detailed Description
The present invention is further described with reference to the following drawings and specific examples so that those skilled in the art can better understand the present invention and can practice the present invention, but the examples are not intended to limit the present invention.
In order to further accelerate the peak regulation construction of the gas storage, solve the problem of large consumption peak-valley difference of natural gas in winter and summer and promote the technical development of seasonal peak regulation of the gas storage, the invention aims to provide a corresponding peak regulation scheme aiming at a mode of 'peak regulation of a gas storage-pipeline system', synthesize a mathematical modeling, a pipe network simulation and a comprehensive evaluation method and determine an optimal/feasible operation (peak regulation) scheme of the gas storage-pipeline system. The peak regulation scheme of the invention is technically implemented by being divided into the following four stages:
1. urban gas load prediction-determining the required consumption of downstream cities in winter, and further determining the total peak load regulation;
2. on the basis of the research on the actual peak regulation operation rule of the underground gas storage, the gas production rate, the operation pressure and other parameters under different peak regulation intensities are summarized by mathematical rules, and a relational expression between the gas production rate and the peak regulation amount (intensity) is fitted. Combining the peak load (intensity) and mathematical rule obtained in the stage 1 to obtain the gas production rate;
3. simulation of peak regulation amount of a pipe network, namely determining the peak regulation rate of a gas storage according to the calculation result obtained in the stage 2, fixing the gas production rate, calculating gas utilization gaps (the part of which the total gas utilization is higher than the designed gas output of a pipeline) at different gas production times to serve as the peak regulation amount of the pipe network peak regulation, and performing simulation of peak regulation operation conditions of the pipe network at different peak regulation amounts by adopting SPS commercial software to obtain a preselected peak regulation scheme;
4. comprehensively evaluating a peak regulation scheme, namely selecting a peak regulation index by combining the stability and the reliability of gas supply from the process angle of ensuring the gas demand of downstream users; and the index weight is given by adopting a subjective and objective weighting method, so that the subjectivity of the index is kept and objective basis is not lost, and the weight assignment has scientificity and objectivity; and finally, carrying out comprehensive evaluation by adopting three objective comprehensive evaluation methods, namely a gray correlation method, a rank and ratio method and an ideal method, wherein different evaluation results may cause different evaluation results, and finally obtaining a peak regulation scheme with the optimal compatibility by adopting a maximum compatibility method comprehensive evaluation method.
As shown in figure 1, the invention relates to a specific implementation flow of a comprehensive evaluation method for peak regulation schemes of gas transmission pipe networks and gas storage reservoirs.
Step1, urban gas load prediction: before predicting the peak regulation amount of the underground gas storage-pipeline, predicting the downstream peak-regulated urban gas load so as to determine the peak regulation amount.
When the urban gas load prediction model is established, an artificial neural network model can be adopted, and the difference evolution extreme learning machine algorithm is used for prediction by combining the difference evolution algorithm on the basis of the working principle of the extreme learning machine. When a mathematical model of load prediction is established, factors such as the average temperature per month in the current year, the average GDP in the current year and the like are used as influence factors.
Neural network training mechanism
The method for predicting the gas load by using the neural network technology is a new research method. The neural network technology has self-adaptive function to a plurality of complex, non-structural and irregular factors, and can memorize information and only has the characteristics of reasoning, autonomous learning, optimized calculation and the like, so that the intelligent processing problem of human brain can be simulated. Particularly, the method has the self-adaptive function and the self-learning function, so that the influence of factors such as temperature and weather change on the gas load can be well solved, and therefore, the prediction of the gas load by the artificial neural network method is determined by scholars at home and abroad. At present, the most studied method is to use an error back propagation algorithm to perform short-term prediction on the gas load, wherein a three-layer artificial neural network model is relatively simple and commonly used.
The problems of low training speed, generalization and the like are the bottleneck for restricting the application of the feedforward neural network, and an Extreme Learning Machine (ELM) is provided for solving the problems. The extreme learning machine randomly assigns values to the input weight and the hidden node offset of the single hidden layer neural network, and the output weight of the network can be solved only by one-step calculation, so that the training speed can be greatly improved. However, in some practical applications, the ELM may need more hidden layer nodes to achieve the ideal effect, which seriously affects the generalization of the ELM network, and deteriorates the reaction capability of the ELM in an unknown sample. The method adopts a differential evolution extreme learning machine algorithm, namely, a learning algorithm combining the optimization of the differential evolution algorithm and the extreme learning machine network is utilized, namely, the input layer weight and the hidden layer deviation of the extreme learning machine are optimized and selected by utilizing the differential evolution algorithm, so that an optimal network is obtained. The training steps are as follows:
step1 population initialization: randomly generating a population, wherein each individual in the population is composed of an input layer hidden layer node and a hidden layer deviation,
θ=[ω11,ω12,…,ω21,ω22,…ω2k,…ωn1,ωn2,…ωnk,…,b1,b2,…bk],
wherein ω ij, bj is a random number in [ -1,1 ];
step2, selecting an objective function: calculating an output weight matrix of the ELM network by using an ELM algorithm for each individual in the population; selecting part of verification samples from the test samples, and setting a Root Mean Square Error (RMSE) of the ELM as a target function of a differential evolution algorithm;
step 3: mutation: initializing a given population ith individual { theta ] for a populationi,GI | ═ 1,2 … NP }, a new individual based on the differential evolution algorithm is generated as follows: v. ofi,G=xr1,G+F×(xr2,G-xr3,G) Wherein the randomly selected subscript r1≠r2≠r3∈ {1,2, … NP }, mutation factor F ∈ [0,2 ]]In order to control the differential variable (x)r2,G-xr3,G) Amplification of (1);
step 4: and (3) crossing: let mu leti,G+1=(μ1i,G+1,μ2i,G+1,…μDi,G+1) Wherein
In the formula (1), b (j) belongs to [0,1], and the cross probability CR belongs to [0,1 ];
step 5: selecting:
comparing the vectors mui,G+1And in the current populationThe target vector of (2) is the vector with the larger objective function value in the optimization process, which is dominant in the next generation population.
Therefore, the differential evolution algorithm is used for network learning of the extreme learning machine, the global optimization capability of the differential evolution algorithm is utilized, the connection weight and the threshold of the extreme learning machine are reasonably coded and used as the fitness index of the differential evolution algorithm for training, and the optimal network is obtained.
② prediction model
After the training mechanism of the artificial neural network is established, an annual peak regulation prediction model of the gas storage is established by adopting a regression method:
the annual peak regulation amount is an amount for compensating seasonal supply and demand difference of natural gas users, and the calculation formula is as follows:
Qt=∑Qti(3)
in formula (3): qtThe unit m3 is the total monthly peak shaving gas storage capacity; qtiThe amount of gas storage required for monthly peak shaving of various users;
the peak regulation amount required by each user depends on the uneven coefficient of the monthly gas consumption of the user, and the calculation formula is
In formula (4): qipThe average gas consumption per month of a certain user, unit m 3; a isijThe average monthly gas consumption coefficient is the uneven coefficient of the monthly gas consumption of a certain user, namely the ratio of each monthly gas consumption to the average monthly gas consumption of the whole year; n is the peak number of the gas consumption (i.e. a)ijMonthly parts > 1).
Step2, optimizing the peak regulation of the gas storage: the method can be used for summarizing the mathematical rules of the main gas storage operation parameters such as gas storage pressure, gas production rate and the like according to the peak regulation operation experience of the conventional gas storage, for example, a relational expression of the main parameters and the peak regulation amount is fitted by adopting methods such as least square method and the like, and the gas production rate under a certain peak regulation amount is obtained by means of the conventional experience summary.
Step3, simulating the peak regulation amount of the pipe network: the tail section of the gas transmission pipe network has certain gas storage capacity and can bear part of the peak regulation task. In order to fully utilize the gas storage capacity of the tail section of the pipe network and avoid large pipeline pressure fluctuation caused by peak regulation, it is necessary to simulate the peak regulation capacity of the gas transmission pipe network under a certain working condition. And (3) obtaining the gas production rate of the gas storage according to the gas storage peak regulation calculation result in the step (2), fixing the gas production rate, calculating gas utilization gaps (the part of which the total gas consumption is higher than the designed gas output of the pipeline) at different gas production times to serve as the peak regulation amount of the pipe network peak regulation, and performing pipe network peak regulation working condition simulation by adopting SPS (SPS) or TGNET (triglycidyl isocyanurate) simulation software to obtain a preselected peak regulation scheme.
One embodiment of the present invention uses SPS software for pipe network simulation. As shown in fig. 2, the present invention uses SPS software to perform a simulation of a pipe network.
Compared with other gas transmission pipe network simulation software, the SPS has the following advantages:
1. the simulation speed is high, and particularly, the precision of a simulation calculation result is high in dynamic simulation;
2. during the operation process, certain parameters can be changed, whether the simulation model operates or not does not influence the change of the parameters, and the trend of the change of the system parameters after a certain parameter is changed can be immediately reflected;
3. the transient working conditions such as automatic opening of a certain valve or automatic stopping of certain equipment can be simulated.
The SPS software can simulate a single fluid medium and a plurality of single-phase mixed fluid media; different types of plumbing equipment, such as pipelines, rotating equipment, shut-off and check valves, sensors, flow meters, PID control and control valves, etc., can be used and corresponding connections can be made between the field device and the analog device to achieve field compliance.
When the SPS software is used for simulating the peak regulation capacity of the gas transmission pipeline, the simulation of the peak regulation capacity of the gas transmission pipeline can be completed only by establishing corresponding pipeline and equipment models according to the pipeline to be simulated and inputting the operation parameters of the pipeline.
When the established large-scale complex pipe network model relates to a plurality of access points, a gas balance area model can be adopted. The gas balance area Model is also called a pipe network inlet and outlet Model (Entry/Exit Model), and the rule is the basis for providing capacity and service for customers by operators, and defines the contents of the service of the operators, the matching mode of customer requirements, system constraints and the like. The pipe network inlet and outlet model is shown in fig. 3, the gas balance area is connected with the adjacent domestic/foreign balance area, and the connecting point is used for conveying natural gas and is divided into a flow-in point and a flow-out point. The natural gas facilities in the gas balance area comprise gas field production, high-pressure natural gas pipelines, gas distribution pipe networks, gas storage pools, demand areas (residents, power plants, industrial users and the like), and the like, wherein different facilities belong to different participants, such as long-distance pipeline network operators, gas distribution pipe network operators, manufacturers, gas storage pool operators, residents, power plant companies and industrial customers. And signing service contracts among all participants, and ensuring that the flow in and out of the natural gas infrastructure is balanced by using the natural gas infrastructure.
The invention can also use TGNET software to simulate the pipe network. The tgnet (transient Gas network) software is a transient simulation software for natural Gas gathering and transportation pipe networks, and can be used for simulating steady-state and transient operation data of pipelines, such as point flow, temperature, pressure and the like. The software can be used for establishing a pipe network model, carrying out simulation verification on dynamic and static operation data of the pipe network, and predicting the operation condition of the pipeline when the structure, the operation condition and the like of the pipe network change, thereby providing a powerful basis for field production operation. The software is the key of an ESI company pipe network SCADA online system, and meanwhile, the software can be used as offline simulation software of the SCADA system.
The TGNET software adopts model elements to represent elements in the actual pipe network, and the connection relation and the operation parameters of each element in the pipe network system are consistent with the parameters of the elements in the actual pipe network system. When the parameters of each element in the pipe network model are reasonable and correct, the actual pipe network can be correctly expressed, and the simulation result is the actual pipe network operation parameter.
Establishing a gas storage-pipeline model in TGNET:
an injection and production gas well system is complex, but when only the gas production working condition in the peak regulation period is considered, the gas production well is simplified into a gas source;
the valve is arranged at the front end of the pipeline for outputting the natural gas after the natural gas is treated, the valve is mainly used for adjusting the pressure of the gas entering the pipeline, and the pressure behind the valve is mainly used as the pressure of the gas entering the pipeline in the scheme, so that a pressure adjusting valve is not arranged;
the software has pipeline elements, model simplification is not needed, and only basic parameters of the pipeline are input;
the pigging station does not increase the gas quantity in the gas transmission pipe network and does not consume the gas quantity in the gas transmission pipe network, so the pigging station is regarded as a structure like a three-way pipe, and the pigging station can be regarded as a whole and simplified into a large node;
and the gas station is simplified into a node, and the gas quantity is not influenced in the whole system.
When the TGNET software is used for simulating the peak regulation capacity of the gas transmission pipeline, the simulation of the peak regulation capacity of the gas transmission pipeline can be completed only by establishing corresponding pipeline and equipment models according to the pipeline to be simulated and inputting the operation parameters of the pipeline to obtain the average gas transmission capacity of the pipeline.
Step4, comprehensively evaluating the peak regulation scheme: and 3, obtaining different peak regulation preselection schemes on the basis of the simulation of the peak regulation amount of the pipe network in the step3, and finally, comprehensively evaluating the peak regulation schemes by adopting a comprehensive evaluation method so as to obtain the optimal peak regulation scheme.
Firstly, in the aspect of peak regulation evaluation indexes, the invention comprehensively considers the manufacturability of peak regulation, the reliability of gas supply and the stability of gas supply, and selects eight process indexes: pipeline end pressure fluctuation rate, air feed point pressure stationary time, pipeline end gas storage volume, gas storage maximum pressure, gas storage minimum pressure, supply and demand unbalance household number, actual air supply volume, pressure boost consumed power, two economic indicator: the total operation cost and the pipe transmission income are ten evaluation indexes.
Secondly, average weighting is adopted to avoid weighting too randomly or blindly, and index weighting is calculated by adopting an objective weighting method based on an analytic hierarchy process and an entropy weighting method, so that the weighting process has subjective reliability and objective scientificity.
Finally, because the number of peak regulation systems which can be referred to at present is very small, in order to ensure that the evaluation process is not limited by subjective knowledge, three objective comprehensive evaluation methods of a grey correlation method, a rank and ratio method and an ideal solution method are adopted to objectively evaluate a peak regulation preselection scheme, and aiming at the problem that different evaluation results are possibly caused by using different methods, the maximum compatibility method is adopted on the basis of the three evaluation results, and the optimal peak regulation scheme with the maximum compatibility is screened out.
Weight calculation principle:
the invention adopts an objective weighting method based on an analytic hierarchy process and an entropy weight method to calculate index weight, firstly adopts the analytic hierarchy process to calculate subjective weight, secondly adopts the entropy weight method to calculate objective weight, and finally adopts the objective weighting to obtain combination weight.
1) Analytic hierarchy process
Analytic Hierarchy Process (AHP) is a multi-criteria decision-making method combining qualitative and quantitative analysis proposed by the famous operational research scientist t.l. satty et al in the 70's 20 th century. The method is characterized in that after the essence, influence factors, internal relations and the like of the complex decision problem are deeply analyzed, a hierarchical structure model is constructed, and then the thinking process of decision is mathematized by using less quantitative information, so that a simple and convenient decision method is provided for solving the complex decision problem with multiple targets, multiple criteria or no structural characteristics. Specifically, it is a decision-making method which decomposes the relevant elements of the decision-making problem into the levels of target, criterion, scheme, etc., and objectively quantizes the subjective judgment of the person by a certain scale, and performs qualitative analysis and quantitative analysis on the basis of the levels. It makes human thinking process hierarchical and quantitative, and uses mathematics to provide quantitative basis for analysis, decision, forecast or control. It is especially suitable for the situation that the qualitative judgment of human plays an important role and the direct and accurate measurement of the decision result is difficult.
When the problem is analyzed by applying the analytic hierarchy process, the problem is firstly layered. According to the nature of the problem and the general target to be achieved, the problem is decomposed into different composition factors, and the factors are gathered and combined according to different levels according to the mutual correlation influence and membership among the factors to form a multi-level analysis structure.
Structure hierarchy analysis structure
Through various researches and demonstrations, the peak regulation system of the gas transmission pipe network and the gas storage can be divided into three levels as shown in fig. 4.
Wherein, the peak regulation scheme of the gas transmission pipe network and the gas storage is evaluated as a target layer, which represents the purpose of solving the problem, namely the target to be achieved by applying AHP; the process type index and the economic type index are criterion layers, namely intermediate links for realizing the preset target; ten evaluation indexes are scheme layers and represent specific schemes for solving the problems.
② constructing judgment matrix
After the hierarchical analysis model is established, pairwise comparison can be carried out in each layer of elements, and a comparison judgment matrix is constructed. The analytic hierarchy process is mainly to judge the relative importance of each factor in each layer, and the judgment is expressed by numerical values by introducing proper scales and written into a judgment matrix. The decision matrix represents a comparison of relative importance between the factor at the previous level and the factor to which the level is related. The basic information of the matrix type analytic hierarchy process is judged, and is also an important basis for calculating the relative importance.
Assume element B of the previous levelkAs a criterion for the next layer element C1,C2,…,CnWith dominant relationships, our intent is to be on criterion BkGiving C their relative importance1,C2,…,CnThe corresponding weight. In this step "importance" is assigned a certain value.
For n elements, we get pairwise comparison decision matrix C ═ C (C)ij)n×n. Wherein C isijRepresenting factor i and factor j relative to the target importance value.
Generally, the constructed decision matrix takes the form:
generally speaking, the judgment matrix is judged pairwise by experts or famous researchers in the field, the subjectivity of the analytic hierarchy process is mainly reflected in the link, and the judgment matrix formed by the scores of the experts not only has higher credibility, but also can objectively reflect the real importance of the index to a certain extent.
In the case of an analytic hierarchy process, in order to quantify the decision making judgment, the above numerical judgment matrix is formed, and the judgment is often quantified according to a certain ratio scale. A typical 1-9 scale method is given below, as shown in Table 1.
TABLE 1 judge matrix Scale and its meanings
Serial number |
Importance rating |
Cij assignment |
1 |
i, j two elements are equally important |
1 |
2 |
The i element being slightly more important than the j element |
3 |
3 |
The i element is significantly more important than the j element |
5 |
4 |
The i element is more strongly important than the j element |
7 |
5 |
The i element is extremely important than the j element |
9 |
6 |
The i element is less important than the j element |
1/3 |
7 |
The i element is significantly less important than the j element |
1/5 |
8 |
i is more strongly insignificant than j |
1/7 |
9 |
i elements are extremely less important than j elements |
1/9 |
Checking consistency of judgment matrix
After the judgment matrix is established, consistency of judgment thinking should be adhered to and maintained. The consistency of judgment thinking means that when the expert judges the importance of the index, the judgment is coordinated and consistent among the judgments, so that the inconsistent results do not occur, inconsistency occurs under the condition of multiple stages, the inconsistency is easy to occur, and the inconsistency degrees are different under different conditions. Due to the complexity of objective things and the diversity of people's recognitions, and the one-sidedness that can result. It is obviously unlikely that every judgment is required to have complete consistency, but it is really true that a judgment with a large topic of consistency should be. Therefore, in order to ensure that the conclusion obtained by the analytic hierarchy process is reasonable, the consistency check of the constructed judgment matrix is also needed, and the check is usually performed in combination with the sequencing step.
According to the matrix theory, when the judgment matrix B has complete consistency, the maximum characteristic root is equal to the order of the judgment matrix, namely lambdamaxM, the remaining feature roots are all equal to 0. When the matrix B is judged not to have complete consistency, lambdamaxNot equal to m, at this point, maximum feature root λ is introducedmaxThe ratio of the difference between the order m of the judgment matrix B and the order m-1 is used as an index for measuring the deviation consistency of the judgment matrix. Ready to use
The consistency of the judgment matrix B is checked. When lambda ismaxWhen m, CI is 0, indicating complete agreement; the more the CI value deviates from 0, the worse the consistency of the decision matrix.
Generally, as the order of the decision matrix increases, the difficulty of keeping the decision matrix perfectly consistent increases. In order to measure whether the judgment matrixes of different orders have satisfactory consistency, a ratio CR between CI and an average random consistency index RI of the same order is introduced, and CR is called a random consistency ratio. The RI values of the 1-10 th order decision matrix are shown in Table 2.
RI value of 21-10 th order judgment matrix in table
Order of the scale |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
RI |
0 |
0 |
0.58 |
0.9 |
1.12 |
1.24 |
1.32 |
1.41 |
1.45 |
1.49 |
When CR is less than 0.1, the judgment matrix is considered to have satisfactory consistency; if CR is greater than 0.1, the decision matrix is adjusted to have satisfactory consistency.
Fourthly, single ordering of layers
After the judgment matrix passes the consistency check, that is, completely conforms to the consistency or has satisfactory consistency, what needs to be done next is to calculate the relative weight between the next lower layer elements related to each element except the scheme layer, and during specific calculation, the maximum characteristic root of the judgment matrix and the corresponding characteristic vector thereof are calculated. Common methods for calculating the maximum feature root and the feature vector include a square root method, a sum-product method, a least square method and the like.
Overall sequence of layers
And repeating the steps, calculating the characteristic roots and the characteristic vectors of the judgment matrixes layer by layer from top to bottom along the hierarchical structure in sequence, and performing total hierarchical sequencing calculation on the basis of the characteristic roots and the characteristic vectors to obtain the relative weight of the lowest-layer factors relative to the highest layer.
Assuming the target layer is layer A; the criterion layer is a B layer with m elements B1,B2,…,BmTheir relative importance ranking values with respect to layer A are b1,b2,…,bm(ii) a The third layer is a C layer which is provided with n elements C1,C2,…,CnThey relate to an element B in the B layeriAre respectively the relative importance ranking values of(if a certain element C in the C layerjAnd an element B in the layer BiIrrespective of whether or not0), the comprehensive relative importance ranking value of the elements in the C layer to the target layer is:
similar to the consistency check of the hierarchical single ordering, a consistency check of the hierarchical total ordering should also be dealt with. It is easy to find that the hierarchical single-ordering consistency check of the second layer (B layer) is a hierarchical total-ordering consistency check. For the third layer (layer C), the random consistency ratio CR is:
wherein, CIiIs BiThe consistency index of a judgment matrix formed by comparing relevant elements of the C layer with the criterion; RI (Ri)iIs BiThe average randomness consistency index of a judgment matrix formed by comparing related elements of the C layer is a criterion.
Similar to consistency check of hierarchical single ordering, when CR is less than 0.1, the judgment matrix is considered to have satisfactory consistency; if CR is greater than 0.1, the decision matrix is adjusted to have satisfactory consistency.
2) Entropy weight method
The method of determining weights using the concept of entropy is called entropy weight method. The starting point is that the importance degree of certain index observation values is reflected according to the difference degree of the same index observation values, and if the data difference of certain index of each evaluated object is not large, the effect of the index on an evaluation system is not reflected.
The entropy weight method is an objective weighting method, and is a method for determining the weight of an index by using the size of information provided by the entropy value of the index. The entropy weight method has the following functions: the indexes are weighted by an entropy weight method, so that the interference of the considered factors of the weights of all evaluation indexes can be avoided, and the evaluation result is more practical; through calculation of each index value, the size of the information amount can be measured, and therefore the established index can reflect most of original information.
The specific steps for determining the index weight using the entropy weight method are briefly described below.
Forming decision matrix
Let the set of objects participating in the evaluation be M ═ M (M)1,M2,…,Mm) The index set is D ═ D (D)1,D2,…,Dn) Evaluation object MiFor index DjIs denoted as xij(i 1,2, …, m; j 1,2, …, n), the decision matrix X is formed as:
② standardized decision matrix
In order to eliminate the influence of different index dimensions on the scheme decision or process some decision problems with negative index values, the decision matrix X is standardized to form a standardized matrix V (V ═ V)ij)m×n. Indexes are classified into two categories according to their properties. One is a greater and more optimal index, also called benefit index; the smaller the index, the more excellent the index is, and the cost index is also obtained.
And (3) adopting a corresponding standardization form according to the index property during standardization treatment:
for larger and more optimal indicators:
for smaller, more optimal indices:
in the formula vijIs xijNormalized value, max (x)j)、min(xj) The maximum value and the minimum value of the j index are respectively.
It can be seen that after standardization, v is 0. ltoreq. vij≤1。
Calculating characteristic proportion of ith evaluation index under jth index
For a certain index j, vijThe larger the difference in value (c) indicates that the index has a greater effect on the object to be evaluated, i.e., the more useful information the index provides to the object to be evaluated. According to the concept of entropy, an increase in information means a decrease in entropy, which can be used to measure the size of such an amount of information.
The characteristic specific gravity of the ith evaluation object is p under the j indexijThen, then
④ calculating entropy e of j indexj
When p isij0 or pijWhen 1, p is considered to beijln(pij)=0
⑤ calculating the difference coefficient d of j indexj
Observe the meter of the entropy valueFormula of calculation for a certain index Di,vijThe smaller the difference of (e)jThe larger. When the j item index values of all the evaluated objects are equal, ej=emax1. According to the concept of entropy, the larger the index value difference of the j-th item of each evaluated object is, the larger the information amount reflected by the index is. Thus, a difference coefficient d is definedj
dj=1-ej(13)
djThe larger the amount of information provided by the index, the more weight should be given to the index.
Sixthly, determining the entropy weight of each index
3) Combining weights
Integrating subjective weight w calculated by analytic hierarchy process1jAnd objective weight w2jThe available combining weight wjCommon combined weighting method with multiplier synthesis normalization method
And finally, obtaining the subjective and objective combination weight of the index.
The principle of the evaluation method is as follows:
1) grey correlation method
The grey system theory is proposed in 1982 by professor Duncuo dragon, a famous scholar in China, and the grey system theory realizes the exact description and understanding of the real world through the generation and development of part of known information. Grey correlation analysis is one of the main aspects of the theoretical application of grey systems. The gray comprehensive evaluation method based on the gray relevance compares and sorts evaluation objects by using the relevance between each scheme and the optimal scheme.
The relevancy analysis belongs to the category of geometric processing. The method is a sort analysis of relativity, and the basic idea is to judge whether the relation is close according to the similarity of the geometrical shapes of the curves of the sequences, wherein the closer the curves are, the greater the relevance of the corresponding sequences is, and the smaller the relevance is otherwise. The specific evaluation steps are as follows:
① determining the evaluation objects and the reference number series (evaluation standard). the evaluation objects are m, the evaluation indexes are n, and the reference number series is x0={x0(k) 1,2, …, n, the comparison column being xi={xi(k) 1,2, …, n, i is 1,2, …, m, wherein the reference list is chosen according to the following principle: the high-quality index is selected as the maximum value, the low-quality index is the minimum value, and the comparison sequence is the peak regulation scheme.
② calculating gray correlation coefficient
For comparing the series xiTo reference number sequence x0Correlation coefficient on k-th index, where ρ ∈ [0, 1%]Is the resolution factor. Wherein, it is calledAndtwo-level minimum difference and two-level maximum difference.
And thirdly, calculating the gray weighted association degree. The grey-weighted relevance is calculated by the formula
Wherein: r isiGray weighted relevance of the ith evaluation object to the ideal object; w is aiThe weights obtained by the subjective and objective weighting method.
And fourthly, evaluation and analysis. And sequencing the evaluation objects according to the grey correlation degree, and establishing the correlation sequence of the evaluation objects, wherein the larger the correlation degree is, the better the evaluation result is.
2) Rank and proportion method
The Rank-sum ratio (RSR) method is a statistical analysis method which is proposed in 1988 by Chinese scholars and original Chinese preventive medicine academy of sciences, and integrates the advantages of classical parameter statistics and recent non-parameter statistics. The key step of the rank comparison method is rank substitution, and the method has the advantages of strong statistical information function, strong pertinence, high flexibility, simplicity and convenience in operation and high application value. The basic principle is that in an n-row m-column matrix, through rank conversion, dimensionless statistics RSR (WRSR) is obtained; on the basis, the distribution of RSR (WRSR) is researched by using the probability and method of parameter statistical analysis, and the quality of the evaluation object is directly ranked or ranked in grades according to the RSR (WRSR) value, so that the evaluation object is comprehensively evaluated.
Arranging m evaluation indexes of n evaluation objects into a matrix. And compiling the rank of each evaluation object, wherein high-quality indexes are compiled from small to large, low-quality indexes are compiled from large to small, and the average rank is compiled when the same index data is the same.
② calculating weighted rank-sum ratio
Calculating probability unit
And compiling a WRSR frequency distribution table, listing the frequency fi of each group, and calculating the accumulated frequency and accumulated frequency of each group.
Fourthly, calculating a linear regression equation
And (3) calculating a linear regression equation by taking the probability unit Probit corresponding to the accumulated frequency as an independent variable and WRSR as a dependent variable, wherein WRSR is a + b multiplied Probit.
Fifthly, sorting in different levels
And calculating the corresponding WRSR estimation value object according to the regression equation to perform grading sequencing.
3) Ideal solution method
The OPSIS (technique for Order Preference by Similarity to an Ideal solution) method is firstly proposed in 1981 by C.L. Hwang and K.Yoon, and the TOPSIS method is a method for ranking according to the closeness degree of a limited number of evaluation objects and an ideal object and is a method for evaluating relative superiority and inferiority among the existing objects. The TOPSIS method is a sort method that approaches the ideal solution, and only requires that each utility function has monotonic increase (or decrease) property. The TOPSIS method is a commonly used effective method in multi-target decision analysis, and is also called as a good-bad solution distance method. The specific algorithm comprises the following specific steps:
① the method of vector programming is used to obtain the standard decision matrix, and the decision matrix A of the multi-attribute decision problem is set as (a)ij)m×nNormalized decision matrix B ═ (B)ij)m×nWherein
② form a weighted normalization matrix C ═ Cij)m×n
cij=wj·bij,i=1,2,…,m;j=1,2,…,n
③ determining a positive ideal solution C and a negative ideal solution C0. Let the j attribute value of the positive ideal solution C beNegative ideal solution C0The j-th attribute value isThen
And fourthly, calculating the distance between each scheme and the positive ideal solution and the negative ideal solution. Alternative di is a distance to the positive ideal solution of
Alternative di has a distance to the negative ideal solution of
Calculating the queuing index value (comprehensive evaluation index) of each scheme, namely
⑥ push againstAnd (4) ranking the priority and the disadvantage of the schemes from big to small, and evaluating and selecting the optimal scheme.
4) Maximum compatibility method
Basic principle of maximum compatibility method: let h +1 be the number of evaluation schemes and n be the number of evaluation targets. Assuming that each evaluation scheme is a point of an n-dimensional Euclidean space, the geometric meaning of the evaluation scheme having the maximum compatibility with h evaluation schemes is: and in the n-dimensional Euclidean space, calculating a point with the minimum weighted average of the squared Euclidean distances of the h points. According to the multivariate statistical analysis theory, the correlation degree metric between the ith evaluation scheme and the jth evaluation scheme can be calculated by the grade correlation coefficients of the two evaluation schemes, wherein the grade correlation coefficient is as follows:
wherein,for the ranking of objects in the ith schema,the ranking of the object in the jth scheme is given.
The compatibility of a certain multi-attribute evaluation scheme is a weighted average of the correlation coefficients of the evaluation scheme and other evaluation schemes. Then a certain evaluation scheme y ═ ykThe compatibility with other h evaluation schemes can be calculated according to the following formula:
whereinwj>0 is the weight of the jth multi-attribute evaluation scheme, and is usually taken when there is no particular preference for each evaluation schemeIf each evaluation method is independent, the greater the compatibility of a certain evaluation scheme is, the stronger the representativeness and the high reliability of the scheme are, and the better the compatibility is.
Evaluation model of maximum compatibility method:
where yk is the result of the final solution ranking of merits calculated using the maximum compatibility model.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.